{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (19, 31), (4, 3), (30, 16), (18, 17), (20, 10), (9, 15), (24, 8), (27, 14), (31, 16), (6, 10), (4, 26), (15, 7), (20, 0), (6, 21), (26, 8), (15, 34), (20, 24), (25, 32), (20, 7), (18, 2), (4, 5), (12, 35), (10, 12), (10, 23), (26, 4), (17, 8), (28, 5), (32, 6), (0, 6), (13, 29), (11, 28), (25, 22), (2, 8), (5, 3), (5, 11), (31, 29), (9, 6), (25, 35), (31, 9), (29, 33), (32, 17), (28, 23), (32, 0), (9, 31), (9, 3), (7, 32), (6, 13), (18, 14), (21, 0), (30, 29), (15, 8), (11, 10), (20, 35), (4, 21), (17, 4), (24, 34), (10, 29), (28, 8), (16, 31), (6, 17), (21, 26), (25, 20), (0, 35), (19, 19), (1, 10), (25, 8), (24, 7), (10, 13), (23, 8), (7, 12), (0, 3), (4, 18), (11, 2), (17, 15), (30, 24), (32, 27), (0, 34), (28, 22), (19, 17), (14, 23), (22, 16), (27, 19), (27, 4), (12, 4), (13, 28), (21, 35), (23, 24), (25, 33), (32, 28), (32, 9), (10, 9), (31, 17), (20, 8), (20, 11), (27, 8), (21, 8), (6, 27), (26, 13), (32, 3), (23, 18), (1, 5), (5, 16), (31, 35), (3, 16), (1, 4), (8, 11), (0, 21), (23, 16), (29, 32), (8, 29), (28, 32), (32, 16), (33, 11), (30, 22), (0, 27), (7, 34), (4, 23), (18, 33), (26, 3), (1, 25), (11, 30), (10, 15), (22, 12), (11, 16), (7, 31), (4, 35), (2, 34), (12, 21), (27, 22), (2, 6), (16, 30), (31, 31), (10, 19), (10, 17), (7, 0), (4, 29), (33, 19), (26, 6), (9, 25), (6, 34), (27, 5), (30, 6), (9, 19), (29, 12), (23, 35), (5, 18), (8, 23), (23, 20), (5, 10), (26, 27), (4, 0), (14, 34), (28, 15), (2, 7), (9, 17), (25, 7), (28, 29), (14, 14), (29, 29), (18, 32), (10, 34), (13, 31), (16, 33), (24, 4), (0, 32), (22, 10), (7, 4), (28, 11), (20, 31), (28, 33), (12, 2), (32, 26), (15, 32), (27, 18), (19, 22), (0, 29), (23, 33), (18, 11), (5, 19), (19, 30), (16, 26), (25, 30), (30, 31), (25, 9), (4, 13), (5, 17), (8, 9), (3, 32), (19, 24), (26, 1), (21, 3), (21, 9), (3, 9), (24, 12), (12, 19), (3, 6), (1, 9), (23, 19), (24, 3), (10, 16), (22, 2), (21, 13), (21, 22), (26, 17), (28, 31), (7, 11), (26, 2), (29, 34), (12, 31), (21, 34), (13, 14), (30, 1), (14, 24), (18, 29), (16, 0), (9, 18), (20, 6), (15, 2), (14, 22), (8, 17), (23, 31), (19, 29), (1, 6), (13, 11), (5, 28), (2, 26), (14, 4), (4, 28), (13, 5), (8, 28), (2, 3), (23, 2), (10, 7), (15, 18), (31, 1), (26, 35), (12, 29), (18, 7), (10, 31), (30, 27), (16, 25), (4, 24), (24, 21), (2, 15), (10, 10), (24, 0), (7, 17), (22, 9), (22, 26), (28, 19), (2, 21), (14, 30), (16, 28), (20, 2), (32, 31), (6, 9), (0, 12), (25, 3), (11, 32), (15, 11), (6, 32), (1, 3), (24, 25), (27, 20), (11, 22), (22, 33), (13, 35), (4, 34), (26, 19), (14, 33), (23, 21), (29, 21), (8, 16), (25, 4), (32, 30), (4, 4), (5, 23), (17, 35), (7, 28), (21, 2), (20, 21), (17, 26), (26, 30), (29, 6), (1, 21), (5, 34), (14, 35), (15, 33), (21, 32), (17, 1), (20, 3), (32, 25), (19, 2), (4, 32), (19, 0), (23, 22), (0, 18), (22, 29), (3, 17), (23, 30), (2, 28), (8, 3), (14, 20), (1, 31), (32, 23), (28, 25), (33, 18), (2, 17), (24, 6), (6, 0), (31, 5), (32, 13), (25, 29), (19, 34), (13, 30), (29, 10), (11, 31), (11, 15), (21, 16), (8, 13), (15, 25), (21, 7), (19, 25), (11, 9), (27, 15), (33, 13), (13, 13), (15, 15), (27, 9), (0, 13), (19, 16), (13, 25), (33, 21), (12, 26), (1, 29), (2, 30), (13, 0), (16, 35), (3, 11), (28, 3), (31, 10), (1, 32), (11, 8), (22, 35), (22, 4), (18, 28), (3, 2), (23, 15), (32, 10), (1, 34), (6, 1), (32, 5), (19, 35), (10, 2), (6, 31), (9, 12), (0, 4), (22, 22), (2, 32), (22, 3), (10, 24), (8, 27), (31, 34), (3, 22), (14, 27), (16, 27), (23, 25), (19, 28), (33, 9), (13, 26), (30, 12), (18, 23), (7, 25), (20, 26), (27, 31), (11, 14), (7, 15), (24, 11), (27, 34), (12, 24), (16, 1), (33, 4), (6, 7), (11, 5), (33, 0), (14, 9), (6, 33), (28, 14), (21, 12), (28, 30), (26, 12), (9, 7), (24, 24), (11, 6), (15, 4), (0, 28), (19, 12), (16, 17), (22, 30), (3, 8), (10, 30), (22, 13), (16, 23), (6, 28), (0, 10), (31, 22), (32, 18), (4, 16), (27, 27), (12, 33), (30, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777600", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 21), (11, 1), (30, 16), (19, 26), (32, 26), (25, 6), (11, 22), (23, 0), (24, 28), (29, 28), (9, 6), (33, 29), (14, 8), (34, 15), (8, 16), (8, 19), (36, 20), (35, 11), (10, 29), (22, 29), (26, 29), (15, 14), (34, 26), (19, 5), (17, 15), (22, 28), (29, 18), (13, 24), (28, 6), (33, 4), (2, 5), (19, 7), (32, 16), (14, 14), (34, 14), (6, 8), (9, 16), (5, 10), (25, 14), (26, 6), (7, 11), (29, 25), (9, 25), (32, 24), (11, 5), (33, 3), (21, 27), (22, 17), (3, 15), (11, 16), (11, 19), (23, 24), (1, 29), (2, 3), (7, 1), (18, 20), (26, 27), (9, 10), (12, 19), (24, 14), (10, 2), (22, 11), (17, 23), (20, 28), (14, 4), (4, 17), (34, 12), (18, 12), (16, 21), (9, 1), (17, 16), (30, 8), (13, 8), (3, 18), (8, 4), (13, 25), (15, 3), (0, 8), (36, 16), (1, 18), (3, 27), (22, 10), (16, 19), (20, 3), (36, 3), (28, 20), (25, 3), (18, 29), (36, 25), (4, 14), (22, 20), (23, 6), (12, 23), (31, 3), (27, 14), (3, 25), (0, 25), (18, 1), (16, 10), (36, 2), (36, 19), (9, 8), (15, 15), (35, 20), (22, 27), (18, 21), (27, 24), (24, 16), (34, 9), (25, 9), (13, 22), (30, 28), (3, 3), (29, 23), (8, 6), (9, 22), (11, 17), (22, 0), (35, 14), (22, 3), (36, 22), (0, 21), (28, 17), (16, 9), (11, 0), (24, 25), (31, 18), (31, 9), (11, 23), (32, 17), (5, 17), (17, 14), (9, 4), (17, 4), (36, 23), (12, 5), (33, 5), (18, 18), (11, 26), (6, 1), (28, 1), (1, 14), (20, 16), (26, 9), (20, 14), (15, 18), (12, 20), (13, 19), (21, 14), (6, 9), (6, 7), (20, 1), (35, 27), (32, 14), (36, 24), (5, 24), (9, 0), (26, 12), (22, 12), (13, 15), (2, 4), (9, 9), (11, 24), (13, 9), (0, 29), (6, 17), (20, 10), (15, 13), (29, 1), (35, 15), (6, 22), (29, 6), (12, 28), (15, 23), (31, 23), (31, 0), (34, 25), (21, 10), (0, 26), (8, 3), (12, 0), (18, 2), (10, 6), (10, 1), (4, 2), (27, 18), (28, 12), (3, 2), (3, 20), (14, 27), (26, 0), (29, 14), (32, 29), (11, 7), (32, 2), (2, 24), (19, 8), (16, 29), (32, 25), (28, 10), (2, 23), (18, 19), (27, 22), (16, 16), (26, 1), (30, 22), (23, 18), (25, 23), (9, 26), (32, 15), (11, 2), (35, 0), (16, 7), (23, 3), (14, 29), (24, 18), (6, 13), (22, 8), (15, 22), (12, 3), (8, 25), (16, 27), (24, 21), (21, 0), (36, 4), (29, 13), (24, 29), (10, 4), (9, 23), (7, 27), (32, 3), (25, 24), (30, 19), (6, 2), (19, 9), (2, 14), (4, 22), (13, 12), (27, 4), (6, 0), (17, 20), (31, 17), (25, 22), (0, 22), (10, 14), (7, 19), (32, 22), (14, 28), (3, 21), (18, 5), (25, 16), (14, 3), (12, 7), (33, 26), (4, 1), (27, 3), (22, 26), (10, 22), (20, 12), (21, 17), (35, 6), (36, 10), (28, 26), (3, 24), (18, 6), (17, 26), (20, 20), (19, 6), (36, 21), (31, 13), (12, 11), (9, 3), (12, 24), (11, 6), (19, 12), (24, 6), (21, 24), (26, 11), (4, 11), (17, 12), (17, 17), (27, 12), (15, 27), (9, 29), (22, 21), (22, 23), (23, 12), (32, 5), (30, 29), (26, 14), (2, 25), (7, 7), (26, 16), (22, 6), (4, 10), (15, 21), (34, 23), (33, 24), (25, 18), (34, 16), (19, 3), (17, 8), (8, 14), (30, 3), (34, 4), (4, 15), (0, 12), (20, 18), (35, 4), (12, 21), (33, 11), (18, 7), (11, 20), (12, 25), (32, 9), (19, 17), (3, 8), (5, 2), (4, 25), (13, 27), (22, 16), (16, 14), (16, 2), (10, 9), (19, 24), (7, 21), (34, 8), (19, 10), (19, 2), (7, 4), (5, 29), (20, 8), (32, 28), (8, 10), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "976200", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 18), (22, 37), (10, 15), (27, 33), (29, 14), (4, 20), (16, 22), (27, 3), (17, 31), (23, 32), (25, 11), (18, 17), (13, 36), (33, 16), (1, 37), (33, 35), (5, 37), (24, 33), (9, 22), (17, 15), (9, 16), (16, 8), (11, 22), (29, 8), (32, 10), (19, 11), (21, 23), (12, 23), (23, 23), (28, 35), (20, 4), (18, 30), (17, 35), (23, 10), (29, 11), (14, 12), (12, 37), (12, 20), (14, 21), (20, 18), (0, 31), (24, 5), (2, 10), (15, 34), (30, 34), (22, 2), (25, 19), (0, 5), (6, 37), (22, 10), (6, 21), (23, 15), (23, 4), (19, 30), (14, 7), (31, 27), (12, 27), (34, 0), (14, 10), (34, 33), (11, 11), (25, 33), (33, 9), (27, 29), (29, 23), (20, 36), (9, 36), (23, 0), (8, 17), (25, 18), (8, 11), (23, 37), (2, 24), (1, 31), (13, 18), (3, 37), (29, 17), (22, 25), (19, 27), (1, 8), (12, 14), (25, 26), (19, 28), (32, 12), (17, 33), (2, 11), (23, 12), (30, 13), (3, 32), (16, 15), (17, 4), (5, 8), (6, 18), (19, 13), (11, 1), (8, 5), (12, 18), (11, 3), (19, 5), (8, 32), (31, 11), (0, 11), (21, 8), (29, 16), (31, 26), (28, 19), (22, 30), (27, 26), (26, 29), (7, 7), (32, 34), (27, 18), (6, 36), (5, 20), (12, 13), (19, 8), (21, 1), (28, 23), (11, 16), (2, 0), (28, 36), (4, 12), (25, 20), (31, 6), (0, 27), (33, 18), (0, 19), (18, 18), (28, 25), (20, 13), (10, 29), (25, 4), (21, 14), (28, 11), (10, 36), (26, 34), (6, 23), (21, 34), (14, 17), (32, 3), (11, 9), (34, 7), (20, 10), (6, 14), (6, 33), (17, 37), (26, 26), (34, 18), (13, 23), (6, 26), (34, 14), (24, 8), (4, 4), (24, 0), (17, 23), (8, 28), (16, 26), (21, 17), (7, 11), (8, 0), (1, 0), (5, 23), (2, 36), (32, 4), (10, 17), (17, 20), (24, 29), (12, 12), (23, 19), (13, 30), (6, 8), (25, 22), (10, 34), (34, 32), (27, 13), (33, 31), (34, 1), (28, 9), (12, 2), (15, 30), (6, 12), (16, 32), (32, 5), (8, 36), (28, 33), (13, 6), (24, 27), (31, 12), (20, 0), (29, 31), (24, 17), (16, 27), (20, 28), (13, 33), (3, 34), (19, 3), (1, 30), (13, 31), (0, 25), (14, 15), (12, 7), (30, 8), (16, 19), (14, 26), (25, 28), (1, 14), (10, 27), (29, 18), (28, 8), (18, 9), (29, 10), (34, 21), (31, 37), (21, 7), (23, 26), (12, 16), (6, 9), (21, 3), (9, 34), (25, 8), (8, 22), (5, 4), (26, 21), (27, 9), (15, 20), (4, 17), (9, 11), (33, 29), (9, 27), (22, 8), (32, 33), (10, 24), (4, 5), (12, 21), (4, 25), (6, 22), (19, 18), (15, 37), (5, 3), (20, 33), (32, 22), (19, 14), (23, 3), (8, 6), (19, 25), (19, 31), (23, 25), (21, 9), (22, 27), (27, 6), (18, 37), (4, 19), (16, 6), (34, 30), (18, 2), (27, 17), (12, 11), (24, 11), (0, 14), (7, 27), (24, 35), (4, 24), (24, 22), (29, 19), (30, 25), (32, 7), (8, 34), (25, 17), (26, 24), (27, 19), (9, 21), (28, 32), (6, 29), (15, 29), (3, 6), (7, 0), (19, 33), (0, 23), (23, 20), (23, 7), (0, 30), (26, 12), (2, 22), (7, 30), (4, 15), (29, 12), (32, 35), (16, 25), (18, 23), (24, 37), (20, 27), (30, 31), (24, 21), (5, 28), (2, 21), (19, 34), (34, 10), (30, 9), (25, 32), (33, 36), (27, 24), (25, 2), (27, 1), (18, 12), (9, 32), (30, 18), (6, 34), (2, 2), (23, 1), (28, 24), (3, 14), (26, 10), (0, 12), (10, 21), (24, 4), (11, 31), (7, 4), (31, 31), (34, 23), (12, 32), (3, 8), (26, 5), (5, 0), (30, 14), (10, 32), (5, 32), (23, 17), (5, 26), (2, 15), (17, 25), (4, 16), (30, 6), (30, 3), (4, 14), (0, 4), (21, 5), (29, 0), (2, 4), (3, 30), (28, 17), (22, 9), (25, 14), (29, 20), (21, 6), (22, 20), (13, 17), (11, 26), (3, 5), (12, 19), (28, 15), (27, 28), (34, 16), (19, 0), (11, 0), (21, 30), (15, 28), (27, 30), (29, 36), (31, 5), (27, 34), (33, 28), (26, 1), (31, 13), (12, 9), (1, 26), (30, 32), (8, 23), (20, 9), (6, 24), (29, 15), (10, 20), (20, 5), (15, 23), (28, 16), (26, 37), (32, 20), (11, 19), (11, 32), (15, 7), (18, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "543244", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 4), (22, 12), (2, 13), (6, 1), (26, 26), (5, 20), (24, 8), (5, 23), (30, 1), (31, 26), (33, 18), (1, 2), (6, 28), (2, 8), (24, 29), (26, 10), (38, 30), (35, 11), (29, 3), (32, 27), (28, 22), (36, 24), (8, 31), (29, 11), (32, 20), (21, 30), (20, 33), (9, 32), (10, 31), (2, 15), (11, 5), (28, 8), (24, 23), (22, 18), (21, 11), (24, 26), (15, 33), (11, 7), (23, 16), (10, 19), (33, 10), (22, 30), (21, 20), (26, 25), (8, 13), (31, 32), (9, 25), (18, 4), (23, 26), (7, 0), (26, 0), (37, 28), (15, 7), (20, 20), (32, 18), (15, 32), (10, 6), (35, 15), (5, 17), (14, 21), (31, 11), (0, 19), (30, 16), (8, 33), (2, 23), (14, 19), (20, 0), (35, 4), (30, 12), (19, 23), (26, 18), (24, 14), (38, 21), (21, 19), (8, 28), (28, 3), (9, 27), (36, 25), (2, 32), (26, 12), (1, 12), (30, 27), (22, 1), (11, 0), (31, 24), (9, 30), (14, 6), (17, 24), (3, 14), (33, 15), (22, 7), (38, 26), (18, 24), (27, 15), (0, 15), (18, 15), (30, 32), (23, 19), (17, 9), (30, 20), (24, 28), (31, 2), (7, 4), (36, 5), (18, 19), (34, 8), (38, 29), (5, 19), (35, 2), (17, 0), (14, 9), (36, 13), (10, 9), (35, 10), (29, 12), (3, 9), (9, 29), (34, 12), (25, 18), (35, 6), (17, 20), (1, 22), (31, 23), (10, 1), (4, 13), (35, 16), (20, 22), (24, 3), (25, 14), (4, 1), (18, 17), (19, 14), (34, 24), (10, 29), (6, 17), (32, 23), (37, 15), (16, 0), (1, 16), (4, 31), (23, 14), (7, 23), (30, 5), (19, 17), (18, 14), (38, 3), (12, 21), (6, 8), (15, 4), (19, 13), (19, 26), (3, 24), (25, 21), (32, 1), (24, 32), (4, 21), (22, 24), (2, 16), (6, 12), (34, 10), (8, 26), (28, 11), (38, 19), (3, 11), (9, 4), (1, 19), (34, 31), (35, 20), (30, 3), (21, 2), (36, 33), (36, 3), (14, 4), (3, 32), (24, 24), (21, 31), (6, 5), (37, 1), (13, 7), (20, 31), (5, 7), (17, 22), (19, 9), (6, 9), (38, 7), (6, 4), (36, 26), (14, 22), (32, 24), (28, 7), (16, 17), (7, 32), (7, 18), (17, 17), (38, 11), (27, 14), (2, 21), (20, 30), (25, 12), (29, 9), (25, 9), (5, 16), (2, 31), (36, 16), (28, 13), (37, 24), (33, 3), (20, 14), (10, 12), (32, 22), (14, 8), (3, 13), (33, 29), (11, 4), (5, 8), (7, 21), (27, 33), (27, 27), (29, 20), (1, 20), (25, 20), (28, 16), (23, 12), (31, 10), (28, 24), (27, 20), (3, 6), (23, 13), (34, 11), (38, 22), (6, 16), (9, 1), (1, 31), (19, 12), (38, 32), (28, 26), (34, 20), (7, 1), (34, 29), (24, 11), (13, 12), (27, 7), (37, 10), (33, 32), (22, 11), (36, 31), (2, 1), (24, 33), (37, 21), (14, 2), (32, 7), (29, 30), (13, 5), (12, 10), (8, 14), (6, 3), (38, 20), (5, 18), (30, 7), (31, 19), (8, 11), (9, 6), (15, 6), (11, 29), (16, 23), (9, 21), (9, 10), (28, 23), (1, 28), (11, 31), (33, 1), (17, 12), (19, 4), (17, 7), (6, 29), (5, 6), (28, 18), (38, 16), (33, 16), (3, 17), (15, 3), (0, 10), (11, 9), (29, 8), (8, 2), (32, 13), (0, 33), (20, 26), (26, 7), (29, 5), (6, 13), (34, 30), (18, 22), (9, 28), (10, 2), (12, 30), (36, 32), (16, 9), (9, 22), (19, 24), (37, 6), (36, 10), (8, 9), (5, 9), (16, 1), (5, 33), (5, 22), (22, 15), (19, 32), (19, 18), (27, 21), (15, 19), (27, 2), (16, 12), (34, 7), (35, 14), (11, 24), (23, 5), (22, 3), (28, 30), (38, 12), (19, 27), (3, 8), (9, 26), (10, 27), (38, 17), (8, 5), (37, 17), (31, 16), (21, 3), (3, 5), (31, 33), (15, 21), (32, 12), (35, 8), (6, 18), (23, 8), (16, 20), (6, 26), (32, 21), (34, 1), (25, 26), (24, 20), (21, 17), (20, 15), (37, 27), (28, 5), (26, 28), (36, 18), (36, 21), (22, 9), (8, 4), (31, 3), (32, 2), (28, 33), (4, 2), (23, 33), (29, 17), (25, 33), (33, 6), (10, 17), (37, 23), (33, 25), (10, 28), (8, 19), (15, 30), (24, 4), (9, 13), (21, 27), (34, 9), (35, 12), (9, 14), (4, 20), (9, 12), (28, 31), (22, 21), (34, 0), (17, 33), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25632", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 25), (6, 25), (25, 17), (26, 3), (13, 30), (27, 36), (7, 30), (35, 14), (28, 13), (27, 17), (21, 12), (25, 23), (26, 18), (29, 6), (3, 8), (35, 10), (29, 2), (32, 31), (31, 28), (33, 7), (9, 11), (15, 34), (5, 22), (28, 15), (17, 13), (19, 10), (21, 11), (35, 13), (16, 29), (14, 27), (26, 27), (6, 14), (30, 19), (1, 27), (1, 36), (20, 26), (34, 5), (0, 7), (26, 21), (24, 11), (31, 33), (13, 19), (5, 8), (20, 6), (18, 15), (5, 36), (18, 22), (1, 21), (21, 13), (26, 22), (1, 2), (16, 13), (1, 18), (16, 36), (13, 26), (29, 17), (11, 5), (24, 35), (24, 6), (23, 10), (35, 35), (29, 23), (24, 8), (12, 19), (27, 2), (35, 17), (10, 18), (24, 18), (18, 31), (18, 5), (33, 24), (30, 8), (5, 15), (33, 19), (6, 6), (31, 3), (17, 28), (22, 8), (18, 8), (19, 35), (3, 9), (25, 5), (3, 30), (16, 19), (32, 2), (14, 21), (8, 15), (4, 16), (31, 10), (30, 4), (27, 23), (22, 16), (11, 34), (19, 27), (30, 29), (27, 15), (11, 7), (30, 23), (18, 29), (7, 20), (25, 11), (10, 3), (0, 16), (20, 24), (28, 22), (17, 3), (3, 20), (24, 31), (17, 37), (29, 22), (25, 37), (30, 11), (15, 5), (3, 1), (15, 35), (13, 13), (6, 7), (35, 11), (20, 36), (5, 5), (1, 17), (3, 31), (1, 11), (1, 23), (11, 33), (26, 29), (27, 16), (1, 9), (17, 30), (10, 36), (28, 4), (9, 19), (11, 18), (32, 7), (32, 23), (30, 27), (13, 27), (26, 7), (4, 30), (22, 1), (12, 32), (33, 21), (17, 9), (8, 34), (5, 30), (0, 10), (8, 33), (11, 2), (9, 2), (35, 27), (14, 5), (13, 23), (12, 3), (4, 3), (31, 24), (13, 34), (2, 27), (23, 14), (0, 35), (31, 11), (8, 5), (7, 11), (35, 26), (0, 22), (4, 31), (18, 21), (29, 18), (19, 1), (10, 19), (14, 23), (33, 27), (10, 11), (20, 34), (30, 36), (32, 15), (7, 22), (6, 18), (21, 19), (27, 34), (12, 30), (2, 3), (30, 16), (6, 4), (24, 5), (33, 12), (2, 32), (19, 21), (29, 26), (13, 4), (10, 30), (24, 26), (0, 15), (19, 8), (11, 23), (20, 35), (10, 15), (3, 6), (34, 15), (32, 1), (27, 24), (3, 10), (13, 15), (4, 27), (14, 18), (20, 18), (29, 29), (6, 37), (25, 19), (12, 24), (4, 36), (35, 9), (8, 29), (8, 2), (31, 27), (8, 6), (33, 15), (6, 13), (3, 7), (22, 36), (19, 5), (35, 34), (26, 31), (7, 18), (28, 23), (29, 16), (6, 0), (9, 18), (4, 2), (34, 24), (28, 34), (13, 10), (27, 5), (4, 5), (14, 32), (10, 14), (34, 26), (19, 24), (0, 14), (21, 16), (11, 30), (6, 12), (27, 22), (10, 33), (33, 13), (10, 17), (28, 7), (25, 8), (7, 5), (29, 9), (9, 22), (11, 25), (18, 12), (7, 35), (0, 8), (11, 20), (27, 11), (32, 11), (19, 37), (33, 9), (0, 25), (35, 12), (28, 29), (0, 33), (25, 13), (27, 20), (15, 12), (18, 0), (16, 0), (18, 25), (8, 1), (31, 5), (9, 1), (33, 23), (22, 18), (22, 22), (21, 18), (23, 19), (8, 30), (12, 29), (10, 16), (20, 3), (13, 2), (1, 12), (28, 14), (24, 3), (0, 24), (0, 17), (13, 32), (9, 10), (21, 21), (4, 32), (5, 26), (35, 2), (12, 27), (16, 22), (18, 16), (10, 8), (0, 37), (8, 25), (2, 25), (3, 32), (33, 14), (14, 24), (6, 30), (13, 21), (23, 8), (17, 34), (8, 32), (29, 30), (31, 2), (21, 6), (34, 10), (1, 16), (34, 20), (11, 37), (13, 31), (20, 15), (22, 37), (14, 0), (3, 0), (32, 5), (22, 35), (11, 24), (27, 9), (8, 8), (22, 12), (29, 20), (30, 7), (12, 7), (8, 37), (17, 19), (15, 32), (18, 36), (32, 29), (3, 19), (27, 14), (7, 0), (31, 6), (6, 11), (30, 14), (28, 12), (24, 16), (11, 9), (34, 6), (11, 8), (9, 24), (1, 35), (8, 3), (22, 7), (28, 28), (33, 26), (15, 11), (6, 17), (32, 36), (15, 33), (23, 21), (6, 19), (8, 20), (7, 33), (16, 28), (34, 3), (13, 33), (35, 31), (32, 20), (4, 20), (31, 18), (5, 27), (19, 26), (20, 28), (34, 14), (22, 30), (25, 28), (32, 35), (10, 34), (34, 28), (30, 20), (32, 6), (21, 28), (3, 29), (9, 35), (0, 12), (10, 23), (1, 13), (5, 1), (19, 9), (7, 16), (2, 21), (22, 27), (16, 20), (3, 37), (24, 29), (5, 35), (24, 9), (23, 24), (1, 22), (22, 33), (14, 26), (12, 22), (4, 15), (15, 13), (13, 12), (25, 0), (12, 8), (2, 34), (8, 21), (22, 29), (20, 21), (24, 12), (34, 33), (22, 3), (4, 10), (8, 23), (7, 19), (18, 34), (26, 33), (30, 35), (27, 33), (15, 8), (0, 4), (27, 0), (26, 11), (28, 20), (27, 1), (28, 19), (28, 36), (2, 17), (11, 16), (3, 4), (25, 12), (21, 15), (25, 16), (16, 16), (17, 8), (9, 27), (17, 1), (24, 27), (8, 36), (15, 36), (26, 36), (12, 36), (16, 12), (14, 31), (23, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "792000", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 25), (23, 6), (25, 18), (5, 5), (9, 5), (25, 11), (22, 36), (6, 7), (13, 1), (5, 35), (34, 27), (8, 35), (2, 35), (23, 14), (1, 26), (13, 30), (20, 24), (27, 23), (26, 5), (5, 13), (34, 1), (8, 30), (24, 18), (31, 25), (12, 30), (18, 0), (33, 0), (26, 33), (6, 29), (8, 33), (13, 14), (10, 1), (27, 30), (31, 29), (16, 17), (11, 29), (18, 7), (20, 4), (32, 13), (27, 10), (30, 0), (5, 28), (31, 26), (6, 25), (10, 21), (11, 14), (8, 16), (34, 23), (16, 16), (8, 24), (4, 20), (29, 4), (9, 14), (24, 26), (26, 0), (31, 8), (31, 11), (28, 4), (8, 21), (7, 11), (1, 10), (1, 33), (17, 35), (14, 36), (33, 18), (10, 23), (8, 26), (2, 9), (21, 8), (9, 2), (34, 32), (5, 19), (2, 32), (11, 17), (17, 14), (34, 28), (22, 13), (27, 28), (10, 22), (28, 31), (22, 17), (27, 6), (4, 25), (19, 15), (26, 26), (7, 28), (34, 2), (33, 20), (4, 7), (28, 22), (13, 34), (15, 21), (3, 30), (34, 7), (5, 18), (22, 22), (20, 17), (1, 8), (3, 14), (15, 10), (24, 16), (9, 21), (24, 3), (13, 36), (32, 11), (15, 36), (23, 19), (24, 12), (34, 17), (32, 3), (26, 22), (8, 4), (29, 20), (10, 31), (21, 24), (10, 28), (0, 36), (29, 12), (26, 23), (25, 28), (29, 6), (5, 23), (10, 8), (7, 8), (20, 31), (30, 14), (21, 3), (1, 21), (23, 31), (5, 6), (23, 15), (6, 34), (11, 22), (23, 18), (4, 9), (17, 20), (8, 17), (31, 10), (20, 26), (22, 1), (11, 2), (15, 5), (30, 3), (9, 10), (9, 8), (10, 24), (6, 6), (21, 14), (34, 29), (8, 5), (5, 32), (8, 22), (0, 24), (4, 27), (16, 33), (15, 15), (7, 33), (15, 18), (7, 0), (33, 7), (32, 24), (32, 5), (28, 12), (0, 20), (1, 32), (9, 34), (2, 13), (5, 22), (14, 8), (11, 3), (24, 27), (23, 22), (14, 10), (29, 2), (6, 18), (4, 26), (23, 4), (33, 4), (31, 28), (3, 16), (2, 27), (13, 29), (6, 9), (1, 0), (17, 0), (32, 34), (3, 24), (19, 18), (16, 19), (7, 9), (27, 13), (17, 21), (19, 32), (7, 31), (10, 15), (7, 35), (16, 9), (8, 25), (27, 18), (16, 18), (30, 36), (20, 22), (22, 34), (23, 12), (18, 9), (29, 34), (20, 1), (20, 34), (14, 12), (25, 25), (21, 6), (28, 3), (15, 8), (30, 19), (34, 18), (27, 29), (17, 24), (0, 10), (12, 34), (11, 28), (5, 10), (2, 4), (20, 12), (12, 24), (20, 2), (31, 3), (28, 18), (4, 11), (19, 2), (28, 19), (17, 13), (32, 20), (18, 24), (12, 27), (0, 9), (31, 2), (27, 16), (14, 1), (27, 36), (5, 7), (2, 30), (0, 8), (13, 4), (27, 4), (18, 10), (16, 31), (21, 21), (1, 12), (6, 30), (13, 26), (27, 17), (34, 13), (12, 14), (34, 35), (30, 16), (22, 15), (16, 13), (11, 13), (30, 8), (26, 9), (23, 0), (15, 32), (29, 35), (4, 36), (11, 12), (11, 31), (27, 27), (21, 27), (15, 16), (12, 6), (18, 33), (34, 30), (17, 7), (8, 0), (6, 21), (3, 6), (26, 1), (10, 10), (19, 6), (34, 21), (12, 11), (5, 15), (11, 15), (6, 26), (5, 12), (19, 11), (18, 17), (17, 27), (25, 33), (5, 36), (34, 20), (10, 6), (15, 6), (22, 5), (20, 20), (12, 7), (5, 24), (30, 28), (7, 27), (32, 31), (4, 21), (17, 36), (27, 9), (7, 10), (14, 2), (31, 19), (23, 30), (1, 36), (3, 13), (7, 16), (3, 9), (5, 33), (17, 2), (7, 15), (24, 4), (27, 11), (26, 34), (2, 31), (15, 22), (15, 35), (23, 27), (6, 16), (20, 18), (30, 18), (7, 21), (32, 9), (21, 30), (34, 11), (8, 1), (31, 22), (29, 31), (18, 36), (18, 32), (20, 32), (22, 28), (12, 32), (27, 15), (21, 35), (4, 31), (19, 28), (7, 34), (18, 2), (28, 27), (25, 23), (33, 10), (0, 13), (12, 18), (21, 11), (17, 15), (13, 3), (26, 19), (24, 22), (7, 19), (25, 29), (25, 36), (16, 3), (27, 19), (18, 27), (7, 32), (1, 15), (7, 26), (15, 7), (24, 17), (16, 22), (3, 34), (6, 0), (18, 1), (14, 31), (22, 21), (11, 19), (17, 25), (11, 0), (28, 15), (18, 29), (23, 29), (16, 7), (2, 34), (34, 25), (31, 1), (4, 4), (1, 11), (24, 36), (5, 20), (24, 10), (21, 32), (22, 2), (5, 3), (3, 5), (31, 6), (15, 27), (25, 1), (10, 16), (26, 7), (20, 16), (3, 12), (31, 35), (27, 32), (9, 22), (34, 5), (3, 3), (26, 2), (21, 4), (0, 33), (4, 16), (12, 16), (19, 34), (14, 24), (24, 21), (17, 16), (18, 26), (4, 14), (29, 36), (12, 1), (29, 15), (16, 28), (11, 30), (19, 17), (34, 22), (18, 11), (7, 7), (17, 31), (2, 28), (7, 30), (9, 9), (24, 19), (16, 34), (21, 1), (19, 8), (30, 31), (20, 19), (22, 31), (25, 13), (5, 2), (26, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657660", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), 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), (2, 5), (6, 29), (13, 10), (28, 15), (19, 18), (38, 1), (3, 29), (17, 19), (5, 23), (31, 12), (9, 4), (31, 0), (1, 21), (26, 7), (26, 4), (24, 24), (25, 20), (23, 7), (26, 9), (20, 9), (26, 16), (27, 0), (1, 14), (7, 9), (9, 25), (32, 5), (7, 25), (30, 2), (36, 19), (12, 28), (2, 22), (6, 20), (11, 11), (32, 23), (12, 22), (25, 7), (36, 25), (6, 15), (3, 20), (17, 27), (34, 7), (21, 31), (15, 24), (36, 9), (32, 13), (3, 9), (35, 18), (7, 12), (35, 31), (10, 0), (10, 20), (14, 11), (10, 11), (6, 21), (33, 29), (31, 26), (20, 16), (18, 25), (22, 16), (15, 25), (37, 4), (6, 26), (9, 11), (3, 23), (32, 18), (7, 21), (29, 21), (1, 6), (25, 15), (25, 19), (11, 7), (21, 6), (7, 16), (19, 28), (32, 15), (6, 0), (37, 31), (21, 7), (35, 4), (22, 18), (33, 22), (7, 14), (9, 9), (32, 16), (15, 14), (1, 11), (14, 21), (8, 24), (18, 15), (36, 28), (2, 19), (17, 3), (4, 2), (22, 7), (34, 15), (26, 2), (35, 21), (36, 18), (24, 3), (4, 7), (22, 22), (35, 16), (23, 22), (35, 24), (16, 27), (3, 0), (17, 7), (38, 16), (17, 9), (5, 21), (29, 26), (31, 31), (11, 23), (33, 23), (5, 6), (7, 5), (3, 25), (16, 29), (37, 30), (4, 27), (37, 20), (26, 19), (25, 3), (8, 16), (28, 20), (16, 18), (16, 5), (10, 29), (22, 17), (23, 18), (15, 18), (20, 29), (25, 22), (14, 18), (31, 23), (27, 8), (23, 15), (7, 18), (20, 12), (25, 23), (9, 27), (6, 9), (5, 22), (27, 30), (19, 6), (32, 14), (30, 1), (29, 23), (0, 13), (13, 3), (32, 8), (21, 29), (26, 24), (7, 30), (16, 24), (3, 28), (7, 7), (2, 21), (11, 6), (33, 8), (12, 0), (27, 5), (30, 16), (19, 23), (34, 28), (23, 8), (8, 8), (1, 15), (28, 5), (17, 20), (12, 20), (19, 30), (17, 15), (33, 18), (22, 13), (12, 30), (28, 14), (4, 8), (21, 10), (16, 28), (29, 19), (4, 15), (30, 12), (27, 15), (14, 8), (30, 6), (22, 4), (37, 19), (27, 18), (36, 8), (4, 11), (5, 19), (29, 10), (28, 24), (3, 1), (16, 3), (2, 9), (32, 2), (16, 31), (17, 14), (19, 24), (18, 9), (13, 23), (34, 24), (3, 31), (4, 6), (26, 28), (37, 10), (23, 2), (8, 4), (16, 20), (9, 12), (35, 14), (13, 25), (25, 2), (18, 26), (38, 17), (14, 0), (21, 15), (34, 29), (26, 8), (17, 26), (22, 19), (19, 0), (9, 22), (2, 30), (14, 20), (37, 2), (32, 7), (19, 20), (8, 1), (38, 26), (30, 20), (6, 13), (14, 10), (15, 16), (31, 4), (30, 8), (0, 24), (36, 21), (35, 23), (12, 2), (19, 15), (10, 30), (14, 26), (26, 25), (37, 6), (11, 13), (11, 18), (30, 4), (10, 15), (30, 0), (13, 29), (33, 13), (34, 11), (34, 25), (27, 2), (25, 11), (31, 8), (25, 18), (34, 3), (38, 22), (34, 30), (25, 17), (10, 25), (10, 13), (5, 2), (9, 26), (15, 28), (31, 29), (2, 15), (21, 25), (11, 4), (37, 27), (14, 1), (17, 21), (27, 28), (7, 26), (19, 12), (16, 13), (28, 22), (23, 10), (35, 10), (15, 30), (35, 17), (13, 28), (38, 0), (19, 19), (11, 9), (3, 8), (31, 14), (28, 13), (1, 19), (28, 27), (9, 1), (3, 11), (23, 0), (18, 20), (14, 22), (27, 26), (29, 16), (5, 13), (21, 22), (0, 11), (0, 30), (0, 3), (17, 17), (11, 1), (2, 26), (38, 20), (16, 12), (19, 8), (5, 27), (23, 25), (36, 24), (15, 9), (23, 23), (26, 6), (16, 10), (5, 18), (27, 11), (8, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766080", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), 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), (14, 24), (1, 11), (24, 16), (9, 31), (31, 32), (12, 32), (5, 16), (29, 20), (26, 0), (17, 15), (30, 24), (13, 11), (20, 0), (6, 28), (11, 26), (23, 7), (5, 36), (17, 4), (3, 23), (10, 7), (14, 23), (30, 8), (17, 35), (19, 37), (19, 8), (26, 37), (28, 36), (30, 19), (17, 34), (1, 15), (22, 14), (25, 9), (11, 21), (11, 19), (12, 15), (19, 12), (32, 8), (24, 21), (30, 23), (32, 36), (22, 6), (19, 15), (20, 36), (32, 35), (16, 31), (31, 26), (21, 35), (0, 35), (7, 21), (7, 34), (7, 22), (8, 3), (21, 21), (5, 31), (30, 37), (22, 0), (23, 19), (7, 4), (1, 5), (20, 17), (16, 20), (14, 14), (19, 33), (20, 23), (18, 32), (25, 16), (31, 7), (16, 23), (14, 31), (0, 12), (23, 11), (23, 18), (28, 2), (6, 34), (4, 11), (17, 16), (30, 27), (19, 35), (22, 33), (6, 33), (22, 11), (9, 36), (11, 20), (25, 21), (29, 30), (5, 33), (25, 36), (25, 1), (25, 32), (10, 16), (15, 4), (26, 35), (2, 33), (22, 23), (30, 25), (9, 10), (30, 16), (2, 19), (3, 6), (19, 14), (2, 32), (25, 25), (22, 1), (29, 37), (18, 10), (23, 25), (29, 18), (28, 32), (30, 36), (31, 17), (25, 23), (23, 17), (6, 3), (5, 13), (4, 8), (17, 21), (7, 30), (30, 4), (13, 30), (7, 31), (17, 24), (16, 0), (4, 35), (24, 17), (1, 31), (5, 0), (3, 13), (32, 30), (10, 28), (29, 14), (0, 5), (27, 37), (17, 10), (14, 29), (13, 1), (17, 13), (21, 32), (15, 5), (28, 5), (17, 12), (15, 35), (30, 14), (31, 8), (13, 26), (19, 31), (29, 23), (0, 8), (13, 29), (32, 14), (27, 36), (28, 29), (16, 3), (16, 28), (11, 15), (25, 24), (31, 31), (26, 21), (17, 29), (1, 26), (10, 37), (13, 36), (31, 9), (0, 6), (7, 36), (28, 20), (18, 26), (17, 5), (8, 29), (0, 4), (21, 13), (19, 6), (29, 21), (21, 34), (15, 25), (24, 14), (2, 16), (1, 19), (14, 20), (27, 9), (17, 25), (13, 9), (30, 26), (19, 0), (8, 36), (25, 0), (3, 12), (32, 23), (2, 15), (5, 7), (31, 30), (20, 20), (11, 25), (5, 25), (13, 33), (28, 28), (28, 35), (14, 7), (15, 0), (4, 13), (31, 19), (11, 37), (4, 4), (32, 19), (26, 16), (19, 7), (21, 2), (12, 0), (11, 14), (22, 17), (4, 19), (8, 37), (12, 22), (4, 21), (3, 19), (23, 26), (14, 32), (31, 22), (17, 17), (6, 26), (13, 23), (15, 6), (20, 26), (25, 18), (23, 15), (1, 21), (22, 30), (19, 29), (22, 37), (21, 25), (2, 6), (8, 14), (32, 0), (4, 32), (12, 2), (18, 5), (9, 21), (29, 29), (27, 22), (6, 35), (8, 7), (14, 27), (29, 15), (7, 3), (14, 21), (32, 18), (5, 21), (23, 5), (24, 29), (9, 12), (11, 17), (30, 15), (7, 18), (5, 19), (12, 7), (25, 14), (23, 8), (16, 27), (0, 22), (15, 24), (32, 7), (21, 11), (20, 34), (23, 2), (30, 10), (30, 2), (31, 18), (11, 32), (7, 23), (2, 37), (4, 16), (20, 37), (15, 20), (1, 22), (9, 22), (25, 31), (19, 19), (26, 28), (12, 20), (15, 34), (32, 27), (9, 8), (17, 23), (11, 29), (8, 5), (20, 9), (26, 14), (15, 17), (9, 33), (10, 18), (17, 20), (9, 20), (19, 13), (14, 35), (16, 32), (13, 31), (27, 25), (4, 36), (17, 14), (14, 11), (6, 23), (22, 7), (22, 21), (21, 22), (7, 25), (12, 1), (32, 16), (22, 24), (2, 26), (31, 23), (15, 12), (25, 22), (31, 0), (1, 17), (25, 12), (16, 25), (12, 37), (18, 31), (18, 13), (15, 2), (28, 8), (21, 0), (16, 33), (18, 0), (7, 33), (21, 26), (18, 15), (2, 24), (4, 3), (22, 12), (32, 3), (17, 37), (8, 15), (30, 22), (11, 8), (12, 18), (21, 19), (0, 30), (31, 12), (5, 34), (5, 24), (19, 5), (4, 33), (11, 0), (30, 5), (15, 10), (13, 15), (26, 13), (17, 1), (2, 4), (30, 34), (7, 35), (22, 35), (25, 29), (14, 2), (13, 32), (7, 1), (9, 27), (6, 31), (31, 34), (7, 13), (18, 17), (32, 25), (21, 24), (5, 35), (18, 4), (32, 11), (0, 29), (30, 13), (30, 18), (6, 15), (21, 15), (12, 33), (11, 9), (4, 27), (26, 9), (16, 35), (28, 18), (9, 30), (3, 37), (20, 11), (9, 37), (31, 28), (18, 20), (16, 34), (27, 2), (15, 13), (7, 24), (29, 19), (13, 19), (17, 0), (11, 11), (19, 28), (0, 36), (10, 15), (14, 16), (8, 9), (9, 9), (18, 34), (12, 31), (7, 12), (10, 21), (17, 26), (1, 37), (20, 8), (4, 25), (27, 32), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), 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), (19, 19), (16, 10), (14, 3), (3, 31), (20, 29), (16, 28), (27, 0), (8, 27), (2, 4), (0, 1), (7, 21), (23, 18), (0, 20), (31, 5), (23, 5), (16, 5), (19, 14), (17, 14), (16, 16), (27, 1), (11, 20), (26, 11), (3, 13), (10, 1), (24, 23), (2, 17), (15, 20), (27, 31), (2, 10), (19, 6), (12, 5), (27, 27), (17, 10), (9, 25), (7, 8), (8, 23), (10, 9), (22, 4), (23, 0), (23, 1), (32, 22), (17, 27), (20, 22), (29, 7), (16, 21), (31, 29), (3, 11), (30, 15), (0, 18), (5, 31), (21, 14), (29, 0), (10, 18), (11, 21), (22, 5), (30, 10), (6, 16), (17, 20), (31, 31), (7, 4), (3, 26), (16, 9), (6, 4), (9, 30), (29, 4), (9, 10), (28, 8), (26, 10), (31, 19), (20, 24), (19, 18), (21, 0), (29, 15), (10, 21), (16, 23), (23, 30), (26, 29), (2, 29), (1, 16), (28, 14), (7, 28), (9, 16), (18, 26), (27, 3), (4, 13), (23, 20), (11, 1), (17, 19), (1, 23), (15, 28), (26, 31), (3, 12), (17, 1), (13, 0), (5, 1), (11, 19), (28, 30), (11, 23), (28, 29), (23, 27), (29, 3), (6, 12), (16, 13), (0, 28), (18, 2), (20, 5), (18, 21), (24, 20), (2, 11), (26, 24), (27, 12), (22, 29), (31, 14), (21, 7), (16, 3), (23, 31), (27, 11), (10, 28), (15, 18), (15, 27), (4, 29), (13, 26), (14, 7), (30, 30), (6, 0), (25, 22), (20, 19), (23, 8), (19, 7), (3, 15), (5, 11), (15, 23), (14, 10), (13, 9), (29, 16), (7, 9), (22, 25), (14, 14), (25, 11), (23, 9), (9, 9), (3, 7), (26, 19), (11, 8), (30, 18), (15, 15), (21, 21), (17, 4), (14, 5), (15, 29), (26, 16), (18, 10), (15, 6), (27, 9), (13, 20), (11, 30), (3, 28), (29, 12), (23, 16), (24, 2), (29, 8), (18, 29), (13, 31), (29, 29), (14, 24), (3, 6), (16, 2), (20, 12), (15, 25), (15, 17), (5, 6), (29, 11), (5, 10), (0, 23), (24, 1), (28, 12), (9, 21), (23, 25), (7, 26), (0, 31), (6, 19), (17, 28), (31, 16), (20, 10), (2, 19), (20, 16), (14, 25), (4, 12), (3, 8), (28, 4), (8, 24), (5, 26), (13, 25), (14, 23), (9, 14), (20, 11), (21, 8), (3, 29), (2, 5), (0, 11), (4, 20), (6, 14), (0, 14), (6, 3), (8, 12), (12, 15), (24, 29), (13, 18), (27, 13), (27, 30), (22, 6), (7, 15), (5, 20), (6, 6), (24, 5), (6, 15), (30, 0), (14, 22), (4, 5), (17, 3), (10, 30), (25, 27), (0, 8), (11, 31), (15, 9), (20, 8), (19, 9), (11, 12), (32, 9), (14, 1), (23, 2), (9, 23), (19, 23), (23, 7), (11, 14), (27, 8), (3, 20), (14, 2), (28, 27), (12, 14), (22, 17), (25, 20), (17, 7), (11, 29), (28, 15), (16, 11), (16, 25), (13, 16), (8, 5), (4, 26), (14, 11), (20, 30), (23, 4), (17, 18), (15, 22), (13, 24), (27, 4), (11, 17), (20, 23), (5, 21), (20, 1), (18, 22), (31, 7), (13, 10), (30, 2), (22, 20), (22, 24), (14, 31), (26, 2), (19, 15), (0, 12), (29, 10), (32, 17), (11, 2), (7, 14), (15, 13), (11, 15), (15, 11), (22, 22), (3, 9), (21, 22), (12, 23), (17, 26), (6, 24), (14, 19), (19, 26), (13, 2), (13, 14), (25, 0), (9, 2), (27, 23), (15, 16), (21, 6), (8, 18), (8, 17), (29, 19), (31, 22), (26, 27), (2, 20), (17, 24), (3, 22), (10, 14), (29, 25), (4, 31), (26, 7), (21, 23), (1, 1), (0, 5), (3, 5), (9, 19), (13, 13), (11, 13), (30, 17), (24, 6), (12, 31), (7, 2), (13, 22), (17, 0), (25, 17), (31, 18), (1, 20), (1, 30), (4, 10), (26, 8), (28, 20), (14, 29), (13, 11), (24, 3), (12, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949536", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 14), (19, 30), (22, 29), (15, 17), (33, 24), (24, 2), (18, 16), (4, 17), (29, 12), (34, 11), (35, 9), (5, 32), (23, 19), (32, 18), (18, 9), (1, 12), (26, 1), (14, 1), (24, 6), (3, 28), (17, 31), (11, 30), (2, 34), (20, 34), (15, 18), (6, 20), (15, 3), (25, 16), (32, 20), (3, 9), (24, 4), (28, 32), (26, 2), (28, 17), (22, 33), (35, 27), (14, 28), (25, 15), (13, 30), (23, 8), (34, 19), (23, 33), (6, 33), (2, 9), (20, 31), (10, 16), (30, 18), (36, 1), (35, 24), (2, 26), (35, 25), (29, 18), (20, 1), (3, 15), (21, 19), (12, 28), (23, 28), (3, 5), (33, 10), (22, 17), (9, 34), (34, 20), (3, 16), (6, 18), (12, 14), (9, 33), (17, 19), (24, 10), (35, 19), (22, 10), (29, 13), (1, 9), (9, 0), (5, 23), (23, 34), (27, 12), (20, 2), (30, 14), (12, 32), (11, 25), (2, 18), (36, 3), (32, 33), (31, 0), (9, 26), (23, 0), (17, 33), (30, 26), (13, 12), (10, 17), (26, 16), (14, 29), (15, 7), (25, 21), (2, 32), (22, 34), (16, 34), (11, 26), (29, 1), (25, 10), (16, 22), (12, 30), (11, 11), (29, 17), (33, 25), (34, 26), (26, 13), (33, 26), (0, 19), (0, 18), (35, 11), (1, 27), (7, 21), (8, 30), (6, 0), (31, 5), (20, 12), (10, 34), (26, 8), (8, 2), (36, 22), (26, 6), (24, 1), (9, 30), (36, 5), (23, 9), (23, 21), (25, 5), (32, 5), (26, 7), (34, 8), (9, 24), (19, 0), (25, 26), (29, 9), (28, 15), (25, 30), (19, 31), (4, 20), (20, 25), (15, 6), (33, 8), (33, 22), (18, 31), (17, 12), (2, 11), (16, 7), (16, 23), (29, 2), (17, 27), (19, 9), (27, 2), (19, 19), (5, 21), (7, 29), (6, 23), (15, 30), (30, 22), (4, 23), (25, 19), (15, 9), (29, 11), (31, 30), (25, 24), (17, 1), (15, 1), (11, 29), (30, 16), (9, 2), (32, 32), (2, 3), (5, 12), (36, 10), (20, 17), (23, 16), (26, 30), (22, 30), (13, 22), (32, 12), (1, 13), (11, 23), (14, 25), (0, 33), (0, 23), (4, 14), (14, 16), (18, 26), (2, 6), (0, 21), (12, 29), (14, 14), (11, 4), (32, 22), (36, 24), (3, 25), (32, 34), (2, 24), (28, 21), (28, 6), (20, 4), (28, 20), (14, 30), (29, 28), (29, 5), (32, 30), (29, 30), (8, 24), (10, 33), (15, 24), (8, 5), (14, 5), (21, 4), (14, 12), (31, 23), (16, 13), (23, 17), (12, 23), (34, 10), (8, 25), (0, 6), (20, 33), (27, 33), (31, 20), (13, 18), (36, 9), (1, 6), (20, 5), (21, 23), (26, 26), (35, 5), (27, 25), (27, 5), (18, 1), (21, 28), (26, 28), (27, 3), (24, 9), (26, 20), (6, 6), (29, 10), (36, 6), (16, 19), (26, 10), (35, 33), (25, 7), (19, 26), (15, 10), (4, 31), (30, 15), (3, 31), (29, 24), (0, 7), (21, 9), (30, 8), (19, 16), (18, 10), (14, 31), (13, 9), (31, 27), (0, 11), (32, 16), (34, 21), (33, 9), (5, 14), (16, 17), (8, 10), (1, 17), (8, 13), (20, 15), (18, 25), (9, 31), (31, 16), (11, 34), (27, 0), (3, 22), (31, 15), (10, 1), (9, 28), (15, 11), (22, 8), (22, 9), (0, 4), (4, 27), (3, 7), (20, 27), (6, 12), (0, 14), (17, 34), (4, 29), (33, 15), (1, 10), (15, 19), (14, 10), (29, 15), (29, 21), (24, 8), (31, 14), (0, 2), (24, 11), (19, 7), (33, 30), (11, 9), (30, 9), (18, 33), (12, 3), (10, 14), (3, 10), (31, 18), (16, 33), (36, 2), (36, 31), (5, 22), (10, 0), (2, 16), (19, 23), (13, 8), (30, 10), (15, 25), (3, 21), (19, 28), (14, 24), (29, 6), (2, 29), (4, 8), (3, 20), (14, 33), (25, 4), (7, 4), (27, 6), (35, 32), (2, 22), (22, 4), (15, 20), (22, 21), (2, 15), (7, 19), (11, 27), (19, 2), (18, 7), (1, 0), (35, 10), (6, 30), (12, 4), (10, 11), (11, 31), (11, 10), (26, 5), (33, 34), (16, 24), (8, 12), (33, 23), (19, 34), (5, 24), (22, 28), (12, 2), (6, 14), (30, 23), (26, 4), (6, 9), (31, 31), (32, 8), (21, 21), (28, 9), (3, 27), (7, 6), (23, 20), (33, 3), (6, 27), (9, 20), (14, 34), (19, 32), (18, 30), (22, 31), (18, 14), (10, 23), (22, 14), (13, 31), (7, 11), (4, 4), (7, 32), (22, 15), (16, 27), (30, 27), (27, 29), (5, 31), (30, 19), (32, 21), (21, 32), (33, 21), (35, 4), (8, 4), (2, 33), (20, 9), (21, 13), (35, 29), (25, 13), (19, 4), (28, 8), (33, 19), (34, 22), (8, 28), (11, 5), (10, 28), (4, 11), (9, 14), (21, 31), (0, 15), (7, 26), (35, 31), (13, 16), (16, 1), (25, 8), (12, 34), (32, 4), (31, 28), (23, 26), (18, 24), (22, 18), (5, 28), (16, 10), (19, 25), (21, 11), (19, 6), (17, 18), (27, 32), (19, 29), (15, 23), (12, 20), (22, 24), (24, 22), (34, 15), (6, 32), (7, 25), (17, 3), (23, 10), (9, 7), (24, 24), (24, 31), (24, 12), (12, 10), (33, 4), (3, 2), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677160", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 30), (17, 22), (22, 16), (20, 7), (8, 10), (1, 26), (17, 26), (28, 10), (15, 1), (18, 9), (28, 9), (0, 26), (19, 17), (21, 27), (5, 19), (34, 9), (31, 14), (23, 19), (0, 8), (8, 31), (7, 24), (5, 21), (32, 3), (27, 19), (29, 5), (22, 29), (2, 1), (17, 11), (18, 20), (25, 5), (26, 6), (1, 23), (3, 25), (24, 16), (28, 20), (25, 25), (14, 17), (31, 19), (0, 12), (26, 8), (24, 28), (35, 26), (29, 22), (3, 4), (15, 17), (19, 27), (30, 31), (17, 17), (19, 20), (18, 18), (6, 14), (16, 17), (6, 21), (10, 1), (22, 24), (27, 16), (5, 26), (3, 14), (25, 4), (30, 5), (1, 30), (7, 0), (32, 28), (9, 27), (24, 3), (15, 3), (13, 12), (2, 16), (8, 18), (28, 8), (18, 7), (3, 10), (27, 29), (3, 1), (3, 26), (35, 9), (7, 15), (34, 2), (21, 2), (19, 8), (26, 13), (30, 12), (10, 15), (17, 24), (14, 1), (31, 27), (20, 27), (5, 14), (29, 18), (30, 16), (4, 21), (5, 22), (0, 21), (17, 10), (21, 6), (10, 13), (1, 22), (23, 10), (30, 11), (5, 27), (6, 7), (17, 0), (33, 26), (6, 4), (1, 11), (14, 15), (26, 0), (22, 4), (8, 28), (26, 25), (27, 30), (18, 17), (26, 17), (5, 4), (25, 14), (16, 11), (35, 28), (32, 30), (22, 10), (12, 13), (0, 17), (14, 21), (2, 3), (6, 17), (4, 3), (6, 20), (15, 14), (1, 29), (20, 20), (17, 7), (8, 30), (30, 29), (18, 13), (13, 7), (14, 19), (22, 28), (32, 17), (28, 22), (12, 19), (22, 14), (9, 9), (35, 3), (24, 27), (3, 30), (31, 31), (24, 7), (7, 13), (14, 0), (32, 23), (31, 4), (20, 15), (16, 18), (10, 26), (34, 24), (24, 14), (29, 9), (15, 19), (11, 27), (5, 16), (8, 26), (11, 13), (6, 23), (17, 2), (2, 7), (11, 22), (34, 29), (25, 10), (5, 1), (13, 3), (6, 29), (35, 18), (11, 14), (17, 21), (28, 1), (10, 2), (25, 23), (22, 11), (34, 6), (0, 2), (24, 0), (12, 11), (8, 1), (17, 31), (33, 23), (32, 15), (15, 25), (15, 9), (33, 2), (12, 24), (28, 23), (30, 24), (32, 19), (8, 25), (17, 8), (26, 23), (26, 30), (7, 31), (17, 23), (33, 20), (19, 9), (29, 24), (25, 15), (21, 29), (21, 0), (3, 31), (23, 5), (30, 2), (10, 7), (19, 19), (3, 19), (12, 29), (26, 3), (11, 10), (21, 18), (14, 10), (23, 26), (7, 8), (6, 28), (29, 4), (33, 0), (4, 26), (12, 14), (21, 30), (21, 28), (28, 31), (29, 17), (1, 13), (14, 12), (15, 15), (2, 6), (33, 9), (3, 9), (32, 20), (15, 11), (13, 2), (13, 13), (18, 8), (22, 12), (6, 13), (21, 15), (7, 29), (20, 16), (6, 10), (19, 24), (8, 12), (9, 11), (5, 24), (5, 9), (4, 28), (15, 10), (5, 31), (10, 6), (11, 7), (26, 11), (4, 25), (7, 19), (15, 5), (28, 6), (14, 29), (10, 21), (25, 28), (9, 17), (3, 18), (13, 15), (18, 23), (1, 27), (16, 31), (29, 8), (13, 9), (18, 22), (22, 31), (18, 26), (28, 29), (3, 17), (4, 24), (25, 29), (1, 15), (14, 9), (21, 31), (0, 20), (22, 17), (33, 25), (27, 10), (32, 16), (24, 23), (2, 24), (24, 26), (22, 7), (26, 29), (7, 18), (27, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277992", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 8), (8, 4), (20, 9), (19, 13), (12, 27), (34, 26), (25, 20), (32, 23), (21, 3), (13, 27), (4, 19), (9, 16), (10, 21), (4, 0), (24, 4), (14, 26), (7, 24), (31, 22), (22, 25), (7, 4), (29, 29), (27, 20), (7, 19), (19, 18), (26, 23), (21, 5), (31, 8), (22, 22), (3, 12), (29, 24), (25, 0), (11, 30), (2, 15), (32, 15), (8, 19), (23, 6), (31, 21), (14, 11), (21, 11), (24, 10), (9, 9), (7, 27), (18, 27), (30, 24), (32, 20), (17, 26), (28, 1), (2, 28), (9, 21), (2, 19), (24, 1), (23, 19), (8, 25), (33, 11), (9, 29), (30, 0), (17, 4), (12, 25), (26, 27), (7, 5), (15, 18), (15, 21), (8, 5), (6, 25), (5, 13), (0, 28), (22, 10), (3, 14), (26, 21), (27, 28), (10, 11), (23, 29), (30, 6), (27, 5), (28, 5), (14, 7), (24, 13), (0, 10), (17, 3), (31, 11), (22, 21), (23, 4), (10, 10), (1, 3), (1, 19), (0, 20), (28, 8), (10, 8), (12, 8), (18, 2), (3, 24), (24, 29), (5, 21), (15, 24), (31, 12), (19, 17), (16, 21), (3, 5), (7, 25), (34, 28), (23, 15), (16, 29), (26, 24), (24, 30), (5, 14), (19, 23), (34, 2), (13, 7), (10, 6), (4, 28), (25, 3), (11, 29), (29, 19), (21, 6), (15, 1), (25, 10), (2, 5), (0, 30), (17, 15), (24, 20), (14, 3), (17, 10), (28, 7), (19, 8), (14, 1), (10, 4), (22, 14), (0, 11), (33, 6), (21, 13), (15, 25), (20, 24), (21, 9), (26, 2), (22, 5), (0, 7), (7, 16), (5, 25), (16, 30), (4, 30), (8, 14), (15, 12), (17, 11), (22, 2), (34, 13), (8, 22), (7, 26), (23, 18), (29, 12), (30, 20), (6, 16), (16, 9), (15, 14), (21, 23), (2, 24), (4, 13), (11, 19), (20, 30), (30, 22), (13, 29), (8, 11), (32, 4), (6, 13), (18, 12), (11, 7), (18, 19), (23, 20), (26, 8), (14, 14), (27, 11), (34, 25), (25, 21), (34, 24), (8, 30), (18, 13), (16, 12), (24, 25), (4, 11), (12, 15), (10, 7), (17, 18), (9, 17), (1, 18), (5, 20), (13, 9), (25, 19), (1, 30), (5, 11), (11, 24), (34, 16), (12, 10), (12, 20), (8, 0), (20, 0), (34, 15), (17, 5), (14, 16), (33, 2), (21, 22), (24, 11), (26, 5), (11, 23), (21, 30), (26, 25), (24, 9), (18, 16), (26, 7), (15, 6), (6, 3), (28, 18), (2, 8), (27, 30), (19, 0), (32, 21), (12, 28), (1, 1), (19, 22), (17, 24), (16, 19), (29, 23), (6, 11), (25, 9), (5, 18), (20, 13), (29, 8), (28, 16), (29, 20), (32, 3), (5, 15), (1, 12), (9, 26), (10, 0), (32, 5), (32, 18), (25, 24), (4, 10), (9, 13), (27, 10), (29, 27), (27, 15), (27, 1), (20, 16), (13, 25), (14, 4), (28, 2), (6, 28), (11, 17), (30, 21), (26, 15), (16, 8), (0, 2), (13, 11), (25, 17), (25, 15), (17, 23), (13, 17), (22, 23), (3, 30), (14, 27), (13, 22), (32, 30), (4, 4), (1, 15), (19, 28), (27, 25), (13, 6), (19, 26), (17, 7), (17, 12), (34, 29), (16, 16), (5, 4), (17, 27), (12, 7), (30, 2), (29, 13), (3, 18), (30, 7), (28, 9), (1, 4), (17, 14), (24, 19), (26, 6), (28, 30), (11, 9), (10, 30), (23, 1), (9, 24), (31, 20), (15, 28), (2, 17), (15, 10), (19, 11), (3, 19), (33, 26), (1, 10), (29, 30), (6, 17), (17, 22), (23, 9), (18, 1), (32, 12), (25, 11), (23, 25), (2, 20), (13, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660504", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 17), (10, 5), (20, 3), (24, 18), (25, 23), (7, 14), (2, 29), (6, 20), (33, 29), (9, 11), (17, 26), (12, 13), (24, 24), (27, 11), (5, 0), (27, 15), (22, 5), (13, 6), (9, 24), (3, 21), (15, 10), (11, 19), (8, 29), (27, 19), (28, 27), (20, 27), (11, 6), (27, 8), (34, 19), (14, 30), (21, 28), (21, 5), (26, 20), (32, 7), (23, 20), (21, 7), (33, 7), (12, 2), (13, 29), (12, 17), (27, 18), (2, 5), (33, 27), (12, 7), (17, 30), (23, 5), (29, 22), (34, 13), (2, 11), (32, 25), (13, 9), (6, 17), (19, 22), (4, 16), (2, 22), (33, 21), (14, 20), (3, 5), (22, 30), (19, 15), (9, 28), (10, 6), (1, 19), (26, 4), (7, 25), (7, 9), (3, 28), (31, 28), (18, 18), (33, 1), (13, 8), (14, 5), (25, 8), (7, 20), (27, 27), (2, 14), (23, 30), (3, 13), (10, 30), (8, 8), (24, 19), (1, 26), (21, 12), (15, 8), (11, 29), (30, 24), (32, 9), (19, 14), (31, 3), (14, 25), (4, 12), (13, 12), (19, 29), (31, 0), (26, 8), (8, 24), (3, 0), (26, 26), (32, 22), (11, 27), (9, 29), (4, 1), (9, 4), (30, 23), (0, 28), (21, 3), (29, 18), (31, 13), (27, 21), (17, 10), (21, 4), (13, 15), (24, 3), (29, 1), (11, 17), (20, 1), (7, 29), (0, 16), (25, 12), (0, 29), (28, 13), (15, 6), (28, 6), (2, 9), (20, 15), (8, 1), (2, 30), (34, 16), (10, 0), (27, 0), (8, 3), (30, 29), (11, 21), (34, 27), (0, 21), (0, 7), (17, 8), (9, 0), (10, 12), (21, 11), (19, 27), (32, 15), (26, 25), (15, 21), (29, 3), (21, 24), (21, 13), (27, 3), (7, 11), (33, 14), (26, 29), (32, 29), (14, 1), (1, 0), (11, 23), (9, 19), (28, 2), (3, 16), (19, 1), (27, 17), (23, 12), (6, 4), (1, 21), (24, 28), (25, 13), (17, 7), (24, 30), (20, 11), (25, 5), (33, 19), (21, 23), (33, 13), (8, 6), (11, 22), (22, 1), (8, 15), (23, 11), (15, 12), (13, 27), (17, 0), (31, 14), (25, 24), (25, 28), (28, 23), (12, 22), (28, 29), (9, 9), (8, 0), (5, 1), (8, 11), (1, 12), (6, 12), (28, 9), (32, 2), (5, 25), (13, 23), (33, 22), (29, 8), (32, 4), (20, 4), (0, 9), (12, 28), (18, 29), (0, 15), (30, 7), (23, 19), (30, 17), (31, 9), (6, 28), (5, 29), (5, 22), (0, 3), (14, 8), (15, 0), (20, 30), (28, 0), (16, 9), (18, 1), (1, 8), (19, 30), (13, 30), (7, 12), (29, 14), (9, 7), (16, 10), (2, 21), (7, 0), (29, 5), (4, 3), (33, 12), (14, 27), (33, 5), (22, 28), (30, 20), (34, 4), (2, 2), (33, 6), (5, 18), (25, 1), (13, 11), (24, 2), (11, 3), (20, 16), (4, 26), (20, 19), (10, 25), (15, 5), (22, 4), (11, 20), (23, 18), (26, 12), (10, 9), (6, 13), (20, 25), (0, 2), (13, 1), (19, 25), (20, 8), (0, 4), (1, 22), (17, 13), (15, 23), (4, 9), (28, 24), (10, 20), (16, 11), (12, 0), (23, 3), (6, 21), (9, 5), (26, 17), (1, 4), (6, 9), (7, 24), (19, 0), (30, 10), (29, 17), (19, 9), (33, 25), (16, 16), (5, 27), (14, 29), (30, 21), (23, 17), (6, 0), (18, 8), (21, 1), (9, 18), (4, 20), (20, 23), (28, 21), (14, 12), (25, 9), (1, 20), (4, 27), (4, 0), (28, 3), (3, 18), (22, 24), (18, 10), (29, 19), (7, 27), (27, 29), (12, 5), (24, 4), (16, 0), (6, 26), (14, 6), (20, 14), (28, 22), (18, 28), (29, 0), (22, 8), (17, 9), (25, 20), (12, 29), (18, 15), (13, 24), (3, 17), (32, 11), (23, 9), (9, 15), (19, 4), (29, 7), (17, 16), (12, 8), (32, 28), (22, 10), (32, 10), (24, 1), (30, 1), (30, 8), (18, 3), (13, 18), (25, 15), (2, 28), (28, 28), (21, 25), (5, 11), (27, 14), (23, 6), (28, 12), (17, 14), (24, 16), (31, 21), (13, 13), (3, 6), (10, 13), (8, 17), (12, 4), (26, 16), (19, 24), (27, 28), (27, 22), (28, 18), (17, 25), (23, 28), (15, 2), (5, 6), (4, 28), (25, 19), (30, 19), (19, 8), (12, 30), (3, 14), (16, 7), (2, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "738576", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 11), (5, 23), (24, 3), (20, 11), (29, 26), (20, 7), (12, 0), (18, 2), (18, 10), (3, 2), (13, 27), (17, 27), (33, 10), (29, 31), (17, 8), (17, 12), (3, 19), (28, 18), (25, 27), (1, 12), (2, 1), (12, 23), (23, 1), (20, 13), (16, 26), (2, 4), (34, 14), (27, 10), (0, 7), (14, 15), (21, 3), (15, 5), (13, 4), (6, 16), (18, 24), (21, 21), (0, 28), (9, 2), (8, 0), (21, 30), (11, 6), (35, 24), (8, 20), (0, 20), (22, 1), (29, 15), (17, 17), (15, 13), (14, 21), (35, 5), (1, 26), (12, 27), (21, 25), (8, 15), (12, 13), (15, 30), (0, 26), (23, 10), (18, 4), (11, 24), (29, 2), (16, 21), (10, 15), (31, 13), (11, 32), (1, 24), (9, 10), (11, 0), (28, 12), (3, 7), (8, 23), (17, 7), (14, 23), (2, 28), (24, 4), (5, 15), (14, 30), (32, 26), (30, 13), (4, 32), (24, 23), (16, 28), (30, 20), (14, 6), (23, 11), (32, 10), (3, 13), (22, 12), (8, 26), (6, 30), (14, 11), (8, 3), (15, 29), (23, 6), (6, 0), (9, 17), (30, 18), (30, 2), (25, 11), (28, 2), (14, 22), (34, 17), (19, 27), (26, 2), (35, 19), (26, 12), (13, 8), (30, 27), (18, 6), (4, 9), (23, 24), (8, 19), (35, 25), (20, 32), (16, 13), (17, 5), (22, 24), (17, 10), (2, 7), (26, 3), (26, 4), (0, 30), (23, 2), (33, 6), (8, 14), (32, 30), (16, 31), (7, 17), (1, 8), (29, 19), (9, 18), (2, 8), (17, 13), (1, 22), (8, 21), (12, 6), (35, 23), (15, 11), (11, 25), (26, 15), (17, 9), (10, 1), (26, 18), (17, 1), (30, 17), (13, 18), (21, 12), (2, 10), (26, 5), (27, 19), (11, 27), (28, 3), (12, 16), (8, 16), (1, 32), (27, 18), (20, 1), (29, 28), (28, 25), (24, 1), (33, 28), (31, 26), (4, 23), (18, 30), (1, 7), (9, 22), (24, 10), (7, 18), (3, 31), (22, 0), (14, 4), (25, 26), (6, 20), (25, 28), (12, 19), (23, 30), (7, 19), (23, 7), (27, 1), (16, 24), (16, 14), (24, 21), (21, 4), (2, 0), (1, 16), (26, 26), (34, 31), (33, 15), (5, 32), (22, 9), (5, 13), (35, 1), (0, 6), (15, 10), (4, 17), (20, 25), (7, 21), (12, 8), (24, 32), (33, 2), (8, 6), (1, 9), (18, 29), (11, 15), (2, 23), (22, 18), (31, 22), (10, 20), (10, 24), (2, 11), (29, 32), (13, 23), (1, 29), (10, 2), (11, 4), (4, 20), (24, 19), (5, 7), (25, 18), (27, 28), (23, 4), (27, 17), (35, 21), (7, 30), (2, 22), (14, 16), (9, 13), (13, 19), (31, 32), (22, 7), (34, 32), (33, 29), (1, 2), (17, 14), (31, 19), (9, 15), (10, 21), (10, 16), (29, 24), (31, 1), (31, 6), (19, 30), (14, 1), (10, 10), (0, 21), (35, 28), (29, 6), (18, 14), (7, 32), (16, 4), (1, 11), (32, 20), (15, 14), (0, 23), (8, 30), (17, 22), (25, 30), (30, 24), (21, 22), (4, 31), (11, 1), (35, 8), (26, 19), (10, 29), (11, 30), (19, 12), (35, 26), (10, 3), (14, 0), (19, 2), (11, 10), (21, 27), (23, 17), (18, 31), (6, 15), (28, 1), (20, 24), (5, 30), (26, 11), (13, 5), (2, 21), (21, 1), (12, 29), (10, 0), (22, 29), (6, 1), (23, 0), (23, 12), (2, 32), (2, 15), (28, 21), (20, 26), (27, 30), (4, 28), (4, 1), (11, 31), (14, 13), (30, 23), (29, 13), (24, 17), (28, 20), (15, 4), (35, 10), (22, 17), (15, 21), (3, 8), (6, 24), (12, 15), (4, 27), (33, 17), (18, 15), (30, 26), (25, 24), (23, 27), (28, 16), (29, 21), (34, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "767760", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 6), (37, 16), (37, 13), (37, 15), (20, 15), (11, 18), (31, 12), (3, 24), (8, 23), (22, 15), (9, 3), (34, 6), (31, 27), (3, 7), (14, 17), (12, 15), (27, 12), (21, 13), (23, 24), (35, 1), (13, 1), (3, 18), (12, 21), (12, 16), (10, 17), (9, 7), (22, 2), (20, 0), (31, 28), (29, 19), (36, 11), (37, 8), (17, 9), (35, 23), (31, 21), (7, 29), (16, 1), (15, 15), (25, 27), (0, 23), (22, 11), (2, 11), (10, 13), (31, 4), (35, 3), (11, 2), (9, 25), (34, 20), (25, 0), (34, 19), (36, 16), (34, 14), (12, 6), (37, 2), (10, 5), (8, 25), (4, 11), (8, 28), (33, 10), (15, 6), (4, 25), (13, 15), (11, 26), (18, 13), (6, 29), (22, 18), (29, 3), (5, 6), (6, 18), (1, 26), (7, 12), (24, 27), (14, 9), (34, 11), (21, 11), (16, 29), (5, 5), (30, 10), (24, 8), (13, 8), (12, 18), (11, 21), (26, 5), (17, 25), (9, 9), (22, 8), (16, 14), (30, 2), (33, 19), (22, 22), (16, 6), (16, 15), (32, 29), (32, 3), (1, 23), (13, 24), (15, 0), (25, 1), (24, 22), (32, 23), (33, 13), (7, 6), (18, 5), (23, 20), (7, 17), (4, 7), (33, 6), (35, 9), (28, 18), (25, 21), (36, 19), (10, 12), (33, 25), (25, 11), (1, 8), (22, 6), (26, 15), (23, 21), (19, 4), (36, 24), (2, 29), (32, 27), (23, 1), (6, 10), (28, 4), (32, 20), (35, 24), (2, 20), (19, 15), (8, 0), (26, 18), (31, 17), (1, 25), (35, 21), (29, 25), (17, 14), (26, 7), (33, 0), (11, 4), (12, 7), (34, 0), (11, 27), (20, 28), (1, 29), (8, 9), (23, 25), (36, 6), (7, 20), (1, 13), (24, 1), (29, 1), (14, 24), (4, 12), (3, 4), (30, 8), (15, 18), (30, 6), (4, 18), (36, 27), (37, 28), (2, 12), (3, 23), (17, 28), (34, 17), (16, 24), (11, 23), (22, 16), (13, 19), (36, 4), (9, 2), (1, 28), (23, 12), (35, 6), (32, 10), (22, 27), (19, 6), (34, 4), (2, 3), (35, 14), (16, 18), (6, 17), (19, 5), (6, 15), (17, 20), (1, 6), (11, 13), (3, 20), (17, 1), (36, 12), (6, 25), (37, 22), (4, 28), (24, 5), (20, 16), (5, 3), (18, 22), (19, 14), (28, 25), (29, 20), (29, 5), (11, 7), (12, 22), (25, 25), (0, 4), (13, 17), (25, 18), (10, 18), (20, 26), (28, 24), (31, 8), (9, 12), (15, 7), (21, 2), (23, 27), (15, 8), (5, 14), (26, 24), (22, 20), (3, 29), (22, 29), (21, 5), (12, 24), (26, 0), (26, 27), (27, 20), (30, 20), (30, 19), (16, 0), (21, 25), (19, 29), (15, 5), (32, 12), (18, 25), (29, 21), (20, 4), (18, 7), (0, 22), (37, 14), (36, 9), (21, 14), (2, 23), (25, 5), (26, 4), (28, 0), (35, 17), (32, 24), (16, 27), (25, 15), (14, 8), (33, 16), (32, 14), (20, 11), (11, 25), (22, 23), (31, 13), (13, 3), (24, 7), (29, 28), (25, 26), (37, 1), (26, 2), (31, 29), (16, 2), (22, 1), (3, 22), (15, 27), (34, 28), (20, 10), (34, 24), (8, 8), (24, 20), (37, 4), (27, 19), (33, 4), (23, 5), (37, 25), (16, 21), (15, 13), (35, 13), (27, 21), (4, 13), (16, 10), (16, 25), (23, 7), (26, 23), (5, 2), (23, 26), (12, 17), (34, 25), (8, 29), (14, 5), (3, 14), (20, 17), (24, 12), (17, 11), (19, 2), (1, 27), (1, 5), (25, 12), (21, 7), (37, 9), (34, 29), (11, 22), (11, 6), (12, 14), (24, 24), (20, 18), (11, 10), (35, 5), (14, 27), (16, 13), (13, 0), (27, 23), (29, 11), (18, 8), (23, 8), (12, 23), (37, 12), (32, 22), (5, 20), (35, 8), (18, 20), (22, 0), (37, 27), (2, 28), (21, 0), (6, 8), (28, 12), (36, 15), (1, 22), (26, 25), (30, 12), (4, 19), (1, 0), (2, 25), (7, 1), (17, 19), (18, 23), (19, 0), (9, 11), (32, 7), (26, 6), (23, 15), (32, 9), (18, 4), (27, 6), (7, 26), (3, 10), (28, 15), (9, 14), (7, 18), (0, 19), (1, 21), (25, 7), (4, 24), (26, 11), (6, 23), (34, 18), (25, 4), (32, 4), (7, 25), (35, 12), (25, 13), (15, 24), (29, 18), (24, 23), (14, 1), (33, 12), (34, 3), (29, 17), (33, 8), (19, 16), (16, 20), (22, 14), (28, 16), (15, 2), (21, 23), (31, 11), (10, 25), (30, 9), (32, 11), (0, 15), (22, 12), (23, 10), (10, 3), (2, 27), (34, 22), (37, 23), (1, 9), (22, 9), (23, 11), (13, 20), (8, 19), (31, 5), (18, 6), (10, 22), (6, 1), (4, 17), (0, 13), (4, 14), (10, 8), (3, 13), (14, 2), (24, 14), (13, 7), (10, 20), (24, 25), (17, 10), (37, 11), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "748440", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 28), (16, 16), (22, 16), (26, 16), (20, 7), (18, 8), (22, 31), (11, 29), (0, 20), (0, 28), (5, 31), (10, 3), (9, 1), (27, 19), (8, 25), (20, 14), (24, 25), (15, 25), (23, 7), (21, 1), (16, 11), (20, 15), (0, 12), (27, 32), (5, 10), (27, 30), (13, 20), (4, 23), (12, 28), (5, 1), (24, 18), (4, 19), (18, 30), (12, 11), (4, 7), (10, 6), (11, 25), (24, 14), (31, 2), (17, 4), (11, 5), (10, 4), (6, 24), (18, 22), (8, 19), (25, 17), (5, 14), (20, 5), (30, 15), (17, 9), (9, 16), (13, 0), (11, 24), (5, 21), (28, 20), (2, 11), (11, 21), (16, 28), (2, 23), (21, 24), (11, 7), (25, 16), (9, 11), (27, 21), (8, 10), (22, 2), (20, 2), (16, 27), (5, 12), (7, 20), (22, 27), (14, 2), (20, 24), (31, 25), (26, 12), (26, 28), (7, 28), (0, 1), (14, 17), (26, 11), (22, 7), (15, 22), (31, 5), (2, 5), (30, 20), (25, 30), (27, 24), (3, 20), (22, 19), (20, 9), (28, 0), (28, 23), (15, 21), (28, 12), (30, 3), (19, 27), (2, 7), (31, 1), (31, 6), (8, 9), (10, 8), (21, 25), (27, 25), (21, 27), (30, 27), (28, 25), (30, 10), (25, 15), (24, 7), (2, 13), (5, 18), (30, 22), (14, 16), (9, 30), (2, 12), (18, 26), (16, 29), (5, 9), (4, 20), (3, 32), (31, 9), (3, 8), (12, 16), (26, 2), (15, 9), (19, 28), (31, 0), (3, 3), (6, 25), (22, 14), (30, 18), (30, 6), (3, 31), (25, 6), (12, 20), (7, 12), (22, 29), (5, 20), (16, 6), (23, 31), (6, 20), (25, 0), (9, 15), (27, 26), (30, 16), (27, 20), (24, 24), (28, 27), (10, 15), (30, 12), (15, 10), (26, 4), (4, 21), (20, 32), (11, 18), (1, 24), (28, 3), (9, 3), (17, 26), (1, 15), (25, 19), (29, 30), (28, 6), (27, 17), (31, 18), (5, 3), (24, 3), (14, 19), (28, 22), (21, 11), (8, 18), (17, 31), (8, 29), (17, 6), (7, 29), (22, 6), (16, 24), (29, 10), (4, 27), (5, 7), (12, 6), (25, 7), (26, 14), (27, 1), (20, 18), (6, 5), (26, 18), (3, 0), (27, 18), (14, 4), (17, 0), (13, 26), (19, 19), (20, 10), (12, 19), (8, 5), (12, 9), (31, 19), (30, 7), (4, 24), (3, 2), (24, 13), (26, 7), (11, 26), (4, 25), (29, 14), (24, 17), (24, 27), (16, 2), (24, 5), (3, 21), (11, 32), (9, 2), (25, 14), (23, 30), (7, 0), (2, 8), (12, 21), (3, 5), (6, 12), (1, 22), (0, 3), (16, 32), (20, 31), (6, 2), (27, 16), (14, 23), (4, 18), (20, 17), (26, 24), (31, 14), (1, 1), (15, 8), (23, 28), (4, 1), (16, 25), (8, 11), (14, 10), (15, 30), (29, 28), (28, 30), (11, 20), (7, 11), (20, 13), (14, 0), (3, 7), (3, 15), (22, 4), (3, 12), (8, 4), (13, 3), (21, 20), (0, 18), (9, 32), (29, 3), (19, 17), (20, 3), (12, 8), (4, 26), (0, 24), (1, 32), (11, 2), (7, 7), (14, 20), (21, 21), (30, 13), (0, 30), (6, 18), (19, 8), (12, 17), (5, 32), (14, 1), (28, 26), (20, 23), (29, 13), (22, 30), (1, 4), (14, 9), (12, 24), (1, 2), (18, 3), (10, 7), (18, 20), (4, 31), (14, 13), (22, 8), (28, 16), (31, 28), (7, 1), (16, 15), (9, 7), (17, 24), (30, 28), (6, 22), (14, 22), (27, 12), (1, 7), (12, 31), (23, 15), (14, 28), (16, 0), (13, 13), (26, 1), (4, 2), (3, 29), (20, 12), (25, 2), (5, 29), (29, 19), (12, 4), (4, 15), (25, 20), (10, 31), (25, 32), (8, 2), (4, 9), (2, 28), (25, 28), (25, 22), (14, 5), (19, 4), (0, 10), (26, 29), (13, 12), (21, 12), (13, 5), (17, 25), (17, 5), (4, 17), (6, 8), (11, 16), (3, 1), (18, 6), (17, 32), (10, 27), (0, 7), (24, 0), (16, 5), (13, 6), (23, 16), (30, 8), (20, 20), (16, 4), (21, 29), (17, 20), (16, 1), (31, 20), (9, 23), (19, 16), (22, 0), (15, 29), (9, 12), (14, 21), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601600", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (35, 26), (14, 4), (14, 11), (13, 25), (33, 14), (11, 6), (8, 2), (2, 14), (33, 28), (34, 2), (14, 10), (9, 31), (23, 0), (27, 20), (27, 8), (13, 21), (24, 10), (26, 15), (18, 22), (28, 2), (27, 11), (9, 0), (24, 16), (19, 23), (24, 23), (17, 13), (24, 2), (10, 15), (34, 27), (26, 14), (4, 29), (14, 27), (27, 10), (17, 23), (11, 22), (2, 25), (11, 7), (19, 25), (17, 25), (28, 29), (2, 20), (12, 21), (16, 12), (30, 3), (32, 21), (35, 20), (14, 13), (10, 20), (26, 29), (7, 20), (6, 11), (27, 24), (9, 6), (2, 29), (32, 30), (10, 26), (34, 24), (25, 25), (17, 4), (30, 1), (8, 30), (3, 24), (6, 24), (23, 24), (23, 1), (4, 4), (29, 19), (25, 20), (12, 10), (2, 13), (27, 4), (35, 21), (3, 10), (27, 23), (8, 0), (31, 14), (22, 30), (9, 9), (14, 26), (34, 15), (0, 2), (30, 11), (30, 24), (35, 12), (15, 8), (12, 8), (12, 12), (5, 24), (28, 21), (25, 26), (27, 15), (26, 20), (18, 31), (8, 20), (6, 28), (17, 29), (18, 5), (5, 29), (23, 6), (11, 14), (28, 9), (13, 14), (17, 12), (23, 17), (35, 2), (19, 12), (7, 25), (21, 2), (18, 6), (7, 27), (14, 5), (15, 20), (11, 15), (12, 23), (25, 18), (20, 20), (6, 0), (35, 13), (34, 8), (26, 7), (29, 29), (28, 0), (5, 9), (7, 9), (1, 31), (23, 5), (19, 19), (5, 26), (22, 5), (9, 28), (2, 28), (12, 27), (3, 15), (10, 9), (25, 3), (0, 24), (25, 7), (2, 4), (23, 14), (9, 12), (24, 24), (17, 31), (8, 27), (14, 0), (29, 8), (14, 19), (19, 8), (17, 3), (10, 4), (29, 24), (2, 27), (1, 11), (19, 4), (28, 5), (7, 24), (1, 20), (9, 8), (20, 2), (30, 30), (27, 18), (6, 27), (13, 3), (23, 2), (19, 7), (28, 17), (27, 21), (19, 2), (30, 22), (7, 30), (20, 15), (18, 17), (22, 17), (16, 1), (5, 21), (2, 16), (34, 28), (35, 30), (18, 8), (34, 22), (2, 15), (12, 3), (34, 21), (6, 9), (15, 1), (7, 15), (18, 30), (26, 2), (10, 7), (35, 28), (35, 5), (34, 29), (10, 17), (25, 19), (11, 20), (16, 19), (8, 6), (24, 4), (19, 27), (33, 13), (16, 7), (8, 14), (12, 14), (6, 17), (18, 4), (15, 14), (21, 17), (10, 18), (6, 25), (10, 23), (11, 4), (9, 24), (31, 20), (34, 7), (35, 15), (8, 26), (10, 28), (11, 8), (32, 20), (34, 23), (10, 8), (28, 26), (2, 5), (32, 18), (20, 27), (32, 7), (27, 19), (24, 17), (11, 27), (21, 19), (22, 11), (12, 16), (15, 16), (19, 20), (20, 21), (1, 18), (32, 13), (2, 11), (27, 16), (15, 5), (8, 17), (14, 1), (5, 6), (11, 9), (31, 5), (14, 28), (3, 7), (28, 11), (3, 18), (32, 29), (9, 2), (8, 7), (11, 5), (25, 23), (16, 6), (26, 0), (23, 13), (24, 29), (15, 6), (10, 2), (15, 11), (22, 24), (16, 11), (20, 13), (17, 5), (1, 19), (29, 27), (22, 10), (1, 26), (6, 12), (24, 9), (3, 5), (34, 11), (12, 4), (33, 9), (24, 8), (30, 13), (14, 20), (6, 4), (5, 19), (21, 13), (6, 13), (11, 28), (0, 13), (34, 25), (30, 16), (24, 20), (19, 10), (12, 6), (10, 6), (24, 19), (5, 18), (10, 31), (29, 4), (17, 18), (12, 13), (27, 27), (34, 3), (11, 19), (20, 23), (3, 4), (13, 29), (32, 14), (27, 6), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476196", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), 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), (30, 29), (20, 29), (36, 9), (18, 11), (16, 26), (27, 2), (15, 19), (20, 3), (28, 26), (27, 22), (18, 4), (5, 24), (6, 3), (4, 13), (28, 29), (17, 12), (12, 3), (4, 5), (35, 21), (8, 25), (36, 7), (5, 1), (7, 4), (5, 23), (35, 0), (19, 12), (33, 2), (5, 6), (10, 29), (8, 8), (24, 7), (16, 5), (2, 22), (12, 1), (11, 16), (3, 17), (4, 12), (23, 17), (20, 13), (9, 29), (19, 23), (32, 10), (4, 4), (4, 20), (23, 13), (10, 15), (15, 11), (3, 27), (29, 10), (7, 12), (11, 9), (24, 1), (27, 23), (35, 7), (31, 26), (17, 0), (6, 24), (7, 28), (11, 11), (1, 12), (3, 1), (19, 11), (3, 25), (12, 20), (20, 22), (7, 26), (23, 15), (20, 15), (2, 19), (26, 6), (35, 16), (8, 6), (33, 1), (13, 23), (28, 28), (11, 15), (6, 30), (15, 1), (1, 8), (7, 30), (25, 11), (23, 11), (21, 31), (18, 1), (0, 12), (20, 1), (14, 14), (29, 21), (18, 20), (0, 15), (7, 3), (25, 22), (29, 30), (9, 21), (28, 21), (17, 11), (4, 8), (19, 29), (18, 25), (10, 5), (14, 13), (29, 26), (20, 18), (10, 17), (15, 7), (13, 21), (27, 7), (28, 13), (23, 4), (16, 25), (4, 2), (36, 16), (36, 27), (10, 28), (2, 14), (29, 28), (1, 20), (30, 21), (4, 29), (11, 24), (22, 0), (26, 13), (26, 8), (6, 7), (18, 27), (34, 23), (19, 3), (19, 6), (0, 19), (23, 14), (24, 4), (11, 7), (21, 25), (32, 27), (18, 3), (0, 2), (13, 14), (5, 16), (2, 2), (17, 17), (11, 19), (32, 17), (11, 17), (14, 5), (11, 25), (7, 8), (9, 14), (10, 18), (17, 27), (31, 20), (27, 26), (7, 21), (25, 7), (36, 21), (34, 25), (33, 14), (23, 19), (36, 12), (16, 15), (5, 11), (19, 1), (2, 11), (27, 11), (13, 30), (11, 20), (18, 14), (7, 23), (34, 12), (3, 2), (23, 9), (19, 21), (31, 18), (4, 25), (28, 11), (5, 0), (26, 21), (31, 17), (17, 13), (27, 16), (28, 9), (16, 18), (30, 4), (14, 20), (34, 5), (32, 20), (25, 0), (21, 13), (1, 4), (26, 2), (30, 5), (36, 1), (18, 31), (5, 10), (31, 23), (15, 10), (3, 14), (9, 9), (14, 29), (24, 26), (3, 16), (11, 8), (28, 6), (14, 31), (34, 15), (14, 3), (21, 10), (9, 23), (17, 20), (9, 2), (4, 18), (17, 29), (20, 24), (33, 9), (10, 1), (2, 6), (8, 5), (9, 4), (23, 26), (16, 6), (12, 15), (15, 8), (31, 1), (22, 21), (17, 2), (1, 7), (11, 26), (25, 19), (2, 13), (16, 20), (24, 17), (13, 9), (1, 13), (32, 3), (4, 27), (35, 4), (25, 4), (32, 16), (33, 28), (21, 15), (22, 16), (21, 27), (27, 0), (12, 16), (24, 2), (17, 5), (31, 31), (12, 12), (2, 20), (30, 3), (23, 31), (25, 29), (8, 24), (32, 23), (24, 13), (31, 29), (28, 15), (31, 12), (5, 15), (1, 30), (10, 25), (14, 8), (13, 31), (25, 8), (31, 30), (30, 30), (4, 0), (16, 28), (30, 13), (31, 16), (24, 5), (12, 10), (16, 11), (34, 9), (9, 17), (13, 15), (21, 12), (3, 15), (0, 20), (35, 5), (29, 31), (16, 21), (13, 20), (15, 17), (16, 2), (18, 12), (29, 18), (18, 7), (24, 10), (9, 22), (8, 26), (13, 29), (9, 27), (7, 11), (20, 5), (22, 3), (36, 25), (26, 20), (27, 31), (22, 17), (30, 7), (3, 4), (8, 3), (5, 3), (1, 16), (10, 22), (29, 22), (35, 12), (2, 21), (26, 3), (16, 22), (34, 13), (23, 1), (15, 20), (17, 4), (19, 27), (32, 4), (1, 25), (6, 29), (1, 24), (13, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402300", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (35, 6), (12, 22), (32, 23), (4, 1), (12, 7), (21, 9), (30, 22), (9, 10), (2, 17), (30, 18), (21, 23), (2, 20), (12, 10), (18, 7), (11, 5), (20, 15), (6, 24), (30, 8), (21, 13), (16, 3), (4, 18), (29, 3), (32, 5), (24, 0), (33, 9), (29, 28), (8, 5), (25, 13), (2, 29), (16, 18), (8, 17), (6, 10), (29, 14), (5, 27), (24, 19), (19, 19), (11, 19), (3, 0), (12, 26), (28, 21), (15, 23), (28, 3), (4, 6), (6, 18), (11, 23), (13, 21), (26, 3), (18, 5), (11, 24), (15, 16), (13, 22), (22, 22), (30, 29), (17, 1), (23, 15), (34, 13), (18, 28), (25, 6), (6, 9), (16, 29), (20, 28), (10, 15), (25, 24), (2, 18), (26, 6), (17, 25), (0, 8), (2, 4), (14, 9), (28, 14), (23, 3), (35, 22), (27, 26), (7, 28), (3, 10), (13, 4), (22, 21), (16, 7), (23, 5), (11, 9), (19, 16), (18, 19), (27, 4), (14, 13), (13, 23), (34, 14), (2, 26), (28, 10), (25, 17), (10, 23), (30, 10), (5, 12), (16, 2), (22, 26), (25, 27), (34, 10), (8, 28), (6, 20), (11, 3), (31, 29), (33, 7), (9, 27), (21, 0), (19, 2), (32, 2), (4, 3), (0, 21), (31, 22), (27, 2), (33, 23), (33, 25), (31, 16), (6, 3), (28, 6), (17, 22), (1, 1), (21, 10), (24, 1), (16, 22), (24, 23), (26, 4), (29, 18), (20, 2), (15, 29), (28, 27), (6, 2), (25, 2), (20, 29), (23, 28), (19, 7), (20, 5), (4, 0), (6, 8), (1, 24), (3, 8), (11, 16), (25, 16), (12, 15), (14, 20), (16, 19), (23, 23), (15, 11), (34, 16), (24, 24), (27, 1), (15, 18), (25, 19), (10, 24), (7, 20), (23, 19), (5, 23), (9, 8), (9, 15), (11, 20), (14, 12), (16, 17), (6, 16), (12, 6), (4, 29), (0, 10), (26, 29), (5, 3), (10, 11), (1, 26), (28, 13), (30, 16), (16, 15), (25, 7), (21, 12), (1, 4), (31, 26), (7, 29), (15, 22), (34, 4), (16, 0), (3, 13), (3, 9), (24, 11), (26, 25), (22, 0), (18, 23), (22, 13), (14, 6), (20, 10), (19, 12), (25, 5), (10, 0), (20, 3), (21, 18), (4, 9), (32, 26), (26, 23), (15, 9), (7, 6), (27, 18), (15, 6), (26, 0), (1, 10), (27, 20), (25, 10), (1, 14), (14, 0), (8, 10), (18, 12), (12, 5), (34, 28), (13, 14), (14, 14), (7, 5), (18, 8), (27, 19), (6, 4), (35, 0), (23, 14), (15, 12), (17, 4), (26, 18), (29, 13), (24, 21), (1, 11), (3, 25), (11, 28), (10, 21), (31, 14), (11, 6), (6, 11), (6, 0), (12, 24), (29, 2), (23, 10), (19, 24), (5, 16), (21, 6), (5, 7), (29, 15), (10, 1), (26, 15), (33, 17), (30, 24), (26, 14), (26, 8), (33, 14), (31, 23), (23, 7), (25, 20), (33, 18), (29, 9), (28, 9), (7, 21), (27, 23), (14, 16), (18, 3), (11, 14), (18, 26), (3, 18), (30, 11), (26, 17), (35, 26), (21, 5), (34, 18), (14, 2), (25, 22), (19, 14), (18, 4), (0, 19), (34, 29), (27, 5), (31, 21), (20, 13), (21, 26), (24, 27), (16, 20), (32, 0), (10, 27), (29, 23), (16, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "850432", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 30), (18, 4), (19, 13), (29, 25), (4, 6), (18, 25), (20, 19), (0, 12), (8, 19), (13, 3), (20, 6), (29, 12), (5, 1), (1, 3), (6, 24), (15, 28), (23, 20), (14, 20), (24, 0), (5, 31), (30, 13), (21, 5), (17, 13), (10, 0), (26, 16), (9, 2), (12, 27), (20, 18), (9, 27), (4, 19), (12, 18), (25, 5), (13, 27), (22, 13), (23, 9), (29, 24), (3, 13), (18, 29), (19, 2), (17, 25), (3, 9), (27, 2), (10, 16), (0, 27), (12, 8), (9, 28), (24, 24), (0, 1), (11, 24), (19, 26), (18, 32), (12, 16), (8, 10), (24, 32), (22, 9), (28, 23), (26, 23), (5, 24), (18, 10), (14, 5), (25, 27), (31, 11), (16, 5), (6, 0), (13, 0), (2, 28), (4, 9), (8, 26), (31, 10), (5, 3), (15, 2), (29, 26), (18, 6), (20, 14), (12, 17), (18, 2), (30, 9), (17, 23), (29, 11), (23, 17), (31, 2), (1, 12), (28, 13), (2, 31), (10, 15), (21, 24), (25, 23), (25, 26), (25, 1), (8, 6), (0, 7), (27, 6), (17, 17), (30, 15), (12, 32), (20, 27), (0, 24), (18, 9), (24, 2), (13, 15), (11, 29), (9, 30), (2, 12), (0, 9), (30, 12), (29, 27), (17, 24), (15, 31), (27, 3), (13, 17), (12, 5), (7, 12), (8, 12), (13, 11), (6, 31), (3, 0), (16, 13), (15, 14), (31, 8), (28, 16), (15, 11), (12, 19), (22, 24), (17, 7), (30, 29), (14, 30), (0, 29), (14, 14), (4, 1), (7, 6), (3, 25), (8, 7), (15, 26), (1, 10), (31, 0), (7, 26), (2, 7), (9, 1), (21, 28), (0, 6), (29, 17), (29, 6), (31, 4), (1, 25), (3, 23), (9, 19), (26, 11), (18, 5), (11, 7), (14, 13), (12, 13), (23, 15), (9, 18), (18, 3), (20, 20), (11, 8), (19, 9), (31, 15), (25, 18), (16, 26), (4, 31), (11, 4), (20, 25), (4, 16), (25, 9), (19, 15), (21, 10), (11, 3), (14, 9), (10, 32), (8, 4), (14, 19), (17, 27), (7, 30), (17, 9), (18, 19), (28, 10), (22, 2), (2, 25), (11, 14), (30, 32), (4, 12), (5, 2), (19, 19), (25, 31), (3, 32), (14, 32), (26, 20), (14, 29), (16, 16), (22, 12), (12, 31), (24, 27), (5, 16), (28, 7), (17, 4), (21, 22), (29, 5), (17, 11), (30, 27), (0, 19), (10, 8), (28, 22), (22, 10), (17, 29), (24, 15), (4, 0), (16, 17), (5, 19), (27, 23), (22, 30), (27, 25), (31, 21), (24, 4), (28, 8), (4, 24), (19, 30), (1, 13), (11, 6), (27, 32), (11, 23), (7, 14), (23, 11), (28, 6), (18, 31), (29, 9), (25, 22), (25, 6), (11, 5), (2, 4), (6, 19), (31, 5), (13, 30), (15, 27), (10, 4), (18, 8), (9, 11), (30, 8), (19, 25), (16, 15), (22, 18), (14, 18), (5, 22), (3, 19), (12, 11), (14, 22), (4, 21), (22, 25), (8, 1), (19, 28), (6, 28), (16, 3), (0, 8), (8, 23), (11, 31), (19, 0), (20, 29), (14, 25), (10, 30), (26, 2), (8, 28), (20, 5), (15, 19), (28, 17), (21, 13), (21, 21), (7, 8), (24, 29), (17, 2), (16, 9), (2, 8), (29, 29), (11, 13), (4, 8), (1, 22), (26, 1), (28, 21), (21, 19), (17, 19), (29, 7), (2, 10), (7, 9), (4, 3), (10, 28), (25, 12), (14, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "490960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (17, 22), (26, 28), (27, 12), (30, 14), (18, 20), (6, 4), (1, 24), (12, 8), (16, 19), (28, 7), (20, 6), (20, 19), (25, 21), (17, 10), (23, 28), (6, 28), (29, 8), (25, 7), (27, 9), (1, 17), (22, 32), (22, 28), (17, 29), (33, 5), (18, 30), (20, 24), (15, 2), (23, 8), (21, 28), (24, 11), (28, 4), (22, 18), (30, 17), (13, 32), (29, 7), (8, 24), (10, 8), (13, 36), (19, 12), (21, 34), (0, 7), (29, 0), (4, 4), (5, 36), (4, 13), (18, 8), (5, 3), (32, 17), (23, 16), (24, 2), (15, 28), (28, 25), (13, 26), (1, 25), (26, 33), (20, 30), (25, 29), (6, 8), (7, 17), (13, 12), (29, 31), (32, 30), (8, 27), (14, 22), (19, 36), (13, 30), (2, 6), (8, 2), (11, 7), (8, 13), (31, 3), (3, 1), (12, 12), (9, 27), (23, 25), (24, 6), (7, 16), (18, 16), (28, 20), (17, 4), (8, 23), (13, 3), (18, 19), (1, 6), (18, 3), (0, 31), (1, 36), (25, 19), (12, 13), (16, 25), (26, 3), (28, 5), (17, 7), (13, 11), (22, 21), (8, 0), (23, 0), (24, 16), (13, 1), (5, 35), (1, 9), (31, 36), (24, 19), (22, 10), (24, 25), (9, 3), (22, 24), (23, 26), (19, 22), (19, 2), (26, 9), (5, 13), (7, 3), (18, 5), (25, 9), (2, 25), (7, 24), (28, 14), (34, 17), (9, 4), (12, 9), (31, 6), (20, 17), (21, 10), (15, 30), (21, 33), (15, 1), (8, 17), (5, 33), (25, 22), (2, 4), (31, 22), (17, 30), (11, 24), (21, 24), (13, 6), (29, 33), (22, 2), (13, 7), (11, 10), (34, 13), (14, 11), (26, 12), (12, 35), (18, 35), (22, 11), (7, 26), (18, 10), (8, 34), (29, 22), (8, 8), (29, 32), (7, 0), (19, 27), (27, 18), (34, 28), (26, 1), (34, 9), (11, 16), (0, 20), (3, 18), (15, 10), (14, 23), (30, 6), (22, 16), (1, 21), (23, 18), (23, 20), (15, 19), (28, 27), (19, 20), (8, 28), (14, 25), (5, 4), (7, 19), (1, 4), (4, 15), (1, 12), (9, 7), (33, 13), (9, 18), (21, 0), (14, 7), (15, 0), (30, 7), (26, 14), (5, 21), (5, 16), (25, 5), (6, 1), (21, 15), (34, 8), (32, 5), (16, 6), (10, 13), (2, 16), (10, 0), (3, 34), (10, 15), (16, 27), (18, 34), (33, 12), (7, 15), (1, 33), (10, 12), (3, 10), (16, 1), (30, 28), (21, 11), (17, 5), (8, 15), (27, 20), (9, 11), (4, 10), (21, 31), (18, 27), (7, 18), (30, 19), (21, 18), (19, 8), (22, 9), (23, 7), (31, 12), (3, 6), (28, 3), (27, 15), (33, 25), (34, 15), (24, 31), (31, 1), (1, 8), (34, 2), (3, 16), (26, 27), (6, 0), (9, 28), (2, 1), (26, 20), (10, 27), (9, 24), (27, 1), (10, 36), (25, 24), (16, 13), (34, 25), (19, 4), (11, 14), (26, 10), (2, 2), (18, 17), (20, 25), (18, 31), (10, 19), (14, 32), (21, 12), (8, 32), (5, 9), (29, 21), (15, 18), (12, 27), (26, 34), (2, 21), (34, 10), (11, 6), (0, 10), (1, 1), (19, 11), (32, 14), (7, 9), (33, 33), (5, 29), (22, 13), (11, 36), (0, 18), (24, 13), (14, 9), (29, 25), (5, 30), (23, 19), (12, 25), (21, 8), (15, 3), (1, 7), (2, 29), (9, 23), (9, 22), (22, 36), (17, 25), (16, 35), (10, 17), (4, 19), (28, 35), (31, 5), (12, 0), (12, 21), (27, 8), (19, 19), (9, 9), (29, 28), (3, 8), (21, 20), (34, 34), (20, 23), (14, 1), (8, 1), (20, 10), (22, 29), (23, 17), (18, 28), (24, 5), (33, 35), (26, 8), (27, 30), (30, 18), (15, 20), (24, 21), (26, 2), (26, 31), (15, 16), (28, 30), (24, 33), (28, 23), (10, 33), (34, 12), (16, 36), (15, 26), (28, 1), (20, 11), (6, 15), (10, 29), (2, 34), (22, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944748", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 27), (26, 18), (27, 30), (11, 3), (4, 26), (11, 15), (16, 1), (9, 12), (7, 5), (6, 6), (6, 22), (10, 1), (4, 1), (28, 9), (27, 13), (21, 11), (10, 23), (2, 17), (12, 1), (20, 10), (14, 8), (12, 25), (19, 10), (30, 2), (15, 19), (23, 20), (1, 1), (10, 10), (25, 31), (25, 9), (6, 11), (13, 10), (16, 25), (2, 15), (12, 18), (28, 21), (27, 24), (9, 2), (11, 23), (27, 5), (22, 13), (6, 27), (17, 5), (19, 4), (7, 7), (30, 7), (9, 15), (17, 7), (15, 26), (5, 18), (29, 29), (5, 23), (28, 13), (4, 2), (17, 2), (1, 11), (22, 17), (18, 27), (12, 11), (0, 11), (4, 3), (12, 6), (5, 10), (24, 1), (24, 23), (20, 2), (26, 13), (6, 13), (4, 32), (23, 13), (0, 7), (16, 3), (26, 2), (25, 19), (25, 15), (23, 28), (22, 33), (8, 2), (26, 8), (16, 21), (30, 16), (14, 14), (4, 30), (1, 18), (12, 22), (30, 6), (30, 26), (14, 26), (13, 13), (7, 16), (27, 23), (21, 22), (25, 2), (27, 20), (15, 9), (6, 4), (28, 30), (15, 7), (11, 0), (10, 32), (7, 31), (30, 4), (14, 2), (22, 23), (0, 1), (19, 32), (15, 29), (29, 26), (7, 30), (0, 5), (24, 19), (30, 32), (10, 4), (17, 28), (30, 21), (28, 1), (30, 10), (1, 6), (27, 3), (18, 25), (23, 17), (7, 20), (21, 5), (7, 23), (28, 15), (30, 27), (8, 13), (4, 18), (9, 30), (27, 10), (29, 8), (30, 30), (28, 2), (14, 9), (8, 16), (12, 28), (3, 20), (17, 4), (23, 33), (9, 9), (14, 12), (8, 29), (19, 17), (8, 32), (8, 31), (21, 1), (4, 19), (7, 0), (15, 27), (25, 16), (25, 4), (26, 32), (1, 8), (19, 19), (12, 29), (26, 6), (25, 12), (10, 2), (2, 18), (19, 29), (28, 7), (24, 7), (0, 23), (3, 30), (3, 10), (7, 10), (5, 15), (25, 1), (19, 24), (12, 4), (1, 20), (9, 8), (18, 16), (11, 25), (30, 15), (0, 31), (21, 10), (23, 31), (0, 20), (11, 21), (6, 28), (28, 14), (3, 8), (1, 14), (20, 18), (2, 29), (9, 20), (13, 24), (1, 13), (20, 21), (17, 31), (12, 0), (17, 19), (15, 31), (10, 29), (8, 15), (6, 3), (26, 10), (27, 17), (1, 27), (22, 11), (22, 6), (13, 26), (15, 16), (5, 31), (15, 24), (29, 18), (14, 27), (4, 13), (25, 10), (29, 1), (23, 10), (20, 7), (13, 14), (27, 16), (20, 25), (28, 20), (21, 25), (10, 6), (24, 25), (6, 23), (9, 27), (7, 9), (4, 14), (25, 32), (2, 14), (6, 14), (8, 30), (4, 8), (14, 33), (12, 24), (9, 14), (12, 32), (18, 10), (1, 22), (8, 12), (27, 4), (14, 31), (25, 11), (21, 7), (7, 18), (26, 17), (27, 1), (29, 16), (5, 32), (0, 3), (6, 33), (28, 8), (29, 19), (27, 31), (9, 6), (16, 23), (13, 9), (15, 11), (26, 31), (3, 2), (11, 16), (22, 14), (22, 31), (15, 12), (17, 25), (6, 2), (19, 22), (1, 28), (13, 0), (0, 16), (6, 29), (11, 22), (8, 23), (13, 27), (29, 17), (1, 3), (5, 27), (23, 8), (15, 17), (20, 30), (12, 10), (3, 1), (15, 8), (28, 32), (0, 6), (19, 33), (14, 21), (5, 5), (12, 8), (29, 10), (0, 8), (21, 18), (26, 1), (11, 8), (17, 12), (16, 0), (21, 16), (1, 30), (14, 7), (2, 24), (5, 14), (9, 25), (0, 28), (23, 2), (13, 20), (23, 14), (12, 27), (19, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "293876", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (13, 31), (10, 24), (7, 11), (5, 28), (27, 35), (29, 10), (10, 3), (8, 31), (5, 27), (26, 30), (27, 16), (22, 33), (19, 25), (11, 36), (20, 31), (10, 31), (2, 4), (10, 16), (21, 3), (10, 30), (4, 2), (22, 20), (17, 6), (29, 22), (14, 24), (27, 19), (19, 8), (27, 31), (16, 4), (12, 20), (12, 13), (25, 29), (5, 1), (10, 21), (9, 18), (6, 2), (28, 29), (26, 8), (21, 12), (22, 19), (5, 22), (7, 7), (18, 13), (8, 7), (6, 31), (28, 30), (14, 11), (15, 29), (2, 35), (19, 18), (25, 20), (25, 14), (3, 33), (2, 32), (19, 2), (5, 14), (7, 4), (12, 33), (25, 6), (9, 33), (7, 32), (11, 26), (11, 3), (29, 27), (15, 30), (15, 9), (12, 26), (10, 11), (8, 20), (0, 25), (3, 31), (16, 32), (25, 24), (20, 22), (16, 29), (14, 7), (5, 31), (4, 22), (29, 3), (21, 22), (24, 23), (15, 22), (10, 10), (0, 23), (12, 3), (28, 26), (21, 16), (21, 26), (23, 31), (11, 33), (27, 14), (24, 15), (11, 5), (29, 9), (2, 36), (18, 31), (18, 32), (19, 15), (8, 10), (19, 27), (19, 30), (22, 2), (17, 34), (8, 2), (0, 19), (6, 20), (13, 13), (18, 23), (6, 33), (10, 29), (6, 12), (23, 26), (19, 6), (9, 21), (14, 0), (16, 17), (26, 18), (3, 13), (25, 5), (9, 10), (21, 2), (1, 33), (22, 10), (3, 35), (17, 13), (4, 31), (25, 15), (18, 33), (27, 2), (7, 0), (23, 22), (13, 20), (2, 19), (0, 33), (2, 29), (21, 4), (19, 32), (10, 22), (5, 21), (14, 17), (22, 5), (22, 17), (9, 32), (1, 18), (28, 14), (3, 18), (2, 17), (28, 32), (13, 19), (19, 1), (27, 13), (29, 25), (22, 34), (17, 11), (19, 35), (20, 3), (4, 0), (1, 34), (1, 12), (13, 22), (27, 22), (23, 17), (9, 31), (16, 16), (7, 6), (21, 18), (18, 18), (0, 32), (13, 29), (15, 0), (24, 0), (13, 9), (4, 20), (9, 8), (15, 14), (28, 34), (14, 9), (9, 16), (4, 32), (4, 11), (12, 6), (17, 9), (12, 35), (29, 33), (27, 7), (7, 10), (2, 7), (26, 26), (25, 25), (13, 0), (6, 11), (5, 25), (21, 1), (1, 36), (1, 32), (18, 19), (20, 29), (26, 17), (17, 27), (3, 32), (7, 22), (15, 5), (22, 8), (24, 16), (28, 16), (20, 0), (24, 24), (4, 1), (17, 17), (24, 20), (5, 10), (0, 10), (4, 5), (1, 11), (21, 27), (13, 1), (18, 4), (10, 18), (14, 26), (29, 12), (16, 0), (20, 19), (7, 25), (9, 36), (9, 13), (8, 18), (22, 26), (20, 1), (29, 14), (21, 31), (24, 21), (19, 0), (13, 5), (26, 35), (13, 12), (23, 8), (17, 26), (16, 2), (29, 30), (29, 23), (28, 1), (18, 29), (6, 14), (15, 7), (16, 30), (15, 23), (1, 27), (29, 28), (14, 5), (16, 8), (19, 10), (25, 9), (9, 28), (23, 28), (13, 25), (20, 14), (20, 35), (13, 27), (21, 25), (5, 6), (14, 15), (13, 21), (15, 35), (8, 36), (14, 6), (20, 26), (22, 0), (18, 14), (6, 35), (9, 11), (26, 24), (1, 24), (13, 7), (6, 6), (5, 29), (26, 11), (20, 18), (0, 14), (29, 18), (14, 25), (29, 6), (16, 5), (8, 21), (13, 16), (8, 5), (16, 1), (12, 28), (7, 23), (11, 10), (25, 10), (7, 34), (3, 25), (14, 19), (0, 4), (7, 17), (7, 31), (15, 28), (9, 4), (14, 8), (11, 31), (17, 30), (16, 35), (5, 30), (14, 14), (28, 10), (5, 18), (18, 10), (25, 13), (3, 28), (10, 9), (9, 25), (7, 5), (19, 31), (27, 30), (22, 14), (0, 12), (9, 3), (17, 31), (15, 3), (15, 15), (0, 29), (29, 5), (17, 36), (28, 13), (6, 9), (9, 2), (2, 28), (15, 11), (22, 22), (2, 18), (11, 28), (9, 35), (21, 6), (16, 13), (3, 8), (6, 0), (9, 19), (21, 15), (8, 35), (25, 3), (7, 2), (18, 21), (5, 20), (27, 15), (26, 1), (3, 24), (20, 32), (28, 12), (23, 23), (3, 29), (15, 25), (4, 36), (6, 18), (4, 17), (21, 14), (11, 1), (26, 3), (26, 9), (10, 28), (24, 27), (2, 5), (20, 25), (3, 15), (0, 31), (21, 11), (25, 27), (2, 34), (5, 8), (20, 6), (22, 31), (18, 5), (10, 17), (27, 6), (4, 6), (0, 24), (5, 19), (1, 21), (24, 25), (26, 16), (9, 9), (5, 16), (25, 23), (28, 20), (23, 3), (5, 24), (16, 18), (0, 1), (22, 24), (13, 24), (14, 32), (9, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987840", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 32), (1, 2), (0, 30), (1, 28), (20, 13), (15, 24), (1, 27), (19, 13), (15, 8), (33, 22), (34, 19), (8, 3), (21, 12), (28, 26), (35, 3), (14, 13), (36, 0), (29, 7), (36, 11), (23, 31), (28, 0), (14, 0), (16, 13), (10, 23), (8, 7), (36, 27), (7, 8), (0, 12), (0, 13), (7, 6), (13, 27), (36, 14), (25, 29), (36, 16), (34, 20), (18, 24), (31, 11), (28, 1), (21, 8), (17, 16), (18, 7), (27, 28), (10, 19), (7, 23), (13, 22), (5, 13), (27, 31), (16, 12), (3, 25), (7, 30), (3, 18), (11, 30), (11, 8), (22, 6), (4, 28), (14, 2), (35, 27), (8, 20), (25, 24), (30, 2), (36, 15), (12, 25), (9, 26), (13, 6), (34, 1), (6, 17), (11, 10), (18, 19), (34, 15), (31, 1), (26, 24), (2, 28), (0, 23), (36, 20), (36, 1), (23, 32), (30, 13), (26, 6), (4, 18), (23, 28), (20, 2), (30, 23), (34, 14), (23, 4), (23, 14), (28, 28), (7, 7), (15, 1), (4, 32), (0, 6), (1, 14), (27, 15), (32, 18), (15, 21), (5, 2), (35, 13), (25, 12), (4, 2), (5, 0), (35, 20), (3, 9), (20, 18), (18, 27), (25, 30), (25, 21), (5, 25), (19, 4), (3, 13), (6, 29), (32, 7), (10, 26), (1, 19), (14, 3), (13, 31), (8, 15), (29, 22), (34, 27), (14, 8), (24, 7), (22, 3), (5, 30), (31, 30), (27, 18), (3, 11), (36, 6), (22, 22), (26, 25), (23, 23), (10, 8), (16, 0), (23, 22), (21, 20), (12, 14), (26, 19), (14, 24), (21, 18), (9, 20), (0, 9), (7, 18), (30, 30), (36, 2), (10, 5), (25, 32), (21, 7), (14, 15), (32, 9), (35, 16), (5, 1), (29, 32), (18, 26), (8, 31), (27, 21), (28, 24), (34, 16), (31, 0), (32, 28), (10, 11), (15, 31), (35, 29), (19, 26), (24, 31), (22, 23), (31, 23), (21, 16), (34, 5), (3, 22), (10, 13), (14, 26), (13, 21), (17, 4), (18, 8), (29, 3), (3, 14), (3, 26), (1, 30), (21, 10), (4, 9), (8, 5), (21, 30), (35, 10), (10, 30), (24, 0), (13, 8), (4, 20), (15, 28), (27, 16), (16, 11), (33, 5), (24, 4), (23, 17), (14, 32), (26, 7), (17, 24), (11, 23), (16, 3), (18, 6), (29, 25), (33, 17), (4, 3), (19, 32), (22, 12), (17, 12), (1, 22), (14, 7), (17, 26), (0, 2), (23, 24), (1, 20), (6, 19), (8, 12), (12, 1), (8, 28), (25, 11), (22, 13), (29, 17), (30, 9), (29, 12), (36, 13), (23, 8), (24, 19), (11, 31), (34, 32), (4, 14), (27, 6), (9, 8), (7, 17), (26, 1), (4, 16), (9, 14), (4, 21), (21, 9), (6, 5), (13, 25), (23, 7), (23, 20), (14, 22), (19, 18), (2, 16), (20, 16), (17, 8), (21, 27), (2, 8), (4, 17), (14, 12), (24, 6), (8, 14), (2, 18), (9, 30), (2, 11), (25, 28), (7, 28), (2, 31), (6, 16), (2, 15), (7, 16), (32, 1), (8, 17), (6, 7), (23, 3), (25, 5), (4, 4), (34, 8), (13, 24), (3, 23), (33, 0), (34, 31), (3, 31), (16, 30), (24, 9), (36, 3), (6, 0), (32, 16), (10, 32), (11, 16), (13, 15), (33, 9), (12, 27), (20, 4), (29, 14), (20, 20), (28, 16), (15, 0), (3, 5), (11, 7), (21, 13), (5, 5), (1, 24), (19, 10), (20, 15), (14, 25), (11, 0), (35, 9), (20, 9), (20, 17), (18, 29), (13, 1), (32, 20), (25, 23), (34, 9), (27, 10), (21, 3), (18, 3), (36, 26), (6, 18), (6, 15), (31, 17), (19, 29), (24, 30), (5, 29), (12, 22), (14, 28), (22, 4), (28, 12), (8, 19), (11, 4), (29, 24), (22, 19), (36, 5), (26, 17), (31, 3), (0, 17), (24, 27), (15, 18), (9, 19), (35, 18), (30, 10), (7, 12), (10, 1), (27, 26), (21, 2), (15, 25), (31, 26), (3, 0), (14, 17), (21, 0), (20, 28), (12, 21), (24, 2), (5, 10), (29, 29), (9, 16), (10, 0), (26, 30), (3, 19), (21, 32), (5, 20), (28, 11), (17, 25), (14, 18), (5, 18), (32, 31), (12, 4), (5, 23), (0, 15), (18, 2), (9, 22), (1, 8), (30, 1), (18, 11), (32, 0), (35, 5), (4, 1), (28, 7), (10, 7), (27, 8), (17, 21), (23, 0), (30, 4), (33, 12), (12, 0), (17, 17), (30, 7), (3, 12), (33, 8), (33, 11), (7, 13), (28, 22), (27, 1), (5, 16), (1, 31), (27, 29), (28, 30), (24, 25), (25, 13), (27, 11), (28, 10), (4, 19), (30, 17), (3, 7), (17, 32), (36, 31), (10, 29), (27, 17), (31, 24), (19, 19), (11, 2), (14, 31), (30, 27), (16, 20), (27, 23), (24, 15), (20, 29), (22, 8), (5, 19), (3, 28), (5, 17), (24, 8), (23, 21), (34, 3), (3, 27), (13, 4), (4, 11), (3, 29), (26, 2), (7, 3), (2, 27), (21, 29), (17, 15), (11, 25), (1, 0), (26, 4), (22, 11), (32, 2), (23, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "623700", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), 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), (20, 23), (20, 6), (3, 20), (28, 17), (8, 16), (30, 20), (5, 22), (8, 29), (6, 29), (9, 21), (1, 0), (22, 10), (15, 24), (10, 3), (13, 24), (23, 22), (9, 33), (17, 32), (31, 0), (29, 22), (15, 7), (4, 1), (7, 20), (3, 25), (22, 30), (7, 11), (29, 0), (28, 24), (10, 20), (29, 21), (27, 4), (6, 4), (12, 21), (26, 23), (27, 16), (11, 5), (6, 33), (2, 23), (16, 14), (16, 30), (6, 27), (15, 25), (9, 10), (28, 14), (32, 0), (10, 4), (6, 18), (11, 15), (2, 14), (25, 26), (18, 32), (8, 9), (24, 1), (5, 10), (18, 16), (31, 22), (28, 30), (4, 19), (29, 4), (13, 6), (19, 1), (7, 22), (14, 31), (18, 13), (25, 27), (15, 1), (14, 8), (32, 14), (13, 0), (6, 1), (18, 23), (16, 5), (30, 16), (24, 8), (32, 25), (25, 23), (27, 7), (1, 3), (15, 20), (21, 19), (19, 28), (21, 14), (11, 4), (29, 11), (12, 7), (28, 33), (7, 25), (29, 27), (29, 15), (1, 15), (30, 19), (26, 24), (5, 17), (15, 31), (7, 28), (26, 26), (19, 31), (15, 16), (28, 25), (24, 17), (3, 10), (20, 32), (14, 33), (9, 12), (0, 7), (28, 20), (0, 20), (24, 26), (19, 25), (11, 6), (12, 22), (27, 3), (7, 27), (31, 20), (30, 8), (5, 1), (23, 2), (18, 9), (29, 33), (19, 0), (11, 19), (23, 14), (21, 9), (21, 6), (8, 1), (13, 23), (20, 9), (18, 0), (12, 27), (23, 33), (11, 23), (4, 9), (21, 29), (5, 32), (20, 16), (28, 18), (18, 27), (8, 15), (3, 13), (7, 15), (14, 3), (0, 31), (11, 2), (9, 23), (9, 6), (32, 29), (7, 8), (3, 28), (2, 3), (26, 28), (20, 10), (30, 28), (10, 22), (18, 1), (14, 16), (12, 4), (4, 16), (31, 8), (24, 5), (4, 26), (17, 29), (16, 7), (26, 29), (24, 16), (8, 10), (12, 28), (8, 28), (10, 6), (1, 33), (18, 11), (29, 30), (0, 27), (10, 13), (12, 17), (26, 10), (13, 15), (31, 1), (1, 17), (5, 15), (8, 8), (23, 16), (7, 23), (7, 30), (6, 12), (29, 29), (28, 31), (3, 5), (10, 7), (16, 19), (18, 24), (22, 19), (4, 14), (24, 31), (27, 19), (14, 5), (25, 13), (32, 21), (32, 23), (24, 19), (23, 3), (17, 20), (24, 22), (22, 0), (7, 19), (24, 20), (13, 19), (21, 12), (5, 2), (30, 25), (31, 14), (23, 6), (30, 7), (17, 14), (32, 9), (25, 33), (4, 25), (31, 3), (13, 32), (10, 14), (6, 16), (27, 17), (9, 9), (2, 0), (20, 19), (26, 11), (6, 26), (21, 27), (13, 33), (3, 23), (5, 20), (30, 2), (28, 27), (11, 13), (17, 7), (23, 28), (2, 15), (20, 27), (21, 8), (21, 11), (10, 5), (23, 7), (15, 29), (28, 9), (28, 21), (11, 30), (4, 5), (9, 20), (17, 22), (14, 19), (9, 0), (32, 1), (11, 29), (4, 11), (6, 17), (23, 10), (8, 18), (10, 23), (4, 18), (22, 12), (14, 29), (23, 30), (27, 1), (29, 26), (28, 19), (28, 4), (9, 8), (22, 9), (19, 12), (15, 4), (24, 3), (12, 11), (5, 9), (7, 1), (24, 29), (26, 21), (24, 0), (24, 14), (21, 20), (3, 33), (18, 28), (2, 28), (19, 19), (12, 16), (21, 23), (11, 9), (6, 0), (17, 1), (28, 28), (22, 32), (6, 30), (12, 10), (27, 18), (10, 28), (2, 21), (11, 1), (1, 27), (31, 27), (19, 22), (11, 25), (26, 32), (18, 22), (32, 27), (11, 12), (21, 7), (4, 15), (30, 23), (20, 31), (11, 17), (15, 2), (8, 25), (13, 22), (3, 2), (23, 15), (1, 10), (0, 21), (32, 24), (15, 18), (31, 24), (23, 18), (7, 16), (22, 29), (29, 1), (26, 2), (19, 11), (2, 5), (29, 7), (18, 8), (17, 15), (8, 19), (7, 3), (7, 31), (18, 19), (15, 8), (18, 15), (18, 25), (26, 6), (20, 0), (30, 31), (18, 30), (7, 21), (19, 30), (13, 11), (5, 16), (15, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864000", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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, 26), (9, 31), (21, 17), (19, 5), (9, 29), (29, 18), (24, 27), (6, 13), (7, 0), (18, 31), (16, 14), (12, 20), (7, 6), (2, 6), (1, 4), (2, 4), (6, 25), (30, 0), (31, 14), (24, 21), (9, 15), (21, 24), (1, 18), (25, 23), (27, 21), (12, 2), (25, 29), (0, 6), (18, 11), (21, 13), (11, 31), (2, 1), (23, 9), (31, 13), (18, 0), (31, 6), (4, 11), (3, 5), (32, 3), (14, 30), (34, 3), (10, 31), (3, 22), (29, 29), (26, 13), (8, 1), (32, 6), (3, 14), (16, 21), (31, 22), (20, 3), (12, 9), (17, 9), (21, 21), (19, 18), (30, 3), (32, 15), (24, 5), (24, 10), (5, 17), (23, 23), (27, 29), (32, 19), (20, 11), (5, 14), (30, 14), (18, 25), (19, 17), (12, 18), (1, 31), (34, 18), (13, 15), (23, 8), (26, 28), (24, 13), (20, 12), (14, 16), (7, 1), (26, 10), (2, 0), (0, 26), (26, 21), (28, 16), (11, 28), (22, 30), (29, 27), (2, 15), (33, 31), (7, 27), (31, 2), (5, 13), (30, 2), (22, 19), (34, 17), (33, 4), (26, 23), (30, 15), (22, 7), (5, 3), (15, 15), (5, 16), (34, 24), (1, 27), (15, 6), (26, 27), (4, 21), (8, 14), (3, 11), (8, 15), (6, 1), (3, 17), (20, 23), (31, 24), (30, 4), (11, 13), (18, 29), (33, 17), (16, 11), (24, 14), (7, 29), (26, 26), (34, 19), (9, 26), (12, 15), (15, 3), (27, 6), (17, 2), (6, 19), (25, 20), (7, 2), (9, 20), (32, 28), (1, 9), (33, 11), (6, 10), (12, 6), (10, 10), (9, 6), (23, 30), (26, 2), (23, 24), (32, 7), (17, 26), (14, 8), (20, 9), (8, 20), (7, 7), (15, 19), (8, 8), (11, 18), (7, 30), (21, 20), (13, 9), (30, 29), (17, 5), (7, 25), (10, 1), (0, 28), (23, 25), (6, 18), (13, 2), (28, 2), (31, 31), (2, 3), (33, 9), (31, 10), (26, 17), (10, 27), (2, 21), (32, 10), (30, 1), (4, 8), (9, 25), (28, 23), (29, 30), (1, 12), (4, 16), (5, 25), (24, 18), (16, 4), (34, 28), (22, 8), (23, 7), (10, 21), (34, 6), (5, 15), (14, 12), (4, 15), (1, 6), (23, 2), (16, 27), (5, 29), (16, 25), (9, 18), (1, 28), (11, 22), (0, 10), (24, 7), (15, 7), (21, 6), (2, 24), (8, 18), (28, 1), (8, 21), (19, 27), (15, 5), (23, 4), (0, 29), (32, 17), (22, 0), (22, 26), (3, 28), (30, 27), (9, 27), (7, 16), (6, 12), (24, 20), (32, 11), (18, 1), (27, 20), (12, 12), (6, 31), (9, 16), (12, 29), (34, 7), (29, 21), (0, 30), (2, 18), (19, 9), (28, 29), (29, 26), (18, 21), (24, 26), (10, 29), (11, 19), (19, 22), (29, 13), (23, 10), (29, 8), (15, 9), (1, 23), (15, 30), (28, 0), (4, 9), (8, 24), (15, 10), (20, 5), (28, 21), (15, 25), (25, 8), (23, 31), (33, 7), (33, 0), (14, 26), (1, 15), (24, 24), (32, 0), (10, 22), (0, 8), (12, 1), (13, 14), (4, 1), (21, 23), (13, 17), (0, 1), (19, 29), (15, 12), (7, 14), (25, 18), (3, 30), (11, 23), (21, 9), (6, 11), (18, 26), (31, 19), (14, 14), (32, 14), (11, 21), (24, 2), (1, 22), (22, 5), (14, 10), (18, 3), (31, 27), (30, 18), (34, 11), (25, 12), (7, 11), (29, 0), (8, 13), (20, 21), (5, 8), (20, 20), (16, 26), (16, 10), (3, 18), (17, 28), (21, 2), (7, 8), (13, 0), (30, 8), (27, 22), (19, 21), (11, 24), (28, 30), (34, 10), (16, 30), (19, 24), (13, 23), (2, 22), (20, 22), (12, 4), (9, 24), (33, 15), (25, 17), (12, 19), (19, 16), (6, 4), (33, 1), (0, 2), (5, 2), (29, 2), (5, 20), (27, 2), (34, 21), (34, 29), (23, 3), (16, 16), (11, 9), (16, 19), (32, 8), (24, 9), (22, 17), (17, 1), (10, 25), (2, 25), (31, 1), (28, 26), (5, 30), (8, 17), (14, 5), (25, 3), (6, 5), (23, 14), (21, 4), (8, 4), (8, 9), (22, 10), (23, 22), (2, 20), (25, 11), (4, 22), (0, 3), (13, 21), (7, 3), (26, 1), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724356", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (23, 28), (27, 19), (30, 15), (29, 20), (25, 31), (2, 34), (32, 22), (19, 23), (12, 34), (31, 27), (10, 0), (2, 1), (28, 20), (22, 27), (32, 27), (15, 12), (7, 2), (6, 33), (6, 21), (24, 16), (30, 25), (3, 4), (7, 8), (18, 7), (4, 10), (20, 1), (25, 29), (16, 13), (19, 4), (23, 9), (32, 32), (32, 17), (31, 15), (13, 26), (26, 22), (1, 33), (9, 12), (19, 0), (19, 11), (14, 24), (24, 15), (4, 22), (17, 34), (13, 30), (5, 20), (3, 5), (19, 20), (2, 16), (8, 30), (13, 25), (33, 32), (29, 27), (14, 4), (2, 0), (24, 28), (6, 13), (2, 19), (13, 22), (11, 14), (3, 16), (29, 14), (17, 20), (9, 5), (32, 5), (19, 24), (26, 0), (8, 32), (18, 0), (28, 10), (26, 29), (8, 34), (10, 18), (24, 12), (4, 11), (28, 12), (12, 1), (16, 11), (0, 24), (11, 9), (20, 0), (20, 32), (3, 14), (4, 2), (15, 11), (3, 3), (33, 2), (1, 13), (27, 8), (14, 23), (32, 2), (15, 10), (28, 14), (18, 4), (12, 23), (26, 35), (16, 20), (24, 9), (5, 2), (22, 22), (26, 24), (25, 24), (4, 35), (28, 11), (14, 25), (24, 10), (11, 21), (21, 10), (9, 14), (27, 4), (26, 12), (13, 7), (7, 13), (6, 5), (30, 17), (30, 14), (20, 6), (17, 17), (14, 31), (5, 22), (15, 13), (15, 9), (5, 30), (7, 27), (15, 29), (1, 10), (23, 18), (19, 27), (32, 28), (26, 27), (12, 6), (17, 27), (29, 19), (8, 20), (6, 12), (5, 3), (4, 3), (7, 11), (27, 16), (1, 28), (25, 35), (12, 35), (11, 11), (31, 17), (23, 29), (4, 32), (24, 4), (18, 19), (30, 7), (8, 31), (10, 17), (33, 31), (31, 26), (19, 33), (15, 17), (17, 25), (25, 19), (6, 23), (27, 14), (24, 2), (2, 24), (23, 32), (6, 0), (8, 3), (6, 11), (10, 22), (9, 29), (22, 7), (18, 27), (20, 22), (26, 2), (31, 9), (16, 15), (17, 24), (12, 17), (29, 5), (4, 23), (29, 29), (7, 25), (12, 27), (23, 2), (18, 24), (9, 35), (25, 18), (27, 26), (17, 9), (13, 20), (18, 22), (12, 8), (9, 27), (18, 33), (28, 35), (33, 29), (17, 30), (6, 8), (9, 0), (9, 1), (18, 9), (9, 20), (10, 34), (22, 6), (13, 19), (29, 4), (10, 11), (13, 23), (15, 2), (13, 0), (21, 19), (18, 15), (18, 34), (32, 20), (17, 35), (2, 26), (23, 19), (9, 17), (8, 11), (12, 25), (28, 30), (9, 15), (4, 21), (15, 5), (21, 4), (11, 7), (19, 5), (0, 8), (28, 16), (30, 4), (1, 2), (8, 19), (6, 29), (1, 5), (27, 2), (33, 19), (25, 23), (30, 20), (16, 31), (19, 26), (26, 7), (9, 13), (4, 0), (6, 16), (20, 7), (4, 5), (1, 22), (10, 27), (20, 20), (15, 8), (16, 24), (13, 35), (26, 9), (7, 21), (0, 29), (16, 6), (33, 33), (14, 5), (24, 27), (1, 9), (6, 35), (3, 2), (29, 15), (25, 3), (33, 8), (23, 13), (27, 11), (33, 10), (17, 4), (12, 5), (29, 32), (31, 34), (19, 2), (18, 12), (14, 18), (22, 0), (32, 10), (20, 33), (28, 27), (20, 8), (24, 32), (24, 25), (8, 18), (0, 7), (12, 16), (6, 30), (13, 34), (6, 4), (28, 15), (3, 20), (28, 6), (29, 6), (32, 29), (0, 25), (28, 24), (6, 17), (28, 23), (20, 2), (20, 34), (5, 9), (3, 0), (16, 1), (19, 30), (8, 28), (33, 30), (31, 23), (32, 9), (2, 8), (21, 22), (5, 13), (6, 34), (33, 21), (0, 21), (33, 26), (24, 14), (13, 3), (32, 7), (6, 2), (23, 24), (2, 11), (6, 6), (24, 7), (11, 5), (14, 20), (10, 19), (9, 3), (17, 7), (5, 10), (21, 9), (25, 20), (21, 11), (2, 18), (20, 9), (4, 33), (28, 5), (12, 20), (17, 22), (23, 6), (26, 6), (12, 26), (21, 29), (10, 6), (3, 22), (27, 9), (14, 7), (31, 6), (3, 33), (4, 25), (25, 21), (8, 1), (21, 6), (31, 19), (27, 0), (1, 34), (11, 12), (19, 9), (3, 12), (5, 27), (14, 12), (18, 32), (11, 25), (17, 18), (27, 3), (23, 3), (21, 31), (22, 21), (31, 16), (17, 15), (25, 27), (25, 5), (5, 0), (4, 13), (31, 11), (20, 16), (14, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "795600", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 21), (6, 1), (2, 4), (36, 25), (12, 16), (17, 15), (5, 12), (24, 4), (6, 9), (11, 14), (28, 30), (13, 26), (17, 18), (29, 20), (8, 8), (34, 16), (33, 27), (19, 21), (32, 7), (23, 25), (8, 9), (14, 20), (5, 24), (24, 1), (20, 32), (12, 4), (26, 20), (13, 8), (32, 15), (28, 22), (34, 7), (30, 0), (37, 25), (21, 29), (31, 14), (16, 18), (12, 25), (25, 28), (10, 12), (28, 13), (18, 4), (19, 25), (14, 7), (33, 16), (17, 28), (16, 0), (25, 13), (31, 0), (29, 4), (27, 19), (20, 13), (31, 7), (33, 7), (32, 5), (31, 17), (2, 1), (10, 21), (0, 20), (35, 6), (27, 20), (29, 8), (37, 6), (24, 10), (33, 26), (27, 9), (30, 1), (7, 28), (21, 28), (26, 9), (7, 30), (7, 20), (32, 24), (35, 30), (16, 22), (9, 2), (10, 15), (18, 25), (16, 15), (21, 8), (20, 17), (33, 11), (15, 7), (7, 26), (3, 25), (4, 8), (32, 18), (0, 25), (15, 22), (21, 20), (24, 13), (25, 23), (21, 12), (33, 20), (8, 6), (13, 13), (2, 28), (16, 10), (19, 27), (25, 19), (3, 3), (14, 32), (20, 25), (20, 9), (13, 0), (25, 26), (30, 8), (24, 21), (1, 3), (5, 29), (12, 2), (32, 1), (24, 9), (18, 22), (23, 26), (9, 24), (17, 17), (19, 19), (28, 5), (4, 15), (26, 19), (28, 7), (11, 12), (36, 7), (14, 11), (16, 9), (29, 6), (0, 1), (0, 3), (12, 15), (5, 31), (0, 24), (23, 12), (8, 16), (10, 1), (28, 25), (27, 21), (8, 4), (37, 18), (14, 27), (20, 16), (14, 24), (9, 4), (36, 17), (32, 4), (17, 6), (14, 3), (0, 23), (28, 17), (4, 18), (8, 32), (22, 21), (31, 19), (10, 19), (29, 32), (17, 1), (23, 6), (27, 17), (37, 20), (4, 29), (23, 22), (3, 28), (27, 7), (4, 17), (3, 11), (16, 25), (27, 23), (19, 1), (15, 25), (27, 4), (35, 26), (30, 10), (12, 11), (21, 2), (3, 5), (32, 19), (14, 26), (11, 31), (2, 32), (17, 21), (28, 23), (33, 6), (27, 32), (0, 7), (6, 6), (18, 11), (19, 29), (8, 29), (21, 16), (6, 13), (1, 25), (4, 23), (4, 26), (21, 22), (24, 5), (19, 22), (24, 24), (22, 16), (29, 26), (11, 22), (2, 13), (22, 3), (10, 22), (10, 9), (2, 5), (11, 5), (25, 18), (12, 6), (6, 12), (22, 1), (31, 8), (16, 32), (3, 4), (2, 18), (11, 25), (23, 29), (4, 9), (9, 5), (16, 5), (20, 30), (5, 9), (24, 29), (18, 13), (5, 26), (13, 27), (4, 3), (5, 0), (20, 4), (28, 12), (19, 13), (27, 2), (36, 11), (9, 30), (27, 30), (23, 0), (33, 14), (2, 17), (7, 27), (27, 11), (11, 30), (35, 29), (4, 4), (20, 10), (19, 7), (28, 8), (21, 3), (28, 20), (1, 11), (17, 16), (29, 25), (26, 10), (34, 20), (11, 6), (10, 2), (14, 19), (4, 19), (31, 16), (11, 26), (13, 19), (20, 26), (22, 2), (18, 23), (16, 28), (23, 11), (7, 7), (18, 16), (10, 0), (28, 27), (23, 13), (9, 9), (8, 19), (31, 30), (3, 29), (20, 28), (7, 15), (31, 3), (1, 12), (18, 2), (20, 3), (28, 28), (19, 9), (17, 8), (8, 10), (12, 27), (19, 2), (7, 19), (25, 25), (34, 31), (36, 24), (7, 22), (11, 13), (4, 2), (16, 29), (1, 29), (36, 15), (7, 0), (6, 15), (17, 23), (36, 2), (25, 21), (19, 8), (34, 10), (20, 5), (12, 5), (13, 18), (10, 14), (36, 22), (32, 17), (15, 18), (35, 9), (36, 8), (19, 32), (21, 1), (8, 1), (21, 32), (14, 12), (22, 15), (12, 0), (26, 28), (2, 30), (28, 26), (36, 18), (22, 24), (31, 13), (19, 16), (30, 13), (35, 13), (11, 1), (37, 9), (1, 30), (18, 7), (29, 18), (23, 31), (2, 21), (35, 5), (15, 10), (11, 3), (0, 17), (27, 6), (30, 12), (21, 9), (35, 19), (8, 18), (13, 28), (25, 7), (26, 14), (34, 19), (9, 13), (26, 15), (18, 26), (18, 21), (18, 14), (34, 1), (33, 24), (24, 8), (0, 14), (18, 31), (11, 7), (10, 4), (7, 4), (27, 8), (20, 6), (9, 29), (9, 32), (35, 3), (16, 12), (36, 9), (2, 25), (31, 21), (10, 20), (30, 22), (4, 30), (37, 12), (16, 2), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303744", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 25), (4, 22), (33, 23), (9, 8), (23, 22), (1, 11), (4, 19), (8, 9), (13, 31), (34, 13), (7, 12), (14, 9), (8, 0), (7, 19), (11, 10), (32, 36), (12, 33), (34, 28), (15, 1), (9, 13), (19, 2), (17, 24), (27, 9), (23, 24), (26, 0), (28, 22), (12, 22), (0, 13), (30, 21), (2, 36), (0, 17), (8, 28), (19, 11), (34, 18), (18, 25), (15, 30), (13, 4), (29, 16), (10, 12), (15, 7), (7, 33), (32, 13), (17, 3), (11, 1), (14, 22), (5, 23), (30, 20), (2, 15), (16, 7), (31, 31), (5, 32), (31, 23), (21, 10), (28, 17), (26, 36), (13, 10), (29, 8), (26, 18), (29, 17), (15, 29), (29, 30), (7, 5), (32, 9), (32, 0), (34, 17), (28, 12), (20, 35), (32, 20), (23, 25), (10, 18), (13, 30), (11, 12), (13, 15), (29, 6), (15, 13), (14, 29), (32, 17), (4, 35), (31, 8), (8, 26), (13, 17), (11, 20), (21, 31), (16, 35), (23, 18), (7, 3), (8, 18), (2, 30), (30, 19), (19, 12), (3, 16), (24, 2), (16, 25), (15, 6), (16, 28), (4, 3), (26, 8), (18, 17), (10, 11), (15, 17), (7, 35), (21, 17), (5, 21), (4, 14), (6, 6), (30, 33), (20, 2), (10, 17), (5, 18), (34, 1), (9, 6), (20, 17), (27, 36), (19, 32), (32, 3), (0, 1), (25, 5), (24, 25), (31, 1), (1, 28), (32, 30), (11, 36), (2, 13), (13, 9), (14, 27), (7, 10), (1, 32), (19, 3), (29, 14), (20, 19), (33, 22), (2, 35), (9, 28), (27, 20), (21, 26), (7, 31), (20, 31), (19, 25), (32, 19), (11, 0), (15, 4), (26, 9), (2, 14), (34, 6), (12, 4), (11, 11), (19, 5), (10, 24), (10, 15), (27, 23), (13, 21), (26, 34), (9, 29), (11, 32), (11, 22), (17, 18), (19, 9), (0, 14), (9, 14), (17, 27), (31, 15), (31, 6), (21, 21), (20, 22), (22, 25), (34, 9), (14, 35), (21, 29), (30, 3), (3, 33), (14, 36), (21, 15), (16, 24), (9, 24), (10, 14), (14, 4), (14, 15), (18, 29), (2, 27), (31, 18), (1, 26), (19, 1), (16, 6), (23, 0), (21, 16), (31, 12), (11, 35), (8, 7), (7, 14), (24, 20), (18, 18), (24, 33), (23, 26), (14, 26), (25, 9), (6, 17), (3, 9), (24, 30), (11, 19), (1, 9), (12, 3), (21, 33), (1, 16), (16, 19), (20, 10), (22, 5), (29, 22), (4, 15), (27, 32), (15, 20), (30, 32), (14, 11), (4, 10), (32, 12), (8, 13), (22, 0), (33, 16), (30, 7), (19, 28), (17, 6), (18, 0), (21, 13), (12, 19), (7, 27), (13, 13), (12, 26), (22, 1), (4, 33), (20, 26), (28, 18), (8, 35), (27, 24), (16, 10), (26, 12), (25, 16), (29, 21), (17, 4), (27, 19), (17, 20), (11, 6), (5, 22), (31, 21), (8, 10), (21, 25), (23, 33), (22, 33), (21, 12), (6, 22), (31, 9), (33, 33), (0, 20), (28, 32), (12, 5), (3, 30), (4, 24), (3, 22), (22, 32), (20, 11), (22, 15), (20, 29), (28, 13), (34, 4), (2, 19), (29, 26), (6, 18), (15, 35), (15, 3), (28, 5), (15, 24), (2, 22), (27, 18), (1, 15), (26, 27), (22, 36), (8, 27), (15, 26), (31, 19), (11, 17), (13, 25), (8, 20), (1, 30), (11, 3), (15, 31), (18, 13), (29, 0), (28, 30), (21, 14), (5, 24), (16, 13), (12, 24), (28, 33), (13, 27), (18, 19), (27, 16), (23, 16), (14, 24), (23, 32), (1, 8), (29, 4), (10, 36), (24, 4), (0, 34), (32, 29), (8, 1), (7, 28), (6, 25), (25, 13), (6, 26), (7, 2), (16, 32), (31, 36), (29, 10), (18, 9), (24, 8), (1, 3), (24, 28), (24, 32), (29, 9), (26, 28), (12, 29), (3, 0), (26, 33), (2, 3), (6, 1), (18, 21), (27, 31), (32, 2), (6, 24), (5, 15), (7, 32), (27, 10), (10, 34), (16, 26), (33, 14), (13, 11), (10, 10), (25, 36), (30, 23), (29, 29), (8, 30), (27, 26), (25, 30), (2, 28), (24, 22), (1, 25), (4, 23), (25, 3), (3, 11), (1, 23), (33, 20), (33, 8), (25, 26), (15, 21), (0, 36), (19, 21), (4, 4), (21, 7), (12, 0), (33, 10), (6, 30), (9, 12), (30, 30), (13, 2), (16, 31), (2, 23), (14, 0), (0, 26), (0, 28), (26, 15), (34, 32), (1, 7), (33, 13), (5, 33), (33, 29), (0, 12), (28, 3), (18, 31), (4, 0), (29, 1), (29, 20), (5, 11), (30, 31), (20, 21), (3, 10), (2, 21), (0, 9), (25, 10), (34, 16), (29, 34), (18, 2), (15, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691200", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 5), (28, 4), (20, 22), (4, 32), (34, 28), (3, 17), (16, 29), (0, 5), (17, 25), (3, 19), (30, 5), (19, 12), (11, 8), (24, 27), (32, 23), (25, 17), (28, 14), (24, 13), (33, 30), (5, 1), (13, 17), (10, 5), (3, 30), (10, 8), (18, 5), (19, 4), (20, 31), (12, 32), (34, 31), (33, 19), (3, 23), (5, 26), (30, 30), (15, 1), (25, 18), (22, 32), (15, 10), (10, 12), (19, 3), (30, 18), (20, 2), (8, 25), (3, 29), (33, 21), (20, 16), (24, 9), (28, 32), (17, 13), (35, 20), (30, 32), (9, 20), (5, 10), (27, 19), (31, 24), (17, 2), (2, 12), (32, 13), (5, 4), (1, 21), (13, 31), (26, 2), (33, 7), (32, 25), (17, 20), (33, 17), (12, 20), (21, 20), (11, 32), (6, 14), (35, 17), (18, 20), (8, 5), (13, 19), (16, 21), (33, 14), (6, 15), (35, 0), (26, 27), (28, 17), (15, 6), (7, 0), (5, 13), (2, 3), (13, 11), (16, 12), (15, 7), (17, 11), (24, 12), (29, 9), (24, 24), (17, 32), (0, 20), (23, 32), (13, 32), (28, 23), (29, 13), (0, 25), (17, 8), (8, 2), (30, 12), (22, 26), (5, 27), (2, 5), (11, 4), (19, 22), (0, 23), (3, 16), (23, 5), (3, 12), (4, 27), (16, 2), (30, 15), (28, 3), (27, 0), (7, 12), (2, 30), (6, 1), (13, 4), (1, 17), (13, 20), (22, 5), (17, 17), (18, 14), (5, 28), (17, 9), (24, 22), (17, 28), (14, 5), (35, 4), (30, 17), (25, 14), (2, 25), (18, 2), (27, 3), (18, 28), (10, 16), (34, 12), (15, 0), (19, 21), (34, 3), (2, 21), (2, 7), (29, 11), (34, 22), (11, 1), (22, 7), (26, 9), (8, 30), (31, 1), (1, 19), (12, 9), (16, 0), (33, 10), (30, 13), (8, 31), (10, 17), (22, 4), (0, 26), (1, 5), (34, 4), (26, 5), (14, 0), (0, 27), (11, 6), (14, 21), (0, 9), (6, 18), (31, 0), (2, 13), (33, 31), (28, 29), (31, 28), (32, 16), (32, 7), (27, 12), (14, 30), (4, 14), (10, 22), (20, 5), (11, 20), (9, 16), (21, 31), (34, 17), (20, 18), (9, 10), (23, 14), (20, 32), (31, 3), (18, 27), (35, 18), (15, 31), (35, 3), (5, 23), (23, 15), (20, 17), (29, 7), (5, 30), (31, 2), (33, 12), (10, 31), (13, 5), (17, 23), (3, 4), (14, 26), (1, 9), (26, 26), (22, 0), (8, 22), (6, 2), (19, 20), (25, 31), (30, 7), (22, 17), (7, 25), (24, 0), (9, 9), (23, 20), (6, 30), (29, 6), (21, 8), (29, 18), (20, 29), (26, 24), (7, 6), (23, 7), (28, 0), (6, 13), (21, 18), (10, 20), (34, 16), (21, 19), (5, 14), (23, 16), (9, 27), (0, 12), (26, 1), (5, 11), (10, 4), (4, 22), (16, 16), (34, 8), (21, 1), (35, 9), (12, 17), (21, 23), (6, 16), (21, 22), (1, 3), (28, 15), (32, 0), (34, 27), (18, 30), (4, 28), (14, 31), (33, 18), (29, 8), (8, 20), (34, 10), (13, 28), (29, 2), (26, 15), (7, 10), (30, 11), (10, 26), (10, 6), (33, 0), (13, 14), (24, 15), (35, 19), (15, 16), (9, 3), (29, 17), (6, 17), (16, 23), (27, 29), (31, 23), (4, 19), (6, 9), (30, 26), (32, 18), (12, 28), (1, 30), (6, 24), (10, 25), (20, 14), (25, 9), (26, 22), (22, 30), (18, 10), (34, 11), (0, 14), (33, 23), (14, 27), (8, 10), (23, 30), (14, 4), (32, 26), (21, 26), (31, 30), (13, 1), (1, 0), (27, 23), (27, 15), (10, 10), (24, 23), (11, 16), (7, 29), (25, 27), (13, 0), (30, 27), (6, 32), (0, 7), (35, 14), (2, 11), (34, 29), (35, 7), (11, 23), (17, 30), (32, 15), (24, 11), (23, 11), (15, 11), (19, 7), (3, 1), (1, 16), (3, 27), (19, 10), (31, 22), (13, 16), (8, 9), (13, 10), (2, 15), (31, 19), (6, 20), (5, 12), (17, 1), (33, 26), (16, 3), (22, 25), (34, 18), (13, 22), (9, 15), (25, 7), (14, 20), (7, 28), (22, 20), (4, 20), (3, 28), (6, 11), (18, 3), (2, 4), (7, 32), (23, 4), (0, 10), (5, 16), (30, 28), (18, 15), (14, 7), (8, 27), (5, 22), (35, 23), (19, 9), (18, 12), (25, 23), (31, 32), (34, 2), (26, 0), (28, 19), (32, 21), (0, 11), (13, 29), (7, 9), (15, 32), (9, 28), (20, 3), (2, 27), (4, 30), (15, 4), (26, 20), (18, 11), (2, 32), (27, 31), (12, 8), (8, 4), (8, 32), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720450", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), 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), (38, 29), (0, 2), (33, 17), (2, 32), (14, 30), (6, 32), (6, 28), (23, 17), (0, 24), (11, 27), (27, 25), (28, 16), (10, 21), (37, 13), (15, 28), (12, 31), (6, 15), (28, 4), (36, 5), (38, 31), (24, 20), (25, 30), (33, 10), (23, 28), (16, 15), (1, 12), (30, 13), (10, 29), (19, 15), (19, 11), (37, 29), (2, 28), (18, 7), (9, 23), (32, 0), (14, 22), (6, 25), (14, 13), (3, 23), (25, 20), (22, 6), (16, 19), (30, 30), (7, 29), (9, 29), (8, 11), (36, 20), (36, 29), (8, 26), (32, 5), (19, 4), (27, 3), (9, 12), (1, 22), (25, 13), (23, 31), (15, 4), (21, 15), (3, 2), (29, 17), (30, 21), (6, 2), (7, 7), (19, 10), (12, 11), (28, 2), (22, 26), (18, 28), (32, 28), (11, 7), (6, 1), (32, 18), (14, 25), (15, 31), (29, 18), (2, 5), (35, 4), (23, 23), (35, 26), (34, 11), (33, 9), (28, 18), (37, 26), (33, 11), (33, 14), (36, 17), (20, 20), (6, 9), (24, 7), (7, 10), (4, 30), (15, 16), (23, 12), (5, 29), (9, 18), (25, 22), (0, 12), (37, 14), (20, 3), (31, 25), (16, 10), (1, 16), (4, 11), (18, 29), (1, 31), (10, 9), (33, 8), (2, 8), (36, 26), (21, 18), (34, 28), (25, 15), (14, 7), (23, 21), (13, 26), (11, 17), (28, 30), (0, 25), (33, 28), (6, 24), (22, 30), (8, 29), (14, 29), (32, 14), (20, 5), (13, 28), (37, 3), (36, 28), (16, 2), (7, 1), (4, 12), (10, 0), (1, 23), (3, 28), (16, 23), (8, 19), (37, 23), (7, 18), (12, 9), (33, 22), (2, 7), (18, 1), (24, 21), (24, 4), (4, 16), (23, 29), (9, 5), (34, 23), (2, 6), (17, 2), (27, 29), (4, 20), (29, 10), (38, 28), (30, 8), (18, 15), (21, 23), (10, 5), (18, 9), (17, 25), (37, 30), (23, 3), (37, 20), (18, 10), (29, 11), (26, 19), (0, 1), (12, 22), (3, 29), (16, 20), (15, 20), (3, 30), (24, 18), (10, 7), (18, 6), (12, 18), (26, 5), (31, 32), (38, 17), (24, 19), (14, 18), (29, 0), (15, 6), (8, 6), (19, 21), (0, 21), (31, 17), (21, 28), (26, 9), (2, 3), (7, 21), (26, 17), (9, 2), (20, 27), (28, 20), (31, 12), (22, 1), (35, 21), (18, 3), (30, 11), (38, 15), (30, 1), (5, 14), (11, 28), (27, 18), (20, 1), (29, 25), (2, 0), (26, 11), (17, 29), (25, 6), (15, 8), (21, 6), (25, 28), (11, 31), (38, 21), (9, 9), (10, 2), (12, 5), (29, 13), (9, 25), (35, 19), (18, 30), (18, 26), (11, 23), (2, 21), (6, 0), (27, 20), (1, 3), (7, 19), (19, 24), (11, 0), (14, 12), (3, 16), (5, 3), (25, 2), (2, 4), (0, 20), (2, 17), (7, 26), (16, 26), (17, 15), (24, 29), (33, 25), (26, 32), (7, 8), (37, 8), (22, 8), (5, 13), (12, 15), (17, 18), (1, 7), (9, 6), (10, 32), (7, 28), (3, 11), (14, 11), (19, 16), (16, 12), (6, 22), (3, 3), (34, 31), (13, 14), (33, 5), (2, 10), (22, 14), (35, 2), (12, 32), (13, 17), (19, 12), (16, 29), (0, 3), (28, 3), (24, 11), (35, 24), (5, 26), (28, 10), (27, 9), (29, 5), (32, 26), (1, 4), (8, 9), (14, 27), (23, 25), (6, 16), (18, 32), (29, 31), (15, 0), (22, 25), (28, 21), (23, 32), (23, 20), (21, 31), (25, 0), (8, 15), (5, 7), (23, 24), (28, 22), (22, 21), (37, 18), (27, 21), (31, 13), (34, 19), (31, 2), (29, 2), (10, 30), (5, 23), (21, 30), (24, 15), (20, 29), (34, 9), (18, 17), (11, 3), (36, 25), (29, 27), (30, 32), (20, 24), (13, 1), (1, 27), (6, 29), (3, 20), (18, 8), (33, 15), (28, 0), (24, 30), (37, 0), (13, 20), (10, 13), (10, 24), (10, 11), (17, 20), (15, 5), (27, 19), (37, 4), (34, 15), (8, 14), (35, 18), (36, 30), (6, 6), (1, 9), (36, 32), (19, 17), (26, 6), (7, 5), (3, 6), (37, 27), (27, 15), (31, 30), (23, 18), (36, 0), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706640", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 13), (26, 27), (19, 12), (23, 10), (16, 24), (1, 21), (1, 4), (17, 30), (6, 1), (12, 7), (26, 17), (21, 27), (12, 20), (11, 17), (5, 11), (23, 14), (29, 17), (28, 20), (7, 2), (0, 25), (7, 28), (29, 8), (11, 5), (17, 10), (7, 23), (26, 30), (27, 16), (10, 10), (11, 1), (21, 0), (18, 24), (16, 8), (13, 10), (20, 25), (11, 8), (12, 6), (0, 10), (6, 31), (14, 2), (24, 21), (16, 11), (3, 22), (20, 17), (13, 6), (2, 27), (8, 25), (4, 1), (21, 17), (4, 27), (5, 12), (2, 0), (21, 7), (16, 9), (17, 17), (13, 26), (11, 28), (28, 28), (5, 2), (1, 25), (26, 16), (5, 6), (11, 19), (29, 7), (7, 30), (17, 14), (21, 26), (23, 30), (14, 4), (7, 19), (21, 13), (9, 9), (22, 6), (13, 2), (27, 24), (24, 9), (15, 27), (1, 8), (8, 20), (17, 24), (29, 14), (25, 4), (16, 15), (21, 20), (17, 13), (14, 19), (18, 14), (3, 19), (0, 17), (27, 18), (14, 14), (22, 24), (1, 28), (10, 13), (21, 11), (28, 19), (26, 9), (17, 0), (27, 13), (8, 28), (15, 2), (22, 16), (28, 6), (4, 9), (24, 28), (1, 26), (25, 1), (28, 29), (6, 8), (29, 28), (18, 16), (22, 4), (0, 21), (10, 21), (17, 5), (1, 24), (18, 26), (20, 31), (14, 23), (5, 25), (1, 7), (14, 29), (1, 2), (6, 29), (21, 23), (13, 20), (12, 0), (14, 6), (15, 12), (21, 1), (14, 10), (18, 28), (2, 2), (11, 15), (9, 10), (6, 11), (18, 11), (15, 22), (4, 12), (1, 15), (18, 18), (5, 9), (13, 0), (9, 7), (22, 7), (28, 11), (25, 29), (10, 0), (13, 27), (1, 31), (25, 21), (18, 10), (11, 12), (10, 3), (22, 19), (8, 2), (15, 21), (20, 24), (13, 28), (15, 26), (5, 7), (21, 25), (26, 24), (23, 15), (11, 9), (17, 26), (21, 3), (20, 28), (8, 6), (23, 31), (20, 23), (29, 29), (19, 23), (20, 11), (17, 27), (27, 27), (5, 18), (22, 26), (16, 14), (8, 9), (21, 16), (12, 16), (24, 13), (16, 26), (1, 29), (3, 8), (12, 15), (22, 21), (28, 15), (23, 17), (2, 10), (0, 18), (27, 12), (0, 29), (21, 31), (16, 1), (7, 13), (24, 25), (16, 2), (11, 2), (18, 7), (21, 29), (5, 22), (19, 15), (29, 22), (29, 24), (6, 17), (7, 27), (29, 15), (18, 19), (10, 24), (10, 31), (14, 3), (26, 26), (5, 26), (6, 4), (29, 23), (3, 7), (4, 13), (7, 7), (29, 6), (25, 25), (24, 30), (23, 3), (3, 24), (13, 17), (6, 15), (14, 31), (5, 16), (6, 27), (17, 3), (18, 31), (5, 15), (18, 0), (6, 26), (25, 22), (11, 22), (0, 15), (3, 13), (26, 8), (3, 20), (0, 12), (24, 31), (0, 30), (5, 27), (10, 28), (0, 22), (16, 4), (19, 11), (11, 31), (2, 8), (16, 12), (25, 17), (29, 25), (3, 31), (26, 14), (22, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867672", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), 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), (22, 5), (7, 25), (34, 13), (20, 1), (11, 3), (25, 16), (8, 18), (19, 1), (4, 27), (26, 11), (17, 11), (22, 24), (19, 15), (12, 13), (22, 2), (37, 3), (12, 27), (6, 0), (24, 29), (23, 19), (23, 16), (31, 26), (2, 0), (35, 15), (20, 19), (1, 20), (12, 5), (21, 6), (31, 13), (25, 11), (22, 14), (20, 27), (22, 9), (21, 1), (33, 8), (6, 28), (10, 12), (21, 0), (18, 27), (21, 7), (31, 19), (36, 28), (29, 27), (26, 4), (6, 19), (20, 7), (26, 13), (11, 17), (24, 10), (16, 29), (35, 25), (21, 16), (9, 18), (7, 17), (17, 7), (37, 1), (15, 2), (27, 24), (27, 5), (26, 25), (5, 25), (16, 9), (31, 10), (14, 5), (14, 16), (0, 20), (25, 10), (32, 6), (4, 10), (3, 3), (0, 17), (0, 25), (12, 23), (30, 19), (21, 21), (37, 15), (35, 2), (22, 11), (33, 21), (7, 12), (27, 11), (17, 27), (18, 14), (12, 9), (36, 2), (5, 28), (36, 8), (28, 17), (14, 1), (16, 2), (15, 0), (20, 13), (18, 13), (20, 17), (30, 22), (30, 20), (23, 26), (6, 14), (7, 29), (28, 9), (9, 20), (11, 11), (36, 22), (35, 19), (16, 26), (14, 20), (29, 7), (22, 25), (0, 21), (26, 16), (13, 27), (13, 21), (6, 9), (30, 28), (16, 21), (23, 23), (12, 7), (22, 4), (22, 12), (28, 8), (36, 27), (8, 20), (3, 29), (19, 8), (10, 26), (3, 7), (17, 2), (27, 2), (0, 9), (21, 27), (37, 11), (5, 18), (2, 14), (10, 17), (37, 17), (35, 4), (8, 1), (4, 7), (24, 4), (9, 6), (19, 23), (29, 14), (33, 9), (31, 23), (10, 28), (27, 18), (31, 2), (20, 23), (10, 8), (2, 24), (4, 6), (5, 26), (9, 27), (24, 24), (34, 29), (35, 1), (16, 12), (31, 16), (21, 4), (24, 17), (13, 23), (10, 27), (15, 21), (36, 20), (1, 25), (22, 10), (35, 16), (21, 20), (32, 2), (9, 24), (28, 0), (36, 3), (20, 21), (16, 6), (30, 11), (28, 24), (30, 17), (27, 17), (9, 19), (16, 11), (16, 24), (3, 8), (3, 0), (19, 18), (5, 14), (3, 5), (27, 25), (8, 24), (37, 21), (2, 10), (0, 13), (20, 0), (25, 23), (23, 1), (13, 15), (31, 21), (19, 29), (11, 6), (8, 6), (23, 25), (13, 1), (4, 22), (20, 14), (20, 26), (9, 17), (35, 20), (24, 28), (19, 7), (11, 15), (4, 16), (33, 0), (33, 26), (30, 0), (4, 18), (4, 25), (19, 14), (4, 4), (21, 3), (13, 24), (33, 1), (16, 3), (1, 5), (16, 14), (27, 16), (5, 23), (5, 2), (32, 1), (0, 15), (1, 14), (0, 22), (19, 22), (0, 16), (18, 23), (8, 22), (29, 10), (34, 26), (27, 3), (6, 29), (1, 3), (7, 16), (24, 0), (6, 23), (5, 8), (12, 3), (18, 1), (0, 6), (8, 25), (32, 25), (2, 7), (17, 0), (6, 7), (37, 10), (3, 2), (24, 20), (14, 14), (34, 15), (17, 5), (7, 2), (14, 19), (3, 12), (16, 19), (32, 22), (11, 25), (11, 2), (32, 21), (6, 15), (36, 12), (10, 1), (31, 11), (25, 22), (22, 3), (10, 25), (36, 0), (33, 15), (21, 22), (32, 17), (28, 7), (35, 9), (26, 21), (11, 28), (20, 18), (32, 23), (33, 14), (17, 10), (12, 16), (22, 29), (30, 29), (17, 28), (25, 8), (32, 9), (5, 12), (19, 6), (22, 28), (10, 13), (4, 3), (28, 19), (25, 27), (9, 3), (24, 8), (29, 15), (1, 27), (31, 20), (22, 13), (27, 4), (27, 13), (21, 19), (9, 9), (9, 28), (2, 25), (32, 12), (0, 24), (18, 6), (6, 20), (37, 22), (4, 21), (18, 0), (13, 25), (23, 3), (34, 11), (2, 13), (14, 24), (36, 26), (27, 22), (29, 0), (10, 18), (34, 1), (26, 10), (3, 19), (10, 14), (33, 5), (16, 4), (17, 19), (15, 8), (22, 23), (9, 8), (16, 16), (19, 19), (26, 20), (2, 8), (35, 7), (2, 23), (28, 2), (0, 12), (32, 14), (17, 15), (27, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967680", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 9), (10, 9), (12, 11), (19, 20), (4, 10), (28, 20), (35, 24), (23, 5), (23, 10), (25, 26), (19, 1), (9, 8), (1, 5), (12, 26), (7, 16), (13, 14), (28, 3), (25, 18), (26, 25), (18, 25), (27, 23), (23, 6), (34, 20), (22, 2), (23, 25), (35, 25), (11, 23), (30, 23), (11, 22), (33, 7), (32, 27), (20, 6), (27, 11), (15, 8), (26, 29), (14, 0), (33, 27), (5, 29), (3, 29), (13, 3), (4, 29), (13, 25), (8, 15), (15, 28), (30, 29), (23, 20), (29, 28), (31, 2), (3, 11), (10, 25), (18, 27), (17, 29), (33, 12), (24, 23), (21, 8), (3, 28), (11, 21), (19, 11), (31, 15), (6, 8), (2, 9), (15, 21), (9, 4), (16, 26), (17, 7), (26, 12), (34, 8), (3, 25), (7, 10), (21, 20), (6, 9), (0, 17), (17, 24), (28, 26), (12, 14), (27, 13), (9, 26), (7, 9), (29, 7), (19, 24), (3, 5), (20, 3), (24, 26), (20, 5), (15, 26), (15, 4), (2, 11), (6, 3), (9, 10), (3, 12), (18, 16), (34, 15), (5, 4), (1, 10), (23, 27), (1, 27), (23, 1), (0, 23), (7, 30), (27, 15), (23, 13), (10, 8), (21, 9), (9, 3), (14, 18), (22, 27), (15, 17), (32, 20), (18, 26), (26, 2), (2, 15), (15, 6), (11, 27), (26, 1), (1, 11), (14, 4), (12, 22), (12, 20), (21, 11), (4, 24), (3, 6), (18, 12), (26, 14), (34, 0), (26, 9), (32, 7), (25, 0), (30, 14), (16, 12), (30, 17), (2, 7), (9, 1), (27, 22), (12, 4), (29, 10), (5, 5), (22, 30), (32, 0), (19, 19), (2, 2), (20, 30), (24, 20), (29, 8), (28, 5), (14, 9), (17, 26), (11, 7), (23, 17), (21, 7), (16, 29), (12, 27), (1, 13), (27, 29), (2, 20), (33, 21), (7, 18), (33, 11), (17, 17), (11, 9), (21, 5), (23, 11), (20, 24), (35, 4), (25, 4), (12, 23), (26, 7), (32, 14), (2, 17), (18, 21), (12, 16), (33, 24), (8, 6), (7, 6), (21, 4), (16, 3), (18, 8), (2, 13), (5, 30), (18, 10), (33, 1), (15, 29), (30, 0), (12, 29), (17, 13), (19, 17), (8, 14), (13, 12), (12, 21), (7, 0), (28, 24), (16, 2), (22, 29), (29, 24), (35, 18), (1, 20), (7, 27), (6, 16), (0, 18), (13, 13), (16, 5), (25, 20), (25, 10), (17, 21), (10, 22), (32, 19), (9, 21), (1, 28), (15, 10), (32, 3), (23, 0), (18, 7), (14, 11), (24, 17), (16, 25), (7, 13), (19, 22), (28, 4), (9, 29), (2, 29), (4, 8), (21, 26), (13, 28), (10, 24), (23, 8), (14, 15), (34, 24), (12, 8), (13, 8), (18, 24), (33, 19), (10, 16), (18, 13), (16, 27), (4, 28), (14, 25), (3, 18), (1, 16), (12, 3), (20, 14), (30, 22), (19, 15), (6, 6), (24, 15), (25, 24), (17, 20), (5, 3), (26, 20), (14, 12), (30, 10), (32, 30), (25, 12), (10, 21), (23, 28), (26, 11), (14, 19), (33, 15), (19, 12), (34, 29), (12, 2), (30, 19), (11, 24), (24, 3), (0, 27), (15, 15), (13, 27), (18, 17), (21, 22), (8, 21), (19, 16), (34, 16), (10, 18), (13, 1), (34, 7), (21, 0), (1, 24), (20, 8), (27, 5), (31, 24), (34, 27), (1, 12), (17, 30), (4, 22), (4, 12), (25, 13), (9, 9), (7, 28), (10, 12), (14, 22), (8, 9), (12, 13), (6, 7), (26, 5), (22, 13), (32, 26), (21, 1), (12, 28), (12, 1), (20, 23), (7, 22), (24, 6), (4, 3), (3, 21), (16, 15), (13, 26), (30, 26), (29, 11), (19, 29), (26, 16), (30, 21), (32, 28), (22, 4), (24, 7), (2, 8), (26, 30), (30, 20), (32, 23), (29, 5), (25, 6), (12, 18), (30, 18), (22, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209916", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), 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), (25, 22), (5, 12), (36, 12), (24, 9), (6, 22), (23, 14), (8, 28), (2, 10), (23, 25), (13, 15), (31, 27), (7, 14), (15, 17), (1, 20), (21, 9), (16, 1), (10, 5), (16, 18), (8, 21), (13, 0), (10, 24), (1, 19), (2, 9), (23, 21), (15, 0), (33, 11), (18, 22), (35, 8), (7, 15), (5, 11), (3, 20), (11, 22), (0, 9), (35, 18), (2, 15), (10, 20), (23, 5), (21, 13), (15, 14), (34, 16), (21, 17), (28, 30), (19, 30), (21, 4), (34, 2), (32, 30), (21, 11), (19, 1), (22, 2), (7, 5), (27, 13), (12, 9), (20, 27), (0, 20), (22, 24), (23, 10), (8, 13), (20, 15), (6, 23), (8, 18), (29, 24), (0, 14), (8, 1), (22, 1), (25, 1), (5, 27), (21, 6), (7, 30), (18, 0), (10, 13), (8, 4), (2, 20), (30, 15), (25, 25), (13, 10), (12, 28), (19, 29), (3, 28), (21, 3), (3, 29), (30, 5), (36, 11), (21, 14), (3, 10), (20, 4), (29, 2), (28, 6), (5, 8), (36, 29), (3, 5), (24, 24), (32, 26), (21, 5), (19, 14), (36, 2), (35, 5), (24, 2), (30, 9), (17, 4), (35, 17), (28, 15), (5, 16), (27, 15), (34, 13), (31, 21), (31, 29), (20, 11), (25, 9), (0, 17), (24, 11), (16, 14), (11, 25), (30, 30), (30, 25), (31, 23), (25, 28), (11, 23), (14, 27), (36, 3), (5, 18), (15, 26), (33, 2), (10, 19), (14, 14), (1, 29), (7, 25), (33, 28), (34, 20), (8, 30), (35, 11), (4, 5), (18, 25), (2, 6), (12, 17), (4, 30), (35, 9), (31, 10), (25, 6), (22, 22), (32, 17), (14, 20), (3, 4), (16, 25), (32, 25), (10, 27), (11, 19), (29, 23), (19, 17), (33, 23), (3, 6), (33, 20), (3, 17), (23, 6), (27, 9), (4, 22), (8, 14), (20, 19), (35, 25), (20, 9), (0, 1), (32, 1), (23, 16), (26, 29), (29, 30), (29, 28), (5, 21), (35, 13), (7, 11), (26, 20), (4, 27), (18, 19), (1, 10), (19, 5), (19, 0), (30, 12), (34, 11), (10, 22), (28, 27), (14, 28), (33, 9), (21, 2), (19, 20), (15, 21), (25, 0), (2, 21), (2, 8), (34, 6), (36, 22), (9, 11), (36, 18), (20, 24), (23, 29), (31, 11), (22, 14), (5, 5), (19, 27), (11, 21), (4, 20), (4, 14), (24, 29), (18, 5), (17, 12), (18, 6), (27, 10), (24, 22), (36, 1), (8, 24), (31, 22), (16, 9), (1, 16), (23, 26), (18, 30), (35, 23), (15, 4), (9, 12), (26, 1), (36, 15), (16, 12), (13, 23), (4, 21), (9, 25), (21, 24), (22, 28), (0, 26), (4, 25), (35, 3), (34, 23), (15, 27), (34, 14), (7, 13), (34, 12), (9, 1), (16, 17), (13, 19), (1, 28), (20, 17), (4, 19), (15, 7), (18, 24), (8, 23), (7, 1), (1, 7), (32, 16), (0, 19), (17, 5), (6, 14), (29, 0), (29, 27), (18, 3), (8, 12), (30, 3), (5, 9), (32, 0), (18, 1), (20, 21), (26, 16), (34, 22), (20, 6), (6, 25), (26, 14), (11, 5), (4, 1), (18, 29), (30, 26), (31, 15), (11, 3), (4, 0), (27, 20), (22, 6), (35, 28), (21, 7), (10, 21), (5, 20), (20, 3), (16, 22), (5, 28), (25, 8), (30, 22), (12, 13), (22, 7), (7, 10), (2, 7), (15, 16), (6, 11), (14, 26), (17, 24), (24, 26), (22, 17), (33, 15), (20, 30), (6, 28), (20, 28), (3, 21), (28, 19), (18, 2), (17, 28), (33, 27), (0, 16), (0, 5), (25, 29), (2, 22), (26, 4), (16, 0), (21, 12), (7, 20), (34, 4), (34, 3), (10, 26), (9, 6), (29, 18), (20, 13), (29, 25), (11, 26), (27, 11), (19, 28), (9, 17), (11, 2), (16, 21), (4, 24), (13, 5), (10, 28), (33, 22), (25, 21), (26, 5), (36, 24), (20, 18), (26, 2), (6, 21), (15, 29), (24, 8), (12, 8), (11, 12), (18, 10), (27, 14), (27, 23), (17, 18), (34, 5), (3, 3), (27, 25), (15, 15), (6, 8), (21, 8), (16, 8), (35, 21), (11, 27), (0, 27), (17, 20), (22, 19), (13, 12), (35, 4), (24, 10), (31, 17), (35, 14), (28, 21), (28, 16), (21, 21), (33, 4), (23, 20), (14, 13), (24, 13), (7, 17), (33, 16), (28, 8), (2, 24), (12, 12), (17, 29), (17, 15), (27, 1), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943488", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), 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), (1, 3), (10, 26), (11, 28), (24, 28), (21, 28), (1, 18), (3, 12), (9, 24), (4, 11), (2, 37), (4, 16), (25, 37), (14, 34), (29, 2), (1, 28), (3, 26), (10, 16), (9, 0), (10, 28), (4, 21), (28, 10), (14, 7), (10, 5), (4, 37), (27, 3), (4, 1), (14, 18), (28, 27), (1, 20), (2, 11), (7, 19), (29, 14), (3, 31), (19, 6), (23, 37), (28, 23), (7, 32), (1, 31), (6, 34), (13, 34), (4, 20), (25, 11), (6, 33), (19, 4), (11, 21), (27, 28), (21, 6), (12, 9), (15, 8), (27, 33), (9, 23), (6, 24), (16, 26), (23, 3), (13, 33), (20, 33), (10, 34), (1, 23), (26, 20), (13, 27), (23, 28), (20, 29), (18, 28), (1, 17), (20, 27), (23, 22), (20, 15), (1, 16), (22, 20), (16, 21), (28, 19), (3, 21), (24, 1), (19, 26), (6, 9), (4, 9), (29, 36), (17, 5), (13, 11), (10, 13), (17, 29), (18, 37), (18, 32), (20, 36), (21, 14), (17, 18), (13, 9), (1, 5), (12, 34), (24, 20), (0, 31), (25, 4), (16, 27), (1, 25), (25, 8), (11, 10), (26, 25), (23, 34), (15, 26), (9, 8), (3, 6), (20, 23), (24, 16), (3, 24), (29, 10), (29, 29), (22, 2), (28, 33), (1, 1), (21, 19), (22, 21), (9, 36), (11, 8), (11, 13), (22, 5), (24, 21), (29, 11), (12, 14), (17, 7), (4, 0), (8, 1), (10, 18), (5, 30), (0, 37), (24, 5), (15, 2), (2, 3), (10, 9), (7, 17), (19, 25), (29, 8), (27, 32), (11, 33), (6, 3), (27, 29), (28, 4), (5, 0), (14, 12), (26, 0), (15, 23), (19, 37), (28, 6), (26, 3), (26, 1), (13, 36), (24, 30), (24, 27), (12, 15), (14, 17), (8, 8), (9, 7), (11, 1), (13, 19), (1, 22), (7, 10), (10, 22), (1, 0), (16, 12), (2, 25), (29, 9), (19, 36), (14, 31), (12, 32), (26, 19), (1, 19), (3, 10), (16, 34), (24, 35), (5, 22), (19, 34), (9, 29), (28, 14), (7, 27), (29, 12), (3, 1), (9, 10), (18, 18), (28, 24), (1, 32), (22, 24), (5, 34), (4, 8), (29, 15), (23, 4), (3, 14), (12, 22), (25, 25), (15, 6), (7, 13), (27, 26), (18, 4), (28, 20), (13, 18), (0, 14), (27, 17), (17, 32), (16, 23), (18, 9), (25, 34), (26, 17), (3, 32), (24, 32), (23, 10), (17, 11), (29, 22), (16, 8), (10, 35), (25, 30), (2, 8), (12, 3), (0, 19), (2, 4), (7, 14), (8, 23), (0, 13), (11, 30), (9, 18), (12, 25), (5, 24), (26, 4), (21, 22), (6, 26), (14, 21), (15, 20), (26, 24), (27, 10), (25, 22), (8, 32), (20, 16), (2, 34), (6, 37), (5, 15), (3, 30), (1, 13), (18, 21), (26, 13), (11, 12), (13, 14), (3, 37), (28, 0), (6, 27), (19, 8), (21, 29), (4, 17), (25, 23), (19, 12), (0, 24), (26, 12), (0, 28), (19, 5), (11, 29), (15, 15), (23, 23), (15, 33), (18, 16), (5, 18), (5, 36), (14, 29), (9, 22), (21, 27), (11, 3), (17, 16), (6, 11), (21, 30), (22, 31), (6, 0), (7, 4), (18, 34), (22, 1), (17, 35), (12, 20), (2, 18), (28, 32), (22, 3), (7, 0), (12, 19), (1, 15), (15, 4), (14, 14), (17, 28), (29, 34), (5, 1), (20, 6), (3, 17), (25, 2), (4, 34), (5, 9), (20, 37), (21, 2), (17, 12), (8, 2), (29, 24), (19, 19), (29, 0), (0, 6), (3, 16), (12, 5), (15, 9), (18, 23), (16, 4), (13, 4), (13, 21), (9, 25), (7, 16), (19, 20), (26, 5), (24, 15), (2, 31), (3, 11), (16, 20), (28, 11), (26, 28), (26, 8), (12, 10), (11, 24), (4, 13), (14, 33), (23, 9), (27, 4), (0, 17), (3, 29), (24, 14), (15, 0), (26, 15), (20, 11), (7, 25), (9, 37), (12, 23), (21, 0), (21, 25), (18, 8), (21, 31), (6, 4), (16, 2), (10, 25), (17, 4), (20, 30), (16, 25), (9, 6), (24, 19), (29, 26), (28, 34), (9, 31), (17, 8), (17, 26), (9, 30), (4, 26), (0, 32), (21, 9), (0, 9), (1, 14), (22, 25), (1, 26), (22, 19), (6, 29), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239184", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 36), (25, 28), (19, 14), (0, 27), (5, 10), (3, 0), (6, 30), (7, 22), (22, 31), (22, 36), (26, 34), (1, 1), (23, 22), (25, 15), (17, 9), (18, 9), (0, 30), (21, 34), (28, 9), (10, 26), (4, 27), (20, 24), (2, 27), (3, 36), (9, 7), (17, 10), (12, 32), (28, 37), (21, 0), (6, 19), (14, 9), (29, 32), (11, 17), (26, 16), (20, 2), (11, 10), (17, 23), (10, 0), (3, 16), (21, 21), (28, 11), (11, 1), (15, 20), (23, 14), (27, 15), (1, 38), (1, 2), (12, 4), (17, 7), (3, 27), (11, 25), (1, 27), (9, 5), (1, 13), (15, 10), (14, 28), (8, 13), (5, 27), (7, 26), (16, 6), (5, 19), (20, 38), (16, 13), (8, 26), (6, 23), (4, 37), (24, 13), (14, 20), (23, 7), (24, 30), (27, 35), (5, 18), (12, 2), (3, 25), (8, 34), (14, 29), (1, 18), (20, 20), (7, 7), (5, 3), (9, 10), (0, 19), (9, 38), (17, 1), (25, 14), (4, 0), (23, 32), (19, 35), (12, 30), (20, 35), (6, 8), (22, 0), (2, 12), (9, 33), (24, 31), (2, 22), (5, 9), (19, 24), (21, 19), (0, 21), (13, 14), (4, 22), (8, 37), (16, 15), (12, 16), (29, 16), (26, 18), (2, 14), (13, 17), (12, 26), (29, 29), (11, 4), (19, 17), (29, 21), (2, 9), (26, 12), (5, 25), (15, 0), (22, 23), (4, 10), (27, 11), (22, 9), (27, 22), (20, 29), (1, 19), (6, 27), (22, 8), (29, 31), (20, 30), (8, 27), (1, 24), (7, 14), (17, 5), (6, 38), (15, 23), (26, 4), (21, 10), (26, 25), (16, 2), (27, 18), (21, 4), (6, 18), (7, 2), (5, 30), (13, 35), (25, 31), (23, 21), (23, 4), (5, 7), (24, 0), (12, 8), (13, 13), (4, 3), (5, 12), (5, 4), (20, 11), (23, 33), (2, 33), (19, 10), (9, 26), (18, 13), (4, 1), (4, 24), (8, 7), (29, 35), (11, 16), (8, 2), (7, 4), (15, 4), (27, 38), (23, 10), (17, 38), (23, 25), (21, 18), (13, 36), (5, 5), (25, 11), (7, 21), (17, 22), (6, 4), (4, 34), (14, 37), (19, 32), (20, 13), (15, 28), (3, 7), (20, 37), (14, 25), (26, 31), (17, 16), (16, 8), (20, 21), (14, 23), (17, 4), (20, 15), (14, 27), (24, 35), (0, 18), (11, 31), (9, 24), (28, 28), (29, 9), (17, 2), (25, 5), (27, 16), (17, 20), (27, 14), (15, 34), (18, 3), (12, 10), (14, 34), (16, 38), (5, 37), (8, 9), (3, 23), (27, 29), (14, 32), (0, 11), (19, 15), (28, 25), (3, 21), (0, 36), (10, 9), (5, 26), (29, 24), (12, 24), (26, 26), (15, 3), (5, 15), (8, 4), (27, 32), (13, 16), (5, 13), (20, 9), (22, 3), (8, 32), (22, 17), (5, 1), (24, 7), (15, 24), (8, 3), (25, 7), (4, 7), (27, 25), (11, 11), (21, 5), (9, 31), (29, 27), (29, 17), (18, 33), (25, 17), (25, 12), (17, 31), (12, 12), (27, 5), (10, 12), (1, 9), (13, 28), (25, 13), (10, 21), (23, 5), (1, 30), (21, 15), (28, 26), (3, 37), (0, 14), (4, 32), (0, 4), (26, 27), (4, 31), (24, 11), (22, 5), (25, 9), (20, 28), (25, 10), (3, 28), (22, 10), (2, 15), (11, 37), (7, 20), (12, 31), (29, 1), (23, 36), (2, 21), (11, 32), (3, 11), (17, 15), (1, 8), (11, 27), (17, 33), (13, 15), (2, 3), (18, 27), (23, 6), (2, 1), (8, 17), (0, 33), (28, 15), (17, 35), (28, 29), (25, 18), (10, 35), (22, 1), (14, 7), (8, 28), (22, 29), (6, 7), (8, 0), (28, 14), (8, 11), (5, 31), (29, 14), (14, 10), (16, 3), (29, 3), (29, 7), (28, 7), (27, 27), (19, 21), (5, 23), (23, 19), (25, 21), (7, 38), (27, 33), (28, 35), (22, 18), (9, 19), (13, 20), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "823680", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 30), (32, 12), (15, 31), (21, 23), (28, 36), (4, 19), (20, 37), (5, 24), (2, 2), (15, 25), (33, 18), (13, 0), (23, 27), (1, 28), (37, 6), (11, 15), (0, 16), (1, 18), (12, 10), (14, 11), (15, 5), (0, 33), (18, 30), (15, 10), (19, 8), (26, 7), (16, 37), (21, 29), (35, 30), (35, 10), (28, 34), (37, 7), (23, 1), (32, 16), (34, 16), (16, 10), (33, 34), (23, 8), (21, 6), (29, 17), (23, 31), (9, 23), (31, 5), (17, 30), (29, 9), (9, 20), (35, 35), (3, 36), (26, 36), (14, 4), (4, 14), (22, 32), (22, 29), (8, 23), (20, 3), (21, 9), (20, 7), (19, 19), (19, 26), (30, 36), (23, 23), (9, 2), (25, 19), (26, 34), (20, 11), (32, 4), (36, 4), (30, 21), (37, 29), (7, 22), (2, 19), (15, 23), (11, 27), (6, 16), (5, 32), (36, 16), (36, 30), (22, 8), (25, 10), (10, 18), (34, 19), (32, 19), (34, 20), (9, 13), (15, 12), (19, 6), (14, 15), (11, 11), (23, 16), (28, 12), (27, 24), (15, 27), (11, 12), (34, 15), (21, 26), (25, 30), (21, 10), (29, 24), (9, 25), (18, 1), (32, 29), (34, 32), (0, 20), (5, 8), (35, 8), (17, 8), (1, 29), (30, 25), (37, 26), (17, 28), (32, 27), (18, 19), (23, 24), (37, 11), (34, 2), (33, 8), (35, 0), (12, 37), (13, 20), (23, 11), (26, 33), (2, 20), (15, 6), (7, 16), (0, 22), (25, 36), (11, 13), (25, 18), (12, 29), (36, 8), (16, 29), (18, 8), (27, 35), (2, 3), (1, 19), (3, 28), (1, 6), (24, 8), (12, 3), (28, 35), (8, 24), (15, 16), (36, 14), (14, 26), (8, 27), (28, 0), (17, 9), (22, 3), (32, 5), (13, 18), (19, 28), (13, 25), (4, 4), (36, 9), (23, 6), (9, 17), (35, 2), (27, 28), (2, 30), (17, 22), (15, 35), (3, 34), (27, 37), (18, 23), (31, 11), (25, 16), (32, 25), (7, 23), (2, 11), (4, 27), (34, 36), (35, 4), (11, 3), (10, 13), (22, 20), (13, 33), (25, 24), (24, 33), (7, 32), (21, 22), (1, 1), (19, 14), (6, 22), (21, 17), (22, 23), (7, 33), (33, 29), (24, 1), (27, 13), (6, 28), (20, 14), (37, 18), (6, 6), (12, 5), (13, 6), (21, 34), (11, 36), (4, 25), (2, 16), (20, 13), (25, 1), (27, 7), (13, 31), (1, 3), (15, 18), (14, 16), (8, 29), (25, 3), (36, 12), (30, 26), (5, 11), (1, 10), (23, 4), (36, 23), (34, 1), (18, 31), (16, 15), (34, 6), (29, 30), (27, 1), (30, 12), (17, 32), (24, 6), (1, 22), (20, 16), (35, 23), (23, 3), (10, 5), (21, 14), (37, 21), (16, 34), (4, 1), (21, 13), (8, 30), (29, 19), (14, 23), (17, 2), (22, 19), (17, 3), (23, 35), (35, 7), (3, 27), (23, 5), (10, 7), (19, 18), (18, 5), (19, 37), (22, 10), (27, 22), (30, 4), (7, 9), (33, 13), (28, 26), (4, 17), (18, 7), (34, 31), (6, 21), (15, 1), (26, 13), (14, 27), (20, 18), (16, 16), (17, 29), (14, 17), (5, 21), (28, 19), (25, 14), (25, 25), (25, 4), (29, 12), (33, 2), (20, 30), (36, 21), (1, 33), (6, 11), (22, 37), (32, 22), (26, 18), (21, 20), (3, 26), (7, 24), (36, 6), (2, 23), (2, 5), (32, 23), (13, 11), (14, 30), (26, 2), (25, 9), (37, 1), (28, 7), (4, 10), (2, 8), (4, 22), (12, 9), (29, 22), (1, 16), (11, 19), (8, 15), (36, 13), (19, 33), (36, 3), (35, 16), (1, 25), (18, 32), (36, 15), (31, 36), (2, 28), (20, 21), (11, 18), (14, 3), (6, 25), (29, 36), (23, 30), (33, 26), (30, 6), (14, 21), (32, 32), (11, 33), (18, 13), (33, 7), (0, 35), (22, 15), (26, 23), (12, 19), (20, 5), (17, 7), (18, 36), (28, 17), (8, 2), (11, 16), (11, 34), (5, 3), (14, 20), (23, 19), (12, 15), (14, 36), (23, 28), (28, 33), (32, 8), (16, 35), (6, 27), (12, 13), (24, 18), (13, 34), (19, 23), (9, 30), (17, 16), (33, 21), (4, 11), (35, 17), (32, 37), (27, 36), (24, 20), (0, 34), (13, 26), (24, 17), (11, 2), (11, 26), (1, 32), (32, 33), (33, 3), (33, 10), (1, 26), (7, 12), (7, 35), (2, 4), (13, 27), (10, 29), (15, 9), (36, 36), (15, 30), (18, 9), (20, 12), (16, 36), (3, 23), (33, 1), (22, 21), (17, 17), (22, 36), (12, 7), (32, 30), (26, 5), (1, 2), (32, 21), (5, 34), (27, 32), (27, 29), (37, 9), (33, 22), (4, 28), (25, 8), (34, 0), (6, 3), (27, 21), (11, 35), (29, 6), (22, 18), (34, 13), (37, 32), (17, 36), (11, 4), (18, 6), (20, 34), (16, 32), (35, 31), (12, 27), (10, 33), (6, 19), (8, 21), (18, 0), (9, 1), (17, 5), (26, 30), (37, 30), (30, 27), (15, 34), (10, 22), (36, 17), (24, 12), (13, 8), (7, 28), (11, 25), (7, 25), (29, 21), (30, 37), (33, 27), (14, 1), (19, 0), (30, 18), (13, 3), (37, 25), (33, 28), (5, 6), (27, 14), (0, 10), (35, 21), (21, 24), (21, 18), (4, 33), (14, 2), (17, 4), (11, 5), (17, 37), (6, 32), (8, 18), (4, 23), (37, 36), (6, 2), (22, 26), (22, 13), (0, 4), (37, 28), (13, 2), (1, 13), (18, 37), (17, 24), (34, 8), (29, 0), (20, 33), (5, 14), (7, 10), (28, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391680", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 5), (14, 21), (35, 21), (0, 21), (24, 24), (18, 20), (12, 30), (21, 15), (28, 27), (24, 12), (11, 26), (18, 9), (33, 32), (4, 28), (2, 24), (1, 21), (19, 10), (32, 26), (8, 13), (25, 13), (32, 12), (12, 22), (19, 21), (20, 20), (25, 4), (2, 22), (13, 10), (16, 30), (31, 21), (12, 13), (33, 13), (12, 19), (35, 10), (16, 0), (3, 9), (23, 18), (27, 25), (9, 13), (4, 0), (7, 0), (20, 17), (27, 31), (8, 30), (35, 9), (24, 19), (29, 22), (15, 23), (23, 6), (26, 20), (12, 3), (4, 18), (11, 1), (37, 19), (31, 17), (15, 14), (27, 27), (34, 7), (21, 31), (17, 11), (23, 22), (30, 15), (14, 9), (32, 7), (3, 0), (19, 29), (23, 28), (29, 5), (25, 12), (25, 15), (0, 7), (2, 31), (21, 13), (7, 18), (21, 12), (9, 4), (30, 18), (30, 4), (33, 24), 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4), (6, 10), (13, 3), (12, 5), (29, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742400", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 27), (29, 3), (24, 27), (21, 24), (4, 6), (9, 24), (8, 4), (2, 23), (28, 27), (22, 3), (0, 25), (28, 15), (13, 12), (1, 15), (0, 19), (20, 29), (5, 25), (13, 8), (25, 22), (7, 28), (2, 0), (18, 28), (27, 10), (28, 20), (23, 21), (28, 5), (3, 25), (20, 22), (7, 14), (12, 0), (16, 22), (9, 7), (29, 10), (16, 1), (12, 7), (3, 28), (5, 30), (2, 31), (12, 12), (18, 7), (14, 17), (0, 6), (1, 10), (27, 17), (15, 14), (8, 19), (15, 30), (20, 8), (18, 24), (25, 12), (11, 13), (9, 28), (6, 4), (19, 13), (12, 13), (28, 19), (19, 27), (17, 9), (11, 4), (4, 29), (5, 31), (13, 14), (21, 10), (6, 20), (3, 14), (14, 25), (20, 25), (17, 20), (24, 15), (17, 17), (29, 6), (9, 18), (20, 4), (27, 4), (3, 12), (0, 29), (2, 11), (17, 25), (20, 13), (13, 0), (18, 18), (1, 14), (28, 4), (17, 7), (3, 21), (24, 17), (11, 19), (12, 14), (6, 8), (10, 7), (3, 18), (17, 4), (18, 29), (14, 7), (21, 14), (25, 15), (5, 23), (6, 28), (29, 7), (1, 5), (7, 25), (1, 7), (19, 6), (17, 15), (25, 10), (27, 13), (1, 29), (0, 3), (9, 30), (4, 23), (16, 8), (26, 16), (5, 12), (0, 16), (28, 23), (13, 4), (27, 19), (10, 25), (5, 10), (19, 18), (3, 16), (26, 26), (9, 21), (25, 6), (21, 23), (1, 22), (11, 27), (16, 29), (15, 11), (3, 0), (23, 6), (21, 21), (10, 14), (5, 5), (5, 29), (26, 5), (1, 3), (23, 26), (7, 31), (7, 19), (0, 11), (13, 18), (4, 2), (4, 11), (0, 26), (7, 20), (15, 25), (23, 8), (19, 1), (27, 25), (25, 16), (9, 0), (29, 29), (26, 8), (10, 26), (26, 4), (6, 15), (14, 27), (17, 13), (3, 8), (9, 2), (8, 25), (29, 9), (7, 3), (27, 15), (24, 24), (29, 4), (11, 29), (20, 23), (3, 17), (11, 5), (25, 30), (12, 9), (27, 11), (15, 13), (28, 9), (12, 15), (1, 6), (15, 6), (20, 28), (29, 8), (14, 4), (27, 20), (2, 2), (2, 9), (19, 17), (6, 6), (8, 10), (1, 13), (17, 5), (19, 28), (15, 7), (1, 26), (25, 11), (15, 21), (27, 3), (11, 1), (0, 21), (5, 7), (5, 18), (23, 27), (2, 19), (18, 19), (21, 13), (11, 20), (3, 15), (29, 14), (1, 12), (21, 29), (29, 0), (3, 3), (17, 0), (22, 20), (10, 3), (5, 0), (17, 31), (11, 10), (0, 18), (18, 1), (24, 0), (21, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "921600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 20), (7, 2), (11, 31), (14, 24), (16, 7), (30, 31), (4, 2), (30, 29), (18, 4), (10, 19), (17, 21), (22, 20), (8, 31), (8, 6), (18, 19), (20, 18), (18, 13), (14, 6), (1, 6), (9, 12), (20, 26), (28, 19), (12, 25), (4, 4), (19, 25), (13, 17), (15, 8), (5, 20), (24, 18), (2, 10), (26, 20), (23, 9), (26, 23), (21, 20), (16, 3), (5, 8), (26, 1), (12, 4), (22, 8), (29, 14), (12, 30), (1, 19), (15, 6), (5, 19), (18, 7), (10, 20), (26, 18), (4, 16), (21, 24), (14, 9), (23, 15), (5, 7), (18, 30), (12, 27), (8, 21), (4, 6), (0, 7), (5, 27), (18, 23), (3, 15), (27, 32), (2, 16), (3, 3), (22, 18), (25, 10), (25, 32), (4, 15), (10, 29), (17, 11), (2, 26), (4, 17), (9, 20), (24, 1), (9, 17), (30, 14), (27, 6), (29, 4), (13, 16), (6, 10), (12, 31), (25, 15), (25, 14), (4, 7), (11, 26), (26, 17), (7, 5), (15, 7), (16, 16), (23, 16), (15, 11), (12, 22), (2, 2), (24, 28), (5, 6), (6, 3), (30, 6), (28, 24), (1, 5), (6, 26), (14, 23), (5, 29), (6, 24), (29, 18), (2, 6), (11, 24), (22, 22), (25, 28), (10, 12), (27, 7), (24, 23), (17, 27), (22, 4), (17, 20), (21, 28), (16, 19), (19, 28), (27, 12), (24, 22), (8, 0), (3, 27), (16, 18), (19, 29), (14, 8), (1, 9), (29, 15), (27, 3), (27, 27), (29, 22), (23, 4), (19, 26), (2, 24), (2, 20), (25, 7), (14, 19), (20, 0), (6, 2), (20, 1), (14, 10), (1, 27), (28, 15), (21, 21), (15, 19), (8, 1), (8, 10), (15, 5), (16, 20), (26, 26), (7, 27), (19, 4), (19, 16), (17, 10), (30, 3), (24, 9), (20, 19), (22, 32), (0, 12), (3, 12), (0, 18), (17, 1), (1, 14), (14, 3), (6, 23), (23, 2), (1, 29), (10, 27), (29, 19), (6, 19), (22, 17), (27, 9), (26, 6), (3, 31), (3, 5), (25, 19), (5, 25), (30, 16), (16, 14), (16, 1), (8, 8), (26, 4), (21, 22), (6, 0), (2, 31), (10, 25), (18, 3), (8, 2), (12, 19), (27, 20), (22, 29), (24, 7), (6, 29), (29, 0), (19, 21), (15, 28), (7, 9), (30, 24), (24, 3), (4, 28), (30, 23), (8, 16), (19, 11), (8, 3), (13, 15), (17, 19), (16, 10), (27, 16), (22, 0), (17, 3), (2, 4), (9, 14), (28, 17), (17, 16), (9, 5), (9, 16), (25, 1), (3, 17), (8, 24), (23, 27), (12, 0), (9, 13), (30, 0), (9, 21), (1, 7), (30, 15), (30, 5), (10, 9), (5, 15), (27, 30), (9, 8), (10, 13), (4, 30), (30, 10), (0, 15), (26, 25), (14, 4), (13, 14), (5, 24), (28, 30), (4, 8), (15, 0), (22, 12), (11, 27), (3, 4), (20, 14), (29, 27), (5, 5), (0, 3), (19, 24), (15, 12), (30, 28), (18, 0), (11, 25), (22, 24), (15, 3), (29, 25), (10, 18), (27, 2), (13, 21), (15, 21), (11, 5), (0, 25), (7, 21), (4, 18), (24, 31), (26, 24), (7, 24), (16, 15), (29, 9), (13, 9), (14, 28), (19, 19), (17, 18), (1, 28), (23, 12), (27, 25), (28, 9), (19, 14), (22, 14), (10, 15), (4, 23), (14, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555738", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (1, 5), (18, 14), (12, 15), (31, 3), (24, 32), (29, 31), (16, 21), (11, 18), (31, 33), (6, 12), (12, 8), (18, 13), (26, 29), (12, 7), (13, 8), (21, 9), (27, 18), (23, 19), (21, 27), (33, 2), (10, 19), (10, 1), (10, 14), (3, 30), (5, 13), (2, 31), (6, 10), (29, 8), (7, 23), (28, 3), (2, 4), (25, 21), (17, 36), (20, 16), (15, 15), (15, 13), (27, 22), (17, 16), (33, 34), (29, 5), (20, 1), (2, 33), (17, 33), (21, 1), (18, 26), (34, 32), (17, 18), (26, 4), (21, 25), (24, 27), (18, 9), (28, 9), (18, 0), (4, 17), (33, 14), (32, 8), (3, 10), (25, 36), (6, 0), (22, 25), (26, 13), (33, 27), (19, 15), (10, 7), (23, 13), (20, 33), (3, 1), (11, 34), (33, 33), (1, 7), (23, 21), (25, 30), (4, 22), (17, 13), (14, 7), (5, 26), (0, 31), (4, 28), (24, 29), (18, 36), (1, 32), (12, 5), (3, 26), (2, 24), (26, 0), (17, 1), (24, 35), (9, 28), (7, 25), (12, 1), (10, 30), (10, 2), (21, 8), (20, 28), (16, 32), (14, 3), (24, 2), (26, 20), (33, 26), (29, 28), (14, 36), (26, 6), (15, 30), (30, 7), (31, 2), (4, 6), (10, 12), (17, 30), (33, 3), (12, 10), (15, 8), (29, 36), (2, 23), (14, 23), (12, 31), (29, 16), (25, 35), (31, 17), (22, 9), (30, 34), (23, 0), (20, 32), (22, 35), (30, 31), (20, 0), (15, 21), (11, 31), (13, 10), (33, 20), (21, 16), (10, 36), (23, 14), (27, 8), (30, 12), (11, 23), (25, 14), (23, 23), (16, 11), (31, 6), (32, 7), (13, 7), (0, 34), (21, 32), (15, 7), (20, 7), (34, 15), (9, 19), (18, 23), (7, 5), (32, 15), (19, 10), (7, 16), (19, 18), (19, 19), (7, 19), (33, 22), (18, 31), (11, 30), (19, 27), (4, 0), (7, 22), (5, 11), (26, 19), (5, 31), (32, 16), (28, 33), (23, 30), (12, 36), (22, 17), (21, 23), (30, 13), (8, 19), (28, 12), (0, 17), (2, 6), (11, 19), (25, 7), (26, 7), (5, 8), (27, 0), (15, 28), (3, 12), (25, 4), (30, 19), (28, 26), (12, 17), (30, 33), (6, 11), (21, 24), (18, 30), (9, 14), (17, 26), (8, 8), (18, 2), (14, 29), (26, 5), (11, 13), (32, 0), (26, 2), (1, 10), (9, 17), (6, 16), (4, 9), (2, 18), (27, 32), (34, 31), (16, 14), (29, 11), (4, 23), (0, 35), (24, 28), (10, 6), (12, 3), (6, 4), (14, 28), (24, 20), (15, 35), (4, 1), (25, 15), (16, 4), (6, 2), (6, 28), (5, 24), (11, 33), (20, 18), (15, 19), (25, 22), (8, 3), (24, 24), (32, 17), (15, 0), (15, 10), (34, 28), (16, 3), (17, 29), (9, 24), (25, 23), (13, 24), (30, 28), (31, 14), (24, 11), (16, 22), (26, 31), (23, 25), (0, 8), (27, 16), (5, 33), (9, 26), (7, 14), (25, 24), (0, 20), (20, 22), (29, 18), (26, 15), (23, 35), (29, 21), (2, 10), (26, 35), (20, 34), (12, 19), (33, 31), (26, 33), (7, 1), (17, 0), (0, 14), (19, 11), (27, 26), (29, 33), (22, 11), (30, 9), (3, 35), (8, 25), (25, 5), (26, 12), (30, 24), (2, 36), (26, 11), (16, 0), (18, 33), (1, 20), (20, 6), (29, 7), (19, 35), (12, 30), (20, 30), (12, 29), (7, 2), (13, 3), (34, 19), (22, 31), (23, 15), (12, 35), (6, 20), (13, 1), (21, 33), (27, 24), (4, 35), (12, 27), (32, 3), (0, 21), (33, 8), (28, 27), (24, 19), (13, 11), (10, 31), (19, 28), (15, 12), (28, 23), (13, 2), (11, 1), (32, 9), (0, 10), (25, 33), (18, 25), (29, 29), (17, 32), (13, 34), (14, 34), (20, 25), (4, 24), (17, 17), (25, 25), (31, 35), (3, 21), (26, 10), (15, 11), (23, 2), (34, 33), (27, 17), (1, 23), (31, 27), (27, 9), (9, 21), (25, 16), (12, 22), (9, 20), (12, 13), (12, 12), (14, 21), (22, 21), (27, 29), (18, 15), (3, 22), (1, 27), (14, 18), (7, 30), (27, 12), (28, 18), (17, 28), (34, 13), (34, 4), (25, 10), (15, 18), (15, 5), (0, 12), (2, 28), (32, 31), (33, 28), (29, 12), (5, 32), (17, 22), (4, 15), (34, 2), (19, 17), (21, 4), (16, 12), (18, 16), (31, 5), (11, 36), (8, 21), (0, 7), (25, 0), (4, 4), (7, 3), (2, 12), (4, 26), (28, 2), (5, 0), (32, 24), (11, 11), (23, 10), (15, 20), (16, 2), (9, 10), (16, 15), (4, 27), (18, 7), (5, 7), (15, 36), (21, 36), (27, 13), (1, 8), (8, 16), (3, 11), (10, 13), (17, 6), (17, 12), (34, 26), (9, 3), (1, 16), (13, 20), (13, 26), (25, 1), (25, 11), (27, 25), (33, 4), (32, 14), (9, 27), (13, 18), (14, 6), (5, 4), (0, 24), (15, 9), (8, 0), (2, 9), (13, 33), (5, 30), (6, 15), (27, 23), (23, 6), (3, 33), (18, 10), (20, 11), (2, 21), (9, 23), (27, 19), (24, 3), (0, 18), (25, 32), (24, 23), (6, 14), (1, 22), (30, 23), (34, 7), (2, 5), (28, 11), (18, 18), (32, 30), (1, 21), (8, 17), (10, 20), (19, 33), (17, 11), (6, 35), (11, 4), (11, 10), (25, 29), (10, 18), (31, 10), (21, 11), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449280", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), 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), (13, 21), (1, 4), (26, 14), (24, 10), (18, 27), (13, 20), (28, 6), (19, 17), (6, 16), (13, 17), (1, 24), (18, 14), (19, 12), (18, 2), (27, 27), (28, 9), (3, 5), (17, 20), (12, 26), (13, 30), (2, 17), (1, 16), (13, 27), (32, 19), (25, 24), (13, 13), (13, 16), (23, 14), (28, 16), (20, 21), (19, 1), (3, 27), (28, 20), (4, 20), (6, 25), (13, 10), (8, 6), (2, 14), (24, 21), (11, 15), (6, 22), (28, 10), (4, 27), (23, 4), (16, 11), (6, 26), (31, 18), (30, 32), (4, 3), (7, 13), (25, 17), (27, 26), (9, 11), (6, 20), (3, 17), (19, 22), (12, 9), (22, 14), (6, 1), (2, 8), (28, 29), (8, 12), (22, 31), (30, 4), (22, 11), (23, 23), (32, 3), (23, 25), (3, 31), (25, 1), (30, 13), (15, 12), (28, 32), (30, 1), (21, 29), (14, 19), (31, 11), (26, 28), (25, 3), (29, 14), (10, 12), (19, 23), (16, 4), (19, 24), (12, 30), (22, 16), (9, 7), (31, 27), (25, 4), (25, 0), (1, 31), (26, 5), (14, 3), (3, 29), (27, 10), (0, 16), (24, 4), (10, 24), (26, 26), (5, 3), (17, 12), (15, 3), (18, 6), (11, 29), (33, 10), (21, 28), (5, 7), (32, 17), (1, 32), (4, 7), (7, 7), (2, 18), (18, 12), (24, 16), (3, 9), (13, 22), (28, 14), (19, 9), (24, 19), (4, 29), (8, 17), (30, 14), (13, 32), (22, 23), (24, 27), (12, 12), (5, 21), (14, 9), (18, 32), (30, 10), (16, 18), (0, 18), (26, 29), (13, 1), (28, 22), (31, 21), (9, 8), (13, 25), (33, 2), (9, 30), (18, 24), (26, 17), (10, 29), (16, 29), (30, 17), (31, 23), (25, 6), (29, 17), (33, 9), (1, 28), (26, 21), (21, 7), (7, 11), (30, 21), (26, 4), (30, 18), (29, 3), (2, 11), (12, 24), (23, 12), (21, 1), (31, 19), (2, 2), (17, 31), (28, 13), (2, 31), (0, 30), (15, 21), (8, 27), (14, 14), (22, 15), (14, 16), (23, 0), (12, 5), (27, 32), (24, 12), (26, 3), (21, 31), (3, 19), (6, 14), (24, 26), (12, 14), (2, 5), (17, 11), (32, 28), (28, 11), (6, 5), (8, 15), (22, 22), (1, 14), (33, 22), (25, 18), (25, 12), (26, 6), (26, 31), (16, 27), (4, 14), (15, 20), (7, 8), (8, 18), (30, 22), (11, 9), (12, 6), (25, 8), (7, 5), (17, 9), (14, 22), (31, 5), (9, 20), (9, 18), (17, 17), (3, 18), (21, 19), (18, 23), (24, 9), (21, 14), (17, 8), (29, 20), (8, 14), (26, 7), (21, 3), (7, 21), (7, 28), (30, 24), (4, 26), (11, 0), (9, 10), (12, 13), (31, 14), (25, 16), (14, 5), (6, 13), (32, 4), (31, 31), (5, 12), (28, 4), (17, 4), (26, 19), (33, 18), (18, 7), (25, 7), (11, 12), (11, 3), (23, 1), (1, 12), (24, 29), (1, 19), (13, 7), (22, 9), (11, 26), (20, 0), (27, 21), (4, 25), (16, 0), (2, 12), (5, 17), (3, 1), (29, 28), (24, 8), (15, 24), (9, 12), (11, 7), (20, 23), (15, 11), (22, 20), (27, 5), (12, 7), (25, 14), (17, 5), (14, 29), (22, 17), (17, 15), (3, 11), (2, 16), (9, 1), (33, 30), (20, 22), (18, 3), (12, 17), (32, 15), (20, 26), (27, 7), (0, 29), (17, 14), (8, 23), (21, 11), (6, 32), (25, 2), (7, 27), (8, 11), (10, 28), (4, 18), (18, 30), (31, 13), (31, 29), (21, 15), (4, 1), (10, 25), (14, 8), (1, 20), (31, 24), (21, 20), (11, 2), (27, 24), (24, 3), (16, 30), (20, 27), (32, 6), (13, 14), (28, 1), (8, 26), (6, 7), (21, 22), (3, 25), (30, 15), (23, 22), (21, 13), (3, 13), (29, 0), (25, 32), (15, 14), (10, 8), (20, 2), (5, 8), (32, 10), (10, 1), (12, 16), (12, 8), (26, 15), (19, 29), (17, 28), (29, 22), (31, 0), (11, 30), (20, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "642024", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (29, 14), (19, 30), (28, 9), (13, 6), (3, 26), (18, 14), (12, 23), (22, 25), (4, 21), (29, 1), (13, 16), (12, 30), (7, 5), (26, 1), (25, 2), (16, 5), (12, 13), (8, 15), (27, 30), (18, 21), (14, 27), (12, 9), (20, 2), (0, 10), (8, 23), (7, 17), (27, 22), (17, 3), (8, 22), (9, 8), (16, 8), (25, 29), (23, 18), (23, 4), (27, 18), (13, 19), (9, 28), (27, 27), (27, 11), (6, 7), (4, 8), (12, 22), (16, 10), (10, 2), (2, 25), (17, 23), (19, 23), (10, 6), (25, 18), (7, 25), (11, 26), (7, 10), (24, 28), (11, 16), (29, 5), (21, 7), (18, 1), (6, 26), (19, 28), (8, 30), (6, 22), (19, 14), (9, 13), (22, 20), (12, 1), (30, 24), (19, 8), (22, 17), (30, 1), (21, 19), (13, 2), (17, 18), (1, 23), (16, 6), (5, 3), (9, 0), (24, 30), (7, 15), (0, 29), (27, 28), (22, 27), (28, 20), (9, 6), (28, 29), (20, 5), (19, 0), (5, 8), (3, 5), (24, 22), (12, 29), (15, 26), (7, 2), (22, 12), (1, 4), (27, 3), (16, 11), (7, 19), (18, 16), (16, 26), (3, 0), (21, 16), (8, 6), (26, 22), (18, 29), (7, 4), (24, 29), (3, 17), (18, 15), (24, 12), (30, 11), (30, 19), (28, 26), (0, 15), (6, 29), (26, 8), (29, 23), (21, 14), (13, 15), (20, 4), (13, 4), (14, 26), (18, 24), (25, 20), (2, 17), (14, 20), (23, 2), (13, 10), (19, 6), (10, 15), (3, 4), (30, 5), (16, 22), (8, 12), (26, 7), (20, 13), (3, 16), (10, 18), (23, 19), (29, 27), (25, 0), (14, 11), (8, 14), (23, 3), (5, 14), (22, 23), (7, 9), (28, 16), (3, 6), (2, 6), (4, 6), (26, 18), (15, 25), (17, 22), (5, 28), (11, 12), (14, 6), (28, 22), (11, 4), (1, 25), (1, 29), (2, 7), (0, 17), (20, 8), (21, 10), (30, 7), (10, 30), (3, 22), (29, 3), (5, 20), (17, 21), (0, 16), (15, 28), (15, 1), (29, 4), (29, 0), (27, 0), (29, 15), (13, 18), (22, 16), (13, 26), (18, 7), (14, 5), (12, 18), (15, 7), (6, 20), (5, 21), (10, 23), (11, 7), (18, 17), (8, 17), (10, 7), (25, 7), (23, 26), (22, 19), (8, 8), (16, 24), (25, 4), (10, 11), (4, 26), (19, 24), (16, 2), (21, 5), (24, 21), (12, 5), (2, 29), (18, 10), (17, 17), (8, 21), (25, 8), (26, 13), (20, 11), (12, 26), (15, 15), (5, 30), (5, 16), (14, 18), (9, 30), (12, 11), (22, 13), (3, 13), (9, 10), (8, 27), (6, 6), (11, 18), (20, 28), (10, 24), (5, 29), (28, 12), (3, 1), (27, 5), (2, 24), (2, 15), (17, 15), (4, 9), (17, 13), (20, 29), (19, 21), (0, 26), (26, 26), (5, 19), (12, 0), (19, 26), (1, 13), (24, 24), (30, 9), (9, 17), (6, 13), (24, 19), (6, 2), (27, 29), (10, 0), (27, 9), (10, 27), (8, 7), (16, 29), (20, 0), (21, 15), (4, 4), (19, 25), (12, 27), (16, 23), (21, 17), (3, 11), (9, 7), (24, 14), (26, 11), (30, 14), (2, 1), (12, 19), (16, 0), (25, 28), (22, 10), (23, 6), (30, 22), (9, 9), (23, 17), (11, 25), (16, 7), (3, 24), (11, 17), (9, 23), (19, 16), (27, 8), (9, 1), (15, 19), (3, 3), (25, 16), (25, 12), (6, 14), (19, 13), (2, 22), (9, 3), (29, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 30), (11, 5), (6, 13), (21, 33), (30, 14), (24, 4), (17, 15), (3, 6), (13, 24), (8, 36), (13, 15), (24, 20), (13, 8), (26, 17), (13, 34), (19, 4), (18, 12), (33, 20), (7, 17), (3, 3), (11, 8), (31, 24), (23, 4), (17, 22), (17, 4), (29, 0), (20, 14), (30, 22), (4, 2), (11, 4), (29, 29), (20, 31), (15, 9), (9, 3), (20, 32), (18, 32), (14, 17), (3, 16), (0, 28), (2, 24), (3, 26), (31, 7), (22, 32), (7, 31), (8, 18), (8, 30), (9, 8), (2, 5), (11, 18), (28, 34), (16, 28), (33, 36), (7, 35), (4, 32), (15, 21), (31, 36), (15, 1), (10, 5), (25, 15), (0, 33), (15, 28), (5, 33), (7, 19), (29, 26), (17, 23), (12, 32), (19, 14), (6, 7), (27, 22), (15, 35), (5, 12), (17, 7), (3, 18), (33, 12), (29, 21), (4, 35), (2, 9), (4, 0), (24, 25), (1, 18), (5, 31), (4, 24), (20, 17), (22, 21), (2, 13), (12, 33), (21, 21), (14, 16), (12, 14), (15, 7), (6, 19), (2, 18), (22, 0), (19, 2), (25, 18), (2, 17), (1, 10), (17, 20), (26, 6), (17, 37), (28, 22), (14, 18), (27, 28), (33, 3), (24, 7), (22, 36), (18, 30), (26, 30), (0, 9), (19, 0), (14, 3), (27, 13), (19, 34), (22, 1), (4, 15), (22, 9), (30, 0), (7, 0), (8, 23), (14, 22), (10, 23), (32, 12), (8, 27), (20, 28), (0, 19), (8, 4), (22, 12), (20, 35), (15, 29), (29, 18), (21, 15), (15, 23), (33, 2), (31, 12), (12, 20), (4, 20), (12, 12), (33, 31), (21, 17), (11, 2), (21, 8), (25, 31), (16, 15), (5, 15), (25, 35), (15, 27), (10, 16), (8, 21), (2, 15), (23, 18), (14, 9), (16, 30), (20, 15), (8, 35), (7, 34), (14, 10), (30, 2), (24, 17), (10, 34), (19, 11), (27, 37), (10, 2), (3, 7), (8, 33), (12, 18), (22, 31), (16, 36), (0, 10), (33, 1), (7, 32), (28, 28), (10, 13), (0, 13), (13, 29), (2, 21), (6, 15), (21, 22), (31, 25), (33, 34), (14, 21), (9, 25), (3, 0), (27, 27), (7, 5), (14, 28), (17, 29), (11, 14), (26, 22), (18, 25), (29, 3), (13, 32), (32, 7), (28, 33), (32, 28), (12, 29), (28, 24), (1, 26), (2, 3), (28, 1), (18, 28), (21, 0), (10, 15), (6, 29), (21, 3), (5, 0), (24, 3), (8, 17), (1, 25), (1, 13), (0, 4), (27, 20), (6, 28), (27, 4), (24, 34), (10, 36), (25, 7), (29, 22), (12, 28), (31, 3), (15, 0), (26, 14), (17, 27), (29, 7), (13, 14), (5, 18), (1, 8), (9, 34), (2, 32), (2, 14), (28, 13), (24, 22), (22, 4), (10, 29), (7, 11), (5, 3), (21, 1), (22, 19), (13, 9), (6, 23), (18, 27), (30, 4), (28, 5), (10, 28), (16, 23), (10, 30), (15, 19), (18, 34), (23, 30), (17, 6), (6, 26), (4, 5), (14, 5), (24, 13), (30, 18), (23, 8), (4, 36), (4, 21), (14, 11), (1, 32), (7, 28), (1, 4), (1, 19), (2, 12), (19, 25), (10, 9), (28, 11), (26, 24), (31, 22), (28, 7), (5, 32), (15, 31), (29, 31), (20, 12), (31, 2), (23, 28), (18, 11), (20, 24), (2, 25), (22, 13), (14, 13), (3, 30), (19, 12), (9, 26), (16, 11), (8, 10), (13, 31), (16, 27), (4, 18), (0, 31), (30, 34), (29, 10), (21, 10), (20, 36), (4, 3), (24, 2), (1, 36), (9, 37), (0, 27), (28, 27), (22, 14), (20, 23), (12, 37), (5, 8), (14, 24), (20, 11), (20, 19), (25, 28), (26, 2), (9, 33), (32, 21), (7, 1), (11, 28), (0, 37), (0, 22), (2, 31), (26, 7), (17, 25), (11, 17), (8, 26), (10, 8), (4, 11), (19, 5), (11, 10), (25, 11), (33, 24), (23, 33), (3, 23), (32, 19), (13, 3), (33, 29), (21, 9), (33, 35), (17, 19), (23, 20), (24, 32), (14, 4), (2, 34), (16, 24), (14, 0), (4, 4), (6, 16), (8, 11), (9, 4), (9, 0), (13, 22), (9, 24), (20, 6), (3, 8), (33, 18), (22, 33), (20, 3), (26, 25), (18, 36), (0, 6), (5, 10), (32, 27), (19, 16), (14, 1), (21, 11), (5, 27), (2, 8), (23, 29), (7, 23), (6, 37), (11, 16), (16, 17), (31, 0), (26, 31), (25, 29), (18, 0), (0, 2), (16, 20), (20, 34), (20, 30), (18, 10), (21, 7), (22, 6), (25, 1), (22, 37), (21, 25), (24, 23), (32, 29), (7, 7), (9, 23), (14, 19), (3, 10), (33, 9), (21, 36), (25, 30), (7, 4), (17, 2), (24, 0), (28, 0), (28, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967104", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 2), (11, 22), (23, 25), (27, 17), (33, 26), (22, 26), (13, 21), (32, 28), (33, 24), (24, 26), (16, 6), (3, 23), (37, 1), (31, 16), (33, 7), (35, 10), (29, 2), (11, 21), (13, 27), (20, 27), (36, 21), (2, 28), (23, 16), (32, 19), (16, 23), (21, 18), (30, 24), (5, 11), (6, 12), (24, 28), (22, 13), (29, 13), (10, 28), (37, 15), (26, 7), (23, 22), (20, 18), (26, 25), (28, 22), (35, 1), (30, 23), (22, 9), (9, 14), (24, 1), (23, 17), (4, 20), (18, 12), (15, 0), (23, 7), (22, 24), (7, 25), (33, 12), (8, 20), (18, 1), (38, 9), (36, 25), (34, 16), (6, 24), (34, 2), (16, 4), (13, 15), (31, 26), (14, 1), (10, 22), (17, 1), (2, 13), (2, 6), (36, 7), (33, 28), (4, 15), (7, 2), (33, 2), (38, 23), (3, 5), (9, 12), (31, 12), (21, 10), (21, 17), (35, 24), (37, 7), (16, 18), (20, 6), (14, 3), (1, 18), (17, 28), (14, 17), (8, 3), (34, 29), (8, 2), (15, 19), (26, 18), (37, 24), (9, 28), (7, 20), (26, 22), (38, 20), (9, 10), (1, 5), (2, 17), (38, 14), (4, 13), (12, 24), (25, 28), (35, 9), (34, 26), (38, 18), (18, 13), (26, 20), (37, 17), (16, 27), (7, 13), (15, 6), (17, 4), (23, 11), (8, 10), (12, 3), (7, 27), (5, 28), (32, 7), (2, 21), (26, 27), (24, 7), (22, 10), (18, 3), (29, 10), (18, 6), (3, 6), (23, 4), (25, 15), (28, 8), (18, 16), (12, 12), (13, 1), (20, 3), (2, 11), (5, 4), (23, 10), (29, 12), (20, 13), (7, 11), (31, 25), (9, 11), (35, 12), (18, 11), (38, 3), (10, 16), (27, 22), (19, 14), (21, 13), (3, 19), (12, 21), (14, 8), (25, 24), (29, 18), (0, 10), (15, 10), (6, 3), (30, 8), (4, 6), (19, 28), (4, 8), (4, 2), (26, 29), (0, 4), (9, 3), (22, 8), (4, 19), (34, 28), (11, 23), (7, 9), (26, 8), (0, 15), (3, 10), (34, 7), (25, 22), (13, 13), (28, 16), (29, 7), (9, 22), (27, 10), (1, 15), (13, 2), (35, 4), (30, 18), (15, 24), (35, 6), (29, 27), (15, 15), (12, 2), (27, 0), (9, 18), (7, 1), (23, 12), (9, 26), (29, 23), (29, 11), (17, 25), (24, 22), (14, 22), (30, 9), (13, 3), (12, 7), (28, 28), (4, 17), (31, 5), (29, 1), (19, 13), (29, 19), (12, 25), (18, 18), (12, 16), (1, 26), (0, 18), (37, 20), (24, 24), (33, 14), (14, 21), (1, 20), (31, 24), (31, 20), (9, 9), (34, 11), (32, 3), (11, 18), (32, 9), (19, 15), (5, 24), (3, 13), (22, 1), (34, 4), (36, 2), (38, 2), (1, 0), (11, 27), (16, 19), (5, 7), (18, 25), (37, 13), (8, 21), (7, 21), (16, 3), (23, 21), (13, 4), (4, 21), (31, 14), (33, 10), (5, 20), (30, 15), (13, 8), (2, 10), (37, 6), (28, 20), (7, 4), (12, 9), (18, 19), (8, 17), (31, 29), (21, 16), (5, 8), (29, 15), (9, 7), (5, 10), (3, 28), (21, 26), (8, 26), (26, 28), (1, 21), (1, 12), (14, 29), (35, 21), (3, 16), (34, 3), (37, 8), (20, 29), (10, 15), (1, 23), (37, 16), (32, 23), (34, 1), (23, 23), (5, 26), (27, 4), (20, 24), (10, 24), (38, 27), (15, 13), (21, 7), (4, 1), (11, 0), (31, 3), (19, 4), (19, 17), (20, 25), (17, 19), (25, 19), (29, 5), (0, 19), (17, 6), (26, 9), (36, 27), (7, 19), (17, 22), (20, 26), (28, 24), (23, 29), (38, 7), (24, 12), (30, 16), (19, 12), (12, 26), (1, 3), (0, 26), (23, 1), (30, 27), (34, 19), (25, 16), (5, 0), (13, 22), (23, 5), (37, 27), (8, 7), (34, 5), (2, 22), (28, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8704", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), 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), (12, 3), (12, 25), (3, 13), (12, 22), (34, 1), (6, 9), (13, 33), (0, 3), (35, 14), (25, 0), (37, 2), (31, 8), (22, 24), (7, 11), (33, 3), (1, 19), (37, 1), (36, 10), (19, 25), (35, 31), (2, 12), (32, 2), (26, 20), (21, 31), (35, 17), (15, 11), (38, 0), (0, 17), (5, 20), (33, 29), (2, 28), (24, 3), (12, 10), (6, 23), (9, 6), (37, 25), (12, 28), (5, 23), (32, 35), (34, 23), (10, 33), (33, 31), (22, 11), (22, 0), (25, 17), (21, 32), (23, 9), (31, 29), (13, 17), (1, 28), (20, 4), (19, 14), (23, 14), (6, 33), (27, 30), (35, 9), (26, 7), (5, 10), (1, 27), (32, 17), (3, 9), (5, 2), (2, 30), (2, 20), (24, 13), (38, 29), (1, 8), (15, 6), (32, 3), (18, 28), (18, 35), (29, 6), (8, 19), (36, 14), (33, 8), (29, 18), (28, 26), (33, 26), (38, 17), (4, 24), (32, 26), (5, 6), (29, 17), (20, 21), (28, 32), (32, 22), (4, 7), (3, 31), (15, 12), (27, 4), (16, 22), (32, 31), (13, 7), (10, 21), (7, 16), (37, 33), (32, 24), (1, 10), (16, 31), (24, 22), (28, 28), (19, 28), (31, 21), (37, 9), (16, 7), (28, 5), (1, 21), (15, 8), (24, 19), (14, 16), (13, 24), (29, 3), (12, 1), (37, 32), (33, 24), (11, 10), (23, 25), (0, 34), (5, 4), (27, 0), (7, 7), (17, 1), (10, 17), (22, 5), (23, 27), (10, 0), (30, 25), (38, 10), (31, 6), (10, 25), (30, 5), (17, 8), (20, 34), (8, 32), (33, 27), (16, 33), (20, 29), (38, 15), (17, 4), (4, 9), (17, 34), (37, 15), (6, 29), (31, 7), (12, 14), (36, 8), (18, 10), (19, 12), (26, 13), (18, 22), (7, 34), (4, 5), (27, 7), (33, 18), (35, 16), (37, 35), (3, 16), (20, 32), (27, 28), (36, 2), (37, 29), (24, 21), (16, 19), (8, 7), (12, 18), (1, 15), (7, 22), (36, 31), (18, 12), (25, 19), (19, 15), (7, 2), (9, 21), (35, 26), (28, 21), (3, 20), (26, 1), (26, 15), (32, 5), (37, 4), (9, 32), (33, 15), (15, 0), (2, 18), (5, 5), (5, 18), (11, 9), (16, 5), (16, 0), (26, 8), (2, 29), (2, 21), (34, 16), (8, 6), (28, 7), (14, 22), (33, 35), (35, 6), (7, 29), (29, 34), (16, 26), (32, 8), (13, 3), (38, 16), (16, 32), (30, 18), (21, 23), (22, 30), (2, 23), (7, 32), (5, 9), (8, 13), (6, 13), (20, 24), (26, 17), (15, 1), (1, 5), (38, 31), (28, 14), (17, 10), (5, 17), (8, 5), (32, 27), (35, 33), (19, 8), (0, 22), (36, 25), (5, 30), (32, 32), (31, 30), (34, 22), (11, 23), (7, 12), (23, 13), (16, 4), (17, 35), (22, 23), (11, 1), (21, 16), (13, 12), (37, 5), (10, 27), (17, 18), (4, 17), (4, 22), (25, 16), (1, 20), (31, 10), (26, 4), (31, 9), (11, 19), (31, 12), (17, 11), (31, 3), (31, 25), (0, 8), (33, 20), (7, 6), (25, 21), (2, 19), (8, 10), (23, 2), (7, 21), (32, 9), (11, 17), (20, 15), (5, 21), (6, 27), (12, 23), (22, 27), (23, 32), (18, 31), (35, 13), (10, 8), (9, 30), (24, 4), (21, 24), (22, 15), (28, 6), (2, 10), (9, 29), (13, 31), (32, 13), (28, 24), (23, 10), (24, 24), (7, 18), (25, 25), (1, 0), (32, 25), (24, 14), (9, 24), (33, 32), (21, 9), (2, 34), (13, 20), (24, 1), (12, 15), (36, 16), (22, 6), (11, 4), (27, 6), (1, 33), (16, 6), (32, 29), (1, 7), (11, 21), (18, 8), (34, 28), (28, 25), (11, 16), (11, 33), (17, 12), (37, 21), (18, 25), (1, 3), (7, 27), (30, 35), (2, 2), (5, 8), (36, 23), (31, 17), (13, 21), (16, 3), (13, 22), (25, 8), (33, 12), (12, 21), (21, 33), (9, 25), (3, 17), (28, 29), (34, 14), (3, 33), (1, 35), (28, 12), (16, 34), (6, 7), (26, 0), (30, 21), (0, 31), (14, 23), (22, 7), (9, 16), (18, 6), (31, 32), (30, 1), (8, 11), (3, 5), (19, 11), (4, 21), (23, 17), (3, 14), (5, 26), (26, 10), (13, 35), (23, 1), (16, 35), (35, 20), (36, 5), (29, 33), (34, 4), (28, 10), (22, 18), (9, 11), (20, 10), (23, 30), (13, 30), (22, 13), (35, 7), (37, 31), (2, 15), (2, 3), (1, 14), (14, 33), (24, 6), (19, 32), (31, 28), (8, 9), (15, 16), (21, 30), (2, 9), (27, 26), (3, 23), (27, 11), (0, 33), (34, 21), (32, 33), (10, 28), (26, 3), (20, 28), (20, 1), (25, 10), (13, 9), (25, 5), (15, 9), (1, 24), (20, 2), (7, 0), (10, 4), (20, 18), (25, 9), (0, 32), (35, 23), (34, 3), (8, 1), (38, 30), (17, 9), (28, 20), (29, 27), (20, 17), (28, 9), (24, 35), (17, 25), (12, 13), (32, 23), (36, 20), (17, 15), (1, 23), (22, 34), (13, 13), (7, 33), (2, 11), (4, 13), (36, 11), (25, 22), (11, 30), (19, 13), (17, 29), (34, 27), (22, 35), (11, 22), (29, 22), (14, 29), (6, 21), (8, 23), (15, 13), (34, 15), (26, 14), (5, 13), (3, 25), (33, 28), (20, 16), (6, 19), (37, 7), (19, 29), (29, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634368", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (13, 27), (11, 2), (9, 7), (9, 36), (14, 34), (5, 30), (13, 28), (17, 30), (29, 15), (17, 32), (22, 36), (27, 1), (2, 8), (24, 2), (8, 36), (10, 8), (19, 20), (20, 22), (24, 36), (24, 12), (27, 9), (22, 13), (24, 3), (29, 8), (29, 20), (10, 15), (2, 33), (23, 27), (22, 0), (23, 24), (29, 33), (13, 37), (8, 29), (7, 1), (13, 0), (11, 0), (13, 4), (12, 3), (4, 17), (16, 14), (13, 14), (5, 31), (28, 6), (20, 30), (10, 7), (9, 14), (2, 28), (6, 13), (26, 33), (24, 29), (14, 3), (7, 29), (7, 34), (27, 27), (20, 37), (4, 27), (22, 3), (14, 20), (20, 0), (24, 5), (24, 32), (14, 9), (25, 20), (16, 20), (25, 24), (9, 1), (0, 22), (17, 36), (0, 17), (16, 26), (17, 1), (0, 1), (26, 19), (22, 11), (11, 33), (5, 37), (17, 15), (10, 24), (21, 23), (10, 4), (1, 37), (25, 9), (9, 24), (2, 15), (12, 18), (19, 8), (14, 19), (29, 14), (5, 27), (14, 4), (23, 31), (13, 29), (14, 14), (12, 1), (12, 16), (27, 12), (17, 35), (7, 24), (3, 3), (0, 30), (16, 9), (8, 26), (23, 30), (0, 29), (0, 2), (8, 5), (18, 5), (29, 4), (20, 31), (29, 26), (24, 23), (14, 21), (17, 27), (4, 23), (16, 11), (27, 33), (0, 26), (21, 36), (5, 4), (11, 26), (4, 7), (24, 28), (9, 31), (14, 11), (19, 0), (6, 32), (1, 23), (6, 34), (19, 17), (3, 29), (17, 34), (15, 24), (12, 22), (19, 21), (30, 26), (22, 23), (29, 3), (28, 20), (15, 16), (25, 31), (14, 2), (24, 16), (9, 29), (10, 28), (26, 13), (19, 10), (6, 25), (8, 17), (25, 4), (9, 34), (16, 35), (5, 33), (15, 14), (12, 30), (4, 1), (3, 33), (23, 21), (7, 22), (26, 17), (4, 37), (5, 14), (12, 33), (28, 26), (9, 10), (1, 14), (17, 0), (25, 25), (13, 17), (2, 20), (1, 8), (23, 15), (3, 32), (20, 26), (30, 14), (2, 1), (13, 1), (7, 31), (15, 17), (0, 15), (15, 2), (16, 27), (17, 23), (1, 33), (7, 2), (21, 8), (18, 7), (11, 18), (17, 17), (12, 11), (25, 37), (26, 4), (9, 23), (1, 10), (16, 16), (23, 5), (15, 1), (1, 21), (25, 28), (25, 2), (7, 18), (11, 17), (13, 24), (26, 14), (22, 17), (30, 34), (19, 29), (2, 37), (22, 22), (15, 34), (13, 6), (18, 22), (16, 28), (11, 27), (26, 35), (8, 25), (11, 28), (18, 34), (9, 9), (27, 7), (2, 31), (11, 12), (30, 27), (19, 13), (15, 37), (27, 0), (12, 10), (0, 32), (1, 15), (28, 4), (3, 36), (2, 27), (0, 27), (22, 21), (20, 32), (4, 35), (19, 15), (9, 6), (10, 27), (13, 21), (20, 2), (13, 15), (4, 19), (21, 33), (12, 32), (28, 30), (10, 6), (2, 4), (30, 1), (28, 31), (26, 21), (21, 21), (19, 1), (17, 22), (15, 9), (15, 15), (27, 3), (8, 22), (4, 18), (11, 34), (29, 12), (9, 26), (19, 36), (30, 4), (4, 11), (18, 29), (18, 37), (21, 6), (27, 8), (10, 17), (30, 31), (23, 19), (7, 35), (29, 2), (28, 9), (13, 3), (8, 21), (11, 4), (23, 36), (27, 13), (25, 33), (26, 10), (18, 6), (24, 7), (6, 2), (9, 25), (12, 2), (25, 32), (22, 31), (19, 23), (30, 29), (5, 32), (18, 33), (0, 19), (24, 10), (14, 6), (0, 9), (2, 30), (19, 2), (11, 3), (18, 9), (16, 21), (26, 20), (26, 0), (29, 18), (22, 9), (27, 35), (15, 28), (7, 3), (2, 25), (27, 24), (5, 5), (10, 23), (6, 15), (21, 15), (5, 16), (16, 19), (0, 25), (22, 28), (0, 34), (8, 9), (14, 1), (30, 8), (0, 7), (7, 7), (1, 17), (3, 15), (0, 12), (3, 16), (22, 5), (13, 16), (22, 24), (1, 3), (16, 15), (9, 12), (29, 10), (0, 36), (18, 20), (22, 35), (8, 16), (13, 20), (21, 7), (1, 30), (21, 2), (19, 16), (8, 3), (4, 24), (20, 14), (21, 16), (24, 8), (9, 32), (18, 28), (0, 10), (14, 30), (2, 19), (22, 32), (15, 18), (1, 24), (16, 5), (18, 0), (2, 7), (6, 35), (4, 33), (21, 13), (17, 10), (3, 10), (10, 18), (27, 37), (15, 6), (18, 10), (29, 25), (23, 6), (15, 12), (18, 15), (12, 37), (7, 10), (30, 10), (14, 28), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), 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), (25, 25), (5, 19), (20, 21), (15, 6), (6, 6), (24, 13), (18, 11), (10, 32), (17, 31), (28, 20), (22, 19), (16, 1), (6, 7), (6, 13), (7, 25), (13, 27), (16, 19), (28, 25), (15, 1), (16, 14), (29, 24), (4, 5), (7, 30), (24, 10), (12, 4), (9, 31), (21, 18), (10, 31), (26, 11), (23, 8), (13, 11), (15, 0), (30, 29), (25, 33), (15, 5), (9, 17), (10, 33), (5, 0), (4, 29), (7, 6), (17, 33), (13, 33), (2, 2), (25, 3), (15, 14), (1, 7), (4, 16), (24, 27), (23, 24), (3, 31), (27, 34), (5, 11), (25, 27), (18, 31), (0, 14), (13, 28), (3, 16), (20, 27), (0, 18), (16, 2), (3, 24), (25, 26), (3, 9), (26, 13), (0, 31), (10, 28), (22, 29), (15, 24), (19, 29), (21, 22), (20, 2), (19, 2), (17, 4), (21, 7), (7, 24), (8, 1), (25, 13), (3, 7), (13, 17), (0, 24), (0, 2), (15, 17), (12, 26), (19, 20), (12, 17), (17, 3), (9, 13), (25, 8), (21, 6), (28, 21), (24, 6), (10, 7), (1, 21), (23, 26), (13, 16), (2, 20), (9, 33), (8, 16), (26, 7), (1, 30), (10, 11), (25, 17), (24, 23), (2, 6), (24, 20), (10, 3), (13, 0), (8, 18), (17, 0), (14, 31), (8, 22), (24, 21), (28, 28), (20, 17), (25, 18), (29, 34), (18, 25), (8, 20), (27, 16), (11, 17), (21, 32), (17, 27), (28, 34), (24, 0), (26, 0), (10, 15), (16, 27), (30, 4), (20, 23), (6, 11), (14, 9), (8, 24), (19, 4), (28, 17), (16, 28), (25, 2), (28, 27), (4, 25), (30, 2), (4, 19), (7, 31), (7, 23), (3, 28), (18, 23), (8, 12), (21, 4), (30, 16), (12, 9), (11, 20), (10, 18), (24, 9), (23, 19), (27, 23), (29, 22), (4, 11), (26, 24), (3, 10), (15, 4), (16, 11), (10, 17), (23, 1), (8, 9), (11, 11), (19, 8), (29, 11), (17, 29), (23, 30), (13, 29), (25, 28), (6, 1), (27, 25), (13, 22), (1, 19), (22, 31), (22, 32), (2, 33), (25, 11), (17, 23), (2, 3), (12, 13), (28, 1), (17, 24), (4, 27), (28, 5), (28, 19), (5, 20), (19, 26), (6, 24), (4, 12), (10, 6), (24, 3), (24, 15), (11, 7), (15, 16), (16, 21), (19, 30), (12, 24), (16, 30), (13, 3), (14, 26), (2, 30), (26, 16), (0, 4), (11, 24), (7, 3), (25, 0), (23, 6), (24, 17), (16, 23), (4, 26), (14, 19), (22, 13), (22, 16), (21, 9), (14, 7), (21, 31), (15, 8), (18, 17), (18, 12), (6, 34), (19, 14), (9, 16), (10, 13), (11, 19), (12, 16), (26, 12), (11, 23), (3, 23), (0, 26), (6, 16), (24, 32), (7, 21), (10, 10), (5, 22), (9, 27), (0, 7), (4, 2), (22, 27), (13, 15), (5, 10), (28, 26), (29, 29), (4, 24), (0, 12), (4, 28), (1, 9), (14, 21), (29, 32), (19, 34), (29, 0), (3, 26), (28, 12), (19, 9), (26, 25), (14, 13), (16, 8), (20, 13), (1, 16), (7, 34), (9, 11), (26, 29), (14, 23), (15, 22), (12, 7), (0, 10), (0, 30), (14, 25), (3, 5), (3, 17), (4, 20), (30, 23), (5, 6), (17, 16), (15, 18), (28, 13), (15, 26), (11, 25), (8, 19), (20, 22), (16, 12), (28, 30), (16, 20), (5, 27), (8, 11), (13, 34), (30, 13), (15, 13), (6, 2), (18, 10), (12, 0), (28, 3), (6, 9), (15, 28), (4, 14), (28, 10), (7, 8), (0, 16), (24, 8), (30, 28), (18, 8), (29, 16), (5, 9), (11, 6), (27, 22), (15, 25), (11, 32), (13, 19), (1, 27), (12, 15), (20, 3), (20, 26), (25, 1), (1, 15), (19, 18), (30, 0), (27, 0), (24, 1), (1, 1), (11, 14), (6, 17), (22, 23), (18, 1), (4, 13), (5, 29), (1, 31), (12, 34), (6, 3), (5, 23), (3, 20), (30, 17), (26, 2), (7, 32), (5, 14), (7, 11), (30, 19), (20, 15), (0, 9), (9, 1), (28, 2), (26, 6), (25, 4), (12, 21), (7, 12), (26, 18), (7, 0), (28, 15), (4, 23), (19, 11), (3, 29), (6, 5), (11, 22), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758160", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 3), (6, 34), (13, 33), (38, 5), (9, 15), (29, 13), (26, 10), (12, 35), (10, 21), (1, 26), (8, 23), (1, 32), (33, 22), (15, 20), (8, 3), (2, 0), (37, 12), (9, 3), (15, 3), (0, 15), (24, 24), (26, 26), (10, 13), (27, 21), (33, 25), (20, 15), (11, 23), (2, 35), (11, 25), (24, 29), (23, 31), (38, 36), (29, 27), (0, 9), (28, 29), (8, 31), (11, 15), (17, 9), (3, 32), (37, 14), (20, 13), (30, 13), (6, 13), (2, 20), (31, 7), (6, 2), (20, 3), (34, 17), (36, 12), (33, 23), (34, 31), (6, 10), (0, 18), (3, 15), (5, 6), (24, 34), (10, 15), (9, 10), (5, 22), (13, 34), (36, 36), (19, 31), (22, 21), (6, 35), (21, 35), (17, 15), (19, 3), (12, 7), (4, 31), (34, 1), (15, 33), (37, 15), (23, 15), (31, 8), (1, 15), (14, 27), (2, 8), (38, 31), (11, 31), (4, 4), (34, 13), (12, 4), (9, 27), (30, 6), (31, 17), (30, 16), (29, 19), (22, 33), (11, 33), (31, 9), (16, 22), (33, 31), (24, 1), (31, 6), (2, 25), (34, 18), (6, 19), (10, 19), (25, 32), (16, 15), (19, 22), (27, 15), (1, 23), (27, 35), (30, 32), (29, 21), (21, 27), (14, 21), (38, 25), (30, 33), (23, 18), (24, 11), (35, 38), (22, 9), (18, 5), (6, 9), (3, 31), (11, 38), (21, 30), (7, 24), (1, 19), (30, 0), (23, 2), (20, 35), (30, 21), (31, 30), (32, 34), (24, 33), (3, 20), (34, 30), (28, 10), (30, 22), (16, 18), (8, 12), (1, 11), (17, 6), (25, 9), (18, 6), (16, 33), (29, 10), (20, 12), (10, 6), (9, 4), (38, 11), (4, 12), (15, 17), (33, 0), (23, 25), (7, 17), (2, 26), (38, 16), (11, 29), (35, 2), (4, 10), (34, 3), (7, 36), (29, 15), (4, 32), (25, 19), (26, 23), (22, 34), (13, 16), (7, 12), (11, 7), (2, 31), (9, 2), (24, 16), (9, 30), (2, 23), (16, 0), (15, 22), (9, 1), (36, 25), (6, 11), (14, 24), (19, 35), (9, 19), (0, 35), (5, 12), (29, 2), (9, 36), (23, 37), (3, 36), (3, 28), (26, 24), (27, 22), (10, 18), (31, 31), (7, 32), (37, 4), (34, 7), (18, 30), (29, 25), (2, 3), (34, 26), (25, 33), (13, 13), (3, 25), (11, 11), (37, 32), (25, 34), (10, 28), (11, 27), (13, 4), (16, 10), (17, 14), (16, 34), (0, 16), (35, 6), (7, 5), (28, 12), (25, 29), (34, 34), (4, 30), (14, 7), (14, 0), (3, 12), (30, 19), (5, 37), (22, 12), (32, 11), (11, 36), (22, 5), (29, 32), (35, 10), (37, 27), (3, 30), (8, 11), (5, 20), (7, 8), (0, 23), (4, 1), (36, 29), (36, 38), (34, 36), (22, 30), (22, 1), (0, 30), (37, 29), (19, 28), (21, 21), (15, 5), (5, 25), (29, 26), (16, 26), (22, 37), (14, 6), (21, 2), (22, 27), (13, 28), (32, 5), (9, 9), (19, 6), (15, 34), (22, 29), (15, 37), (29, 35), (13, 31), (13, 6), (6, 3), (10, 4), (19, 33), (13, 24), (22, 38), (28, 17), (36, 3), (12, 3), (15, 10), (4, 2), (17, 17), (6, 27), (14, 2), (8, 17), (15, 30), (10, 10), (23, 0), (14, 19), (30, 4), (25, 28), (7, 6), (32, 18), (33, 10), (37, 25), (1, 28), (3, 7), (6, 14), (1, 0), (19, 25), (22, 0), (22, 31), (7, 18), (20, 33), (17, 3), (28, 2), (3, 33), (17, 31), (31, 33), (20, 20), (29, 12), (14, 23), (33, 27), (17, 10), (19, 21), (2, 4), (32, 7), (25, 4), (28, 6), (1, 16), (11, 14), (16, 2), (8, 1), (4, 5), (17, 30), (8, 26), (12, 37), (27, 10), (10, 11), (11, 3), (20, 4), (14, 26), (34, 0), (25, 15), (34, 37), (22, 8), (23, 10), (20, 2), (24, 0), (7, 4), (17, 34), (30, 1), (12, 15), (17, 22), (35, 9), (9, 18), (20, 1), (25, 2), (31, 24), (38, 6), (26, 37), (26, 29), (28, 31), (5, 5), (25, 5), (32, 1), (36, 31), (22, 3), (7, 25), (34, 2), (29, 31), (26, 11), (3, 14), (2, 5), (36, 1), (14, 30), (11, 26), (9, 26), (23, 12), (20, 27), (38, 17), (35, 17), (35, 3), (12, 2), (36, 30), (5, 35), (22, 6), (29, 18), (25, 18), (31, 10), (28, 11), (28, 38), (27, 4), (21, 33), (10, 2), (25, 21), (18, 31), (0, 36), (22, 28), (0, 2), (13, 1), (0, 24), (25, 7), (15, 7), (1, 20), (6, 22), (2, 28), (35, 33), (9, 38), (5, 3), (32, 30), (7, 27), (6, 16), (30, 29), (19, 16), (7, 38), (12, 11), (5, 23), (28, 36), (10, 32), (19, 13), (4, 23), (36, 17), (31, 22), (38, 29), (5, 15), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "467808", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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, 22), (12, 15), (21, 24), (29, 20), (22, 35), (22, 17), (30, 11), (14, 10), (27, 17), (28, 16), (21, 7), (24, 28), (3, 25), (27, 30), (13, 13), (1, 27), (15, 8), (18, 17), (8, 14), (15, 33), (8, 8), (24, 9), (13, 3), (24, 5), (8, 27), (18, 10), (0, 20), (8, 26), (1, 2), (15, 35), (0, 13), (7, 2), (29, 34), (30, 35), (22, 11), (14, 36), (23, 4), (18, 9), (13, 6), (5, 0), (13, 23), (26, 21), (7, 14), (17, 26), (26, 16), (5, 27), (21, 0), (18, 30), (30, 27), (3, 9), (27, 1), (16, 3), (28, 28), (0, 9), (2, 29), (8, 29), (2, 3), (26, 24), (20, 29), (8, 10), (29, 28), (16, 29), (5, 5), (17, 0), (0, 11), (13, 36), (2, 36), (27, 4), (23, 33), (16, 37), (30, 13), (21, 8), (2, 17), (25, 21), (10, 23), (18, 23), (18, 16), (23, 19), (9, 0), (27, 37), (17, 14), (19, 33), (20, 28), (8, 17), (6, 12), (6, 17), (0, 19), (11, 2), (10, 9), (10, 16), (6, 8), (29, 2), (12, 4), (14, 34), (20, 24), (25, 4), (27, 8), (7, 36), (2, 20), (16, 23), (1, 30), (28, 32), (17, 21), (14, 0), (7, 0), (13, 5), (17, 36), (29, 29), (0, 17), (15, 27), (25, 8), (1, 16), (9, 20), (12, 17), (9, 29), (21, 6), (7, 32), (4, 35), (0, 35), (30, 28), (15, 21), (18, 33), (20, 13), (15, 31), (10, 30), (28, 27), (19, 36), (4, 3), (20, 2), (28, 12), (24, 30), (7, 8), (17, 20), (26, 0), (21, 28), (5, 12), (7, 20), (26, 27), (0, 36), (12, 0), (8, 9), (27, 33), (25, 30), (9, 19), (19, 5), (21, 3), (20, 18), (0, 33), (23, 29), (6, 30), (25, 27), (14, 12), (6, 1), (20, 3), (6, 9), (10, 8), (4, 36), (8, 7), (1, 14), (18, 7), (12, 33), (12, 21), (19, 30), (28, 25), (23, 25), (28, 7), (6, 31), (25, 5), (24, 15), (5, 15), (20, 21), (12, 13), (6, 37), (15, 20), (12, 23), (13, 20), (2, 33), (5, 13), (5, 3), (3, 21), (4, 4), (9, 3), (14, 30), (3, 5), (27, 29), (23, 20), (21, 12), (19, 21), (20, 16), (11, 12), (14, 5), (11, 24), (20, 23), (11, 26), (18, 34), (30, 19), (3, 20), (3, 35), (30, 22), (16, 15), (4, 6), (8, 4), (11, 31), (19, 4), (10, 36), (30, 9), (3, 37), (21, 13), (18, 15), (4, 20), (1, 31), (21, 17), (9, 6), (2, 14), (13, 35), (29, 4), (12, 11), (1, 9), (14, 33), (19, 18), (30, 10), (3, 7), (8, 30), (5, 30), (26, 5), (6, 24), (20, 10), (25, 20), (16, 22), (5, 19), (12, 2), (5, 33), (26, 20), (15, 0), (2, 0), (19, 37), (13, 26), (17, 27), (8, 33), (9, 5), (14, 29), (30, 4), (14, 15), (26, 9), (5, 16), (20, 36), (14, 28), (16, 13), (18, 5), (10, 32), (20, 31), (5, 24), (25, 25), (5, 22), (29, 33), (1, 17), (21, 4), (24, 32), (30, 24), (13, 2), (11, 16), (22, 26), (1, 25), (27, 20), (27, 9), (28, 21), (20, 25), (9, 30), (5, 34), (23, 6), (26, 37), (3, 34), (11, 20), (28, 10), (12, 37), (29, 13), (16, 9), (7, 5), (9, 28), (30, 21), (2, 18), (19, 7), (10, 13), (6, 21), (19, 1), (28, 24), (29, 23), (10, 22), (27, 36), (19, 12), (7, 35), (18, 2), (22, 21), (4, 8), (4, 19), (23, 1), (29, 32), (21, 30), (12, 19), (30, 25), (25, 16), (16, 1), (6, 35), (22, 20), (24, 14), (3, 8), (24, 35), (1, 5), (15, 16), (12, 24), (16, 35), (10, 20), (28, 0), (12, 28), (16, 11), (2, 2), (26, 12), (11, 30), (23, 27), (30, 14), (3, 23), (6, 26), (1, 37), (7, 24), (23, 23), (3, 24), (25, 3), (9, 17), (23, 10), (13, 32), (1, 23), (2, 7), (14, 27), (0, 10), (15, 5), (2, 34), (17, 16), (10, 6), (20, 1), (8, 12), (14, 18), (10, 29), (11, 5), (0, 22), (23, 12), (13, 22), (10, 4), (8, 5), (2, 5), (0, 18), (12, 16), (24, 20), (9, 25), (21, 5), (2, 22), (4, 11), (24, 6), (28, 20), (28, 37), (14, 6), (10, 31), (7, 34), (27, 22), (29, 21), (27, 14), (3, 14), (29, 12), (24, 12), (2, 30), (28, 1), (2, 27), (17, 22), (21, 37), (18, 12), (3, 1), (1, 4), (18, 24), (6, 33), (26, 28), (20, 27), (4, 15), (15, 7), (14, 16), (22, 19), (5, 25), (2, 1), (25, 18), (29, 31), (12, 5), (26, 25), (9, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535248", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 16), (33, 2), (25, 8), (31, 22), (10, 24), (11, 22), (22, 0), (16, 22), (11, 4), (4, 18), (1, 24), (0, 26), (10, 14), (37, 23), (21, 29), (35, 2), (35, 17), (24, 24), (21, 15), (2, 9), (10, 12), (31, 5), (0, 3), (17, 27), (35, 0), (28, 15), (0, 29), (20, 20), (34, 16), (36, 30), (9, 10), (32, 24), (21, 10), (15, 22), (13, 9), (36, 6), (13, 26), (0, 5), (15, 5), (22, 25), (5, 9), (3, 28), (14, 6), (29, 10), (12, 24), (15, 24), (22, 14), (22, 10), (16, 0), (0, 16), (8, 12), (15, 9), (17, 16), (3, 15), (6, 21), (8, 26), (25, 26), (21, 25), (4, 30), (30, 1), (5, 21), (34, 11), (11, 8), (19, 0), (5, 10), (19, 9), (7, 12), (12, 14), (26, 16), (18, 25), (12, 10), (11, 25), (36, 4), (28, 20), (13, 12), (3, 7), (19, 17), (23, 25), (0, 23), (18, 1), (11, 11), (17, 14), (16, 17), (32, 11), (27, 1), (20, 8), (14, 13), (31, 28), (9, 21), (11, 2), (11, 9), (19, 12), (38, 2), (27, 6), (12, 29), (2, 3), (11, 0), (2, 8), (35, 7), (31, 25), (32, 29), (32, 12), (15, 18), (26, 1), (12, 5), (11, 15), (34, 22), (19, 23), (36, 15), (14, 29), (28, 12), (15, 10), (7, 4), (11, 17), (27, 9), (33, 1), (22, 20), (13, 15), (25, 15), (33, 21), (33, 11), (0, 30), (16, 5), (3, 2), (38, 22), (25, 25), (28, 29), (27, 23), (36, 3), (22, 29), (28, 26), (33, 4), (19, 30), (33, 17), (30, 6), (12, 23), (29, 23), (28, 7), (1, 26), (4, 7), (7, 16), (25, 0), (5, 6), (2, 6), (18, 15), (32, 23), (4, 24), (16, 29), (37, 1), (9, 8), (4, 27), (9, 0), (4, 23), (5, 17), (6, 15), (18, 9), (25, 18), (0, 15), (2, 30), (19, 28), (31, 20), (10, 4), (3, 20), (19, 7), (29, 12), (3, 22), (29, 22), (28, 30), (15, 26), (0, 13), (10, 2), (18, 0), (10, 20), (10, 7), (17, 18), (13, 16), (7, 30), (0, 2), (34, 25), (10, 13), (15, 23), (6, 28), (6, 27), (19, 2), (26, 2), (6, 20), (31, 15), (3, 21), (12, 11), (10, 9), (23, 11), (20, 15), (3, 30), (24, 10), (33, 15), (32, 20), (26, 30), (3, 13), (2, 16), (1, 27), (11, 19), (32, 6), (4, 19), (28, 5), (9, 3), (38, 17), (33, 27), (36, 26), (24, 3), (33, 7), (5, 20), (13, 20), (4, 26), (27, 8), (2, 28), (26, 12), (36, 14), (5, 26), (13, 3), (24, 6), (16, 6), (10, 22), (37, 6), (9, 4), (15, 11), (2, 14), (17, 20), (21, 4), (24, 19), (13, 4), (8, 18), (22, 11), (3, 0), (16, 26), (24, 0), (19, 16), (27, 22), (2, 26), (18, 8), (35, 9), (27, 12), (31, 16), (14, 5), (5, 23), (0, 21), (1, 1), (17, 17), (23, 16), (9, 24), (38, 4), (29, 28), (3, 25), (29, 13), (22, 22), (16, 9), (2, 11), (19, 11), (21, 13), (25, 14), (0, 24), (14, 25), (14, 9), (30, 5), (38, 25), (18, 23), (12, 4), (38, 10), (34, 14), (22, 15), (18, 11), (11, 30), (36, 24), (27, 7), (4, 25), (38, 12), (0, 9), (1, 8), (9, 5), (26, 4), (11, 29), (21, 6), (3, 3), (15, 16), (29, 18), (28, 22), (34, 27), (14, 7), (30, 11), (23, 14), (20, 7), (33, 13), (24, 13), (19, 19), (5, 15), (1, 15), (1, 13), (21, 14), (30, 27), (26, 24), (0, 19), (8, 25), (5, 25), (5, 2), (6, 12), (25, 3), (36, 17), (38, 13), (9, 22), (5, 24), (30, 18), (12, 12), (32, 2), (7, 18), (21, 7), (2, 10), (9, 26), (21, 28), (12, 26), (20, 17), (38, 28), (19, 25), (38, 23), (31, 3), (15, 13), (4, 4), (13, 10), (15, 2), (32, 16), (37, 10), (27, 25), (29, 24), (4, 15), (0, 7), (2, 4), (33, 25), (8, 21), (31, 21), (32, 25), (15, 28), (12, 0), (32, 19), (17, 10), (38, 27), (10, 16), (6, 6), (18, 20), (13, 25), (5, 30), (28, 2), (16, 10), (22, 9), (18, 28), (25, 28), (3, 23), (14, 8), (21, 2), (24, 12), (17, 0), (31, 23), (0, 14), (31, 0), (3, 5), (31, 8), (3, 17), (26, 18), (0, 28), (20, 19), (37, 28), (8, 17), (27, 26), (26, 25), (22, 18), (32, 4), (23, 3), (31, 1), (23, 26), (22, 13), (8, 11), (16, 24), (3, 16), (4, 6), (31, 24), (0, 1), (17, 4), (9, 9), (16, 19), (38, 9), (6, 18), (9, 30), (14, 26), (35, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399360", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 23), (6, 4), (16, 21), (20, 27), (22, 24), (18, 27), (1, 28), (16, 15), (12, 31), (18, 10), (26, 34), (7, 1), (0, 7), (24, 21), (33, 15), (24, 15), (12, 0), (10, 23), (17, 8), (5, 34), (27, 24), (28, 8), (31, 0), (4, 15), (35, 12), (7, 2), (20, 5), (28, 22), (27, 22), (19, 25), (19, 26), (27, 5), (23, 12), (16, 26), (2, 11), (2, 21), (0, 21), (34, 7), (35, 3), (25, 20), (10, 5), (17, 34), (23, 13), (32, 13), (7, 8), (15, 17), (3, 11), (3, 0), (0, 1), (0, 29), (4, 4), (8, 32), (18, 11), (26, 0), (26, 10), (7, 16), (30, 18), (21, 20), (8, 22), (22, 28), (9, 6), (5, 23), (1, 19), (13, 24), (14, 7), (31, 3), (36, 20), (21, 13), (29, 12), (26, 22), (7, 7), (32, 18), (7, 27), (7, 28), (1, 18), (5, 9), (17, 12), (11, 2), (18, 12), (22, 20), (10, 13), (13, 19), (2, 34), (22, 5), (24, 26), (14, 3), (8, 17), (5, 2), (30, 34), (10, 10), (28, 18), (21, 8), (32, 6), (15, 0), (1, 9), (16, 6), (27, 21), (18, 14), (27, 23), (20, 4), (9, 25), (36, 16), (6, 34), (11, 33), (31, 13), (2, 12), (21, 4), (11, 15), (3, 27), (2, 32), (2, 27), (36, 5), (21, 1), (21, 15), (14, 10), (35, 2), (25, 18), (25, 3), (19, 1), (21, 33), (1, 23), (31, 16), (4, 31), (18, 25), (35, 10), (12, 27), (14, 13), (34, 3), (29, 31), (0, 19), (9, 3), (20, 26), (31, 31), (34, 20), (9, 17), (10, 11), (7, 33), (5, 24), (35, 6), (29, 6), (33, 2), (26, 6), (1, 34), (29, 26), (18, 23), (2, 25), (22, 1), (27, 33), (0, 2), (35, 34), (11, 32), (16, 33), (14, 12), (14, 29), (23, 10), (15, 19), (6, 13), (14, 28), (25, 19), (10, 14), (20, 25), (8, 5), (29, 7), (21, 22), (9, 31), (16, 13), (31, 29), (4, 10), (10, 16), (7, 14), (35, 1), (23, 3), (3, 16), (32, 19), (24, 8), (9, 4), (11, 16), (12, 29), (17, 7), (11, 26), (4, 18), (19, 16), (17, 22), (25, 15), (31, 7), (14, 20), (29, 11), (5, 5), (23, 6), (31, 6), (32, 3), (23, 19), (5, 18), (34, 0), (17, 18), (25, 6), (34, 4), (27, 20), (21, 12), (7, 13), (19, 18), (9, 21), (16, 4), (1, 11), (33, 13), (35, 16), (33, 4), (24, 30), (18, 6), (13, 30), (6, 19), (34, 22), (1, 13), (32, 23), (20, 0), (31, 32), (22, 30), (2, 28), (9, 5), (36, 24), (34, 27), (18, 5), (29, 24), (27, 17), (24, 6), (7, 4), (4, 19), (9, 23), (36, 31), (17, 28), (15, 25), (34, 19), (18, 20), (17, 31), (31, 17), (4, 16), (32, 16), (23, 24), (14, 18), (26, 32), (17, 33), (9, 15), (19, 24), (0, 13), (4, 29), (11, 23), (11, 13), (13, 22), (6, 27), (29, 16), (26, 9), (21, 9), (15, 2), (1, 15), (23, 0), (4, 24), (36, 12), (20, 10), (27, 30), (24, 19), (10, 15), (14, 2), (24, 1), (22, 14), (29, 23), (13, 2), (30, 12), (25, 11), (11, 20), (29, 32), (36, 3), (9, 24), (3, 17), (2, 22), (17, 13), (6, 14), (9, 10), (8, 26), (30, 11), (13, 6), (7, 22), (30, 8), (3, 4), (7, 17), (4, 25), (4, 30), (36, 17), (34, 18), (14, 19), (3, 25), (35, 8), (22, 11), (9, 32), (8, 23), (35, 18), (7, 0), (27, 31), (0, 26), (1, 21), (17, 4), (27, 15), (32, 0), (17, 24), (25, 26), (21, 29), (15, 6), (7, 32), (22, 15), (7, 29), (25, 9), (28, 0), (4, 20), (36, 26), (29, 20), (26, 20), (26, 25), (11, 9), (28, 1), (11, 11), (24, 5), (8, 11), (29, 13), (12, 26), (15, 21), (2, 33), (5, 27), (27, 27), (13, 3), (7, 23), (17, 26), (11, 27), (12, 11), (12, 34), (9, 8), (14, 22), (26, 16), (28, 4), (5, 29), (4, 28), (9, 29), (22, 4), (13, 1), (16, 23), (16, 0), (6, 9), (9, 28), (19, 23), (23, 31), (35, 26), (31, 4), (14, 11), (22, 29), (30, 4), (4, 34), (21, 0), (23, 20), (15, 24), (1, 22), (18, 30), (5, 4), (26, 33), (5, 20), (35, 20), (33, 26), (27, 25), (19, 6), (21, 11), (16, 14), (0, 11), (26, 23), (14, 4), (25, 10), (25, 1), (11, 14), (24, 2), (22, 0), (16, 28), (26, 28), (1, 6), (17, 27), (13, 20), (6, 15), (15, 14), (8, 25), (34, 12), (3, 19), (22, 13), (17, 14), (27, 19), (24, 28), (32, 15), (33, 12), (0, 17), (33, 1), (20, 30), (4, 23), (31, 8), (20, 21), (33, 19), (31, 21), (29, 8), (3, 34), (4, 7), (10, 6), (30, 3), (35, 33), (2, 23), (2, 2), (10, 24), (18, 21), (24, 33), (29, 33), (23, 14), (3, 15), (34, 17), (7, 10), (30, 9), (6, 21), (3, 7), (33, 5), (27, 18), (14, 21), (30, 31), (4, 21), (11, 1), (10, 3), (27, 11), (0, 20), (34, 8), (25, 8), (14, 27), (35, 14), (16, 30), (29, 22), (25, 7), (19, 32), (28, 5), (31, 20), (33, 6), (20, 12), (23, 9), (36, 14), (10, 22), (20, 6), (25, 32), (15, 26), (36, 18), (8, 3), (22, 32), (5, 1), (24, 25), (5, 11), (5, 17), (2, 13), (30, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864000", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), 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), (37, 22), (2, 20), (21, 22), (4, 5), (30, 19), (34, 16), (25, 14), (10, 24), (2, 19), (12, 6), (28, 17), (30, 20), (37, 29), (1, 5), (3, 22), (0, 3), (12, 8), (1, 17), (26, 3), (37, 12), (26, 30), (29, 27), (35, 26), (28, 21), (26, 18), (26, 11), (10, 20), (22, 2), (35, 25), (11, 5), (16, 6), (36, 11), (25, 31), (4, 9), (29, 21), (27, 9), (15, 9), (8, 33), (32, 7), (14, 13), (20, 6), (31, 7), (11, 9), (4, 14), (31, 26), (10, 1), (37, 9), (7, 8), (23, 17), (7, 30), (36, 10), (8, 29), (15, 3), (3, 13), (8, 7), (11, 8), (24, 20), (6, 5), (7, 14), (5, 5), (18, 29), (32, 27), (22, 32), (8, 16), (13, 10), (12, 34), (4, 0), (24, 8), (33, 9), (28, 25), (28, 7), (10, 23), (24, 10), (23, 22), (34, 17), (3, 15), (23, 16), (22, 12), (17, 21), (24, 16), (17, 11), (8, 1), (27, 5), (22, 8), (30, 16), (7, 11), (33, 11), (2, 25), (11, 27), (8, 26), (6, 25), (31, 6), (4, 28), (13, 16), (2, 8), (25, 15), (34, 4), (3, 1), (30, 29), (14, 1), (9, 14), (19, 34), (25, 3), (4, 26), (6, 3), (15, 20), (37, 31), (19, 23), (0, 11), (34, 26), (15, 2), (8, 25), (31, 24), (22, 26), (5, 10), (8, 28), (14, 22), (18, 2), (25, 28), (36, 31), (12, 18), (16, 14), (15, 7), (5, 0), (6, 14), (37, 28), (15, 1), (19, 0), (20, 24), (28, 28), (20, 23), (11, 29), (35, 23), (35, 16), (12, 4), (8, 30), (18, 13), (1, 27), (28, 10), (3, 14), (12, 27), (30, 34), (15, 27), (26, 23), (24, 26), (1, 2), (11, 15), (34, 12), (8, 8), (28, 27), (13, 17), (20, 15), (32, 28), (14, 29), (36, 16), (34, 27), (34, 19), (21, 16), (0, 12), (7, 29), (26, 5), (24, 12), (0, 21), (9, 27), (36, 20), (32, 9), (3, 7), (36, 19), (1, 24), (37, 5), (22, 5), (19, 13), (17, 31), (19, 21), (26, 0), (26, 28), (22, 15), (28, 6), (33, 6), (3, 23), (13, 26), (35, 19), (12, 17), (13, 23), (21, 17), (24, 6), (37, 23), (5, 19), (28, 32), (21, 15), (26, 27), (32, 34), (19, 16), (8, 12), (27, 3), (13, 31), (14, 28), (4, 12), (30, 25), (29, 30), (18, 20), (27, 10), (18, 23), (10, 16), (8, 24), (23, 3), (24, 32), (24, 24), (18, 1), (15, 28), (2, 28), (3, 17), (28, 33), (17, 13), (3, 18), (17, 10), (10, 21), (4, 2), (27, 8), (2, 23), (33, 21), (21, 25), (21, 9), (15, 29), (35, 9), (32, 15), (33, 2), (10, 9), (19, 20), (0, 28), (26, 26), (12, 24), (10, 11), (0, 25), (12, 11), (16, 13), (36, 27), (23, 1), (21, 30), (14, 10), (2, 4), (29, 19), (27, 7), (5, 21), (1, 32), (30, 30), (10, 32), (19, 15), (10, 4), (12, 31), (26, 4), (18, 7), (6, 23), (31, 16), (35, 33), (14, 2), (19, 2), (2, 17), (14, 6), (31, 15), (31, 30), (16, 8), (19, 6), (22, 9), (8, 2), (7, 22), (21, 23), (26, 22), (10, 3), (37, 6), (13, 33), (30, 18), (25, 5), (36, 9), (32, 14), (22, 33), (3, 31), (11, 10), (4, 6), (24, 18), (21, 13), (19, 3), (29, 1), (16, 16), (31, 12), (17, 3), (22, 21), (17, 6), (7, 23), (13, 24), (5, 25), (26, 19), (32, 3), (5, 6), (22, 30), (19, 27), (21, 11), (22, 6), (7, 31), (5, 7), (11, 34), (31, 18), (3, 11), (16, 2), (15, 16), (4, 16), (21, 24), (6, 28), (37, 26), (21, 33), (24, 25), (34, 0), (11, 20), (27, 1), (4, 27), (25, 20), (29, 29), (16, 29), (9, 4), (32, 16), (8, 4), (5, 11), (2, 18), (36, 12), (36, 14), (6, 21), (16, 31), (33, 34), (13, 32), (0, 7), (12, 12), (2, 6), (28, 30), (21, 31), (17, 25), (35, 4), (22, 16), (32, 23), (15, 10), (2, 15), (9, 34), (28, 31), (1, 14), (1, 11), (32, 33), (1, 15), (9, 24), (23, 8), (24, 30), (34, 31), (23, 13), (4, 7), (25, 21), (33, 17), (31, 22), (30, 13), (15, 26), (12, 21), (17, 20), (3, 32), (1, 19), (30, 32), (33, 31), (16, 30), (21, 27), (4, 25), (13, 34), (11, 32), (5, 9), (36, 8), (3, 34), (15, 22), (8, 27), (26, 12), (7, 20), (1, 31), (14, 26), (17, 2), (34, 13), (14, 14), (29, 6), (2, 16), (30, 14), (23, 6), (21, 4), (24, 19), (20, 30), (2, 13), (16, 33), (7, 34), (25, 18), (32, 8), (6, 16), (24, 7), (20, 8), (26, 24), (17, 30), (28, 18), (21, 1), (15, 4), (19, 1), (4, 15), (32, 22), (8, 5), (2, 9), (17, 34), (29, 2), (16, 3), (35, 21), (5, 27), (13, 20), (21, 14), (15, 19), (16, 15), (2, 14), (5, 17), (2, 26), (4, 22), (11, 30), (9, 26), (18, 25), (23, 11), (27, 20), (13, 29), (3, 8), (36, 33), (3, 16), (12, 30), (11, 6), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "555408", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 6), (21, 16), (20, 27), (21, 20), (25, 17), (32, 0), (9, 7), (20, 36), (9, 11), (7, 22), (31, 31), (33, 2), (8, 8), (27, 1), (14, 34), (28, 9), (26, 30), (5, 33), (9, 28), (8, 10), (8, 24), (30, 31), (16, 36), (33, 30), (26, 34), (18, 23), (25, 31), (37, 3), (14, 21), (19, 31), (1, 2), (15, 28), (10, 33), (37, 11), (15, 10), (10, 8), (0, 3), (28, 15), (4, 28), (15, 0), (6, 32), (13, 16), (26, 1), (14, 28), (27, 6), (32, 35), (0, 32), (28, 33), (12, 2), (34, 14), (18, 10), (2, 2), (5, 22), (6, 20), (1, 29), (7, 23), (6, 33), (10, 19), (25, 1), (18, 4), (21, 7), (18, 37), (10, 20), (12, 5), (11, 32), (9, 38), (37, 21), (33, 28), (29, 21), (0, 33), (12, 35), (21, 10), (25, 9), (32, 19), (9, 29), (26, 13), (25, 35), (5, 10), (34, 25), (16, 5), (36, 36), (3, 31), (21, 14), (0, 14), (9, 12), (1, 7), (32, 12), (8, 16), (4, 38), (29, 35), (18, 3), (36, 18), (9, 16), (33, 19), (32, 20), (2, 30), (12, 36), (16, 15), (34, 35), (13, 26), (18, 18), (33, 34), (18, 7), (15, 24), (16, 21), (30, 12), (5, 19), (4, 6), (27, 27), (10, 6), (7, 17), (28, 18), (36, 2), (26, 8), (1, 15), (27, 10), (6, 35), (17, 0), (1, 9), (17, 20), (35, 29), (36, 23), (16, 32), (18, 30), (34, 1), (3, 8), (6, 29), (13, 25), (3, 10), (37, 13), (35, 16), (16, 1), (7, 29), (8, 23), (0, 30), (7, 11), (19, 19), (11, 18), (2, 4), (3, 37), (14, 22), (30, 6), (31, 19), (15, 17), (8, 14), (30, 2), (22, 12), (29, 12), (9, 22), (20, 14), (19, 38), (9, 6), (36, 25), (5, 37), (5, 3), (27, 28), (33, 14), (22, 25), (22, 32), (20, 3), (13, 1), (14, 14), (25, 12), (29, 16), (25, 10), (4, 33), (1, 37), (23, 29), (8, 20), (11, 27), (25, 6), (26, 4), (0, 36), (19, 11), (30, 30), (6, 8), (9, 25), (20, 10), (26, 11), (22, 0), (23, 27), (3, 13), (18, 11), (10, 37), (23, 14), (23, 16), (20, 15), (33, 6), (30, 13), (14, 13), (0, 27), (24, 14), (4, 8), (0, 5), (8, 1), (1, 30), (34, 36), (18, 15), (12, 30), (27, 15), (7, 20), (31, 18), (2, 32), (24, 21), (11, 6), (9, 37), (2, 5), (21, 33), (15, 14), (32, 3), (29, 29), (30, 34), (33, 20), (8, 19), (12, 32), (17, 3), (6, 30), (25, 11), (10, 24), (26, 24), (16, 31), (19, 21), (24, 24), (14, 38), (33, 35), (37, 14), (36, 17), (20, 9), (21, 18), (29, 14), (1, 13), (19, 37), (2, 8), (13, 15), (6, 3), (20, 29), (23, 24), (23, 28), (2, 7), (17, 2), (37, 12), (0, 18), (35, 35), (8, 33), (22, 4), (18, 2), (16, 19), (21, 38), (36, 29), (9, 1), (23, 31), (24, 35), (13, 8), (13, 14), (24, 15), (20, 6), (34, 9), (27, 2), (16, 37), (26, 26), (37, 24), (29, 9), (11, 17), (0, 22), (1, 11), (2, 14), (3, 19), (6, 16), (3, 34), (22, 5), (22, 37), (37, 33), (21, 35), (2, 37), (12, 22), (15, 18), (19, 2), (11, 3), (30, 16), (34, 21), (32, 13), (11, 36), (24, 19), (33, 13), (7, 25), (25, 25), (37, 35), (4, 24), (17, 12), (10, 14), (29, 33), (1, 26), (27, 31), (13, 10), (25, 33), (15, 11), (36, 9), (17, 4), (28, 20), (32, 27), (19, 35), (8, 3), (30, 18), (18, 31), (21, 30), (23, 0), (18, 13), (8, 9), (16, 2), (14, 36), (3, 1), (28, 16), (30, 10), (29, 13), (37, 22), (25, 21), (6, 14), (2, 20), (17, 30), (37, 8), (21, 9), (15, 32), (37, 7), (21, 24), (0, 28), (11, 26), (22, 6), (26, 21), (31, 14), (25, 15), (3, 33), (5, 15), (35, 20), (10, 16), (11, 37), (18, 38), (37, 30), (28, 29), (27, 33), (10, 26), (2, 28), (24, 34), (11, 38), (13, 34), (21, 8), (34, 28), (0, 19), (28, 17), (0, 35), (18, 14), (8, 38), (4, 31), (32, 17), (5, 31), (14, 20), (3, 36), (12, 21), (14, 16), (19, 13), (31, 33), (4, 23), (18, 1), (5, 27), (31, 4), (28, 30), (13, 30), (37, 25), (15, 33), (10, 31), (30, 4), (1, 23), (35, 24), (36, 38), (29, 19), (13, 38), (31, 27), (4, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94512", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 27), (31, 28), (1, 8), (15, 27), (10, 30), (20, 16), (20, 28), (26, 3), (27, 12), (8, 13), (25, 22), (10, 20), (27, 28), (3, 27), (28, 27), (18, 7), (32, 5), (29, 28), (18, 1), (19, 27), (18, 27), (32, 29), (8, 16), (20, 13), (33, 18), (21, 16), (14, 19), (16, 16), (22, 25), (9, 11), (3, 28), (2, 7), (16, 1), (7, 6), (15, 16), (34, 27), (19, 5), (22, 23), (1, 29), (6, 27), (31, 5), (15, 26), (20, 1), (7, 18), (0, 11), (1, 19), (7, 12), (17, 8), (10, 4), (21, 21), (16, 15), (2, 17), (5, 23), (18, 16), (15, 4), (10, 26), (2, 30), (34, 19), (14, 17), (27, 30), (8, 23), (21, 6), (21, 10), (8, 8), (16, 29), (3, 7), (25, 12), (29, 0), (1, 4), (10, 16), (0, 12), (23, 10), (2, 16), (31, 29), (18, 15), (9, 21), (10, 27), (0, 4), (1, 16), (25, 3), (28, 3), (10, 25), (22, 14), (6, 16), (8, 30), (31, 8), (32, 2), (5, 11), (0, 26), (4, 12), (27, 10), (13, 26), (19, 14), (14, 26), (1, 22), (16, 22), (34, 24), (27, 3), (29, 3), (1, 21), (8, 15), (3, 2), (11, 10), (22, 21), (2, 10), (25, 9), (13, 10), (31, 9), (11, 4), (30, 13), (11, 14), (7, 7), (30, 3), (16, 13), (12, 13), (21, 19), (26, 8), (4, 16), (28, 7), (16, 14), (2, 21), (29, 11), (30, 11), (30, 1), (28, 1), (1, 17), (0, 23), (24, 4), (23, 28), (12, 3), (19, 28), (7, 5), (19, 1), (14, 0), (6, 21), (14, 8), (5, 28), (17, 21), (18, 30), (4, 8), (18, 12), (20, 23), (8, 17), (22, 2), (11, 8), (30, 6), (1, 12), (28, 2), (9, 17), (9, 8), (28, 14), (9, 30), (5, 24), (26, 21), (30, 12), (8, 7), (23, 12), (29, 26), (15, 5), (24, 3), (17, 4), (31, 19), (19, 17), (23, 3), (18, 8), (10, 13), (7, 14), (5, 21), (8, 25), (33, 26), (17, 1), (33, 13), (26, 2), (13, 9), (23, 17), (21, 3), (18, 23), (31, 26), (25, 1), (6, 29), (7, 28), (0, 8), (23, 9), (26, 4), (13, 29), (3, 20), (12, 19), (10, 3), (15, 1), (21, 29), (16, 26), (17, 14), (5, 17), (27, 4), (20, 11), (14, 28), (28, 4), (11, 16), (14, 12), (18, 6), (26, 20), (26, 5), (20, 9), (19, 16), (21, 15), (24, 22), (9, 2), (11, 19), (23, 18), (0, 19), (27, 25), (25, 27), (26, 27), (34, 0), (29, 1), (27, 17), (3, 26), (13, 25), (6, 3), (4, 17), (5, 4), (7, 11), (0, 17), (2, 8), (15, 7), (9, 0), (33, 22), (21, 27), (17, 15), (20, 22), (22, 4), (19, 24), (23, 14), (2, 9), (29, 8), (8, 14), (9, 10), (18, 5), (7, 26), (7, 29), (9, 26), (31, 6), (27, 9), (32, 17), (24, 7), (16, 28), (21, 4), (2, 25), (22, 16), (6, 8), (26, 1), (9, 7), (17, 16), (0, 24), (7, 16), (22, 12), (28, 16), (18, 29), (17, 7), (33, 8), (3, 9), (22, 5), (33, 15), (30, 7), (21, 23), (9, 20), (8, 3), (31, 2), (0, 14), (23, 20), (24, 5), (28, 13), (27, 15), (31, 1), (11, 27), (1, 20), (32, 26), (22, 19), (25, 13), (9, 23), (23, 13), (15, 14), (31, 13), (16, 7), (2, 11), (8, 1), (8, 29), (25, 4), (6, 24), (16, 30), (7, 30), (19, 8), (1, 23), (22, 13), (10, 23), (29, 25), (4, 9), (32, 14), (33, 10), (10, 29), (5, 27), (14, 4), (34, 17), (14, 11), (34, 21), (31, 16), (34, 15), (12, 21), (4, 22), (9, 16), (10, 28), (27, 13), (29, 29), (17, 10), (26, 15), (26, 19), (27, 26), (4, 14), (28, 18), (21, 20), (24, 23), (7, 8), (15, 29), (34, 4), (29, 24), (16, 6), (0, 18), (23, 16), (10, 11), (2, 4), (20, 17), (19, 3), (30, 8), (5, 15), (12, 2), (5, 25), (27, 22), (22, 8), (32, 15), (11, 15), (26, 14), (12, 6), (34, 14), (3, 30), (30, 4), (2, 24), (33, 6), (28, 0), (2, 28), (29, 22), (27, 19), (6, 26), (12, 1), (0, 22), (10, 21), (5, 16), (11, 24), (22, 6), (17, 23), (8, 5), (25, 16), (6, 19), (24, 20), (30, 14), (27, 0), (13, 4), (0, 16), (20, 24), (31, 18), (19, 19), (4, 19), (5, 0), (33, 2), (13, 11), (0, 13), (4, 29), (8, 2), (29, 6), (27, 20), (11, 26), (28, 22), (22, 18), (31, 12), (28, 17), (13, 6), (29, 9), (3, 11), (7, 19), (32, 22), (12, 5), (24, 6), (7, 13), (3, 29), (23, 2), (8, 24), (24, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369495", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), 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), (13, 19), (0, 23), (15, 32), (18, 27), (8, 20), (25, 23), (20, 6), (16, 11), (10, 32), (22, 9), (28, 12), (27, 8), (16, 4), (6, 13), (14, 20), (21, 24), (28, 30), (23, 12), (6, 0), (16, 24), (1, 23), (1, 10), (20, 2), (22, 11), (9, 27), (21, 7), (19, 32), (2, 28), (20, 26), (16, 8), (31, 19), (31, 26), (10, 7), (23, 24), (31, 20), (3, 8), (27, 25), (9, 2), (27, 26), (23, 6), (21, 17), (28, 21), (12, 7), (29, 33), (27, 17), (12, 5), (27, 13), (18, 15), (7, 22), (29, 17), (32, 30), (19, 31), (29, 31), (2, 14), (31, 11), (5, 12), (33, 27), (16, 0), (29, 6), (31, 13), (13, 4), (33, 12), (14, 27), (17, 28), (30, 32), (20, 1), (5, 26), (9, 28), (11, 11), (22, 32), (5, 2), (7, 18), (22, 24), (11, 13), (10, 6), (2, 8), (12, 32), (8, 21), (24, 11), (31, 3), (20, 11), (14, 14), (18, 18), (22, 19), (32, 22), (1, 27), (8, 16), (29, 18), (5, 30), (33, 10), (19, 16), (16, 20), (13, 15), (15, 0), (6, 6), (6, 11), (3, 9), (1, 26), (25, 28), (7, 13), (24, 32), (3, 3), (27, 30), (2, 33), (9, 17), (3, 23), (25, 7), (18, 16), (1, 3), (17, 22), (21, 33), (21, 32), (11, 20), (11, 19), (25, 29), (9, 30), (3, 14), (2, 7), (10, 3), (14, 23), (24, 23), (20, 25), (17, 7), (21, 0), (9, 8), (4, 4), (18, 7), (14, 11), (25, 30), (8, 8), (4, 30), (26, 24), (4, 10), (4, 9), (27, 33), (2, 12), (33, 5), (24, 4), (13, 23), (8, 3), (0, 33), (31, 12), (23, 28), (21, 26), (32, 28), (16, 26), (2, 15), (0, 24), (33, 19), (9, 6), (7, 16), (28, 6), (21, 4), (30, 19), (6, 26), (1, 31), (23, 1), (11, 30), (25, 2), (13, 2), (18, 10), (28, 26), (24, 2), (4, 0), (22, 2), (30, 2), (17, 1), (24, 21), (28, 4), (11, 9), (7, 28), (29, 20), (12, 2), (5, 9), (8, 7), (7, 8), (17, 25), (13, 6), (3, 17), (24, 14), (1, 21), (7, 21), (3, 5), (1, 2), (9, 15), (28, 2), (26, 33), (1, 28), (21, 25), (20, 7), (3, 20), (9, 20), (5, 29), (23, 10), (7, 6), (24, 15), (4, 2), (6, 27), (17, 6), (5, 7), (31, 29), (21, 5), (28, 17), (20, 18), (12, 33), (12, 14), (16, 19), (14, 2), (5, 27), (30, 6), (25, 32), (0, 21), (20, 27), (23, 31), (12, 12), (17, 5), (32, 17), (7, 9), (23, 33), (16, 3), (26, 23), (32, 14), (27, 27), (17, 19), (32, 2), (10, 13), (33, 31), (5, 31), (5, 25), (8, 12), (24, 6), (32, 0), (8, 14), (29, 25), (16, 23), (4, 31), (26, 21), (15, 4), (29, 4), (13, 25), (28, 0), (19, 15), (1, 12), (28, 25), (30, 5), (18, 8), (15, 11), (14, 5), (24, 1), (9, 23), (27, 16), (11, 32), (10, 33), (6, 12), (24, 29), (10, 20), (28, 29), (25, 4), (1, 7), (1, 22), (20, 21), (14, 6), (28, 33), (4, 21), (13, 27), (4, 27), (9, 14), (16, 22), (29, 30), (11, 22), (1, 19), (18, 26), (26, 13), (19, 5), (15, 24), (25, 27), (18, 12), (1, 4), (33, 1), (24, 20), (1, 8), (24, 3), (28, 11), (9, 16), (29, 14), (19, 33), (23, 23), (28, 8), (20, 20), (13, 16), (16, 25), (14, 0), (29, 21), (28, 3), (17, 31), (7, 3), (17, 20), (20, 23), (28, 9), (24, 22), (11, 14), (5, 0), (10, 23), (20, 4), (2, 1), (20, 16), (14, 22), (31, 27), (10, 5), (22, 1), (8, 29), (21, 11), (6, 4), (23, 30), (31, 1), (33, 8), (5, 11), (3, 18), (30, 11), (27, 19), (23, 13), (25, 20), (15, 26), (7, 12), (19, 22), (24, 26), (26, 4), (0, 28), (26, 5), (11, 7), (10, 27), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984000", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 4), (6, 24), (2, 14), (26, 13), (24, 15), (17, 25), (4, 21), (10, 5), (2, 18), (12, 0), (26, 2), (8, 12), (11, 14), (0, 3), (29, 5), (22, 18), (34, 4), (5, 22), (8, 2), (16, 5), (31, 23), (5, 12), (4, 23), (6, 9), (7, 4), (7, 19), (9, 26), (14, 29), (11, 26), (4, 3), (6, 21), (19, 10), (1, 5), (35, 1), (2, 3), (22, 10), (17, 6), (9, 19), (8, 1), (25, 24), (0, 12), (22, 9), (27, 25), (22, 7), (35, 23), (28, 19), (16, 21), (18, 28), (1, 20), (14, 20), (20, 23), (11, 12), (23, 2), (16, 3), (18, 26), (9, 8), (33, 27), (8, 22), (24, 20), (28, 13), (2, 25), (9, 4), (17, 4), (33, 22), (3, 17), (18, 8), (8, 14), (18, 11), (18, 4), (33, 24), (12, 11), (20, 0), (28, 3), (7, 12), (29, 3), (27, 0), (11, 19), (19, 29), (4, 6), (3, 5), (3, 8), (19, 3), (9, 16), (13, 2), (7, 24), (0, 29), (34, 12), (8, 7), (11, 23), (23, 27), (3, 4), (31, 22), (24, 1), (33, 7), (19, 26), (1, 25), (22, 21), (12, 14), (33, 2), (15, 1), (10, 21), (13, 3), (27, 29), (28, 15), (33, 14), (5, 19), (8, 19), (19, 17), (22, 13), (15, 24), (23, 10), (20, 8), (32, 0), (11, 8), (20, 28), (6, 25), (15, 19), (23, 6), (7, 18), (10, 15), (5, 28), (11, 21), (34, 19), (24, 21), (25, 8), (9, 5), (17, 12), (23, 3), (16, 24), (15, 8), (25, 4), (24, 17), (18, 6), (9, 13), (4, 22), (0, 23), (31, 21), (18, 5), (12, 26), (23, 15), (32, 28), (28, 28), (19, 19), (6, 22), (5, 29), (8, 28), (21, 26), (31, 19), (21, 29), (11, 16), (4, 28), (34, 23), (11, 22), (26, 14), (2, 22), (3, 12), (30, 3), (1, 3), (8, 24), (5, 17), (16, 19), (34, 16), (13, 6), (19, 12), (31, 15), (10, 19), (13, 5), (16, 2), (9, 12), (20, 18), (18, 20), (29, 7), (30, 10), (8, 20), (3, 20), (21, 24), (20, 27), (22, 26), (3, 21), (2, 8), (4, 19), (19, 13), (33, 10), (26, 29), (26, 11), (25, 0), (22, 3), (3, 3), (16, 0), (19, 27), (3, 6), (28, 11), (31, 29), (26, 6), (3, 15), (2, 4), (28, 9), (20, 10), (35, 27), (4, 26), (24, 14), (35, 16), (31, 0), (14, 4), (0, 9), (13, 14), (33, 29), (1, 12), (23, 21), (18, 21), (30, 7), (5, 0), (11, 5), (18, 19), (18, 23), (26, 19), (13, 16), (27, 28), (6, 27), (21, 11), (6, 17), (0, 17), (23, 9), (19, 25), (4, 12), (8, 25), (25, 27), (24, 27), (32, 14), (31, 25), (16, 18), (6, 8), (12, 9), (31, 9), (19, 2), (32, 24), (0, 6), (14, 24), (3, 16), (14, 21), (32, 2), (20, 13), (22, 16), (26, 18), (8, 8), (18, 0), (32, 17), (14, 7), (25, 29), (9, 14), (7, 27), (28, 12), (23, 14), (23, 13), (30, 8), (15, 12), (2, 10), (3, 23), (23, 4), (4, 14), (27, 20), (14, 26), (11, 7), (17, 23), (21, 17), (21, 3), (15, 17), (4, 27), (13, 20), (30, 1), (1, 27), (33, 20), (4, 17), (32, 11), (28, 29), (13, 13), (35, 18), (28, 2), (16, 22), (29, 17), (17, 3), (20, 20), (12, 4), (13, 21), (12, 22), (30, 17), (19, 1), (30, 29), (21, 22), (24, 7), (15, 13), (35, 19), (2, 1), (33, 5), (11, 29), (28, 8), (26, 3), (25, 14), (2, 24), (32, 13), (9, 15), (13, 0), (1, 21), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327872", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 8), (7, 25), (6, 10), (28, 35), (28, 7), (27, 2), (11, 13), (9, 8), (29, 30), (1, 27), (15, 28), (24, 33), (15, 18), (1, 16), (12, 5), (17, 26), (18, 25), (30, 8), (27, 8), (19, 32), (23, 9), (22, 37), (31, 11), (21, 31), (27, 32), (7, 19), (23, 21), (32, 11), (11, 36), (13, 4), (34, 4), (21, 28), (11, 15), (20, 13), (2, 2), (21, 19), (17, 3), (33, 3), (8, 10), (17, 13), (5, 1), (32, 29), (0, 37), (27, 13), (1, 30), (7, 2), (13, 23), (26, 13), (6, 33), (22, 8), (4, 2), (31, 14), (16, 2), (0, 4), (1, 17), (15, 36), (5, 21), (18, 32), (15, 24), (15, 32), (15, 16), (10, 6), (30, 26), (32, 33), (15, 25), (33, 6), (12, 11), (32, 27), (17, 1), (13, 2), (16, 11), (4, 17), (31, 34), (10, 18), (22, 2), (29, 7), (4, 1), (1, 31), (12, 10), (25, 0), (11, 4), (12, 30), (22, 32), (11, 6), (30, 31), (2, 26), (25, 6), (27, 34), (6, 24), (9, 14), (16, 22), (33, 29), (22, 1), (0, 9), (33, 14), (12, 20), (1, 37), (6, 31), (1, 28), (20, 32), (32, 31), (4, 7), (25, 3), (21, 29), (28, 37), (13, 15), (31, 18), (34, 1), (6, 4), (16, 16), (25, 20), (7, 22), (6, 22), (33, 0), (12, 4), (31, 8), (22, 10), (33, 16), (28, 3), (31, 19), (32, 6), (32, 28), (2, 36), (31, 9), (18, 4), (29, 36), (21, 15), (33, 15), (34, 34), (21, 18), (0, 19), (21, 20), (9, 3), (14, 11), (0, 10), (14, 13), (22, 30), (34, 13), (1, 25), (26, 12), (4, 35), (34, 16), (23, 13), (26, 30), (30, 28), (29, 11), (13, 9), (28, 25), (18, 24), (3, 18), (6, 2), (27, 23), (11, 19), (26, 10), (13, 12), (3, 20), (21, 13), (16, 30), (34, 6), (16, 14), (31, 24), (17, 19), (23, 7), (17, 37), (4, 4), (18, 16), (9, 2), (31, 3), (25, 31), (26, 18), (24, 7), (29, 14), (15, 26), (6, 5), (19, 33), (3, 13), (24, 0), (3, 26), (24, 14), (32, 36), (33, 4), (6, 36), (29, 0), (9, 28), (25, 17), (0, 34), (31, 33), (5, 10), (22, 29), (11, 14), (18, 5), (15, 0), (6, 8), (12, 28), (8, 6), (21, 37), (15, 6), (16, 28), (28, 32), (9, 24), (34, 29), (25, 8), (23, 23), (10, 20), (26, 23), (0, 5), (34, 21), (10, 11), (2, 5), (0, 11), (9, 7), (17, 31), (18, 19), (31, 36), (7, 36), (11, 23), (2, 21), (7, 24), (9, 30), (14, 23), (17, 0), (21, 3), (4, 20), (14, 12), (5, 27), (19, 5), (32, 4), (2, 8), (19, 0), (29, 22), (22, 22), (1, 29), (16, 29), (25, 32), (20, 25), (21, 32), (26, 25), (5, 32), (34, 5), (1, 18), (1, 1), (25, 4), (4, 32), (10, 16), (27, 33), (3, 0), (24, 24), (18, 31), (25, 21), (6, 32), (11, 12), (4, 31), (29, 3), (29, 23), (27, 10), (17, 24), (29, 2), (1, 15), (9, 32), (12, 35), (12, 1), (8, 3), (30, 14), (28, 16), (14, 1), (13, 13), (5, 17), (16, 31), (11, 10), (19, 1), (6, 6), (25, 1), (14, 32), (28, 5), (28, 11), (6, 37), (25, 30), (4, 27), (4, 29), (32, 26), (20, 10), (31, 37), (27, 30), (20, 15), (24, 30), (22, 17), (3, 10), (31, 5), (5, 15), (20, 4), (25, 26), (22, 36), (3, 22), (33, 34), (6, 3), (34, 28), (14, 5), (31, 7), (3, 11), (2, 37), (32, 30), (34, 12), (23, 17), (30, 11), (9, 16), (24, 2), (2, 20), (7, 20), (10, 0), (33, 9), (25, 18), (6, 26), (22, 9), (24, 9), (0, 31), (25, 9), (23, 14), (24, 36), (6, 34), (33, 21), (32, 20), (8, 12), (8, 24), (11, 37), (20, 37), (10, 17), (21, 14), (31, 6), (30, 12), (33, 12), (1, 21), (16, 35), (15, 22), (6, 29), (26, 26), (24, 28), (28, 17), (0, 2), (5, 12), (33, 20), (26, 17), (4, 23), (14, 25), (31, 32), (27, 15), (14, 29), (16, 26), (27, 31), (4, 13), (19, 28), (27, 9), (11, 32), (4, 12), (29, 34), (27, 17), (19, 25), (32, 5), (19, 14), (25, 11), (3, 23), (29, 24), (24, 10), (9, 0), (34, 36), (25, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998142", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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, 28), (10, 25), (21, 6), (23, 24), (0, 30), (4, 8), (23, 16), (27, 20), (2, 4), (14, 13), (8, 19), (20, 12), (26, 10), (12, 19), (25, 13), (11, 30), (33, 12), (5, 17), (8, 14), (6, 19), (15, 26), (6, 30), (3, 23), (7, 18), (30, 9), (16, 22), (24, 25), (23, 7), (25, 26), (31, 2), (13, 21), (3, 14), (20, 22), (11, 16), (14, 26), (29, 9), (21, 21), (14, 24), (9, 29), (20, 0), (12, 26), (24, 14), (1, 21), (6, 23), (20, 16), (24, 12), (7, 22), (0, 27), (8, 27), (18, 30), (3, 25), (14, 6), (21, 8), (9, 24), (5, 0), (2, 5), (4, 27), (26, 25), (22, 10), (6, 15), (11, 25), (9, 3), (4, 9), (12, 8), (16, 18), (1, 18), (13, 25), (29, 17), (20, 19), (10, 3), (0, 28), (1, 14), (30, 24), (9, 9), (32, 21), (11, 23), (33, 21), (6, 17), (8, 21), (17, 9), (28, 16), (27, 10), (25, 3), (5, 10), (12, 22), (24, 24), (4, 0), (27, 1), (31, 6), (25, 10), (22, 17), (31, 18), (27, 24), (0, 23), (17, 29), (25, 24), (15, 19), (21, 29), (32, 28), (28, 13), (30, 8), (11, 17), (14, 28), (28, 23), (29, 8), (10, 21), (20, 15), (25, 0), (20, 13), (33, 15), (4, 26), (29, 7), (13, 10), (22, 18), (19, 14), (4, 25), (8, 0), (11, 28), (7, 16), (6, 27), (2, 1), (6, 24), (31, 14), (18, 1), (24, 3), (4, 7), (2, 30), (4, 30), (0, 22), (16, 4), (5, 15), (15, 28), (31, 7), (7, 15), (22, 23), (13, 8), (17, 14), (32, 14), (0, 10), (30, 14), (19, 3), (2, 19), (29, 3), (29, 27), (10, 22), (24, 4), (12, 30), (12, 7), (18, 16), (10, 15), (3, 1), (28, 19), (33, 11), (25, 19), (30, 3), (7, 21), (13, 20), (14, 3), (31, 9), (28, 15), (31, 28), (31, 4), (18, 29), (25, 18), (30, 4), (13, 5), (8, 26), (11, 1), (11, 10), (20, 29), (6, 16), (14, 27), (17, 10), (19, 10), (26, 24), (28, 14), (8, 22), (1, 5), (5, 5), (12, 24), (15, 3), (9, 22), (13, 14), (32, 1), (0, 6), (30, 1), (33, 17), (19, 2), (23, 8), (25, 11), (11, 6), (18, 20), (5, 4), (3, 10), (17, 1), (31, 23), (13, 2), (4, 29), (11, 8), (32, 25), (16, 19), (3, 27), (29, 21), (18, 22), (31, 15), (16, 10), (10, 8), (16, 12), (23, 22), (13, 17), (12, 2), (29, 13), (16, 8), (27, 21), (14, 0), (19, 8), (26, 4), (20, 8), (3, 2), (24, 20), (31, 22), (25, 4), (28, 17), (4, 21), (18, 27), (26, 11), (4, 6), (23, 13), (2, 14), (17, 19), (12, 5), (22, 13), (1, 19), (14, 20), (25, 9), (10, 11), (17, 15), (15, 29), (4, 14), (10, 26), (7, 1), (31, 11), (5, 27), (17, 17), (9, 2), (2, 0), (1, 30), (22, 28), (20, 3), (1, 23), (24, 22), (17, 28), (31, 26), (16, 25), (18, 2), (23, 17), (15, 25), (15, 13), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 25), (9, 27), (8, 26), (4, 27), (14, 26), (24, 19), (5, 11), (4, 5), (9, 19), (26, 3), (31, 29), (25, 7), (0, 16), (22, 23), (5, 8), (20, 4), (28, 26), (19, 14), (11, 30), (14, 8), (9, 7), (31, 30), (11, 25), (17, 24), (28, 1), (3, 27), (28, 5), (9, 32), (7, 21), (9, 22), (30, 20), (34, 15), (11, 20), (0, 14), (17, 35), (24, 26), (31, 3), (0, 34), (34, 26), (6, 5), (7, 24), (4, 24), (14, 13), (12, 35), (13, 23), (33, 1), (30, 36), (23, 7), (21, 36), (16, 18), (9, 23), (34, 24), (4, 0), (4, 19), (12, 19), (13, 6), (6, 10), (17, 22), (10, 15), (20, 13), (15, 13), (19, 5), (27, 5), (33, 2), (2, 1), (10, 35), (16, 11), (22, 37), (32, 15), (0, 18), (27, 1), (29, 26), (15, 18), (20, 34), (10, 21), (16, 26), (14, 28), (17, 3), (24, 9), (32, 23), (9, 38), (14, 2), (8, 21), (15, 11), (12, 10), (9, 3), (34, 28), (29, 6), (28, 18), (18, 36), (11, 32), (4, 28), (3, 19), (2, 36), (30, 13), (29, 3), (7, 14), (33, 30), (31, 24), (23, 17), (34, 32), (31, 18), (16, 14), (15, 22), (22, 7), (21, 28), (22, 1), (33, 37), (20, 28), (28, 20), (12, 28), (7, 38), (7, 3), (35, 33), (10, 1), (28, 34), (27, 13), (21, 2), (26, 8), (8, 12), (19, 12), (27, 34), (2, 32), (0, 35), (33, 8), (9, 8), (13, 11), (29, 16), (35, 7), (9, 6), (12, 6), (8, 16), (30, 17), (25, 16), (31, 31), (3, 1), (20, 3), (2, 25), (20, 7), (16, 31), (8, 25), (33, 24), (18, 4), (7, 26), (11, 21), (13, 4), (7, 9), (3, 7), (6, 4), (20, 23), (5, 38), (27, 12), (11, 14), (30, 25), (8, 34), (12, 17), (4, 9), (5, 36), (29, 12), (5, 10), (6, 3), (25, 32), (21, 35), (5, 3), (15, 35), (22, 28), (14, 6), (13, 2), (26, 16), (13, 24), (8, 37), (1, 28), (13, 20), (23, 22), (30, 29), (18, 9), (27, 35), (21, 17), (30, 0), (7, 33), (34, 4), (16, 22), (23, 16), (4, 30), (28, 24), (25, 28), (12, 32), (5, 15), (0, 29), (8, 0), (34, 2), (30, 38), (10, 20), (0, 12), (24, 7), (29, 19), (33, 21), (31, 5), (6, 30), (22, 19), (22, 9), (32, 13), (11, 12), (34, 21), (15, 33), (16, 30), (16, 21), (10, 7), (2, 16), (27, 24), (5, 30), (24, 11), (35, 35), (22, 29), (27, 23), (14, 12), (6, 28), (16, 19), (20, 17), (1, 10), (24, 25), (17, 26), (32, 26), (12, 0), (29, 20), (6, 25), (6, 1), (16, 1), (23, 12), (1, 21), (21, 22), (18, 29), (13, 0), (35, 36), (23, 10), (23, 2), (35, 17), (30, 21), (29, 13), (28, 17), (18, 8), (34, 31), (12, 20), (32, 32), (9, 36), (1, 18), (29, 31), (31, 12), (11, 18), (21, 12), (0, 7), (20, 38), (20, 14), (24, 4), (0, 30), (22, 25), (29, 30), (1, 34), (33, 5), (29, 8), (33, 3), (18, 19), (2, 17), (18, 34), (1, 24), (8, 33), (34, 10), (16, 7), (4, 11), (19, 29), (23, 18), (33, 4), (18, 17), (27, 37), (31, 38), (16, 6), (3, 23), (8, 13), (29, 10), (17, 15), (17, 2), (17, 31), (17, 12), (30, 6), (29, 21), (6, 15), (12, 38), (20, 1), (34, 22), (11, 17), (14, 9), (2, 19), (27, 33), (31, 23), (35, 9), (25, 5), (32, 12), (14, 24), (21, 8), (25, 37), (28, 37), (7, 29), (32, 11), (24, 3), (34, 1), (27, 25), (0, 38), (13, 12), (17, 25), (12, 37), (14, 34), (3, 36), (2, 29), (23, 36), (24, 13), (11, 10), (1, 3), (22, 4), (6, 6), (22, 32), (12, 13), (30, 33), (35, 32), (22, 20), (4, 31), (28, 32), (16, 33), (23, 6), (19, 25), (27, 3), (28, 22), (23, 32), (33, 28), (6, 21), (28, 13), (23, 3), (16, 25), (31, 14), (7, 4), (19, 21), (8, 27), (30, 31), (17, 7), (10, 31), (5, 13), (8, 23), (6, 31), (27, 16), (34, 16), (35, 0), (0, 1), (35, 26), (19, 6), (5, 25), (27, 6), (3, 14), (24, 5), (23, 19), (11, 38), (22, 27), (19, 35), (5, 32), (7, 23), (20, 16), (6, 27), (25, 3), (18, 28), (7, 22), (27, 38), (12, 5), (29, 7), (22, 18), (6, 33), (7, 25), (16, 4), (1, 6), (2, 7), (2, 24), (16, 2), (23, 1), (20, 26), (20, 21), (8, 4), (7, 1), (34, 30), (17, 6), (13, 26), (2, 21), (17, 28), (12, 16), (20, 22), (35, 37), (35, 25), (15, 7), (11, 6), (35, 31), (35, 28), (25, 18), (28, 16), (18, 32), (1, 38), (12, 26), (5, 12), (19, 13), (20, 25), (31, 33), (20, 12), (27, 17), (11, 34), (34, 19), (14, 21), (16, 35), (31, 34), (30, 16), (31, 16), (3, 25), (17, 23), (7, 34), (25, 38), (29, 18), (16, 13), (17, 4), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854670", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), 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), (21, 26), (17, 13), (21, 30), (8, 5), (21, 1), (20, 22), (12, 22), (1, 3), (18, 20), (26, 8), (10, 11), (12, 26), (25, 11), (17, 11), (26, 6), (20, 24), (2, 19), (1, 18), (21, 4), (7, 16), (3, 4), (29, 11), (18, 7), (21, 18), (18, 12), (27, 33), (28, 6), (29, 2), (1, 21), (26, 14), (5, 14), (29, 3), (28, 5), (17, 2), (21, 6), (18, 27), (26, 19), (24, 25), (20, 15), (13, 4), (18, 11), (6, 25), (12, 9), (7, 10), (8, 27), (13, 14), (3, 12), (29, 15), (19, 24), (3, 10), (24, 10), (3, 17), (8, 19), (25, 16), (4, 25), (24, 1), (22, 15), (21, 14), (27, 11), (7, 15), (24, 18), (7, 1), (6, 11), (8, 23), (14, 26), (2, 6), (19, 30), (28, 2), (27, 14), (3, 29), (25, 31), (11, 6), (12, 20), (4, 9), (3, 0), (13, 18), (6, 5), (13, 24), (4, 23), (26, 11), (8, 25), (7, 9), (11, 27), (1, 20), (15, 20), (18, 3), (27, 20), (3, 20), (3, 32), (20, 10), (2, 26), (15, 7), (16, 4), (18, 25), (27, 29), (6, 10), (13, 7), (9, 17), (4, 0), (14, 5), (0, 16), (22, 24), (0, 30), (4, 6), (20, 3), (12, 21), (21, 21), (9, 16), (23, 10), (1, 31), (23, 9), (8, 15), (20, 0), (15, 31), (14, 1), (22, 8), (14, 33), (4, 14), (11, 24), (8, 16), (28, 12), (5, 32), (10, 10), (28, 25), (3, 13), (16, 22), (12, 15), (0, 13), (7, 20), (18, 13), (11, 19), (15, 9), (20, 16), (2, 16), (4, 27), (19, 27), (3, 9), (14, 21), (21, 23), (22, 33), (0, 5), (4, 12), (13, 6), (7, 3), (24, 30), (20, 20), (29, 25), (13, 13), (29, 8), (22, 22), (17, 5), (0, 11), (2, 9), (5, 9), (22, 1), (24, 15), (22, 13), (21, 31), (13, 9), (0, 15), (11, 20), (27, 0), (5, 28), (25, 28), (27, 12), (27, 21), (13, 23), (11, 4), (5, 21), (9, 8), (19, 17), (27, 2), (18, 21), (6, 12), (12, 1), (25, 18), (5, 19), (16, 31), (29, 27), (1, 5), (15, 3), (27, 30), (14, 22), (16, 25), (17, 26), (6, 8), (0, 20), (27, 7), (22, 11), (9, 4), (17, 16), (5, 18), (24, 8), (9, 6), (6, 0), (12, 10), (28, 20), (21, 27), (28, 32), (10, 29), (1, 16), (1, 17), (24, 29), (11, 16), (17, 0), (26, 10), (18, 9), (2, 11), (14, 11), (19, 33), (2, 30), (15, 15), (23, 28), (1, 7), (16, 19), (4, 31), (13, 2), (25, 15), (10, 21), (4, 15), (25, 2), (5, 25), (9, 21), (2, 23), (11, 0), (17, 25), (5, 30), (13, 17), (29, 1), (21, 17), (5, 33), (2, 25), (20, 9), (6, 19), (19, 18), (10, 6), (7, 31), (20, 7), (27, 18), (17, 17), (7, 12), (17, 33), (26, 12), (23, 27), (27, 8), (22, 28), (18, 2), (2, 12), (21, 32), (13, 21), (28, 29), (15, 30), (28, 16), (20, 17), (10, 8), (21, 16), (19, 21), (10, 30), (5, 1), (21, 2), (29, 26), (21, 10), (26, 31), (16, 0), (28, 14), (15, 6), (6, 33), (29, 18), (9, 25), (17, 23), (0, 21), (15, 10), (3, 26), (19, 23), (5, 24), (5, 17), (10, 14), (10, 19), (28, 26), (29, 14), (24, 16), (24, 19), (29, 21), (13, 5), (21, 12), (2, 2), (14, 19), (3, 21), (11, 13), (23, 7), (6, 23), (5, 12), (9, 7), (17, 30), (28, 21), (25, 17), (12, 32), (15, 8), (26, 30), (7, 0), (6, 3), (8, 28), (23, 3), (9, 24), (14, 13), (27, 26), (16, 20), (2, 14), (24, 5), (25, 20), (23, 30), (10, 5), (20, 27), (7, 22), (8, 26), (1, 10), (28, 17), (11, 17), (21, 0), (8, 3), (27, 32), (8, 22), (22, 17), (25, 25), (26, 0), (2, 5), (16, 7), (24, 27), (8, 33), (28, 1), (12, 31), (28, 15), (27, 3), (11, 9), (24, 2), (1, 25), (7, 25), (25, 7), (28, 30), (17, 3), (8, 1), (16, 32), (24, 23), (19, 13), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476010", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 37), (35, 24), (26, 35), (12, 27), (25, 25), (14, 33), (0, 8), (35, 19), (32, 36), (15, 2), (7, 6), (26, 6), (23, 20), (9, 20), (29, 4), (5, 6), (0, 6), (26, 13), (12, 24), (12, 33), (4, 3), (32, 15), (33, 28), (19, 0), (23, 5), (29, 29), (1, 28), (11, 35), (12, 11), (10, 33), (28, 11), (11, 3), (3, 34), (16, 2), (24, 9), (24, 35), (24, 31), (30, 27), (22, 34), (21, 12), (20, 16), (30, 4), (22, 9), (30, 17), (5, 34), (26, 14), (10, 18), (11, 12), (19, 36), (33, 16), (10, 13), (17, 22), (7, 1), (25, 13), (17, 5), (1, 22), (0, 9), (28, 7), (26, 2), (28, 30), (30, 11), (21, 5), (19, 2), (0, 4), (27, 9), (15, 12), (19, 6), (16, 8), (12, 2), (18, 35), (2, 16), (34, 25), (19, 17), (29, 25), (27, 1), (33, 29), (11, 10), (16, 13), (25, 20), (25, 30), (1, 14), (27, 24), (8, 9), (4, 7), (8, 0), (9, 26), (9, 21), (18, 28), (34, 6), (24, 6), (22, 29), (28, 3), (32, 33), (5, 8), (25, 6), (14, 27), (24, 34), (16, 32), (6, 27), (34, 24), (13, 18), (22, 37), (34, 27), (17, 23), (33, 33), (4, 27), (6, 30), (14, 26), (12, 12), (7, 14), (13, 32), (25, 31), (23, 26), (30, 23), (23, 3), (13, 16), (33, 3), (8, 31), (18, 11), (14, 36), (28, 27), (28, 21), (3, 15), (11, 5), (11, 29), (5, 36), (17, 2), (10, 24), (34, 18), (26, 19), (19, 33), (17, 12), (16, 21), (20, 7), (3, 23), (23, 14), (17, 18), (15, 27), (1, 5), (22, 11), (19, 13), (2, 17), (0, 15), (35, 31), (15, 17), (4, 26), (10, 10), (21, 13), (13, 4), (16, 26), (28, 4), (7, 25), (29, 26), (33, 21), (16, 33), (21, 33), (30, 15), (24, 0), (4, 36), (15, 37), (29, 15), (12, 34), (19, 16), (12, 26), (31, 36), (2, 30), (21, 3), (12, 17), (19, 4), (1, 26), (33, 20), (3, 1), (23, 10), (7, 20), (1, 4), (6, 33), (7, 23), (18, 19), (4, 11), (5, 33), (30, 13), (28, 17), (29, 3), (29, 31), (30, 0), (4, 10), (26, 4), (0, 19), (31, 26), (11, 18), (6, 17), (25, 4), (26, 11), (14, 4), (34, 20), (32, 0), (8, 12), (31, 14), (7, 30), (34, 21), (11, 14), (5, 0), (27, 35), (32, 26), (25, 26), (7, 29), (0, 20), (26, 31), (7, 33), (4, 13), (8, 13), (25, 7), (10, 5), (30, 8), (24, 10), (21, 11), (10, 11), (10, 22), (29, 30), (1, 19), (25, 19), (6, 19), (0, 21), (28, 1), (29, 1), (1, 21), (28, 13), (32, 28), (9, 29), (15, 19), (19, 12), (11, 7), (24, 29), (20, 29), (35, 13), (26, 16), (29, 19), (1, 7), (5, 13), (3, 12), (35, 20), (15, 6), (7, 37), (4, 17), (9, 7), (23, 32), (26, 15), (17, 35), (28, 18), (23, 27), (28, 24), (6, 25), (32, 24), (24, 24), (17, 34), (14, 10), (5, 12), (25, 36), (16, 12), (34, 33), (9, 30), (18, 10), (34, 17), (15, 28), (32, 2), (26, 27), (2, 19), (17, 20), (15, 13), (29, 14), (35, 25), (14, 31), (24, 21), (3, 8), (31, 30), (34, 12), (3, 3), (24, 30), (10, 26), (29, 23), (27, 25), (13, 25), (11, 2), (33, 24), (18, 2), (2, 27), (17, 31), (31, 11), (6, 3), (2, 4), (14, 35), (15, 7), (24, 22), (35, 6), (11, 25), (0, 37), (12, 16), (31, 34), (16, 30), (14, 29), (17, 24), (5, 7), (19, 18), (32, 29), (28, 32), (15, 30), (29, 2), (6, 5), (28, 6), (30, 26), (12, 6), (30, 14), (21, 8), (30, 28), (6, 36), (8, 14), (30, 31), (5, 35), (9, 22), (20, 19), (32, 31), (34, 9), (6, 6), (21, 25), (30, 20), (22, 5), (6, 13), (26, 21), (2, 11), (0, 16), (22, 27), (4, 23), (34, 35), (31, 9), (25, 1), (15, 32), (35, 32), (28, 37), (9, 5), (5, 22), (1, 36), (9, 34), (19, 1), (7, 13), (1, 16), (5, 20), (16, 16), (27, 33), (22, 21), (1, 35), (7, 22), (34, 32), (33, 13), (28, 0), (19, 7), (4, 33), (7, 32), (12, 35), (21, 6), (4, 5), (11, 26), (5, 29), (7, 16), (26, 0), (15, 16), (24, 1), (21, 17), (8, 24), (30, 22), (20, 30), (13, 22), (22, 23), (27, 18), (23, 36), (18, 6), (3, 11), (15, 1), (31, 4), (24, 14), (10, 20), (13, 36), (32, 13), (32, 3), (32, 37), (25, 3), (14, 25), (16, 27), (26, 24), (32, 7), (28, 5), (4, 15), (13, 10), (12, 10), (23, 1), (7, 5), (9, 24), (3, 30), (35, 0), (18, 0), (28, 33), (29, 24), (21, 32), (25, 32), (17, 17), (7, 19), (6, 15), (17, 15), (24, 3), (11, 16), (26, 9), (15, 20), (16, 3), (21, 28), (23, 9), (8, 18), (9, 25), (23, 31), (18, 14), (27, 5), (33, 9), (21, 36), (26, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "661815", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 13), (17, 8), (4, 13), (23, 20), (31, 8), (28, 22), (21, 19), (32, 19), (11, 7), (14, 11), (29, 26), (10, 7), (18, 9), (20, 5), (14, 22), (27, 8), (33, 26), (0, 19), (1, 15), (24, 21), (24, 18), (33, 3), (14, 7), (14, 2), (19, 4), (8, 20), (27, 7), (21, 13), (0, 11), (11, 15), (18, 25), (29, 11), (25, 23), (7, 8), (6, 10), (17, 2), (33, 16), (3, 19), (5, 6), (16, 0), (20, 20), (13, 23), (31, 6), (32, 5), (11, 14), (4, 2), (21, 18), (8, 12), (21, 2), (25, 22), (5, 26), (1, 8), (28, 26), (25, 28), (18, 5), (33, 10), (29, 3), (24, 17), (15, 13), (28, 16), (11, 13), (21, 5), (15, 6), (12, 11), (14, 24), (0, 17), (32, 2), (32, 17), (30, 0), (32, 9), (15, 8), (6, 16), (9, 12), (28, 29), (25, 1), (21, 4), (24, 6), (9, 14), (4, 8), (2, 28), (29, 28), (17, 25), (25, 12), (6, 18), (26, 5), (14, 15), (17, 29), (12, 28), (28, 8), (28, 0), (6, 26), (7, 21), (27, 2), (1, 21), (15, 9), (3, 0), (6, 29), (27, 16), (7, 13), (17, 28), (9, 27), (21, 0), (29, 13), (0, 9), (26, 22), (33, 28), (17, 14), (22, 27), (12, 20), (22, 18), (12, 10), (7, 14), (15, 15), (7, 11), (27, 11), (14, 10), (5, 23), (13, 12), (17, 15), (5, 25), (2, 0), (12, 0), (2, 4), (13, 15), (26, 15), (21, 14), (7, 5), (10, 4), (32, 7), (3, 15), (19, 29), (15, 1), (29, 20), (4, 6), (11, 8), (30, 11), (11, 29), (8, 27), (26, 12), (16, 11), (25, 9), (20, 16), (32, 11), (17, 19), (28, 1), (20, 29), (29, 8), (25, 2), (17, 26), (30, 3), (25, 24), (3, 14), (29, 17), (9, 20), (23, 14), (4, 14), (14, 9), (28, 2), (1, 10), (18, 17), (15, 17), (15, 24), (16, 1), (16, 29), (3, 9), (11, 25), (31, 28), (23, 6), (15, 25), (25, 26), (26, 4), (21, 25), (8, 15), (9, 7), (29, 7), (3, 24), (15, 11), (30, 19), (27, 10), (23, 7), (11, 24), (10, 22), (11, 27), (3, 3), (8, 13), (27, 29), (18, 20), (10, 10), (2, 8), (23, 0), (4, 10), (16, 6), (6, 17), (1, 28), (4, 25), (28, 4), (19, 18), (11, 20), (9, 23), (22, 19), (24, 7), (2, 16), (6, 23), (2, 9), (6, 5), (19, 13), (18, 26), (13, 22), (4, 15), (0, 20), (15, 20), (13, 29), (0, 25), (17, 11), (31, 5), (33, 1), (28, 23), (6, 1), (13, 11), (5, 14), (22, 16), (32, 22), (26, 17), (27, 24), (14, 6), (33, 7), (12, 22), (18, 13), (21, 9), (32, 4), (10, 0), (11, 0), (30, 23), (13, 5), (31, 24), (31, 25), (23, 10), (0, 28), (12, 8), (10, 9), (3, 12), (13, 19), (30, 9), (9, 8), (12, 12), (28, 12), (14, 29), (12, 16), (2, 10), (10, 29), (32, 15), (12, 9), (5, 19), (29, 12), (17, 9), (19, 0), (25, 13), (19, 10), (4, 21), (25, 10), (18, 0), (3, 2), (3, 20), (12, 27), (9, 16), (21, 3), (2, 20), (6, 22), (22, 5), (33, 15), (0, 16), (23, 9), (28, 21), (14, 18), (3, 1), (1, 6), (27, 6), (22, 25), (3, 26), (24, 28), (31, 21), (27, 17), (27, 19), (26, 26), (28, 20), (13, 28), (30, 8), (16, 14), (31, 26), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908160", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 5), (20, 9), (21, 26), (4, 14), (13, 13), (28, 37), (14, 27), (29, 13), (4, 22), (1, 35), (16, 3), (27, 38), (2, 36), (23, 35), (0, 26), (6, 8), (20, 21), (27, 12), (9, 38), (29, 21), (27, 35), (29, 20), (24, 26), (7, 27), (21, 34), (27, 6), (2, 9), (11, 29), (21, 0), (11, 11), (29, 26), (16, 27), (26, 34), (14, 21), (9, 26), (16, 18), (7, 23), (4, 3), (9, 2), (1, 12), (19, 5), (10, 7), (6, 15), (13, 32), (28, 9), (11, 10), (28, 33), (20, 7), (4, 28), (15, 27), (9, 36), (16, 16), (0, 1), (14, 37), (8, 21), (27, 9), (7, 10), (25, 11), (4, 2), (13, 19), (18, 30), (22, 9), (15, 25), (5, 2), (0, 12), (19, 2), (4, 26), (17, 0), (5, 6), (20, 6), (6, 30), (1, 10), (23, 11), (3, 35), (3, 13), (10, 10), (14, 16), (22, 32), (12, 20), (20, 18), (28, 4), (11, 16), (9, 33), (10, 32), (22, 2), (1, 18), (22, 31), (5, 17), (26, 9), (5, 37), (9, 12), (10, 8), (27, 32), (7, 6), (3, 38), (14, 11), (15, 16), (7, 33), (18, 34), (11, 18), (24, 27), (21, 6), (6, 3), (23, 17), (1, 3), (17, 3), (11, 35), (4, 27), (19, 23), (5, 7), (16, 0), (9, 3), (2, 22), (24, 33), (13, 31), (15, 0), (21, 11), (10, 3), (20, 20), (26, 28), (19, 19), (1, 32), (8, 12), (14, 35), (18, 8), (14, 22), (4, 13), (21, 36), (9, 23), (21, 38), (19, 6), (27, 25), (0, 5), (24, 35), (9, 10), (29, 5), (23, 7), (15, 38), (24, 6), (28, 5), (9, 30), (3, 30), (11, 3), (9, 37), (19, 37), (9, 35), (10, 34), (29, 11), (28, 14), (15, 32), (25, 2), (22, 3), (15, 8), (2, 8), (20, 17), (9, 8), (29, 4), (6, 36), (3, 3), (29, 12), (1, 20), (14, 30), (23, 21), (27, 37), (28, 15), (28, 20), (22, 1), (27, 4), (28, 18), (0, 30), (27, 21), (12, 22), (10, 11), (27, 34), (26, 11), (25, 33), (20, 3), (16, 1), (18, 20), (26, 1), (10, 1), (28, 23), (4, 16), (6, 22), (23, 20), (7, 9), (12, 19), (23, 0), (21, 18), (1, 23), (0, 15), (26, 18), (21, 3), (27, 31), (25, 24), (18, 37), (27, 28), (23, 26), (28, 13), (5, 13), (6, 13), (0, 34), (5, 31), (7, 4), (15, 37), (13, 30), (25, 25), (8, 33), (26, 38), (2, 17), (12, 29), (25, 7), (14, 34), (15, 17), (27, 16), (7, 38), (17, 11), (22, 16), (18, 5), (28, 10), (4, 5), (0, 10), (10, 37), (7, 32), (1, 38), (23, 34), (14, 38), (24, 4), (21, 25), (10, 15), (2, 16), (9, 22), (18, 29), (4, 35), (24, 2), (13, 37), (22, 8), (22, 28), (23, 31), (10, 4), (14, 31), (7, 22), (10, 21), (14, 28), (9, 1), (10, 0), (2, 27), (3, 34), (8, 29), (21, 28), (26, 5), (5, 8), (17, 13), (29, 30), (15, 19), (4, 18), (20, 26), (4, 33), (19, 12), (15, 29), (23, 28), (1, 36), (16, 5), (12, 18), (28, 3), (0, 35), (8, 5), (24, 37), (3, 33), (20, 14), (14, 14), (14, 29), (0, 9), (2, 35), (28, 22), (12, 1), (14, 6), (9, 31), (7, 5), (18, 15), (2, 38), (16, 15), (26, 27), (29, 9), (26, 10), (16, 2), (23, 8), (0, 19), (14, 7), (10, 13), (29, 8), (17, 34), (27, 1), (9, 19), (26, 32), (4, 29), (11, 24), (18, 13), (4, 11), (27, 36), (16, 24), (12, 11), (5, 38), (22, 27), (20, 0), (15, 11), (22, 15), (16, 32), (1, 8), (9, 9), (5, 28), (14, 33), (24, 38), (10, 23), (9, 25), (27, 0), (28, 11), (12, 36), (21, 23), (19, 34), (24, 30), (11, 26), (16, 34), (28, 21), (11, 4), (12, 35), (20, 36), (21, 12), (10, 22), (10, 20), (23, 15), (0, 7), (3, 9), (7, 28), (18, 31), (15, 20), (12, 4), (0, 36), (20, 25), (5, 30), (10, 25), (17, 38), (7, 3), (3, 17), (24, 5), (2, 26), (6, 28), (3, 31), (27, 5), (5, 34), (22, 21), (12, 5), (20, 10), (21, 33), (1, 15), (6, 24), (17, 8), (23, 6), (22, 0), (23, 37), (2, 1), (16, 21), (14, 13), (7, 2), (16, 31), (17, 21), (28, 29), (7, 36), (20, 15), (6, 0), (8, 31), (5, 1), (20, 24), (28, 17), (4, 7), (29, 17), (8, 17), (13, 26), (5, 18), (15, 31), (22, 36), (7, 21), (15, 35), (10, 16), (27, 24), (21, 32), (13, 16), (22, 11), (3, 22), (16, 38), (19, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "901152", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 0), (6, 28), (7, 28), (14, 1), (23, 28), (12, 6), (31, 10), (20, 17), (24, 33), (5, 4), (23, 18), (14, 18), (12, 11), (22, 21), (18, 14), (5, 5), (11, 21), (26, 14), (32, 8), (20, 9), (14, 26), (30, 31), (14, 5), (33, 17), (27, 11), (4, 32), (24, 25), (32, 20), (10, 7), (7, 4), (19, 12), (17, 8), (34, 10), (27, 19), (3, 2), (19, 19), (13, 19), (5, 32), (14, 2), (16, 15), (28, 22), (17, 4), (12, 10), (27, 4), (1, 18), (18, 8), (34, 29), (1, 5), (21, 16), (18, 26), (26, 11), (20, 7), (7, 33), (12, 21), (27, 2), (21, 25), (10, 0), (28, 23), (23, 0), (25, 26), (33, 33), (31, 0), (26, 16), (36, 10), (23, 20), (36, 24), (13, 2), (13, 27), (31, 21), (9, 1), (24, 0), (16, 6), (9, 27), (25, 8), (3, 15), (35, 14), (6, 33), (4, 17), (20, 0), (13, 23), (0, 20), (14, 29), (11, 22), (22, 27), (3, 29), (17, 18), (22, 26), (35, 12), (8, 4), (32, 2), (4, 22), (3, 26), (16, 27), (14, 13), (19, 16), (27, 32), (31, 26), (8, 6), (18, 16), (5, 33), (15, 21), (27, 3), (30, 23), (35, 9), (7, 1), (27, 30), (29, 32), (26, 6), (35, 11), (0, 33), (3, 30), (32, 25), (25, 14), (5, 30), (19, 24), (8, 33), (8, 28), (17, 6), (1, 3), (6, 23), (34, 14), (26, 10), (31, 9), (4, 3), (10, 24), (20, 18), (30, 3), (16, 20), (34, 12), (17, 25), (19, 32), (24, 27), (0, 12), (15, 3), (23, 16), (13, 5), (11, 17), (17, 17), (23, 8), (28, 14), (8, 32), (26, 7), (21, 27), (4, 5), (3, 14), (1, 25), (24, 10), (11, 16), (24, 21), (21, 23), (11, 6), (1, 12), (16, 13), (25, 20), (24, 20), (22, 32), (21, 20), (29, 31), (6, 21), (5, 3), (23, 15), (27, 5), (33, 9), (25, 6), (23, 23), (6, 13), (24, 30), (32, 12), (27, 7), (15, 27), (32, 0), (11, 2), (10, 29), (30, 9), (29, 1), (22, 30), (13, 31), (5, 27), (24, 16), (20, 4), (21, 7), (17, 28), (11, 12), (23, 5), (32, 23), (10, 18), (16, 14), (10, 17), (26, 21), (1, 14), (10, 10), (30, 13), (0, 15), (8, 11), (14, 9), (33, 6), (18, 31), (2, 4), (24, 15), (32, 5), (6, 20), (35, 26), (34, 31), (17, 11), (32, 1), (25, 18), (13, 17), (29, 22), (4, 21), (3, 24), (2, 15), (10, 5), (36, 29), (35, 13), (2, 23), (14, 25), (8, 14), (31, 28), (0, 4), (4, 13), (2, 7), (9, 9), (10, 4), (24, 26), (5, 25), (10, 25), (4, 4), (27, 25), (1, 24), (19, 2), (5, 8), (14, 22), (15, 14), (15, 32), (3, 25), (29, 20), (19, 10), (0, 27), (19, 21), (15, 23), (19, 15), (5, 15), (25, 3), (27, 18), (22, 15), (19, 25), (34, 3), (33, 20), (30, 29), (1, 22), (19, 29), (14, 7), (29, 29), (13, 29), (23, 11), (28, 1), (3, 31), (12, 22), (9, 11), (30, 27), (33, 13), (15, 0), (23, 30), (25, 27), (32, 26), (21, 24), (21, 29), (34, 11), (12, 29), (35, 17), (30, 16), (22, 18), (0, 5), (35, 6), (25, 16), (4, 26), (33, 29), (2, 25), (7, 23), (3, 13), (7, 11), (36, 21), (1, 27), (20, 21), (6, 3), (17, 0), (16, 33), (8, 0), (35, 21), (22, 17), (32, 24), (2, 32), (29, 13), (5, 24), (19, 4), (30, 25), (6, 5), (20, 16), (24, 22), (22, 33), (33, 15), (0, 25), (11, 33), (6, 26), (34, 8), (26, 20), (33, 27), (21, 2), (21, 21), (6, 27), (27, 15), (30, 15), (29, 6), (36, 0), (5, 17), (18, 21), (33, 4), (29, 15), (20, 24), (20, 20), (33, 16), (32, 17), (29, 23), (26, 9), (11, 5), (12, 8), (23, 19), (13, 22), (6, 14), (3, 32), (36, 23), (25, 1), (32, 6), (30, 14), (17, 22), (21, 6), (28, 6), (27, 9), (35, 19), (9, 2), (34, 32), (33, 31), (4, 2), (26, 1), (3, 28), (30, 8), (9, 30), (18, 25), (0, 32), (1, 31), (16, 8), (7, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613088", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), 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), (29, 12), (32, 26), (2, 26), (17, 5), (30, 12), (29, 4), (14, 28), (4, 19), (6, 17), (6, 13), (13, 9), (34, 12), (9, 21), (15, 13), (6, 23), (0, 22), (27, 7), (29, 30), (17, 21), (26, 7), (1, 7), (23, 2), (21, 12), (14, 2), (9, 2), (7, 25), (25, 25), (34, 1), (24, 5), (27, 14), (27, 22), (17, 4), (24, 0), (34, 7), (26, 14), (7, 23), (33, 29), (29, 15), (10, 13), (11, 8), (3, 8), (10, 17), (8, 4), (17, 25), (27, 23), (10, 16), (22, 26), (21, 26), (5, 14), (1, 25), (26, 5), (27, 9), (28, 16), (15, 30), (7, 6), (29, 18), (20, 11), (15, 24), (27, 26), (4, 13), (27, 6), (24, 28), (28, 11), (13, 8), (1, 21), (7, 7), (31, 6), (27, 25), (17, 18), (14, 15), (12, 15), (16, 24), (20, 29), (20, 18), (11, 27), (15, 18), (23, 20), (9, 4), (12, 18), (10, 12), (14, 11), (13, 21), (16, 27), (1, 4), (19, 3), (18, 13), (15, 3), (32, 20), (30, 22), (0, 23), (33, 5), (25, 8), (2, 11), (19, 11), (14, 22), (7, 16), (15, 16), (16, 21), (3, 9), (8, 26), (7, 10), (8, 30), (29, 10), (28, 4), (10, 18), (27, 11), (16, 3), (30, 1), (5, 28), (18, 23), (15, 28), (30, 15), (12, 2), (6, 9), (22, 22), (23, 29), (34, 24), (30, 27), (26, 15), (10, 28), (18, 2), (24, 13), (30, 24), (27, 28), (0, 9), (8, 6), (32, 14), (12, 19), (21, 27), (29, 0), (26, 18), (4, 30), (25, 12), (11, 22), (19, 30), (24, 14), (15, 27), (14, 1), (6, 28), (23, 17), (19, 1), (24, 12), (19, 9), (26, 24), (22, 6), (27, 4), (34, 18), (34, 9), (23, 10), (5, 6), (8, 29), (11, 26), (10, 14), (26, 19), (30, 4), (21, 2), (20, 10), (2, 21), (2, 13), (19, 13), (33, 12), (8, 19), (33, 13), (6, 24), (33, 10), (5, 16), (24, 10), (30, 29), (25, 28), (2, 25), (17, 14), (2, 27), (1, 16), (32, 29), (10, 5), (14, 25), (26, 1), (21, 9), (14, 23), (4, 20), (3, 27), (5, 15), (34, 2), (27, 20), (1, 2), (13, 3), (27, 2), (34, 23), (28, 27), (33, 6), (19, 18), (3, 30), (10, 6), (17, 17), (7, 11), (10, 9), (33, 17), (8, 2), (3, 25), (24, 26), (16, 8), (26, 10), (18, 8), (19, 12), (11, 24), (15, 17), (31, 2), (20, 9), (7, 18), (17, 20), (21, 4), (7, 17), (29, 26), (3, 23), (30, 11), (28, 22), (0, 18), (7, 15), (21, 13), (21, 25), (6, 3), (34, 11), (21, 18), (22, 14), (21, 10), (2, 24), (2, 19), (24, 2), (20, 22), (27, 10), (20, 6), (32, 10), (11, 15), (4, 16), (21, 1), (6, 18), (17, 11), (19, 2), (33, 25), (9, 25), (9, 22), (19, 8), (1, 30), (33, 1), (3, 11), (27, 29), (29, 28), (32, 23), (19, 24), (7, 13), (34, 5), (16, 22), (8, 5), (34, 25), (34, 6), (29, 17), (26, 25), (6, 27), (6, 14), (6, 25), (34, 3), (25, 9), (15, 14), (2, 20), (19, 0), (7, 1), (0, 2), (15, 7), (32, 8), (32, 28), (10, 15), (32, 17), (26, 6), (25, 27), (33, 28), (24, 15), (29, 2), (18, 9), (19, 6), (33, 0), (10, 25), (7, 27), (20, 0), (25, 22), (22, 11), (18, 25), (30, 23), (29, 3), (34, 14), (21, 22), (27, 1), (29, 16), (15, 2), (9, 20), (13, 29), (29, 8), (9, 26), (15, 8), (9, 27), (21, 24), (24, 3), (4, 18), (30, 18), (6, 7), (8, 18), (2, 15), (29, 21), (31, 14), (28, 17), (20, 24), (4, 27), (25, 3), (1, 1), (18, 28), (32, 27), (20, 26), (30, 19), (28, 5), (21, 3), (6, 0), (6, 5), (2, 5), (16, 28), (23, 0), (5, 18), (32, 25), (10, 2), (2, 9), (28, 1), (6, 12), (10, 4), (13, 30), (17, 6), (22, 5), (13, 24), (14, 4), (25, 18), (0, 3), (21, 0), (2, 18), (14, 20), (12, 23), (3, 29), (13, 19), (2, 23), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986624", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (24, 11), (20, 30), (0, 3), (16, 15), (4, 35), (15, 6), (24, 12), (7, 6), (20, 23), (31, 26), (26, 2), (13, 33), (17, 15), (14, 3), (9, 22), (19, 15), (29, 14), (33, 5), (11, 12), (7, 13), (30, 33), (13, 26), (8, 13), (4, 31), (15, 21), (4, 14), (1, 24), (28, 16), (28, 11), (29, 22), (13, 35), (23, 14), (26, 32), (10, 26), (28, 31), (5, 3), (15, 18), (30, 4), (7, 34), (5, 2), (16, 23), (27, 28), (28, 30), (7, 3), (17, 26), (3, 3), (26, 17), (3, 11), (15, 31), (0, 27), (24, 7), (25, 2), (13, 6), (22, 24), (16, 16), (13, 28), (20, 8), (6, 34), (1, 15), (21, 15), (12, 19), (24, 36), (32, 17), (20, 5), (1, 19), (4, 10), (2, 12), (22, 33), (20, 21), (33, 21), (2, 13), (5, 20), (17, 19), (18, 34), (20, 18), (16, 36), (8, 28), (5, 13), (23, 15), (19, 23), (17, 14), (6, 20), (2, 15), (8, 17), (15, 26), (27, 23), (22, 27), (25, 10), (32, 2), (12, 22), (6, 12), (27, 13), (17, 22), (15, 19), (0, 13), (10, 29), (6, 30), (24, 5), (22, 35), (21, 30), (20, 15), (1, 28), (1, 11), (10, 8), (17, 0), (30, 19), (27, 19), (23, 10), (22, 6), (2, 31), (21, 24), (26, 13), (31, 19), (30, 28), (0, 1), (19, 5), (33, 3), (3, 32), (14, 23), (31, 12), (26, 36), (31, 34), (27, 3), (19, 25), (18, 28), (24, 13), (27, 18), (13, 7), (32, 30), (10, 20), (12, 15), (9, 1), (3, 16), (6, 11), (14, 26), (21, 14), (8, 34), (31, 14), (26, 25), (5, 0), (3, 27), (17, 1), (7, 14), (30, 7), (29, 1), (14, 16), (16, 17), (20, 13), (23, 29), (22, 11), (6, 6), (26, 29), (18, 20), (7, 25), (13, 1), (11, 22), (23, 35), (0, 16), (24, 30), (26, 15), (18, 30), (5, 25), (12, 18), (28, 24), (21, 36), (9, 18), (5, 24), (7, 19), (13, 15), (13, 34), (20, 36), (12, 1), (27, 26), (24, 23), (32, 27), (29, 32), (26, 19), (11, 13), (25, 33), (2, 24), (5, 30), (20, 25), (0, 5), (28, 35), (0, 26), (15, 12), (32, 19), (24, 26), (23, 21), (22, 5), (32, 28), (11, 33), (30, 5), (24, 6), (9, 27), (31, 24), (4, 4), (17, 35), (2, 32), (7, 0), (30, 6), (12, 0), (6, 2), (22, 15), (0, 4), (22, 23), (32, 3), (10, 10), (2, 34), (23, 13), (20, 19), (8, 26), (15, 24), (8, 35), (15, 20), (8, 7), (7, 36), (32, 24), (21, 16), (6, 28), (18, 22), (15, 28), (15, 1), (2, 19), (24, 27), (1, 18), (8, 36), (16, 13), (24, 28), (25, 9), (24, 31), (33, 2), (22, 3), (32, 11), (14, 31), (9, 7), (13, 16), (21, 35), (11, 36), (31, 35), (27, 34), (9, 5), (16, 24), (23, 30), (15, 14), (14, 14), (16, 12), (25, 13), (0, 25), (30, 30), (22, 7), (32, 0), (12, 24), (18, 10), (23, 20), (28, 25), (6, 8), (6, 23), (23, 27), (20, 12), (11, 11), (33, 33), (21, 9), (6, 27), (7, 27), (18, 19), (13, 4), (1, 5), (21, 22), (2, 5), (0, 29), (0, 14), (12, 3), (1, 20), (1, 1), (33, 22), (11, 34), (9, 9), (30, 13), (30, 34), (27, 30), (14, 30), (4, 33), (24, 15), (31, 31), (23, 25), (22, 32), (12, 8), (27, 1), (24, 3), (33, 35), (28, 4), (4, 32), (16, 14), (20, 6), (31, 9), (28, 15), (13, 32), (16, 35), (4, 13), (14, 34), (28, 5), (17, 30), (19, 28), (21, 3), (2, 11), (10, 22), (31, 2), (8, 2), (31, 22), (30, 2), (13, 20), (15, 30), (11, 15), (6, 1), (18, 21), (14, 27), (7, 5), (22, 25), (32, 23), (1, 6), (23, 34), (2, 9), (14, 35), (11, 6), (18, 7), (0, 36), (9, 10), (15, 36), (18, 12), (13, 18), (15, 33), (25, 1), (29, 25), (13, 11), (23, 26), (17, 17), (17, 11), (27, 4), (29, 24), (28, 9), (18, 14), (9, 14), (19, 34), (18, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551808", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 34), (31, 8), (33, 15), (26, 18), (12, 8), (6, 19), (12, 0), (6, 22), (6, 8), (16, 29), (10, 21), (29, 1), (15, 6), (22, 13), (27, 20), (22, 30), (4, 33), (2, 35), (16, 16), (9, 10), (14, 9), (19, 23), (9, 15), (7, 25), (29, 24), (31, 27), (5, 32), (4, 19), (24, 23), (22, 4), (13, 8), (3, 21), (1, 32), (25, 21), (21, 11), (22, 27), (14, 11), (4, 13), (0, 32), (28, 9), (18, 20), (28, 12), (32, 14), (30, 9), (29, 6), (6, 31), (20, 27), (8, 2), (13, 35), (35, 24), (17, 28), (16, 6), (25, 27), (13, 13), (1, 19), (3, 17), (20, 3), (27, 18), (15, 27), (16, 30), (28, 18), (21, 7), (4, 27), (9, 13), (23, 7), (6, 35), (6, 29), (17, 19), (11, 5), (8, 25), (5, 28), (13, 22), (35, 25), (33, 0), (3, 11), (13, 23), (13, 12), (6, 20), (7, 2), (15, 7), (31, 35), (22, 12), (5, 11), (2, 32), (31, 24), (27, 25), (28, 28), (13, 0), (24, 12), (27, 3), (31, 16), (9, 8), (1, 9), (30, 18), (4, 18), (29, 16), (5, 3), (17, 22), (9, 17), (16, 12), (19, 17), (34, 32), (24, 33), (35, 28), (15, 34), (16, 35), (31, 18), (15, 8), (20, 5), (23, 28), (17, 32), (19, 24), (2, 8), (31, 28), (18, 4), (34, 30), (3, 0), (11, 21), (23, 2), (22, 16), (17, 18), (30, 27), (17, 12), (22, 6), (9, 25), (27, 24), (26, 34), (19, 5), (13, 1), (30, 17), (34, 33), (33, 34), (10, 8), (20, 22), (25, 18), (17, 27), (26, 9), (1, 4), (14, 4), (33, 17), (4, 1), (11, 22), (18, 22), (35, 29), (11, 18), (14, 26), (34, 10), (7, 17), (7, 12), (35, 11), (16, 0), (8, 14), (21, 3), (15, 29), (2, 26), (26, 31), (30, 4), (7, 28), (2, 34), (15, 12), (4, 6), (2, 12), (35, 30), (10, 3), (8, 31), (12, 35), (31, 11), (4, 14), (4, 32), (7, 4), (22, 28), (14, 29), (9, 21), (3, 18), (22, 34), (9, 18), (16, 19), (19, 30), (7, 30), (35, 19), (26, 13), (1, 11), (33, 18), (33, 23), (2, 6), (7, 0), (22, 26), (27, 0), (2, 22), (14, 28), (21, 32), (34, 12), (16, 10), (1, 26), (2, 33), (7, 34), (21, 28), (14, 10), (21, 18), (0, 22), (10, 22), (31, 17), (3, 33), (23, 16), (11, 25), (30, 29), (0, 17), (14, 25), (1, 24), (22, 11), (9, 16), (19, 20), (28, 8), (15, 14), (15, 1), (5, 4), (30, 8), (5, 15), (15, 23), (2, 21), (15, 3), (2, 24), (31, 6), (24, 6), (31, 23), (17, 25), (2, 10), (20, 16), (20, 20), (20, 19), (35, 21), (18, 35), (14, 27), (28, 5), (35, 0), (17, 1), (18, 29), (25, 28), (12, 20), (33, 22), (17, 35), (12, 1), (17, 21), (24, 21), (8, 34), (4, 35), (1, 25), (25, 12), (4, 26), (28, 21), (29, 32), (27, 6), (19, 18), (28, 7), (26, 23), (30, 11), (16, 7), (26, 24), (15, 10), (18, 13), (29, 12), (11, 24), (13, 25), (29, 29), (23, 17), (11, 16), (3, 15), (3, 12), (24, 19), (7, 29), (15, 32), (18, 0), (0, 3), (2, 29), (23, 0), (28, 6), (2, 28), (5, 19), (15, 24), (12, 34), (28, 20), (25, 30), (25, 4), (34, 25), (34, 5), (13, 26), (31, 33), (29, 30), (1, 18), (5, 14), (18, 17), (2, 2), (24, 27), (20, 28), (15, 18), (7, 22), (6, 15), (10, 4), (23, 30), (1, 29), (31, 19), (35, 7), (4, 22), (1, 0), (22, 7), (1, 27), (34, 7), (24, 16), (34, 22), (26, 21), (6, 33), (25, 3), (10, 29), (10, 1), (18, 14), (27, 2), (4, 12), (28, 3), (16, 14), (21, 19), (24, 13), (10, 7), (32, 7), (29, 25), (0, 6), (13, 24), (27, 4), (14, 2), (1, 22), (18, 18), (2, 31), (34, 29), (14, 6), (22, 5), (2, 3), (5, 25), (22, 14), (30, 10), (8, 11), (33, 25), (18, 11), (1, 34), (0, 24), (16, 17), (11, 20), (20, 13), (15, 2), (15, 31), (24, 34), (35, 12), (5, 5), (28, 14), (18, 26), (11, 0), (32, 24), (0, 28), (10, 6), (18, 19), (12, 25), (5, 29), (21, 29), (1, 31), (21, 0), (17, 9), (9, 35), (26, 16), (32, 0), (26, 7), (11, 9), (32, 2), (8, 8), (8, 28), (34, 20), (15, 19), (35, 27), (12, 28), (29, 31), (6, 16), (15, 0), (24, 9), (6, 3), (15, 15), (28, 33), (33, 27), (23, 10), (32, 29), (8, 7), (26, 6), (17, 5), (19, 19), (0, 26), (27, 12), (11, 2), (17, 13), (29, 10), (21, 8), (6, 26), (25, 34), (8, 4), (22, 29), (18, 28), (26, 20), (34, 11), (12, 2), (35, 2), (16, 25), (30, 15), (34, 3), (22, 2), (23, 25), (7, 23), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69120", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 34), (1, 25), (29, 7), (4, 36), (24, 12), (8, 13), (19, 4), (11, 35), (30, 25), (10, 12), (8, 24), (8, 7), (6, 2), (27, 31), (26, 24), (18, 35), (8, 31), (0, 33), (18, 3), (9, 13), (7, 2), (29, 15), (9, 5), (11, 28), (17, 22), (8, 9), (7, 1), (14, 34), (11, 13), (13, 22), (8, 4), (10, 27), (10, 24), (25, 32), (4, 34), (19, 32), (10, 34), (26, 16), (21, 17), (4, 4), (27, 11), (4, 17), (15, 6), (21, 5), (23, 16), (15, 7), (7, 23), (9, 31), (22, 36), (2, 33), (9, 26), (11, 36), (19, 8), (6, 35), (19, 9), (4, 20), (8, 2), (14, 22), (10, 21), (7, 3), (24, 21), (22, 19), (8, 3), (6, 1), (30, 27), (0, 7), (2, 3), (3, 10), (8, 22), (5, 5), (25, 2), (14, 12), (29, 35), (24, 5), (1, 30), (28, 8), (3, 7), (16, 5), (28, 27), (12, 34), (8, 30), (11, 21), (3, 28), (14, 0), (30, 32), (11, 29), (24, 6), (5, 30), (11, 18), (4, 11), (27, 25), (7, 18), (21, 30), (2, 7), (17, 4), (23, 31), (28, 12), (7, 32), (18, 18), (29, 31), (3, 20), (12, 16), (25, 8), (29, 21), (12, 22), (20, 25), (14, 2), (4, 24), (3, 24), (5, 32), (5, 8), (20, 9), (21, 27), (16, 22), (1, 8), (18, 31), (8, 18), (9, 0), (10, 7), (0, 32), (8, 35), (23, 6), (12, 8), (11, 12), (25, 12), (13, 2), (25, 33), (15, 30), (26, 18), (24, 28), (29, 33), (10, 23), (16, 4), (28, 34), (14, 18), (0, 23), (3, 6), (24, 7), (20, 33), (26, 19), (5, 1), (27, 24), (23, 24), (8, 11), (2, 12), (8, 17), (5, 28), (14, 14), (0, 15), (3, 5), (29, 34), (1, 12), (30, 17), (28, 16), (26, 4), (26, 28), (16, 6), (5, 13), (26, 14), (30, 23), (17, 31), (12, 13), (18, 8), (2, 30), (20, 12), (26, 8), (22, 25), (13, 15), (8, 8), (12, 19), (10, 2), (26, 25), (0, 12), (25, 6), (26, 7), (6, 33), (12, 31), (22, 33), (16, 33), (13, 8), (2, 17), (30, 2), (26, 35), (6, 22), (27, 27), (27, 19), (15, 21), (2, 31), (20, 14), (6, 7), (11, 10), (24, 9), (9, 22), (27, 20), (7, 14), (10, 25), (6, 36), (18, 14), (13, 36), (17, 14), (18, 24), (25, 7), (5, 2), (29, 5), (9, 8), (5, 23), (24, 27), (21, 6), (20, 32), (20, 29), (7, 20), (15, 28), (13, 19), (10, 4), (13, 26), (6, 6), (13, 29), (23, 0), (16, 0), (15, 32), (17, 10), (2, 19), (14, 13), (24, 36), (25, 9), (7, 9), (23, 4), (22, 11), (18, 33), (14, 36), (13, 0), (20, 1), (19, 30), (19, 35), (12, 29), (8, 27), (22, 32), (20, 15), (15, 33), (24, 14), (17, 36), (1, 11), (7, 31), (5, 17), (1, 34), (19, 36), (17, 30), (21, 3), (28, 22), (26, 22), (10, 28), (3, 18), (25, 29), (28, 31), (12, 0), (21, 29), (1, 24), (28, 26), (30, 20), (0, 30), (18, 30), (22, 6), (20, 30), (29, 11), (3, 23), (25, 25), (12, 1), (18, 29), (16, 9), (30, 0), (3, 13), (27, 5), (18, 20), (10, 11), (21, 2), (21, 23), (27, 6), (11, 14), (22, 8), (16, 19), (3, 2), (10, 8), (23, 32), (15, 16), (24, 8), (18, 21), (8, 33), (25, 16), (4, 13), (20, 0), (18, 22), (5, 19), (21, 12), (26, 3), (6, 27), (5, 29), (19, 33), (0, 25), (18, 0), (10, 35), (16, 31), (12, 30), (17, 6), (30, 1), (5, 20), (8, 29), (0, 29), (3, 3), (9, 34), (28, 30), (10, 36), (27, 4), (1, 22), (10, 20), (11, 17), (21, 9), (7, 28), (22, 22), (24, 15), (19, 22), (16, 2), (1, 10), (11, 9), (27, 33), (15, 1), (21, 8), (30, 26), (16, 21), (24, 29), (26, 33), (2, 18), (3, 1), (18, 4), (10, 19), (21, 13), (27, 1), (8, 1), (11, 5), (6, 32), (0, 8), (28, 20), (3, 12), (0, 3), (20, 31), (6, 8), (13, 11), (14, 26), (29, 19), (13, 9), (16, 10), (26, 5), (15, 5), (16, 3), (23, 36), (28, 25), (15, 27), (14, 31), (28, 4), (25, 15), (11, 15), (21, 22), (4, 8), (1, 19), (29, 27), (13, 16), (18, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706560", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 26), (21, 33), (0, 19), (13, 19), (19, 10), (16, 14), (5, 23), (27, 8), (26, 7), (18, 32), (7, 22), (15, 26), (16, 13), (21, 30), (12, 10), (26, 33), (3, 10), (26, 29), (11, 17), (22, 25), (25, 28), (21, 9), (25, 23), (3, 14), (2, 25), (25, 0), (15, 2), (25, 19), (24, 30), (25, 21), (18, 4), (27, 14), (5, 26), (17, 17), (18, 14), (26, 24), (13, 14), (16, 12), (15, 10), (1, 32), (10, 14), (7, 24), (17, 0), (21, 3), (2, 32), (11, 16), (17, 33), (12, 7), (2, 28), (23, 1), (11, 11), (20, 25), (29, 8), (7, 2), (4, 6), (13, 11), (16, 8), (17, 18), (19, 34), (9, 22), (15, 24), (10, 24), (3, 11), (6, 9), (4, 3), (16, 31), (7, 33), (7, 12), (18, 8), (24, 2), (5, 29), (28, 20), (17, 23), (7, 25), (3, 0), (29, 6), (1, 15), (6, 5), (16, 25), (11, 26), (6, 21), (6, 10), (14, 7), (17, 22), (5, 21), (19, 16), (3, 9), (19, 0), (8, 14), (13, 7), (1, 27), (2, 30), (22, 24), (5, 30), (2, 7), (13, 16), (23, 11), (18, 19), (14, 13), (20, 23), (15, 11), (25, 1), (15, 0), (13, 24), (26, 34), (17, 27), (10, 3), (0, 8), (27, 9), (27, 26), (21, 34), (11, 29), (4, 24), (1, 28), (22, 32), (7, 20), (10, 7), (20, 17), (22, 5), (24, 18), (15, 30), (21, 5), (19, 12), (28, 19), (1, 19), (11, 2), (20, 30), (19, 13), (1, 25), (29, 24), (14, 16), (0, 17), (26, 10), (29, 22), (2, 19), (6, 34), (11, 30), (24, 25), (6, 17), (15, 22), (18, 17), (13, 31), (26, 6), (14, 9), (16, 33), (2, 22), (28, 2), (8, 5), (12, 2), (12, 26), (17, 8), (10, 18), (7, 11), (24, 9), (14, 30), (6, 1), (21, 13), (25, 16), (27, 30), (9, 21), (16, 23), (10, 2), (13, 22), (27, 15), (9, 14), (23, 5), (10, 20), (17, 14), (24, 14), (22, 19), (3, 25), (6, 14), (16, 32), (20, 3), (18, 23), (21, 27), (13, 17), (20, 34), (28, 25), (14, 21), (25, 8), (20, 8), (20, 22), (5, 11), (2, 27), (9, 32), (14, 17), (2, 14), (24, 28), (7, 10), (25, 32), (4, 33), (9, 7), (29, 28), (12, 16), (23, 14), (2, 3), (25, 12), (3, 4), (19, 6), (8, 27), (22, 27), (18, 21), (1, 18), (2, 13), (15, 18), (1, 7), (13, 5), (18, 24), (10, 19), (10, 29), (5, 14), (6, 31), (7, 34), (25, 11), (8, 16), (15, 16), (17, 20), (17, 7), (12, 1), (29, 27), (11, 21), (19, 21), (0, 28), (10, 25), (20, 27), (5, 31), (22, 30), (23, 28), (10, 4), (9, 12), (21, 14), (1, 23), (1, 24), (0, 4), (14, 8), (26, 11), (24, 23), (13, 20), (28, 30), (8, 30), (2, 29), (17, 3), (4, 16), (26, 19), (19, 19), (18, 29), (22, 22), (24, 1), (15, 28), (19, 17), (9, 10), (13, 8), (1, 34), (1, 20), (21, 11), (19, 20), (24, 32), (23, 6), (20, 1), (5, 24), (10, 8), (16, 30), (22, 8), (14, 15), (0, 33), (20, 29), (0, 32), (16, 1), (6, 22), (15, 4), (2, 9), (1, 30), (20, 0), (11, 31), (23, 33), (26, 17), (0, 13), (14, 11), (9, 30), (15, 17), (21, 15), (20, 18), (24, 5), (0, 26), (6, 27), (23, 18), (22, 13), (24, 13), (21, 4), (15, 5), (10, 28), (20, 19), (1, 5), (2, 4), (2, 16), (28, 3), (0, 20), (28, 26), (12, 28), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979200", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), 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), (0, 11), (30, 12), (3, 22), (22, 29), (7, 11), (13, 21), (20, 20), (21, 17), (29, 23), (15, 14), (3, 1), (13, 31), (31, 12), (3, 17), (27, 15), (0, 14), (26, 19), (6, 7), (28, 14), (1, 28), (0, 5), (12, 2), (7, 26), (0, 1), (14, 29), (31, 29), (4, 30), (31, 3), (24, 0), (6, 8), (13, 18), (20, 4), (0, 6), (5, 4), (13, 17), (26, 7), (20, 13), (18, 21), (11, 5), (20, 18), (26, 9), (19, 29), (26, 22), (22, 22), (11, 16), (5, 12), (9, 18), (3, 11), (2, 28), (2, 15), (17, 28), (27, 28), (0, 16), (28, 17), (26, 0), (5, 14), (29, 16), (27, 0), (22, 31), (7, 17), (27, 16), (21, 20), (30, 2), (27, 4), (27, 30), (31, 18), (20, 14), (19, 3), (5, 6), (27, 6), (0, 8), (22, 32), (17, 21), (31, 13), (22, 16), (2, 9), (20, 5), (28, 4), (7, 8), (18, 32), (30, 23), (6, 21), (16, 32), (8, 2), (21, 4), (12, 19), (22, 30), (16, 25), (30, 8), (10, 1), (30, 21), (16, 23), (28, 26), (23, 9), (11, 20), (18, 20), (2, 17), (27, 7), (11, 22), (30, 30), (13, 23), (1, 19), (28, 27), (29, 32), (23, 23), (16, 24), (16, 4), (26, 10), (19, 14), (13, 13), (30, 32), (10, 28), (16, 27), (31, 19), (1, 3), (10, 23), (17, 19), (13, 19), (8, 22), (12, 11), (4, 21), (22, 20), (24, 31), (15, 19), (3, 0), (3, 23), (3, 30), (8, 20), (18, 31), (27, 26), (16, 7), (25, 6), (20, 0), (21, 14), (3, 12), (0, 13), (21, 8), (15, 4), (6, 10), (10, 24), (0, 18), (3, 2), (15, 9), (18, 14), (4, 23), (21, 25), (7, 12), (11, 14), (10, 16), (27, 8), (10, 30), (13, 3), (22, 27), (14, 11), (27, 31), (20, 1), (25, 30), (14, 3), (5, 20), (13, 8), (17, 5), (18, 8), (6, 14), (14, 18), (25, 15), (21, 2), (10, 0), (21, 28), (12, 4), (14, 16), (24, 3), (25, 22), (14, 15), (14, 26), (20, 26), (20, 9), (18, 11), (23, 26), (15, 10), (2, 12), (14, 25), (10, 8), (0, 26), (16, 9), (28, 22), (29, 24), (26, 23), (23, 6), (8, 0), (31, 22), (29, 4), (15, 25), (25, 8), (17, 22), (20, 27), (31, 24), (23, 18), (31, 8), (27, 13), (0, 19), (18, 19), (4, 26), (15, 26), (26, 12), (11, 30), (14, 6), (12, 14), (2, 20), (14, 7), (10, 27), (15, 5), (12, 16), (7, 0), (3, 28), (8, 1), (14, 31), (6, 27), (4, 3), (20, 29), (7, 23), (0, 15), (10, 25), (16, 19), (25, 1), (29, 1), (21, 31), (7, 3), (21, 6), (27, 10), (1, 21), (10, 9), (12, 17), (1, 14), (19, 28), (30, 3), (12, 22), (15, 27), (7, 25), (1, 11), (27, 22), (8, 4), (14, 17), (22, 4), (30, 26), (17, 2), (7, 7), (5, 18), (22, 6), (9, 13), (1, 29), (8, 18), (5, 3), (13, 22), (14, 13), (4, 11), (19, 0), (5, 30), (29, 25), (20, 32), (20, 28), (2, 22), (7, 4), (4, 17), (15, 11), (5, 11), (21, 13), (17, 25), (15, 20), (11, 32), (7, 1), (26, 6), (31, 26), (27, 18), (11, 18), (21, 5), (25, 27), (24, 9), (24, 26), (7, 19), (20, 21), (22, 21), (6, 25), (15, 15), (22, 12), (13, 6), (20, 3), (3, 4), (18, 29), (6, 32), (12, 29), (19, 11), (28, 1), (10, 3), (18, 12), (30, 18), (4, 29), (31, 27), (1, 4), (19, 27), (26, 13), (9, 27), (8, 8), (26, 15), (24, 24), (19, 24), (21, 23), (1, 24), (30, 27), (4, 7), (0, 27), (23, 1), (23, 5), (1, 12), (9, 7), (1, 18), (8, 11), (23, 30), (10, 2), (19, 5), (30, 13), (5, 32), (11, 24), (14, 24), (27, 1), (8, 32), (28, 19), (15, 2), (9, 15), (27, 5), (22, 17), (4, 31), (28, 25), (16, 11), (14, 22), (5, 21), (19, 6), (12, 6), (26, 30), (25, 3), (23, 22), (0, 23), (10, 5), (12, 8), (27, 20), (24, 16), (15, 6), (23, 16), (31, 28), (31, 7), (11, 29), (6, 6), (13, 14), (18, 24), (21, 16), (11, 0), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (18, 21), (29, 2), (10, 33), (29, 5), (1, 32), (29, 17), (11, 8), (25, 11), (26, 0), (30, 15), (8, 6), (12, 27), (29, 14), (5, 5), (29, 29), (2, 13), (18, 8), (5, 29), (24, 15), (22, 35), (5, 14), (14, 2), (3, 27), (6, 22), (2, 6), (9, 21), (29, 20), (19, 22), (20, 12), (22, 10), (29, 13), (19, 26), (0, 25), (13, 9), (22, 29), (0, 9), (2, 14), (16, 14), (16, 29), (13, 0), (16, 32), (3, 16), (17, 36), (26, 37), (27, 3), (2, 4), (1, 2), (6, 17), (30, 12), (9, 13), (21, 5), (21, 9), (13, 22), (2, 36), (16, 1), (22, 5), (2, 5), (18, 15), (14, 15), (18, 10), (8, 10), (2, 31), (22, 23), (7, 17), (5, 28), (25, 20), (12, 9), (10, 11), (24, 32), (18, 3), (2, 15), (14, 34), (28, 21), (27, 19), (20, 36), (10, 25), (0, 18), (25, 25), (3, 30), (2, 30), (28, 34), (16, 20), (6, 10), (29, 34), (0, 21), (25, 33), (18, 19), (4, 14), (1, 35), (7, 25), (10, 6), (25, 18), (26, 8), (7, 11), (16, 17), (7, 26), (13, 20), (3, 31), (22, 34), (21, 7), (21, 31), (13, 31), (9, 3), (27, 7), (18, 6), (23, 7), (27, 17), (17, 10), (8, 23), (4, 37), (28, 5), (12, 30), (7, 28), (7, 27), (2, 10), (18, 9), (19, 30), (13, 30), (26, 22), (4, 35), (18, 14), (17, 32), (12, 4), (11, 0), (7, 37), (6, 19), (3, 35), (29, 16), (3, 14), (29, 27), (25, 26), (23, 12), (11, 1), (7, 29), (25, 15), (2, 17), (13, 24), (10, 15), (3, 10), (21, 21), (11, 3), (11, 29), (18, 12), (20, 32), (1, 34), (25, 12), (15, 4), (11, 30), (30, 22), (11, 6), (10, 26), (8, 19), (15, 33), (7, 20), (8, 13), (23, 17), (15, 30), (24, 21), (1, 26), (10, 30), (2, 23), (23, 33), (28, 30), (26, 2), (17, 22), (28, 23), (22, 28), (30, 14), (7, 34), (21, 27), (26, 33), (23, 36), (20, 35), (27, 12), (6, 9), (22, 19), (3, 19), (26, 9), (6, 37), (7, 21), (19, 24), (0, 14), (24, 3), (28, 29), (5, 31), (21, 14), (8, 33), (3, 28), (5, 10), (0, 36), (25, 29), (17, 2), (17, 11), (28, 15), (1, 3), (6, 2), (6, 34), (6, 33), (22, 25), (7, 33), (6, 8), (25, 21), (28, 20), (17, 1), (25, 0), (5, 23), (22, 13), (29, 3), (15, 25), (6, 14), (9, 31), (1, 31), (8, 32), (1, 19), (15, 6), (22, 16), (14, 16), (15, 29), (30, 32), (3, 1), (6, 4), (21, 8), (4, 34), (17, 12), (8, 30), (28, 8), (9, 23), (8, 28), (25, 31), (23, 21), (30, 8), (18, 5), (24, 8), (17, 18), (5, 22), (5, 6), (5, 16), (26, 27), (16, 34), (21, 28), (4, 32), (12, 18), (12, 17), (21, 1), (2, 26), (10, 29), (30, 28), (11, 13), (22, 1), (27, 18), (24, 36), (15, 11), (13, 7), (16, 10), (21, 10), (18, 31), (6, 21), (9, 4), (8, 31), (27, 21), (26, 11), (26, 12), (20, 17), (24, 18), (24, 37), (20, 1), (22, 33), (4, 21), (24, 24), (13, 13), (10, 37), (25, 3), (4, 5), (9, 8), (8, 11), (9, 1), (14, 31), (14, 5), (8, 36), (7, 6), (10, 35), (25, 7), (26, 32), (14, 21), (14, 0), (23, 24), (13, 32), (24, 34), (12, 10), (16, 16), (23, 14), (14, 35), (9, 14), (5, 2), (0, 23), (19, 14), (5, 15), (20, 27), (1, 5), (27, 0), (7, 4), (3, 20), (20, 37), (3, 34), (20, 14), (13, 35), (29, 9), (5, 12), (5, 30), (9, 6), (21, 19), (13, 34), (1, 10), (0, 2), (21, 15), (7, 36), (0, 16), (0, 20), (12, 32), (28, 35), (21, 13), (3, 33), (12, 0), (12, 6), (25, 5), (12, 22), (24, 4), (19, 4), (21, 4), (26, 3), (7, 14), (8, 20), (27, 33), (13, 3), (26, 30), (24, 5), (11, 35), (23, 37), (13, 27), (19, 6), (19, 29), (6, 35), (2, 2), (11, 19), (23, 19), (24, 33), (28, 6), (4, 33), (7, 18), (16, 31), (24, 1), (3, 2), (24, 31), (2, 33), (4, 27), (30, 13), (25, 24), (20, 16), (17, 3), (24, 35), (25, 4), (1, 13), (13, 2), (15, 20), (5, 19), (26, 18), (27, 27), (11, 18), (25, 36), (7, 10), (25, 14), (16, 37), (23, 25), (1, 37), (19, 36), (17, 24), (10, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739200", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 6), (30, 4), (31, 13), (30, 13), (19, 20), (33, 24), (1, 13), (1, 27), (10, 10), (23, 15), (30, 3), (3, 10), (4, 11), (10, 12), (13, 19), (17, 5), (17, 26), (33, 14), (4, 3), (7, 0), (21, 11), (7, 27), (17, 10), (29, 13), (7, 23), (15, 27), (35, 14), (21, 29), (1, 16), (13, 5), (3, 17), (13, 7), (35, 5), (13, 11), (1, 22), (22, 18), (12, 8), (32, 24), (9, 1), (30, 1), (4, 25), (19, 16), (2, 21), (3, 1), (9, 5), (34, 11), (5, 14), (10, 19), (31, 2), (11, 2), (1, 25), (31, 16), (11, 8), (13, 1), (25, 15), (6, 25), (15, 14), (3, 9), (22, 9), (34, 22), (6, 14), (31, 23), (11, 10), (27, 5), (32, 25), (22, 12), (27, 19), (16, 6), (36, 3), (29, 28), (8, 10), (34, 8), (8, 7), (1, 14), (15, 13), (16, 18), (17, 0), (24, 17), (10, 16), (14, 24), (32, 11), (30, 12), (7, 13), (9, 15), (34, 18), (26, 11), (36, 8), (6, 9), (16, 11), (1, 8), (27, 12), (18, 25), (13, 25), (34, 4), (21, 26), (18, 24), (0, 4), (12, 16), (8, 13), (10, 11), (24, 23), (15, 8), (13, 23), (28, 5), (14, 13), (28, 11), (0, 18), (32, 15), (3, 25), (34, 14), (25, 7), (23, 26), (9, 19), (24, 15), (0, 29), (15, 15), (4, 2), (23, 6), (22, 10), (26, 15), (8, 0), (31, 1), (12, 19), (11, 27), (18, 10), (32, 16), (10, 0), (35, 20), (5, 18), (18, 1), (8, 1), (32, 6), (23, 23), (21, 20), (4, 14), (22, 28), (36, 18), (32, 29), (3, 26), (26, 0), (35, 6), (0, 22), (2, 11), (4, 24), (18, 26), (23, 11), (29, 8), (16, 17), (14, 12), (26, 10), (21, 18), (7, 28), (19, 21), (33, 8), (33, 4), (36, 13), (0, 12), (22, 5), (29, 15), (16, 1), (9, 27), (8, 15), (34, 6), (18, 20), (26, 1), (24, 18), (14, 18), (36, 21), (36, 27), (28, 18), (18, 14), (6, 24), (18, 0), (30, 11), (26, 14), (25, 28), (2, 16), (30, 19), (11, 28), (33, 5), (28, 7), (30, 14), (22, 7), (17, 24), (12, 18), (29, 26), (25, 3), (31, 10), (11, 14), (25, 12), (32, 17), (15, 2), (20, 13), (33, 11), (31, 22), (27, 15), (29, 7), (16, 25), (0, 1), (36, 24), (36, 11), (21, 9), (23, 17), (18, 15), (26, 4), (16, 20), (36, 15), (16, 14), (18, 17), (18, 23), (12, 29), (25, 19), (10, 7), (23, 0), (18, 21), (30, 16), (20, 12), (22, 19), (8, 5), (33, 19), (9, 9), (15, 12), (25, 22), (25, 21), (27, 17), (12, 14), (35, 12), (36, 12), (12, 20), (32, 19), (13, 13), (35, 24), (34, 23), (16, 29), (16, 4), (3, 21), (22, 24), (13, 18), (24, 0), (6, 28), (32, 28), (16, 23), (6, 4), (11, 12), (12, 6), (2, 3), (25, 14), (12, 2), (3, 14), (7, 1), (33, 21), (25, 1), (27, 29), (11, 16), (2, 17), (28, 14), (36, 23), (8, 26), (31, 26), (2, 1), (6, 29), (14, 16), (20, 14), (10, 26), (6, 21), (31, 6), (33, 12), (18, 5), (7, 22), (20, 0), (7, 17), (26, 28), (7, 9), (32, 23), (33, 10), (22, 17), (16, 0), (19, 9), (19, 5), (22, 0), (21, 2), (23, 25), (32, 21), (8, 24), (35, 11), (20, 1), (5, 17), (8, 3), (17, 7), (6, 22), (34, 29), (29, 18), (23, 29), (6, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "558912", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 1), (29, 18), (14, 34), (15, 32), (35, 14), (31, 13), (21, 7), (29, 1), (22, 26), (4, 0), (38, 4), (20, 14), (30, 14), (1, 21), (16, 7), (33, 19), (16, 34), (34, 34), (24, 16), (23, 27), (38, 27), (13, 18), (8, 18), (23, 29), (3, 15), (34, 33), (13, 16), (19, 31), (35, 28), (27, 7), (16, 17), (34, 3), (24, 11), (15, 12), (35, 24), (21, 19), (8, 23), (25, 0), (14, 21), (22, 34), (14, 10), (30, 26), (19, 4), (18, 34), (11, 13), (5, 22), (34, 14), (22, 12), (2, 18), (19, 33), (38, 33), (8, 13), (38, 6), (2, 17), (13, 33), (6, 6), (36, 12), (37, 25), (21, 28), (33, 24), (33, 26), (23, 31), (33, 14), (22, 18), (28, 1), (17, 12), (30, 0), (7, 34), (0, 27), (12, 5), (18, 24), (30, 24), (29, 7), (8, 22), (28, 26), (23, 21), (22, 25), (16, 6), (1, 13), (6, 3), (25, 25), (11, 34), (21, 8), (14, 17), (6, 4), (16, 19), (11, 32), (20, 7), (10, 22), (15, 8), (13, 32), (34, 7), (2, 16), (27, 8), (22, 32), (2, 1), (8, 21), (25, 30), (9, 0), (24, 0), (4, 31), (26, 1), (20, 32), (21, 17), (26, 28), (10, 6), (22, 27), (3, 11), (35, 13), (24, 5), (4, 27), (4, 6), (24, 22), (23, 28), (18, 21), (4, 24), (37, 29), (33, 7), (0, 22), (18, 15), (30, 10), (37, 11), (14, 2), (0, 7), (16, 25), (14, 8), (7, 10), (20, 26), (29, 20), (21, 21), (2, 9), (32, 29), (3, 28), (6, 13), (23, 10), (37, 17), (14, 29), (18, 2), (33, 2), (26, 13), (27, 20), (13, 30), (7, 27), (31, 23), (4, 34), (0, 34), (32, 8), (17, 7), (22, 29), (2, 21), (10, 27), (17, 9), (21, 16), (7, 3), (9, 25), (37, 3), (38, 13), (32, 7), (36, 28), (11, 23), (37, 10), (26, 7), (33, 11), (7, 28), (23, 19), (31, 31), (36, 24), (36, 33), (29, 24), (23, 16), (13, 12), (28, 15), (14, 22), (13, 17), (36, 30), (8, 5), (20, 15), (17, 30), (15, 0), (29, 25), (34, 20), (34, 12), (1, 24), (26, 17), (19, 6), (35, 1), (23, 4), (12, 9), (0, 5), (28, 3), (24, 24), (26, 19), (21, 11), (0, 2), (8, 30), (11, 6), (4, 33), (12, 7), (23, 15), (37, 2), (32, 31), (28, 16), (17, 16), (7, 29), (17, 23), (2, 6), (4, 5), (2, 12), (10, 24), (5, 8), (12, 21), (8, 20), (3, 4), (18, 13), (30, 6), (29, 17), (10, 20), (15, 9), (35, 4), (8, 4), (36, 17), (32, 3), (22, 11), (3, 10), (27, 26), (2, 19), (7, 23), (29, 8), (24, 15), (9, 32), (26, 20), (35, 25), (27, 25), (34, 13), (15, 30), (19, 20), (6, 21), (29, 23), (9, 24), (37, 7), (20, 0), (25, 20), (34, 5), (13, 15), (36, 2), (0, 4), (11, 27), (4, 17), (31, 5), (33, 17), (8, 8), (29, 30), (35, 29), (37, 4), (20, 6), (29, 14), (26, 6), (26, 15), (9, 29), (19, 16), (36, 21), (18, 7), (0, 12), (38, 8), (38, 24), (25, 3), (13, 5), (16, 20), (19, 7), (17, 21), (30, 23), (1, 34), (4, 22), (32, 4), (36, 15), (27, 18), (34, 11), (7, 17), (35, 31), (16, 32), (5, 32), (13, 20), (8, 34), (33, 28), (31, 20), (32, 18), (12, 6), (37, 31), (3, 30), (15, 31), (1, 7), (16, 3), (0, 23), (19, 14), (5, 23), (37, 13), (4, 13), (13, 22), (33, 22), (12, 14), (27, 29), (16, 0), (29, 10), (18, 10), (0, 9), (20, 24), (13, 27), (16, 16), (28, 19), (17, 15), (12, 31), (0, 20), (36, 9), (17, 0), (5, 16), (20, 30), (36, 4), (38, 10), (24, 9), (4, 16), (2, 27), (1, 10), (33, 29), (29, 27), (21, 25), (11, 12), (18, 29), (32, 26), (8, 29), (10, 14), (18, 1), (14, 27), (27, 21), (10, 7), (7, 33), (1, 18), (26, 9), (5, 1), (32, 12), (1, 6), (12, 15), (5, 24), (24, 17), (23, 5), (30, 9), (9, 22), (12, 28), (32, 28), (20, 11), (17, 24), (16, 24), (22, 22), (2, 5), (7, 14), (0, 21), (38, 1), (11, 25), (24, 1), (28, 24), (15, 1), (7, 30), (5, 9), (5, 25), (14, 11), (26, 4), (3, 24), (13, 29), (3, 17), (38, 23), (16, 28), (10, 21), (16, 21), (19, 13), (3, 21), (34, 28), (19, 15), (16, 10), (34, 23), (4, 9), (16, 18), (30, 20), (10, 15), (3, 16), (26, 14), (35, 18), (10, 33), (9, 31), (28, 30), (34, 6), (28, 8), (28, 20), (0, 10), (27, 33), (19, 2), (4, 28), (35, 3), (19, 30), (13, 25), (17, 1), (10, 5), (27, 19), (22, 23), (20, 28), (33, 13), (32, 2), (11, 33), (20, 19), (1, 29), (22, 30), (23, 3), (14, 0), (1, 5), (3, 19), (7, 24), (5, 3), (13, 24), (28, 2), (31, 11), (25, 29), (26, 29), (11, 31), (33, 31), (3, 2), (34, 18), (15, 3), (17, 25), (7, 0), (38, 26), (0, 16), (32, 9), (23, 6), (27, 5), (26, 33), (35, 22), (11, 1), (14, 33), (24, 34), (6, 22), (26, 27), (20, 33), (27, 11), (23, 23), (38, 19), (7, 19), (31, 30), (1, 26), (0, 29), (21, 30), (36, 25), (0, 8), (11, 30), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "273280", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), 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), (5, 22), (9, 5), (9, 20), (5, 16), (6, 32), (18, 19), (30, 24), (4, 8), (33, 1), (13, 20), (19, 6), (20, 0), (30, 32), (6, 13), (23, 27), (8, 9), (3, 10), (26, 21), (5, 9), (18, 1), (11, 13), (4, 2), (35, 0), (15, 36), (18, 2), (14, 7), (12, 23), (22, 24), (8, 12), (22, 3), (9, 32), (26, 36), (35, 5), (8, 30), (11, 3), (10, 3), (29, 23), (19, 17), (2, 0), (32, 19), (19, 36), (21, 27), (32, 27), (27, 23), (20, 6), (12, 8), (1, 0), (7, 9), (6, 28), (25, 24), (14, 4), (6, 35), (8, 35), (19, 1), (10, 21), (21, 21), (5, 18), (29, 3), (32, 30), (14, 28), (17, 0), (16, 23), (20, 21), (8, 11), (3, 18), (12, 21), (21, 23), (13, 24), (22, 31), (0, 34), (34, 27), (7, 26), (33, 14), (21, 0), (20, 28), (13, 26), (6, 16), (5, 13), (24, 12), (10, 1), (27, 18), (27, 25), (8, 27), (35, 16), (16, 32), (13, 13), (12, 35), (8, 20), (8, 34), (6, 7), (2, 27), (26, 30), (21, 14), (25, 34), (18, 32), (13, 30), (28, 24), (18, 25), (25, 18), (22, 5), (24, 32), (11, 10), (15, 27), (11, 16), (22, 35), (0, 21), (20, 35), (15, 12), (22, 28), (9, 9), (32, 20), (22, 6), (32, 36), (6, 14), (5, 31), (24, 19), (22, 10), (22, 34), (4, 21), (14, 13), (2, 33), (15, 2), (8, 14), (31, 20), (0, 25), (17, 24), (32, 25), (31, 17), (0, 19), (8, 4), (7, 33), (1, 2), (26, 26), (2, 26), (35, 6), (16, 3), (19, 10), (30, 7), (22, 20), (12, 17), (35, 8), (21, 30), (32, 32), (24, 3), (18, 17), (17, 22), (3, 31), (13, 18), (5, 15), (17, 19), (35, 30), (2, 11), (25, 20), (29, 24), (19, 35), (14, 14), (10, 35), (31, 35), (18, 16), (27, 6), (29, 18), (13, 32), (1, 17), (16, 12), (9, 10), (16, 16), (10, 33), (15, 14), (9, 30), (29, 13), (17, 34), (23, 5), (10, 7), (13, 28), (23, 7), (30, 11), (11, 26), (3, 26), (31, 7), (14, 24), (11, 19), (32, 35), (2, 7), (20, 15), (6, 31), (17, 30), (2, 16), (32, 31), (12, 32), (25, 29), (30, 21), (15, 0), (25, 33), (22, 21), (7, 19), (9, 1), (30, 5), (23, 1), (27, 13), (27, 1), (22, 14), (20, 25), (29, 20), (17, 26), (12, 9), (12, 13), (20, 18), (5, 3), (29, 21), (20, 27), (6, 8), (3, 8), (26, 31), (0, 14), (8, 28), (19, 26), (2, 10), (4, 11), (28, 35), (16, 24), (21, 36), (32, 0), (30, 13), (31, 21), (18, 20), (11, 7), (6, 25), (13, 29), (24, 24), (10, 25), (32, 17), (22, 18), (1, 18), (34, 8), (26, 8), (11, 9), (14, 0), (8, 22), (20, 3), (19, 22), (1, 15), (19, 19), (4, 27), (5, 36), (0, 17), (27, 29), (8, 2), (23, 35), (25, 36), (6, 11), (35, 1), (11, 11), (4, 29), (23, 18), (15, 6), (25, 7), (28, 26), (19, 23), (2, 31), (29, 5), (4, 34), (31, 25), (1, 21), (3, 28), (23, 11), (9, 12), (27, 8), (22, 0), (31, 23), (25, 25), (32, 34), (28, 23), (28, 5), (4, 20), (12, 36), (4, 17), (32, 7), (7, 2), (25, 12), (29, 1), (1, 30), (30, 9), (30, 6), (28, 9), (30, 20), (2, 14), (4, 12), (29, 31), (12, 15), (34, 19), (31, 1), (6, 6), (31, 26), (3, 21), (7, 5), (26, 18), (20, 29), (34, 9), (14, 34), (10, 12), (30, 17), (28, 32), (13, 33), (26, 1), (28, 28), (4, 7), (28, 8), (27, 22), (24, 5), (15, 26), (33, 19), (34, 17), (34, 31), (19, 30), (20, 19), (2, 6), (25, 31), (10, 18), (21, 5), (13, 25), (9, 3), (7, 27), (19, 31), (34, 36), (0, 11), (18, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98904", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 26), (26, 4), (11, 19), (32, 12), (29, 25), (21, 18), (22, 14), (22, 19), (2, 4), (18, 31), (1, 28), (20, 29), (12, 20), (19, 6), (14, 29), (13, 26), (20, 0), (33, 26), (0, 27), (19, 17), (33, 30), (3, 0), (13, 6), (23, 20), (23, 31), (15, 16), (9, 22), (29, 1), (8, 10), (10, 9), (20, 24), (30, 9), (6, 0), (29, 6), (26, 10), (28, 25), (7, 24), (25, 14), (0, 14), (14, 17), (6, 22), (26, 0), (10, 13), (32, 19), (5, 23), (15, 0), (24, 14), (25, 24), (4, 24), (9, 26), (25, 31), (22, 2), (22, 12), (2, 2), (3, 32), (20, 31), (31, 31), (5, 24), (31, 2), (28, 0), (18, 15), (12, 29), (7, 32), (13, 32), (2, 7), (16, 12), (14, 2), (8, 6), (6, 7), (22, 5), (14, 4), (18, 30), (25, 20), (10, 27), (26, 24), (8, 4), (27, 29), (21, 31), (27, 14), (14, 12), (30, 3), (19, 16), (4, 2), (8, 24), (0, 15), (26, 26), (18, 16), (28, 9), (29, 26), (31, 12), (13, 13), (28, 13), (7, 5), (18, 32), (3, 1), (13, 28), (32, 5), (13, 27), (19, 20), (12, 1), (11, 12), (18, 1), (0, 18), (34, 20), (29, 7), (12, 24), (14, 8), (4, 27), (30, 27), (24, 13), (30, 17), (26, 13), (22, 1), (16, 8), (1, 27), (16, 4), (5, 27), (14, 14), (14, 10), (25, 18), (25, 21), (28, 12), (1, 0), (8, 13), (16, 17), (21, 26), (9, 14), (32, 13), (9, 27), (8, 19), (15, 17), (27, 12), (31, 0), (16, 13), (24, 0), (13, 7), (15, 23), (14, 20), (16, 11), (24, 20), (21, 19), (11, 21), (5, 31), (15, 13), (31, 16), (33, 24), (16, 21), (20, 6), (4, 14), (19, 1), (33, 13), (8, 16), (29, 11), (8, 30), (22, 20), (10, 28), (30, 28), (4, 20), (9, 7), (7, 17), (26, 21), (29, 32), (6, 4), (27, 24), (25, 29), (17, 8), (31, 10), (3, 29), (33, 29), (18, 6), (5, 7), (27, 23), (25, 3), (17, 28), (7, 0), (5, 9), (28, 18), (25, 11), (8, 11), (14, 19), (2, 20), (20, 21), (16, 28), (33, 0), (29, 10), (25, 27), (4, 6), (32, 17), (15, 25), (33, 12), (26, 23), (5, 25), (2, 5), (7, 19), (12, 2), (29, 9), (32, 2), (33, 11), (2, 18), (20, 7), (17, 6), (16, 15), (2, 9), (26, 31), (4, 12), (6, 31), (19, 28), (32, 10), (8, 20), (27, 2), (28, 6), (9, 12), (7, 25), (3, 22), (20, 10), (23, 25), (14, 6), (31, 27), (30, 13), (18, 27), (0, 3), (30, 0), (27, 21), (28, 19), (13, 22), (23, 32), (12, 12), (24, 32), (29, 14), (6, 5), (8, 26), (10, 31), (12, 32), (2, 31), (21, 15), (28, 30), (4, 15), (31, 22), (12, 9), (28, 26), (18, 28), (14, 31), (7, 30), (29, 24), (31, 18), (22, 6), (3, 9), (16, 7), (13, 11), (19, 13), (3, 21), (20, 11), (14, 28), (21, 6), (32, 4), (14, 22), (4, 16), (33, 6), (28, 5), (11, 30), (14, 30), (22, 25), (16, 5), (13, 23), (6, 32), (26, 8), (24, 23), (12, 21), (12, 22), (27, 8), (29, 22), (28, 2), (9, 30), (24, 10), (4, 19), (5, 32), (23, 26), (21, 25), (7, 23), (15, 26), (13, 18), (8, 8), (9, 10), (15, 14), (9, 16), (23, 23), (30, 16), (31, 8), (31, 3), (3, 2), (32, 23), (4, 32), (30, 5), (1, 15), (9, 29), (30, 4), (16, 2), (34, 30), (4, 3), (22, 29), (11, 29), (24, 18), (27, 16), (32, 29), (31, 24), (5, 12), (7, 31), (9, 18), (0, 31), (30, 20), (4, 1), (2, 1), (5, 10), (15, 18), (0, 11), (23, 12), (21, 9), (5, 30), (28, 24), (28, 28), (11, 32), (28, 11), (5, 8), (28, 3), (7, 10), (1, 17), (15, 19), (27, 1), (3, 30), (2, 22), (24, 11), (27, 25), (20, 25), (19, 22), (34, 0), (34, 27), (3, 15), (10, 18), (6, 15), (1, 16), (15, 12), (13, 5), (19, 24), (1, 11), (7, 3), (12, 16), (27, 15), (9, 17), (22, 16), (4, 18), (32, 16), (3, 16), (6, 16), (30, 15), (17, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563232", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 15), (10, 22), (0, 14), (30, 26), (9, 6), (10, 21), (25, 7), (7, 10), (19, 25), (17, 28), (38, 0), (23, 20), (25, 3), (20, 16), (19, 12), (4, 27), (32, 21), (0, 25), (27, 28), (35, 7), (29, 3), (6, 4), (19, 32), (20, 15), (18, 2), (1, 18), (36, 31), (33, 21), (24, 13), (4, 24), (27, 32), (9, 18), (14, 12), (9, 26), (10, 24), (10, 10), (30, 22), (16, 30), (32, 19), (1, 0), (19, 14), (20, 26), (31, 10), (23, 32), (16, 27), (1, 16), (11, 29), (17, 3), (30, 27), (5, 18), (0, 10), (15, 17), (29, 5), (19, 19), (22, 31), (0, 26), (11, 0), (3, 7), (13, 18), (22, 27), (9, 28), (19, 29), (27, 21), (37, 3), (24, 25), (6, 30), (37, 25), (36, 16), (32, 4), (13, 13), (8, 5), (1, 6), (1, 7), (29, 30), (29, 11), (37, 0), (22, 11), (19, 31), (38, 18), (25, 25), (34, 31), (5, 24), (0, 15), (29, 24), (20, 19), (10, 30), (34, 15), (1, 24), (23, 31), (35, 18), (4, 4), (15, 24), (28, 2), (7, 27), (1, 26), (20, 32), (35, 6), (20, 25), (7, 12), (16, 23), (35, 12), (30, 30), (1, 20), (2, 19), (31, 12), (33, 17), (19, 5), (10, 14), (5, 5), (8, 18), (34, 18), (24, 0), (3, 10), (13, 32), (36, 2), (10, 13), (0, 3), (16, 21), (14, 24), (33, 12), (1, 21), (19, 6), (30, 9), (13, 20), (10, 29), (18, 23), (21, 3), (24, 4), (3, 11), (26, 29), (20, 3), (17, 9), (26, 28), (12, 14), (17, 22), (3, 0), (3, 9), (12, 24), (11, 9), (25, 11), (3, 29), (12, 31), (36, 23), (11, 32), (18, 17), (14, 13), (26, 24), (25, 17), (34, 17), (31, 5), (4, 30), (32, 13), (20, 9), (9, 7), (7, 28), (6, 1), (38, 8), (10, 5), (24, 16), (20, 18), (28, 17), (13, 1), (35, 24), (12, 0), (3, 12), (3, 3), (0, 4), (21, 19), (24, 12), (35, 28), (0, 21), (27, 17), (14, 20), (15, 11), (5, 15), (28, 9), (5, 17), (32, 0), (36, 10), (0, 28), (11, 21), (25, 23), (33, 4), (20, 29), (13, 9), (32, 23), (11, 18), (15, 7), (21, 26), (33, 6), (9, 29), (13, 26), (16, 19), (10, 7), (35, 2), (0, 9), (9, 22), (27, 3), (4, 2), (8, 3), (6, 9), (8, 10), (36, 24), (32, 31), (11, 7), (7, 18), (25, 6), (5, 27), (12, 11), (24, 7), (8, 8), (38, 30), (0, 32), (10, 1), (21, 20), (32, 16), (38, 13), (30, 25), (36, 30), (25, 13), (19, 8), (7, 8), (23, 17), (28, 27), (34, 2), (26, 0), (20, 12), (5, 16), (20, 6), (35, 0), (28, 23), (6, 21), (36, 32), (0, 17), (2, 24), (8, 22), (31, 25), (13, 6), (32, 2), (27, 14), (5, 25), (7, 23), (36, 18), (12, 13), (21, 4), (10, 18), (32, 8), (8, 25), (15, 13), (34, 7), (28, 26), (33, 18), (12, 9), (2, 10), (8, 31), (10, 3), (10, 2), (36, 1), (31, 20), (15, 18), (15, 23), (8, 27), (13, 21), (6, 17), (23, 2), (31, 28), (4, 21), (23, 23), (38, 23), (5, 29), (5, 14), (26, 8), (2, 5), (7, 19), (7, 21), (27, 31), (0, 7), (20, 7), (12, 15), (37, 12), (6, 14), (34, 3), (30, 8), (21, 9), (22, 3), (2, 29), (33, 2), (28, 15), (25, 2), (11, 28), (23, 26), (17, 30), (24, 14), (23, 16), (32, 12), (6, 5), (3, 23), (34, 30), (37, 26), (29, 15), (17, 23), (2, 6), (7, 22), (22, 32), (36, 28), (7, 14), (26, 3), (21, 6), (23, 28), (32, 17), (27, 8), (23, 7), (33, 9), (21, 7), (20, 17), (33, 8), (38, 14), (20, 8), (24, 21), (28, 16), (19, 0), (7, 6), (13, 27), (13, 4), (16, 10), (32, 25), (24, 1), (31, 22), (26, 11), (34, 27), (5, 23), (19, 17), (3, 5), (20, 0), (19, 24), (28, 24), (5, 7), (21, 12), (28, 32), (22, 17), (21, 22), (36, 12), (20, 27), (34, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "880000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 34), (14, 25), (21, 5), (7, 10), (33, 27), (37, 33), (36, 20), (34, 4), (12, 24), (37, 32), (4, 9), (16, 31), (9, 31), (6, 34), (22, 30), (35, 6), (16, 11), (13, 29), (6, 18), (1, 13), (29, 21), (36, 0), (19, 0), (13, 27), (27, 14), (16, 5), (13, 3), (22, 8), (30, 32), (4, 21), (25, 8), (28, 30), (24, 21), (25, 5), (5, 5), (23, 4), (25, 34), (13, 4), (6, 1), (30, 19), (5, 16), (1, 34), (32, 25), (21, 21), (22, 26), (10, 0), (18, 33), (19, 35), (10, 18), (4, 4), (10, 14), (23, 19), (10, 17), (26, 17), (38, 26), (38, 0), (12, 31), (24, 9), (32, 16), (1, 24), (37, 13), (3, 35), (25, 18), (33, 22), (32, 14), (29, 12), (23, 12), (7, 16), (8, 0), (20, 1), (10, 9), (36, 2), (12, 6), (24, 30), (2, 2), (16, 0), (36, 25), (17, 6), (23, 35), (35, 33), (32, 15), (9, 26), (23, 32), (33, 26), (25, 24), (21, 19), (22, 5), (5, 34), (7, 29), (35, 31), (31, 27), (36, 1), (30, 35), (35, 22), (20, 18), (8, 28), (25, 32), (2, 33), (26, 21), (14, 1), (31, 29), (30, 26), (1, 2), (19, 16), (15, 30), (35, 18), (28, 1), (0, 34), (38, 32), (38, 34), (13, 30), (5, 29), (5, 22), (27, 32), (5, 17), (32, 19), (3, 22), (32, 1), (9, 1), (15, 18), (35, 29), (15, 13), (35, 23), (30, 31), (23, 5), (31, 14), (36, 19), (17, 23), (28, 4), (3, 14), (27, 17), (0, 4), (21, 6), (25, 35), (1, 22), (28, 18), (17, 24), (1, 16), (10, 19), (34, 15), (21, 17), (36, 18), (29, 6), (12, 13), (32, 27), (15, 14), (37, 7), (5, 9), (7, 34), (32, 0), (35, 16), (15, 8), (32, 5), (12, 32), (18, 12), (6, 4), (24, 6), (6, 3), (14, 29), (37, 17), (13, 8), (1, 26), (8, 31), (16, 29), (6, 35), (12, 10), (24, 7), (1, 28), (0, 29), (26, 6), (38, 25), (32, 30), (38, 31), (35, 2), (9, 6), (3, 30), (23, 6), (38, 30), (28, 7), (18, 31), (10, 33), (34, 29), (3, 20), (31, 12), (8, 23), (8, 32), (9, 30), (21, 18), (2, 24), (23, 16), (12, 20), (12, 25), (23, 25), (18, 29), (34, 20), (20, 8), (20, 21), (23, 0), (26, 13), (37, 10), (36, 27), (24, 14), (15, 23), (38, 5), (17, 27), (10, 30), (2, 34), (6, 2), (9, 15), (32, 20), (21, 28), (28, 5), (20, 15), (12, 30), (38, 4), (3, 28), (32, 29), (34, 30), (26, 22), (12, 22), (25, 13), (0, 19), (31, 3), (3, 27), (2, 27), (36, 4), (13, 25), (21, 34), (16, 13), (15, 21), (11, 12), (9, 18), (20, 34), (20, 19), (25, 19), (11, 25), (4, 3), (38, 19), (22, 16), (19, 26), (27, 15), (32, 3), (25, 14), (3, 2), (34, 28), (22, 33), (30, 6), (30, 33), (34, 34), (29, 35), (37, 23), (9, 28), (8, 8), (7, 25), (19, 25), (26, 20), (18, 21), (19, 15), (38, 24), (18, 11), (35, 17), (19, 21), (33, 32), (14, 9), (4, 11), (17, 17), (22, 21), (32, 21), (32, 35), (4, 10), (2, 16), (30, 25), (2, 5), (2, 30), (21, 4), (11, 20), (37, 1), (16, 9), (4, 31), (10, 20), (27, 12), (38, 11), (1, 0), (14, 35), (9, 5), (15, 4), (22, 28), (2, 1), (24, 29), (27, 1), (2, 23), (17, 35), (34, 1), (23, 30), (30, 9), (2, 32), (0, 12), (7, 4), (5, 8), (35, 9), (17, 7), (20, 27), (16, 24), (15, 11), (27, 0), (23, 26), (37, 2), (37, 26), (35, 10), (1, 17), (5, 14), (21, 26), (15, 0), (22, 35), (36, 6), (34, 21), (35, 20), (5, 10), (6, 33), (35, 15), (30, 28), (34, 13), (30, 1), (27, 29), (19, 10), (35, 35), (8, 1), (33, 23), (0, 18), (13, 18), (21, 0), (37, 11), (23, 7), (24, 19), (4, 13), (33, 1), (25, 6), (10, 16), (17, 25), (32, 24), (34, 16), (9, 24), (24, 8), (31, 33), (2, 19), (29, 9), (6, 0), (13, 17), (34, 27), (8, 3), (26, 31), (20, 6), (8, 34), (28, 9), (7, 28), (13, 10), (6, 27), (20, 10), (20, 32), (35, 11), (8, 24), (10, 13), (33, 29), (23, 21), (2, 29), (15, 32), (26, 28), (8, 25), (22, 34), (28, 24), (32, 6), (15, 19), (31, 26), (29, 15), (25, 30), (20, 4), (19, 33), (18, 1), (26, 3), (9, 14), (10, 2), (32, 34), (21, 32), (13, 24), (22, 11), (18, 26), (31, 28), (31, 20), (24, 23), (17, 18), (33, 20), (1, 8), (8, 21), (30, 7), (11, 26), (4, 19), (29, 28), (37, 5), (31, 23), (19, 17), (31, 10), (21, 16), (7, 15), (19, 14), (4, 34), (37, 14), (29, 4), (17, 4), (16, 27), (23, 20), (4, 23), (11, 3), (28, 20), (35, 8), (1, 35), (13, 9), (1, 32), (4, 24), (9, 20), (16, 2), (8, 33), (18, 6), (12, 9), (10, 26), (25, 10), (0, 22), (26, 25), (37, 21), (24, 28), (27, 13), (28, 11), (28, 10), (19, 6), (33, 2), (24, 22), (5, 0), (7, 7), (25, 25), (11, 27), (14, 10), (10, 31), (23, 3), (16, 19), (18, 20), (4, 2), (23, 27), (31, 24), (17, 16), (12, 19), (18, 0), (4, 20), (12, 5), (11, 5), (36, 17), (7, 3), (37, 24), (35, 12), (24, 17), (21, 29), (3, 23), (2, 11), (9, 29), (3, 5), (3, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997920", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), 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), (18, 32), (24, 24), (4, 20), (24, 15), (17, 1), (11, 3), (5, 26), (20, 8), (10, 26), (27, 5), (16, 13), (18, 16), (6, 28), (7, 28), (4, 16), (27, 10), (20, 9), (29, 29), (10, 8), (0, 19), (22, 26), (26, 27), (14, 15), (0, 25), (12, 8), (28, 10), (13, 12), (3, 17), (10, 25), (28, 16), (18, 11), (24, 0), (25, 12), (4, 25), (4, 1), (12, 32), (1, 10), (3, 25), (22, 24), (6, 4), (14, 9), (27, 27), (17, 21), (11, 11), (22, 1), (5, 4), (23, 19), (24, 14), (24, 21), (10, 6), (24, 22), (13, 26), (26, 18), (10, 23), (11, 23), (16, 9), (2, 3), (10, 13), (26, 7), (22, 5), (2, 24), (25, 21), (29, 20), (15, 4), (16, 21), (21, 18), (12, 0), (31, 6), (1, 6), (2, 28), (9, 11), (25, 15), (6, 11), (28, 23), (6, 9), (8, 28), (25, 29), (23, 12), (3, 9), (13, 17), (27, 20), (11, 15), (22, 2), (19, 9), (13, 23), (30, 27), (25, 28), (2, 13), (6, 3), (27, 6), (0, 26), (5, 5), (4, 28), (31, 25), (30, 17), (9, 30), (25, 32), (30, 12), (16, 1), (22, 7), (30, 2), (9, 14), (14, 2), (24, 11), (0, 32), (14, 8), (31, 19), (22, 12), (25, 25), (19, 7), (12, 12), (16, 3), (1, 28), (5, 3), (24, 12), (29, 32), (10, 10), (0, 20), (15, 32), (28, 25), (12, 4), (4, 10), (20, 23), (5, 25), (25, 22), (19, 24), (5, 9), (17, 2), (26, 14), (16, 2), (17, 23), (30, 10), (15, 28), (23, 1), (0, 6), (17, 30), (10, 9), (22, 14), (25, 30), (11, 0), (23, 0), (7, 21), (14, 32), (31, 0), (19, 17), (9, 7), (10, 0), (16, 25), (26, 15), (17, 26), (21, 11), (21, 10), (10, 22), (4, 27), (8, 14), (20, 20), (0, 9), (12, 7), (22, 9), (22, 15), (5, 24), (9, 4), (20, 19), (29, 10), (29, 6), (17, 11), (8, 29), (4, 2), (8, 19), (21, 8), (26, 21), (20, 16), (14, 4), (14, 18), (28, 7), (22, 27), (13, 30), (17, 18), (17, 3), (0, 4), (14, 23), (5, 7), (29, 25), (6, 17), (18, 20), (12, 13), (2, 25), (27, 13), (18, 9), (2, 1), (12, 24), (30, 29), (11, 13), (22, 4), (12, 1), (22, 16), (3, 20), (18, 7), (27, 9), (30, 31), (18, 30), (0, 2), (18, 29), (9, 3), (15, 8), (18, 21), (6, 20), (20, 11), (8, 20), (4, 17), (13, 20), (29, 21), (21, 29), (16, 0), (6, 29), (9, 24), (2, 7), (13, 19), (7, 32), (31, 13), (11, 1), (31, 29), (15, 14), (9, 32), (2, 20), (4, 0), (2, 6), (12, 9), (24, 6), (27, 12), (0, 29), (18, 8), (18, 15), (28, 5), (22, 23), (18, 25), (15, 25), (0, 5), (8, 27), (6, 2), (26, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645380", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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, 28), (5, 29), (9, 30), (22, 15), (20, 10), (9, 6), (13, 9), (1, 30), (23, 36), (4, 13), (24, 8), (15, 9), (17, 29), (24, 3), (18, 12), (4, 2), (4, 31), (17, 6), (5, 10), (20, 32), (15, 25), (9, 21), (3, 36), (25, 19), (4, 18), (22, 8), (19, 23), (22, 30), (14, 16), (17, 16), (6, 11), (13, 34), (24, 10), (18, 8), (1, 15), (14, 14), (26, 11), (13, 11), (27, 10), (0, 28), (29, 14), (3, 13), (4, 9), (24, 12), (1, 14), (19, 14), (18, 17), (27, 5), (14, 32), (10, 7), (17, 32), (14, 7), (6, 2), (13, 7), (2, 6), (28, 27), (20, 0), (18, 23), (13, 31), (22, 5), (16, 16), (25, 17), (10, 13), (5, 32), (26, 27), (17, 12), (5, 16), (26, 16), (20, 12), (15, 11), (27, 15), (6, 32), (21, 13), (21, 1), (24, 28), (0, 13), (2, 3), (30, 2), (24, 31), (3, 6), (26, 23), (29, 23), (27, 32), (1, 1), (16, 32), (28, 12), (10, 24), (3, 1), (12, 3), (23, 25), (3, 34), (29, 1), (9, 4), (28, 3), (12, 2), (8, 3), (29, 27), (2, 10), (7, 27), (21, 24), (11, 30), (28, 6), (11, 6), (9, 26), (6, 19), (9, 24), (18, 18), (16, 26), (24, 23), (21, 16), (21, 23), (14, 19), (28, 19), (2, 26), (24, 20), (14, 13), (13, 33), (27, 31), (2, 19), (0, 30), (27, 12), (12, 36), (4, 3), (2, 24), (22, 29), (28, 23), (14, 6), (5, 0), (14, 8), (1, 35), (25, 8), (24, 26), (2, 21), (18, 6), (26, 7), (15, 12), (19, 11), (10, 30), (15, 35), (6, 34), (29, 35), (25, 35), (6, 9), (24, 4), (8, 16), (15, 7), (21, 32), (11, 13), (25, 22), (8, 26), (9, 5), (5, 24), (9, 14), (20, 21), (8, 28), (27, 6), (5, 5), (2, 4), (19, 26), (29, 17), (23, 15), (6, 0), (22, 0), (30, 27), (7, 21), (5, 17), (19, 8), (8, 0), (18, 9), (5, 6), (8, 34), (10, 2), (7, 9), (6, 3), (14, 33), (28, 1), (18, 5), (30, 18), (0, 4), (8, 25), (17, 7), (1, 34), (12, 13), (23, 20), (17, 15), (29, 32), (16, 4), (15, 6), (27, 27), (1, 2), (27, 2), (15, 17), (3, 28), (4, 28), (28, 13), (25, 16), (0, 22), (10, 14), (8, 8), (16, 12), (11, 10), (20, 19), (21, 3), (18, 3), (4, 36), (21, 0), (0, 15), (26, 4), (9, 33), (11, 7), (12, 35), (23, 14), (21, 36), (4, 32), (19, 30), (12, 20), (1, 22), (17, 2), (22, 21), (19, 4), (18, 32), (22, 26), (26, 0), (9, 3), (12, 24), (4, 21), (11, 15), (20, 27), (14, 23), (0, 19), (0, 21), (21, 7), (1, 7), (30, 26), (6, 4), (19, 22), (30, 22), (17, 8), (26, 34), (27, 13), (7, 6), (15, 8), (11, 11), (5, 33), (29, 26), (15, 2), (12, 33), (13, 10), (25, 6), (23, 26), (1, 21), (24, 19), (27, 22), (15, 26), (10, 21), (7, 3), (12, 30), (10, 10), (29, 22), (28, 2), (2, 7), (11, 27), (17, 17), (30, 35), (12, 23), (7, 17), (30, 28), (30, 6), (14, 12), (0, 1), (14, 25), (13, 8), (0, 32), (6, 24), (13, 22), (10, 19), (18, 11), (29, 25), (18, 34), (10, 5), (23, 11), (1, 31), (6, 16), (26, 26), (26, 35), (5, 15), (25, 33), (6, 35), (3, 19), (14, 35), (10, 36), (18, 14), (27, 9), (5, 34), (0, 26), (15, 19), (20, 14), (19, 16), (17, 14), (29, 0), (21, 21), (10, 4), (9, 9), (5, 12), (8, 19), (17, 33), (26, 29), (8, 21), (30, 3), (29, 29), (3, 9), (16, 27), (13, 21), (3, 20), (30, 23), (16, 20), (15, 28), (14, 36), (20, 22), (0, 31), (23, 7), (30, 5), (3, 8), (28, 5), (6, 29), (24, 17), (23, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931304", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 27), (5, 18), (12, 21), (15, 16), (27, 25), (7, 15), (1, 21), (25, 22), (12, 22), (30, 24), (29, 18), (30, 20), (14, 17), (14, 14), (16, 10), (14, 24), (23, 29), (17, 16), (28, 3), (13, 32), (0, 16), (1, 16), (27, 16), (32, 34), (4, 7), (32, 0), (31, 18), (24, 32), (31, 12), (28, 25), (29, 31), (0, 7), (5, 27), (17, 17), (15, 28), (4, 3), (9, 6), (23, 28), (12, 9), (27, 26), (30, 33), (8, 22), (18, 18), (30, 1), (26, 0), (16, 0), (17, 22), (19, 20), (6, 16), (11, 7), (20, 16), (27, 18), (18, 35), (6, 31), (27, 28), (12, 14), (1, 26), (25, 9), (17, 25), (18, 7), (11, 35), (19, 23), (15, 1), (31, 31), (5, 19), (5, 17), (32, 24), (24, 10), (10, 17), (25, 3), (12, 15), (23, 19), (28, 9), (28, 34), (12, 17), (10, 9), (13, 30), (9, 14), (4, 14), (28, 8), (8, 19), (23, 27), (28, 23), (21, 13), (30, 22), (30, 29), (14, 35), (32, 21), (32, 31), (6, 33), (21, 20), (13, 25), (8, 4), (28, 30), (25, 31), (25, 1), (20, 4), (29, 12), (21, 5), (12, 19), (21, 33), (22, 14), (23, 14), (23, 30), (8, 9), (11, 6), (32, 30), (3, 25), (0, 10), (30, 12), (9, 11), (7, 20), (22, 32), (16, 14), (15, 33), (9, 26), (17, 9), (20, 1), (5, 5), (12, 24), (10, 6), (0, 30), (4, 26), (6, 27), (8, 18), (20, 27), (32, 7), (21, 10), (22, 33), (3, 17), (21, 2), (16, 18), (31, 23), (23, 20), (3, 4), (10, 5), (15, 17), (6, 23), (10, 11), (12, 28), (19, 35), (7, 6), (1, 6), (22, 21), (5, 29), (27, 4), (18, 22), (4, 30), (1, 17), (20, 19), (32, 17), (16, 30), (24, 12), (1, 20), (5, 10), (24, 16), (29, 23), (29, 10), (11, 10), (17, 27), (14, 21), (17, 0), (31, 13), (19, 34), (18, 28), (7, 30), (26, 1), (24, 27), (26, 34), (5, 32), (26, 25), (22, 4), (12, 35), (12, 11), (4, 2), (24, 19), (16, 8), (6, 2), (14, 34), (32, 19), (29, 26), (18, 34), (19, 13), (32, 14), (25, 18), (28, 2), (29, 27), (8, 32), (17, 23), (27, 7), (10, 15), (18, 8), (22, 19), (15, 29), (32, 13), (28, 6), (0, 35), (7, 31), (32, 11), (17, 29), (11, 22), (9, 8), (29, 13), (6, 6), (11, 25), (24, 14), (23, 2), (26, 20), (3, 22), (9, 21), (26, 30), (0, 2), (6, 9), (2, 19), (5, 6), (1, 19), (21, 28), (2, 5), (5, 21), (13, 3), (8, 33), (21, 31), (1, 23), (23, 12), (8, 17), (18, 13), (3, 26), (28, 11), (19, 19), (3, 21), (31, 0), (24, 2), (20, 3), (3, 28), (0, 4), (30, 26), (12, 26), (2, 14), (32, 12), (20, 17), (29, 33), (28, 32), (15, 10), (31, 8), (13, 2), (14, 16), (11, 20), (23, 35), (14, 31), (25, 8), (14, 20), (20, 20), (2, 25), (28, 13), (10, 27), (22, 23), (18, 32), (19, 2), (2, 2), (1, 3), (22, 34), (29, 35), (28, 16), (14, 15), (10, 2), (6, 13), (26, 17), (20, 25), (8, 3), (29, 4), (7, 2), (1, 8), (14, 29), (22, 24), (5, 12), (4, 0), (6, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152820", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), 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), (28, 27), (0, 16), (6, 23), (13, 5), (4, 3), (29, 18), (13, 23), (5, 27), (1, 7), (12, 15), (12, 2), (9, 14), (21, 12), (8, 29), (1, 19), (32, 3), (9, 24), (26, 30), (7, 9), (27, 24), (32, 17), (27, 18), (21, 18), (6, 27), (11, 11), (29, 12), (32, 26), (28, 26), (16, 15), (19, 23), (14, 10), (30, 8), (3, 1), (16, 5), (4, 28), (16, 12), (13, 13), (24, 20), (29, 11), (34, 19), (34, 9), (22, 3), (0, 12), (32, 20), (29, 19), (9, 10), (2, 23), (10, 25), (14, 13), (12, 24), (0, 3), (27, 8), (17, 29), (11, 10), (4, 5), (33, 19), (5, 2), (22, 10), (9, 11), (10, 17), (15, 22), (10, 10), (5, 29), (18, 3), (25, 10), (16, 10), (15, 2), (29, 15), (13, 3), (0, 5), (23, 15), (25, 1), (15, 9), (33, 12), (23, 12), (11, 24), (32, 15), (18, 14), (22, 17), (18, 30), (24, 26), (17, 18), (6, 21), (16, 7), (15, 14), (10, 26), (15, 8), (9, 12), (1, 8), (11, 18), (13, 16), (11, 29), (30, 28), (4, 13), (7, 27), (24, 10), (18, 1), (4, 17), (34, 10), (33, 5), (14, 8), (2, 20), (0, 20), (6, 2), (22, 5), (10, 29), (26, 25), (5, 21), (4, 21), (23, 16), (3, 0), (25, 16), (26, 15), (6, 4), (6, 1), (5, 16), (19, 10), (28, 6), (20, 20), (20, 5), (24, 13), (12, 5), (4, 11), (27, 15), (33, 16), (20, 30), (4, 6), (19, 9), (0, 10), (23, 5), (25, 11), (12, 25), (7, 13), (31, 3), (20, 25), (33, 3), (23, 25), (9, 13), (22, 23), (5, 13), (2, 2), (15, 10), (7, 30), (33, 7), (31, 24), (25, 20), (17, 17), (23, 7), (21, 13), (31, 18), (12, 0), (31, 17), (11, 5), (0, 30), (34, 27), (4, 29), (9, 29), (9, 16), (30, 16), (14, 15), (19, 1), (2, 8), (1, 30), (15, 30), (12, 9), (15, 24), (27, 0), (32, 5), (1, 13), (6, 15), (34, 22), (23, 28), (9, 23), (30, 14), (17, 9), (2, 25), (10, 3), (23, 17), (0, 8), (6, 22), (27, 10), (20, 19), (1, 1), (30, 2), (25, 4), (24, 27), (11, 15), (33, 6), (4, 10), (3, 12), (23, 27), (15, 11), (22, 27), (8, 28), (28, 15), (23, 9), (23, 13), (23, 8), (28, 12), (20, 2), (29, 3), (8, 22), (12, 6), (13, 1), (29, 27), (18, 12), (18, 2), (30, 27), (28, 28), (7, 2), (15, 5), (11, 30), (6, 3), (33, 13), (16, 29), (32, 30), (17, 15), (5, 9), (11, 22), (31, 7), (17, 5), (1, 9), (25, 19), (12, 28), (4, 0), (13, 0), (28, 14), (4, 15), (30, 5), (26, 20), (4, 22), (8, 18), (8, 12), (25, 22), (1, 10), (22, 21), (15, 7), (5, 30), (27, 3), (20, 15), (33, 23), (34, 25), (27, 11), (26, 11), (7, 17), (31, 11), (6, 13), (6, 20), (1, 27), (22, 11), (4, 26), (20, 23), (15, 6), (19, 14), (32, 21), (7, 8), (10, 16), (33, 15), (1, 14), (19, 7), (28, 3), (8, 20), (31, 27), (21, 15), (12, 29), (19, 16), (22, 16), (4, 24), (14, 3), (10, 23), (23, 20), (7, 7), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604044", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (21, 11), (28, 30), (29, 5), (8, 24), (25, 14), (27, 9), (9, 12), (17, 15), (3, 6), (25, 7), (12, 13), (2, 12), (15, 12), (14, 13), (0, 26), (12, 12), (13, 4), (4, 28), (28, 22), (14, 3), (31, 26), (15, 26), (2, 21), (29, 4), (9, 21), (20, 17), (11, 5), (2, 22), (29, 28), (16, 1), (32, 21), (22, 27), (6, 28), (3, 1), (29, 27), (19, 29), (6, 11), (15, 0), (27, 15), (0, 12), (13, 5), (32, 29), (28, 26), (12, 9), (17, 30), (18, 30), (15, 13), (30, 13), (23, 2), (16, 24), (11, 4), (22, 5), (32, 20), (20, 9), (13, 2), (10, 29), (0, 19), (32, 8), (26, 17), (15, 23), (31, 11), (26, 16), (10, 26), (14, 18), (26, 3), (17, 25), (1, 0), (7, 19), (23, 27), (24, 5), (13, 18), (22, 7), (29, 15), (9, 28), (18, 9), (15, 29), (12, 15), (22, 30), (31, 1), (17, 24), (15, 19), (12, 25), (5, 28), (21, 4), (18, 3), (1, 7), (3, 3), (22, 15), (7, 18), (32, 2), (3, 11), (21, 8), (6, 9), (28, 13), (11, 0), (10, 11), (9, 24), (25, 5), (13, 9), (8, 12), (27, 29), (25, 23), (5, 23), (6, 29), (1, 26), (3, 4), (14, 14), (24, 18), (30, 2), (30, 1), (7, 9), (4, 24), (24, 22), (8, 8), (18, 13), (4, 29), (32, 10), (28, 27), (0, 28), (0, 25), (4, 10), (4, 21), (13, 7), (26, 14), (4, 8), (4, 11), (18, 11), (9, 11), (31, 13), (11, 17), (2, 18), (5, 29), (1, 5), (22, 3), (15, 18), (27, 0), (26, 28), (4, 23), (28, 20), (19, 6), (32, 9), (7, 28), (13, 23), (26, 24), (8, 9), (27, 6), (17, 27), (19, 23), (18, 8), (14, 25), (20, 16), (27, 22), (27, 11), (10, 9), (23, 7), (13, 3), (24, 15), (3, 19), (29, 2), (31, 28), (16, 29), (30, 19), (10, 23), (5, 11), (10, 6), (8, 18), (12, 7), (27, 30), (20, 27), (19, 2), (0, 11), (6, 2), (16, 8), (14, 19), (1, 12), (10, 7), (21, 25), (28, 5), (4, 17), (10, 21), (12, 18), (29, 11), (25, 29), (4, 19), (14, 8), (5, 8), (1, 9), (3, 29), (28, 0), (22, 24), (28, 4), (7, 24), (28, 8), (24, 19), (5, 24), (4, 15), (28, 25), (18, 19), (15, 9), (32, 24), (20, 22), (7, 11), (5, 3), (11, 25), (20, 18), (25, 12), (22, 20), (6, 0), (13, 16), (30, 23), (11, 23), (30, 25), (30, 11), (3, 22), (0, 18), (24, 28), (25, 22), (24, 2), (17, 23), (17, 9), (16, 11), (25, 25), (20, 7), (16, 20), (16, 6), (0, 10), (24, 1), (11, 15), (0, 9), (0, 4), (10, 15), (12, 26), (22, 21), (29, 21), (11, 19), (32, 4), (31, 27), (2, 2), (25, 19), (5, 26), (16, 3), (0, 8), (19, 14), (13, 12), (12, 24), (6, 1), (11, 6), (7, 6), (26, 21), (7, 12), (11, 8), (32, 6), (1, 17), (3, 12), (5, 30), (13, 27), (14, 24), (25, 15), (27, 24), (24, 25), (8, 11), (6, 18), (20, 0), (14, 7), (11, 3), (24, 13), (16, 12), (9, 29), (5, 6), (32, 15), (28, 9), (0, 6), (24, 9), (16, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966168", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (1, 2), (19, 6), (4, 16), (26, 15), (12, 27), (14, 0), (8, 24), (14, 23), (21, 4), (31, 4), (24, 6), (3, 13), (30, 3), (31, 26), (23, 27), (13, 18), (12, 26), (6, 12), (28, 27), (29, 16), (16, 20), (16, 7), (31, 14), (16, 15), (28, 12), (20, 19), (28, 2), (1, 9), (11, 8), (7, 19), (2, 2), (26, 12), (3, 9), (28, 22), (3, 19), (25, 9), (16, 12), (24, 24), (26, 6), (4, 28), (25, 15), (6, 15), (18, 25), (17, 6), (11, 26), (2, 26), (14, 14), (25, 12), (29, 28), (0, 12), (2, 20), (7, 14), (13, 20), (12, 20), (14, 11), (30, 9), (19, 14), (24, 12), (2, 1), (11, 7), (11, 12), (16, 2), (31, 20), (9, 6), (17, 26), (17, 20), (6, 8), (0, 22), (29, 4), (27, 13), (6, 25), (8, 26), (22, 16), (12, 15), (19, 21), (27, 1), (6, 20), (12, 12), (26, 21), (15, 3), (17, 18), (18, 19), (26, 26), (28, 1), (23, 11), (31, 28), (20, 10), (9, 27), (30, 11), (3, 20), (26, 7), (13, 10), (17, 19), (23, 25), (2, 14), (10, 27), (9, 17), (12, 0), (7, 28), (23, 24), (27, 22), (8, 23), (11, 29), (20, 9), (29, 22), (17, 4), (9, 23), (5, 13), (17, 12), (2, 29), (24, 9), (14, 6), (6, 18), (10, 18), (18, 26), (31, 25), (31, 6), (22, 2), (15, 16), (9, 7), (22, 21), (6, 14), (29, 12), (31, 0), (30, 19), (25, 18), (8, 9), (3, 18), (26, 13), (14, 24), (31, 21), (2, 17), (18, 18), (0, 21), (27, 10), (0, 6), (27, 0), (4, 13), (23, 1), (23, 17), (5, 12), (4, 1), (29, 14), (18, 24), (16, 28), (17, 8), (7, 6), (17, 5), (1, 14), (21, 17), (13, 19), (2, 11), (27, 3), (20, 17), (22, 23), (29, 25), (28, 14), (31, 16), (15, 5), (14, 15), (18, 14), (21, 13), (25, 7), (22, 15), (30, 14), (13, 1), (30, 1), (5, 17), (28, 26), (29, 23), (11, 19), (30, 13), (9, 22), (26, 22), (9, 9), (25, 28), (14, 9), (8, 25), (3, 3), (16, 6), (19, 17), (20, 5), (17, 22), (10, 28), (9, 2), (22, 4), (12, 25), (8, 19), (2, 22), (23, 4), (4, 11), (7, 4), (11, 28), (21, 28), (20, 15), (27, 7), (20, 23), (27, 5), (22, 26), (1, 20), (20, 28), (21, 9), (21, 10), (4, 8), (22, 1), (24, 2), (1, 15), (26, 23), (4, 17), (28, 9), (9, 5), (2, 12), (24, 25), (16, 24), (16, 25), (23, 21), (7, 24), (1, 18), (7, 1), (7, 7), (21, 3), (6, 10), (28, 23), (13, 17), (10, 11), (15, 26), (23, 5), (21, 21), (3, 8), (0, 8), (12, 4), (14, 28), (7, 5), (14, 3), (15, 4), (1, 22), (0, 20), (24, 26), (25, 5), (30, 23), (31, 12), (29, 13), (19, 3), (10, 25), (14, 10), (20, 27), (21, 22), (31, 17), (0, 26), (10, 12), (14, 5), (13, 25), (1, 10), (31, 23), (9, 28), (26, 11), (27, 14), (28, 8), (31, 15), (17, 0), (24, 18), (1, 4), (13, 8), (27, 21), (25, 3), (6, 7), (13, 13), (1, 16), (0, 9), (2, 25), (11, 13), (30, 4), (7, 11), (23, 8), (16, 8), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466032", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 35), (21, 34), (4, 18), (36, 5), (21, 28), (1, 11), (30, 21), (35, 10), (13, 13), (21, 30), (18, 30), (9, 26), (16, 12), (21, 37), (25, 36), (0, 36), (23, 34), (4, 13), (9, 32), (36, 29), (16, 26), (3, 14), (21, 35), (31, 2), (20, 23), (24, 26), (29, 1), (30, 34), (4, 0), (26, 34), (2, 3), (30, 17), (37, 23), (25, 30), (29, 23), (29, 32), (25, 8), (8, 10), (28, 27), (28, 30), (5, 34), (30, 9), (3, 15), (1, 9), (12, 5), (21, 9), (22, 1), (34, 23), (26, 26), (28, 6), (37, 1), (24, 4), (24, 12), (34, 35), (6, 25), (5, 21), (0, 5), (5, 29), (31, 20), (15, 16), (1, 33), (35, 37), (3, 4), (22, 33), (26, 21), (15, 34), (16, 30), (35, 16), (37, 27), (5, 20), (23, 22), (7, 5), (6, 8), (24, 33), (30, 32), (32, 7), (4, 35), (18, 36), (19, 31), (8, 2), (7, 21), (24, 37), (8, 14), (28, 19), (13, 30), (37, 21), (17, 7), (0, 11), (1, 17), (38, 29), (25, 24), (2, 2), (17, 14), (22, 26), (9, 8), (21, 29), (6, 14), (16, 31), (19, 21), (37, 26), (31, 17), (27, 27), (0, 1), (31, 11), (8, 23), (25, 12), (26, 31), (7, 4), (18, 19), (38, 7), (36, 27), (24, 24), (7, 1), (24, 20), (17, 30), (10, 27), (4, 25), (36, 23), (32, 1), (16, 0), (16, 2), (6, 28), (29, 6), (1, 21), (20, 19), (38, 13), (30, 19), (36, 32), (9, 2), (23, 25), (17, 18), (17, 36), (14, 13), (18, 27), (12, 28), (25, 2), (12, 24), (4, 12), (20, 8), (6, 7), (35, 12), (33, 0), (11, 31), (4, 9), (23, 31), (27, 2), (22, 32), (31, 4), (2, 18), (7, 24), (19, 37), (35, 14), (15, 6), (11, 25), (7, 10), (10, 10), (11, 28), (16, 5), (1, 14), (30, 11), (32, 22), (24, 1), (26, 0), (8, 28), (4, 34), (38, 8), (29, 31), (7, 3), (14, 11), (22, 22), (25, 7), (28, 3), (15, 35), (28, 25), (19, 12), (24, 5), (32, 25), (37, 25), (4, 3), (28, 20), (9, 3), (3, 17), (14, 18), (21, 4), (34, 24), (11, 17), (9, 1), (32, 19), (15, 27), (2, 31), (3, 31), (22, 30), (0, 16), (8, 30), (10, 7), (21, 19), (28, 36), (0, 26), (35, 33), (36, 12), (4, 31), (23, 2), (21, 20), (36, 7), (29, 22), (20, 24), (0, 32), (11, 36), (13, 3), (18, 25), (1, 22), (33, 27), (14, 6), (6, 20), (27, 30), (37, 31), (5, 26), (16, 27), (5, 15), (11, 16), (26, 2), (14, 5), (30, 28), (30, 31), (37, 10), (12, 21), (2, 36), (11, 6), (15, 0), (13, 37), (17, 31), (24, 13), (34, 17), (7, 19), (34, 13), (13, 6), (37, 7), (30, 1), (37, 29), (6, 5), (36, 22), (14, 12), (25, 26), (35, 4), (13, 23), (33, 36), (12, 9), (18, 23), (2, 33), (34, 7), (27, 22), (8, 25), (31, 8), (2, 22), (7, 29), (36, 37), (23, 21), (28, 26), (7, 13), (16, 32), (18, 1), (32, 3), (33, 7), (37, 18), (2, 26), (0, 18), (16, 10), (15, 30), (8, 37), (36, 15), (34, 12), (20, 22), (34, 30), (28, 18), (28, 37), (3, 13), (5, 6), (19, 5), (10, 19), (30, 5), (10, 25), (21, 8), (31, 27), (26, 24), (30, 6), (19, 15), (0, 17), (3, 0), (3, 6), (35, 21), (34, 5), (15, 14), (2, 28), (11, 37), (11, 1), (18, 7), (26, 1), (4, 19), (15, 13), (6, 21), (14, 25), (22, 14), (18, 4), (27, 20), (25, 14), (18, 26), (27, 33), (20, 32), (4, 2), (21, 13), (2, 34), (31, 35), (33, 37), (22, 9), (23, 15), (29, 5), (34, 29), (20, 13), (13, 0), (12, 1), (6, 10), (17, 20), (9, 22), (29, 34), (27, 37), (18, 17), (5, 30), (11, 26), (14, 24), (29, 19), (22, 27), (15, 9), (5, 16), (30, 35), (31, 15), (6, 31), (31, 1), (3, 28), (22, 34), (37, 28), (38, 23), (38, 26), (36, 9), (13, 17), (6, 2), (16, 25), (9, 17), (5, 27), (25, 34), (12, 7), (36, 30), (30, 22), (23, 12), (19, 10), (37, 35), (1, 12), (8, 32), (23, 10), (14, 17), (17, 37), (12, 19), (1, 15), (30, 2), (16, 35), (11, 20), (15, 3), (5, 25), (23, 36), (20, 37), (35, 1), (12, 37), (3, 3), (9, 25), (24, 32), (7, 11), (10, 35), (27, 3), (38, 28), (27, 14), (3, 16), (19, 1), (16, 6), (20, 29), (8, 21), (37, 34), (13, 12), (33, 31), (25, 21), (22, 28), (9, 11), (28, 17), (15, 2), (34, 36), (32, 9), (10, 5), (7, 27), (27, 8), (18, 0), (35, 15), (13, 34), (35, 11), (31, 33), (3, 32), (25, 32), (22, 15), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72576", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (8, 18), (37, 26), (12, 15), (11, 15), (13, 35), (34, 26), (28, 36), (15, 12), (19, 11), (10, 26), (10, 8), (12, 4), (11, 2), (18, 27), (2, 13), (32, 35), (1, 26), (34, 11), (30, 12), (28, 38), (13, 23), (2, 32), (14, 15), (23, 24), (12, 38), (32, 32), (27, 34), (21, 18), (18, 4), (3, 36), (22, 38), (23, 5), (32, 34), (24, 35), (11, 25), (1, 14), (36, 0), (11, 21), (37, 30), (12, 11), (38, 23), (2, 14), (4, 12), (12, 0), (29, 31), (23, 17), (22, 11), (0, 18), (8, 4), (17, 15), (7, 22), (36, 27), (30, 21), (37, 19), (21, 13), (28, 33), (15, 18), (12, 7), (33, 10), (26, 4), (5, 20), (31, 4), (8, 38), (17, 28), (22, 10), (37, 8), (28, 17), (14, 33), (14, 5), (10, 22), (15, 35), (10, 35), (8, 20), (35, 33), (28, 11), (26, 0), (1, 12), (12, 13), (22, 13), (30, 27), (20, 19), (34, 21), (8, 23), (28, 32), (17, 16), (26, 15), (37, 24), (38, 3), (22, 2), (23, 20), (12, 5), (10, 9), (14, 32), (38, 35), (13, 8), (38, 26), (2, 33), (10, 32), (16, 4), (23, 10), (37, 29), (32, 5), (8, 14), (2, 31), (35, 30), (15, 14), (33, 14), (22, 18), (13, 4), (1, 30), (6, 16), (26, 9), (16, 24), (0, 9), (9, 29), (13, 1), (32, 26), (20, 28), (11, 30), (6, 5), (9, 3), (27, 29), (38, 37), (11, 28), (3, 20), (34, 23), (13, 19), (10, 20), (26, 21), (31, 16), (38, 14), (0, 38), (4, 0), (26, 37), (17, 25), (12, 26), (30, 11), (28, 3), (35, 3), (6, 0), (19, 37), (30, 0), (19, 7), (21, 6), (2, 23), (28, 34), (21, 31), (12, 10), (19, 13), (18, 38), (18, 19), (37, 21), (24, 26), (26, 6), (35, 28), (25, 23), (19, 34), (1, 23), (28, 12), (35, 31), (31, 1), (13, 7), (5, 36), (23, 1), (1, 31), (33, 36), (16, 15), (3, 33), (7, 35), (11, 32), (10, 29), (37, 10), (6, 25), (10, 0), (20, 32), (0, 27), (33, 16), (24, 19), (0, 20), (20, 4), (33, 35), (6, 33), (19, 8), (30, 32), (6, 8), (22, 22), (4, 5), (3, 25), (15, 23), (26, 26), (36, 31), (10, 33), (0, 3), (32, 22), (21, 7), (4, 3), (16, 13), (3, 3), (18, 7), (26, 10), (16, 34), (9, 23), (24, 6), (10, 37), (1, 21), (34, 14), (22, 24), (21, 23), (2, 34), (14, 12), (18, 5), (29, 0), (38, 30), (36, 15), (17, 13), (30, 18), (25, 0), (0, 30), (10, 5), (10, 34), (24, 13), (37, 14), (37, 37), (0, 6), (38, 4), (29, 9), (2, 10), (15, 20), (4, 7), (23, 13), (15, 16), (20, 15), (18, 34), (30, 3), (7, 6), (30, 37), (7, 15), (5, 31), (18, 20), (38, 6), (12, 27), (34, 13), (8, 13), (26, 27), (36, 6), (25, 30), (21, 37), (27, 12), (23, 30), (1, 32), (38, 10), (27, 37), (7, 27), (14, 27), (35, 22), (35, 17), (19, 27), (30, 26), (12, 37), (16, 12), (24, 3), (30, 8), (33, 1), (22, 23), (14, 21), (21, 20), (23, 21), (35, 26), (4, 24), (24, 15), (28, 5), (9, 37), (9, 34), (5, 25), (6, 38), (13, 12), (2, 28), (1, 34), (3, 7), (15, 11), (7, 17), (12, 16), (23, 27), (3, 28), (14, 23), (37, 28), (18, 1), (18, 37), (15, 6), (16, 36), (23, 7), (13, 30), (7, 37), (15, 26), (21, 26), (17, 11), (0, 36), (16, 20), (23, 33), (11, 13), (25, 13), (29, 17), (16, 21), (19, 20), (28, 7), (5, 10), (38, 27), (19, 28), (34, 0), (2, 6), (16, 19), (2, 15), (25, 18), (3, 32), (32, 28), (33, 15), (31, 38), (15, 37), (33, 33), (20, 25), (38, 1), (35, 5), (19, 18), (29, 8), (16, 35), (6, 35), (0, 23), (38, 8), (13, 11), (7, 5), (1, 16), (9, 21), (28, 18), (34, 25), (7, 10), (19, 19), (34, 4), (27, 8), (7, 26), (36, 32), (20, 30), (8, 27), (0, 8), (0, 17), (29, 34), (35, 2), (18, 30), (2, 21), (37, 31), (1, 8), (31, 10), (34, 31), (1, 3), (31, 37), (13, 29), (24, 38), (20, 36), (33, 7), (19, 4), (34, 12), (36, 28), (12, 36), (23, 31), (21, 14), (16, 33), (32, 4), (27, 19), (35, 25), (4, 38), (15, 22), (0, 11), (8, 5), (5, 12), (29, 29), (6, 32), (25, 5), (27, 20), (4, 15), (22, 29), (38, 17), (25, 32), (0, 14), (37, 4), (35, 32), (23, 38), (6, 4), (8, 28), (6, 13), (37, 35), (8, 34), (3, 29), (36, 25), (20, 3), (26, 17), (29, 7), (36, 37), (37, 25), (29, 1), (18, 3), (26, 8), (27, 24), (19, 3), (29, 16), (25, 28), (38, 9), (22, 8), (4, 35), (19, 29), (22, 3), (4, 21), (27, 18), (29, 38), (17, 34), (29, 20), (29, 5), (36, 20), (2, 16), (27, 35), (12, 3), (36, 14), (13, 32), (28, 1), (24, 9), (7, 30), (11, 7), (20, 18), (29, 37), (5, 11), (34, 8), (0, 19), (13, 16), (28, 2), (5, 2), (4, 32), (5, 35), (1, 19), (2, 19), (0, 33), (14, 13), (6, 37), (16, 28), (10, 27), (33, 31), (25, 12), (3, 0), (4, 4), (5, 5), (32, 30), (17, 37), (8, 24), (6, 31), (19, 35), (28, 23), (25, 8), (24, 20), (20, 12), (12, 9), (28, 22), (4, 10), (14, 0), (29, 24), (31, 26), (34, 36), (3, 16), (4, 33), (31, 23), (20, 17), (0, 1), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557568", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), 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), (16, 6), (1, 32), (33, 0), (18, 22), (26, 34), (9, 36), (1, 6), (13, 2), (30, 37), (26, 32), (4, 3), (1, 15), (20, 11), (11, 36), (13, 19), (6, 35), (24, 11), (34, 19), (10, 15), (5, 29), (25, 11), (1, 10), (19, 6), (29, 36), (33, 33), (32, 15), (10, 26), (0, 25), (13, 31), (13, 16), (20, 34), (29, 33), (13, 5), (19, 2), (4, 38), (28, 9), (30, 31), (18, 10), (34, 20), (2, 32), (18, 7), (2, 37), (16, 11), (21, 24), (3, 14), (20, 4), (8, 22), (25, 19), (18, 28), (13, 1), (1, 8), (4, 21), (27, 17), (35, 6), (21, 4), (26, 5), (3, 27), (1, 19), (33, 12), (35, 29), (26, 19), (22, 29), (14, 32), (18, 23), (16, 20), (2, 10), (7, 0), (29, 28), (28, 34), (16, 13), (21, 33), (28, 24), (20, 3), (20, 5), (15, 22), (23, 13), (18, 25), (32, 38), (4, 9), (9, 6), (15, 28), (5, 15), (21, 19), (21, 1), (6, 1), (6, 27), (29, 4), (29, 37), (11, 22), (13, 35), (14, 1), (22, 12), (27, 33), (12, 30), (15, 5), (9, 27), (22, 34), (3, 37), (30, 21), (27, 25), (31, 23), (4, 22), (9, 24), (27, 5), (24, 38), (30, 34), (31, 19), (9, 12), (4, 0), (20, 21), (22, 10), (28, 18), (35, 7), (34, 22), (16, 36), (35, 4), (4, 19), (8, 21), (3, 19), (17, 25), (34, 21), (24, 32), (26, 23), (23, 32), (15, 3), (29, 7), (27, 22), (34, 36), (14, 11), (6, 8), (0, 15), (35, 16), (27, 7), (33, 18), (17, 20), (7, 24), (15, 34), (19, 4), (31, 10), (31, 6), (12, 37), (29, 24), (28, 36), (3, 30), (12, 14), (10, 19), (30, 38), (0, 33), (33, 9), (2, 9), (21, 38), (9, 37), (7, 4), (5, 13), (30, 16), (27, 9), (34, 4), (10, 37), (15, 12), (17, 37), (8, 36), (10, 36), (29, 0), (19, 21), (8, 20), (31, 33), (22, 18), (3, 0), (23, 36), (19, 22), (20, 10), (5, 31), (15, 21), (5, 21), (31, 2), (13, 25), (31, 30), (14, 29), (35, 31), (11, 20), (22, 28), (9, 11), (5, 6), (2, 6), (10, 27), (17, 12), (28, 16), (16, 38), (14, 34), (32, 10), (27, 0), (14, 9), (1, 21), (19, 25), (17, 10), (21, 8), (26, 7), (34, 25), (16, 3), (14, 3), (22, 24), (16, 27), (23, 17), (34, 35), (11, 2), (28, 33), (2, 36), (2, 0), (0, 19), (14, 24), (24, 22), (35, 3), (23, 37), (20, 6), (27, 6), (14, 36), (13, 14), (31, 32), (15, 37), (22, 38), (3, 33), (3, 25), (31, 26), (5, 12), (1, 2), (35, 1), (33, 22), (17, 30), (33, 14), (2, 35), (2, 38), (21, 7), (22, 21), (1, 7), (10, 0), (9, 5), (33, 24), (3, 13), (25, 30), (25, 17), (0, 10), (10, 22), (29, 19), (21, 29), (22, 9), (24, 31), (19, 37), (19, 14), (2, 21), (20, 32), (9, 18), (14, 15), (6, 30), (30, 4), (17, 17), (18, 38), (33, 35), (21, 6), (14, 30), (16, 10), (22, 4), (1, 38), (34, 5), (23, 22), (25, 34), (21, 37), (9, 0), (8, 11), (12, 23), (4, 4), (5, 34), (3, 22), (25, 23), (24, 25), (13, 17), (0, 36), (35, 30), (4, 17), (28, 7), (22, 13), (1, 23), (19, 35), (11, 15), (15, 13), (11, 19), (26, 37), (6, 36), (2, 13), (32, 29), (13, 9), (9, 17), (2, 15), (16, 1), (4, 28), (19, 28), (14, 27), (14, 19), (1, 18), (24, 35), (26, 21), (15, 33), (19, 12), (13, 22), (22, 20), (33, 34), (31, 12), (22, 5), (14, 35), (8, 33), (34, 31), (20, 24), (34, 3), (6, 33), (1, 28), (23, 29), (12, 10), (21, 12), (34, 16), (15, 18), (30, 13), (15, 4), (5, 8), (23, 8), (29, 38), (30, 1), (1, 4), (25, 22), (4, 37), (20, 36), (8, 14), (19, 27), (24, 27), (13, 11), (16, 37), (13, 34), (21, 13), (25, 37), (16, 28), (11, 33), (20, 15), (22, 2), (8, 35), (14, 2), (10, 32), (18, 5), (25, 9), (2, 19), (14, 21), (17, 38), (2, 14), (27, 1), (2, 33), (26, 2), (32, 37), (7, 6), (21, 3), (15, 11), (19, 7), (23, 14), (34, 13), (0, 32), (35, 8), (24, 6), (0, 30), (30, 2), (33, 6), (23, 27), (13, 32), (12, 2), (10, 30), (32, 19), (16, 8), (19, 32), (25, 6), (22, 1), (19, 10), (1, 35), (18, 1), (18, 8), (16, 9), (18, 35), (26, 3), (4, 10), (34, 30), (9, 1), (16, 2), (17, 11), (11, 9), (10, 35), (24, 1), (18, 3), (24, 7), (30, 36), (25, 27), (10, 25), (7, 16), (11, 17), (7, 13), (2, 16), (5, 10), (2, 17), (15, 2), (6, 5), (12, 13), (30, 5), (16, 7), (2, 28), (31, 15), (5, 1), (14, 37), (29, 34), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226800", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), 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), (7, 25), (7, 19), (17, 6), (0, 18), (2, 1), (8, 25), (6, 1), (30, 1), (8, 22), (1, 12), (33, 0), (35, 18), (11, 14), (14, 0), (3, 15), (16, 13), (3, 28), (32, 12), (3, 10), (13, 29), (25, 10), (9, 26), (11, 15), (7, 24), (32, 14), (24, 25), (10, 6), (10, 12), (23, 15), (28, 28), (6, 3), (17, 22), (3, 18), (37, 10), (14, 27), (32, 25), (21, 28), (18, 3), (21, 16), (22, 17), (33, 7), (22, 8), (34, 18), (34, 24), (0, 15), (12, 1), (20, 10), (8, 30), (13, 6), (21, 30), (16, 29), (36, 6), (14, 15), (18, 5), (1, 23), (34, 12), (35, 28), (35, 19), (18, 30), (23, 26), (8, 1), (22, 21), (2, 20), (16, 30), (19, 28), (17, 23), (21, 7), (36, 10), (5, 5), (33, 25), (18, 20), (28, 5), (34, 5), (5, 29), (8, 3), (32, 24), (10, 14), (9, 4), (32, 6), (30, 8), (0, 20), (4, 2), (5, 23), (36, 22), (38, 3), (35, 12), (24, 15), (5, 16), (20, 7), (32, 21), (35, 8), (0, 14), (14, 1), (3, 22), (37, 2), (33, 29), (7, 21), (20, 8), (25, 28), (5, 4), (31, 15), (26, 19), (25, 7), (18, 7), (30, 26), (13, 4), (31, 14), (38, 16), (19, 24), (24, 22), (18, 21), (28, 9), (25, 21), (6, 15), (7, 14), (33, 16), (27, 23), (30, 22), (38, 26), (32, 23), (32, 11), (15, 9), (30, 14), (30, 10), (18, 15), (12, 28), (8, 19), (15, 3), (24, 18), (25, 20), (12, 17), (17, 27), (29, 6), (27, 12), (20, 20), (19, 25), (30, 9), (16, 1), (16, 22), (19, 15), (30, 4), (27, 24), (38, 24), (8, 13), (23, 5), (37, 23), (18, 23), (25, 11), (36, 25), (28, 12), (24, 17), (7, 9), (29, 5), (35, 0), (30, 24), (3, 21), (19, 14), (35, 26), (22, 4), (4, 16), (2, 22), (36, 18), (6, 10), (4, 21), (24, 2), (12, 12), (36, 0), (2, 25), (6, 21), (12, 14), (0, 29), (37, 22), (3, 23), (0, 12), (29, 17), (11, 27), (34, 10), (37, 11), (4, 25), (19, 12), (19, 9), (19, 7), (10, 22), (26, 30), (34, 4), (14, 8), (31, 4), (9, 13), (8, 0), (34, 20), (37, 18), (1, 4), (17, 10), (31, 27), (13, 22), (20, 9), (0, 8), (25, 13), (8, 4), (8, 9), (21, 19), (16, 25), (37, 17), (19, 21), (8, 15), (20, 28), (20, 24), (28, 10), (32, 0), (10, 11), (16, 17), (9, 1), (30, 3), (17, 7), (2, 18), (27, 30), (9, 18), (25, 22), (18, 10), (33, 20), (36, 8), (19, 3), (29, 2), (30, 7), (2, 24), (27, 26), (0, 16), (27, 7), (28, 17), (2, 27), (36, 16), (32, 26), (3, 19), (38, 23), (12, 6), (17, 13), (3, 4), (14, 24), (26, 13), (11, 25), (24, 6), (27, 20), (35, 17), (5, 12), (7, 17), (5, 10), (16, 14), (21, 12), (35, 15), (30, 2), (11, 0), (20, 3), (38, 15), (31, 16), (20, 13), (17, 2), (22, 3), (37, 26), (32, 22), (21, 25), (32, 13), (15, 15), (14, 28), (16, 28), (38, 8), (36, 29), (30, 5), (22, 0), (18, 4), (11, 17), (3, 0), (23, 0), (10, 15), (11, 5), (38, 9), (20, 26), (22, 2), (3, 29), (27, 4), (33, 3), (24, 13), (32, 5), (4, 26), (36, 19), (25, 4), (19, 22), (34, 3), (37, 12), (0, 21), (34, 28), (32, 29), (14, 20), (37, 27), (20, 18), (20, 2), (29, 10), (2, 12), (10, 23), (18, 27), (13, 19), (2, 2), (30, 27), (23, 29), (34, 16), (9, 2), (34, 15), (23, 8), (24, 23), (0, 6), (33, 14), (34, 7), (35, 22), (28, 21), (7, 13), (0, 11), (2, 6), (9, 23), (37, 9), (7, 10), (1, 5), (22, 15), (38, 29), (28, 0), (21, 18), (23, 4), (22, 26), (20, 15), (26, 28), (6, 0), (28, 30), (1, 19), (36, 9), (5, 24), (5, 6), (17, 21), (9, 24), (12, 19), (17, 25), (26, 23), (10, 10), (36, 11), (18, 9), (2, 13), (35, 25), (22, 11), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "243000", "dataset": "MATH"}
{"messages": [{"content": "In a 38x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 25), (24, 21), (5, 31), (34, 7), (27, 19), (35, 30), (5, 24), (24, 30), (17, 23), (21, 13), (18, 29), (1, 6), (13, 5), (14, 6), (30, 9), (34, 3), (18, 20), (27, 13), (10, 16), (24, 9), (36, 0), (13, 0), (28, 6), (28, 3), (16, 16), (15, 8), (11, 0), (6, 11), (29, 14), (16, 0), (16, 13), (26, 27), (37, 8), (21, 18), (4, 9), (12, 29), (20, 27), (24, 26), (19, 9), (33, 27), (14, 9), (15, 16), (16, 9), (9, 9), (3, 5), (10, 9), (5, 9), (37, 20), (26, 29), (0, 2), (0, 8), (11, 13), (17, 15), (0, 25), (1, 7), (11, 8), (37, 17), (8, 21), (21, 20), (22, 2), (16, 12), (10, 2), (37, 6), (31, 15), (3, 6), (36, 13), (34, 30), (10, 30), (28, 26), (22, 9), (14, 30), (7, 22), (28, 7), (28, 1), (17, 21), (3, 28), (25, 20), (33, 16), (19, 2), (16, 14), (7, 16), (17, 8), (1, 18), (4, 4), (26, 24), (8, 14), (13, 11), (8, 25), (14, 5), (8, 0), (19, 31), (30, 10), (15, 0), (21, 4), (6, 18), (1, 23), (8, 31), (32, 24), (6, 7), (11, 6), (21, 23), (29, 2), (17, 17), (27, 23), (28, 27), (34, 2), (29, 1), (24, 19), (7, 25), (25, 0), (31, 12), (14, 17), (12, 17), (7, 8), (2, 22), (25, 28), (25, 6), (4, 11), (31, 24), (23, 4), (7, 10), (27, 24), (18, 2), (2, 18), (16, 6), (25, 3), (34, 21), (8, 15), (23, 8), (33, 4), (26, 0), (16, 18), (10, 31), (21, 7), (7, 6), (1, 19), (6, 2), (20, 21), (24, 5), (9, 16), (36, 3), (11, 12), (21, 26), (16, 5), (32, 27), (7, 9), (32, 14), (17, 29), (20, 24), (20, 3), (24, 29), (10, 4), (33, 23), (6, 30), (3, 12), (35, 17), (3, 0), (1, 11), (3, 10), (36, 2), (31, 11), (9, 28), (21, 29), (36, 4), (33, 10), (17, 20), (26, 13), (8, 29), (29, 19), (12, 19), (12, 23), (23, 15), (34, 9), (22, 12), (16, 31), (0, 20), (36, 23), (33, 18), (18, 22), (23, 13), (9, 14), (11, 5), (5, 4), (15, 3), (0, 26), (8, 20), (23, 31), (3, 9), (35, 15), (37, 28), (18, 24), (30, 2), (1, 28), (33, 2), (25, 9), (8, 12), (27, 27), (12, 5), (34, 25), (1, 14), (22, 19), (7, 7), (14, 21), (13, 24), (27, 14), (1, 8), (34, 28), (32, 25), (6, 25), (5, 30), (5, 17), (18, 27), (7, 11), (23, 2), (29, 25), (32, 10), (4, 19), (12, 22), (0, 19), (9, 20), (19, 23), (10, 8), (1, 9), (3, 25), (15, 24), (7, 27), (1, 10), (34, 6), (11, 18), (14, 15), (26, 15), (14, 8), (18, 14), (32, 9), (6, 0), (4, 15), (25, 8), (35, 26), (11, 27), (14, 13), (5, 20), (11, 1), (35, 19), (29, 21), (36, 25), (18, 18), (35, 3), (21, 8), (35, 5), (18, 26), (10, 15), (31, 6), (2, 9), (14, 7), (5, 0), (8, 11), (2, 5), (14, 1), (19, 3), (11, 22), (35, 25), (5, 6), (12, 8), (4, 28), (18, 6), (0, 28), (15, 13), (34, 18), (13, 2), (15, 30), (36, 31), (32, 1), (29, 3), (25, 24), (20, 6), (11, 26), (15, 11), (18, 23), (21, 30), (1, 29), (1, 16), (33, 31), (21, 12), (29, 15), (10, 7), (29, 7), (35, 2), (4, 16), (34, 0), (36, 15), (31, 30), (23, 18), (2, 27), (19, 16), (33, 15), (29, 28), (22, 14), (26, 19), (31, 2), (19, 25), (35, 11), (22, 4), (27, 2), (1, 3), (0, 16), (29, 29), (31, 4), (29, 31), (16, 28), (33, 0), (28, 8), (29, 20), (4, 30), (23, 11), (28, 28), (16, 17), (10, 12), (34, 19), (32, 12), (4, 10), (10, 10), (22, 1), (13, 26), (9, 30), (20, 22), (5, 14), (28, 16), (27, 30), (17, 18), (2, 8), (12, 3), (9, 11), (18, 7), (27, 0), (19, 29), (17, 6), (22, 16), (30, 21), (28, 25), (11, 14), (21, 10), (34, 31), (2, 12), (5, 2), (15, 10), (19, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766080", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 28), (6, 25), (26, 3), (15, 12), (20, 27), (21, 26), (29, 22), (31, 23), (30, 14), (27, 11), (27, 4), (26, 16), (13, 0), (5, 9), (26, 14), (9, 9), (22, 8), (13, 7), (11, 0), (33, 9), (34, 5), (25, 10), (3, 23), (10, 28), (18, 2), (29, 6), (3, 9), (14, 0), (32, 13), (3, 10), (24, 14), (21, 23), (10, 13), (11, 16), (9, 22), (8, 13), (23, 12), (19, 25), (18, 12), (14, 5), (23, 21), (15, 6), (15, 22), (13, 26), (5, 17), (18, 21), (10, 5), (30, 7), (11, 15), (7, 22), (34, 13), (2, 18), (27, 22), (10, 15), (16, 15), (21, 10), (3, 24), (16, 27), (10, 18), (21, 19), (23, 28), (20, 7), (12, 5), (1, 1), (31, 7), (13, 18), (12, 17), (30, 26), (18, 17), (8, 4), (34, 25), (12, 8), (3, 17), (28, 29), (25, 29), (12, 4), (19, 18), (9, 18), (18, 16), (26, 25), (29, 20), (16, 20), (5, 27), (9, 16), (0, 12), (20, 3), (19, 20), (23, 8), (19, 28), (5, 19), (27, 26), (21, 29), (8, 10), (33, 16), (1, 3), (4, 28), (1, 26), (22, 6), (33, 24), (4, 5), (20, 20), (10, 11), (22, 25), (18, 14), (14, 6), (15, 9), (34, 18), (23, 27), (8, 22), (31, 0), (15, 14), (2, 27), (12, 0), (31, 17), (15, 0), (32, 20), (32, 7), (18, 22), (4, 17), (29, 29), (0, 13), (26, 5), (31, 8), (9, 17), (6, 20), (3, 2), (4, 9), (27, 21), (27, 16), (31, 29), (5, 16), (20, 11), (3, 12), (31, 28), (15, 4), (2, 20), (28, 28), (10, 24), (13, 1), (6, 19), (27, 3), (25, 15), (21, 28), (1, 15), (28, 19), (32, 5), (32, 28), (13, 29), (14, 24), (3, 21), (23, 25), (30, 12), (32, 17), (25, 16), (10, 7), (7, 16), (3, 22), (17, 21), (19, 17), (1, 13), (21, 2), (3, 29), (17, 19), (6, 22), (19, 13), (10, 19), (5, 6), (22, 13), (29, 1), (26, 23), (9, 20), (8, 0), (5, 21), (11, 9), (10, 27), (11, 7), (34, 3), (34, 1), (21, 21), (9, 11), (5, 10), (33, 25), (19, 24), (27, 20), (32, 22), (27, 19), (24, 23), (0, 27), (23, 22), (14, 4), (7, 4), (22, 7), (10, 20), (23, 17), (21, 15), (17, 11), (13, 4), (34, 17), (28, 2), (29, 3), (11, 17), (2, 1), (16, 3), (13, 27), (29, 18), (24, 17), (3, 18), (20, 28), (4, 16), (3, 4), (34, 23), (15, 3), (24, 24), (1, 10), (3, 28), (0, 9), (13, 16), (16, 6), (19, 19), (11, 18), (4, 27), (4, 25), (25, 26), (24, 25), (20, 22), (11, 25), (21, 3), (25, 8), (19, 16), (3, 7), (23, 11), (5, 0), (29, 4), (15, 10), (33, 13), (17, 0), (10, 21), (32, 16), (28, 24), (6, 18), (31, 21), (14, 11), (26, 18), (21, 18), (12, 19), (25, 6), (12, 26), (29, 14), (26, 15), (18, 7), (23, 19), (9, 28), (0, 24), (4, 23), (23, 2), (16, 5), (0, 4), (8, 15), (14, 18), (34, 12), (4, 20), (2, 28), (1, 23), (29, 24), (33, 26), (5, 8), (17, 5), (21, 25), (28, 13), (29, 0), (24, 29), (30, 15), (5, 7), (31, 18), (22, 0), (2, 26), (20, 1), (24, 3), (10, 1), (17, 26), (19, 14), (13, 11), (19, 29), (4, 18), (7, 1), (16, 14), (24, 20), (11, 3), (8, 27), (1, 5), (29, 17), (16, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "962280", "dataset": "MATH"}
{"messages": [{"content": "In a 33x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 29), (30, 10), (15, 1), (20, 28), (18, 10), (21, 0), (10, 4), (31, 0), (3, 22), (5, 5), (15, 2), (14, 23), (4, 4), (31, 31), (22, 26), (22, 21), (1, 5), (26, 27), (14, 6), (9, 3), (6, 30), (18, 16), (3, 23), (1, 4), (8, 31), (18, 11), (18, 3), (11, 17), (16, 29), (30, 15), (23, 25), (8, 19), (13, 32), (23, 30), (21, 1), (6, 27), (0, 33), (32, 15), (3, 3), (18, 14), (17, 15), (3, 6), (23, 9), (7, 16), (16, 25), (15, 5), (9, 9), (10, 13), (28, 20), (1, 13), (12, 19), (17, 31), (31, 25), (2, 8), (30, 6), (19, 11), (31, 14), (10, 1), (19, 5), (32, 2), (25, 30), (23, 18), (3, 14), (14, 19), (10, 22), (0, 34), (10, 12), (22, 23), (29, 33), (17, 32), (23, 6), (13, 8), (18, 1), (17, 7), (13, 16), (25, 5), (6, 31), (15, 25), (22, 12), (25, 17), (29, 3), (19, 16), (8, 7), (3, 34), (21, 6), (9, 24), (19, 25), (12, 10), (3, 32), (15, 3), (7, 1), (5, 29), (19, 14), (25, 31), (28, 11), (18, 17), (13, 29), (20, 2), (0, 13), (15, 12), (7, 24), (32, 4), (26, 29), (10, 15), (17, 21), (28, 28), (2, 30), (23, 29), (9, 1), (25, 9), (3, 30), (0, 15), (22, 4), (27, 31), (28, 3), (18, 33), (14, 14), (4, 5), (6, 25), (31, 20), (8, 21), (25, 11), (1, 23), (26, 26), (20, 13), (17, 12), (32, 14), (10, 25), (26, 8), (16, 21), (7, 20), (20, 22), (10, 21), (21, 32), (31, 28), (28, 31), (17, 4), (22, 11), (2, 16), (15, 15), (27, 15), (13, 34), (30, 8), (16, 11), (7, 19), (15, 21), (13, 25), (21, 27), (16, 26), (17, 29), (19, 27), (17, 11), (28, 9), (2, 23), (4, 16), (32, 22), (12, 21), (19, 32), (16, 33), (25, 18), (7, 28), (15, 30), (3, 8), (4, 19), (31, 8), (29, 0), (31, 15), (13, 13), (5, 8), (8, 3), (21, 26), (32, 32), (23, 23), (7, 5), (25, 27), (25, 4), (7, 9), (0, 27), (10, 6), (8, 11), (14, 31), (16, 7), (20, 9), (10, 31), (24, 11), (26, 28), (30, 2), (0, 6), (7, 30), (22, 10), (32, 29), (20, 8), (28, 6), (21, 4), (32, 20), (18, 12), (4, 10), (17, 19), (20, 30), (28, 25), (8, 10), (24, 0), (22, 6), (6, 19), (11, 14), (25, 20), (30, 21), (29, 18), (0, 25), (24, 10), (12, 25), (23, 26), (0, 19), (11, 11), (31, 21), (25, 23), (13, 22), (1, 32), (14, 5), (4, 33), (3, 20), (14, 7), (5, 1), (0, 1), (8, 29), (12, 24), (0, 16), (1, 31), (18, 0), (18, 13), (28, 29), (27, 29), (0, 9), (22, 1), (14, 8), (2, 25), (1, 18), (13, 20), (5, 21), (11, 4), (24, 34), (31, 26), (6, 16), (27, 8), (29, 16), (24, 7), (31, 32), (9, 31), (22, 25), (7, 8), (30, 17), (3, 24), (12, 5), (5, 26), (20, 1), (2, 22), (20, 34), (1, 29), (30, 31), (31, 4), (30, 22), (17, 18), (11, 16), (2, 32), (20, 11), (28, 21), (6, 14), (10, 3), (27, 13), (6, 22), (12, 34), (31, 10), (19, 20), (22, 15), (25, 6), (8, 13), (25, 26), (3, 1), (4, 1), (9, 28), (9, 20), (5, 9), (24, 12), (17, 6), (14, 25), (17, 9), (23, 34), (11, 5), (6, 9), (12, 6), (1, 33), (4, 32), (16, 18), (22, 18), (15, 23), (24, 19), (17, 8), (15, 13), (23, 2), (28, 4), (22, 34), (12, 3), (27, 28), (28, 7), (11, 9), (19, 23), (1, 26), (31, 2), (4, 20), (14, 32), (12, 0), (23, 4), (20, 15), (18, 9), (13, 0), (14, 11), (13, 19), (23, 11), (22, 14), (19, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574500", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 27), (11, 29), (22, 13), (32, 21), (17, 26), (4, 20), (29, 36), (10, 22), (30, 28), (35, 17), (29, 34), (3, 35), (33, 4), (12, 17), (6, 11), (5, 27), (16, 35), (32, 23), (5, 5), (6, 13), (3, 26), (9, 5), (3, 2), (26, 15), (25, 7), (24, 37), (27, 2), (26, 31), (30, 20), (2, 14), (12, 32), (11, 15), (21, 30), (7, 15), (25, 28), (11, 8), (35, 7), (30, 34), (4, 33), (16, 16), (29, 9), (5, 25), (6, 20), (0, 4), (3, 24), (7, 26), (27, 26), (1, 17), (31, 22), (1, 0), (33, 3), (33, 17), (33, 13), (3, 16), (7, 20), (31, 31), (2, 13), (18, 4), (14, 8), (17, 25), (23, 32), (14, 3), (4, 3), (11, 10), (13, 29), (23, 20), (14, 24), (20, 10), (0, 19), (36, 6), (13, 24), (4, 14), (20, 18), (7, 25), (27, 7), (20, 30), (36, 26), (17, 33), (26, 2), (21, 24), (9, 31), (22, 3), (14, 6), (27, 29), (25, 11), (36, 7), (12, 2), (17, 11), (3, 28), (17, 24), (32, 33), (20, 33), (25, 10), (16, 12), (22, 7), (33, 35), (2, 19), (33, 11), (12, 37), (19, 30), (1, 35), (15, 35), (13, 34), (28, 13), (35, 33), (28, 0), (32, 6), (10, 35), (15, 32), (28, 23), (15, 12), (11, 30), (14, 14), (34, 0), (24, 23), (20, 35), (15, 19), (32, 26), (14, 28), (19, 20), (29, 17), (11, 26), (36, 4), (4, 24), (33, 27), (5, 37), (5, 14), (21, 13), (23, 30), (2, 24), (33, 36), (10, 6), (27, 19), (32, 9), (21, 9), (26, 12), (29, 35), (21, 10), (13, 8), (12, 6), (34, 30), (27, 35), (20, 27), (6, 31), (35, 34), (29, 3), (10, 30), (1, 27), (10, 9), (8, 13), (19, 19), (15, 22), (3, 10), (24, 2), (17, 20), (1, 10), (20, 5), (29, 4), (19, 25), (9, 4), (26, 21), (8, 31), (17, 10), (31, 5), (5, 7), (20, 24), (1, 32), (16, 22), (5, 17), (19, 11), (9, 2), (34, 37), (16, 15), (1, 19), (33, 34), (30, 3), (13, 36), (31, 34), (18, 28), (13, 26), (34, 32), (8, 9), (13, 1), (8, 26), (18, 14), (20, 1), (6, 15), (27, 37), (24, 35), (2, 17), (3, 6), (31, 2), (10, 17), (28, 21), (35, 28), (4, 19), (36, 23), (0, 21), (2, 7), (10, 27), (36, 27), (11, 31), (14, 13), (13, 10), (28, 14), (33, 33), (30, 22), (4, 36), (36, 3), (1, 29), (1, 7), (11, 12), (25, 0), (12, 29), (35, 2), (1, 36), (10, 25), (30, 0), (16, 25), (14, 33), (32, 13), (30, 23), (22, 20), (24, 17), (32, 19), (10, 24), (22, 25), (9, 10), (4, 1), (24, 24), (5, 33), (12, 34), (22, 18), (33, 21), (6, 7), (11, 0), (22, 1), (30, 14), (25, 24), (14, 22), (17, 18), (10, 23), (20, 12), (27, 16), (0, 32), (16, 27), (33, 8), (31, 30), (25, 12), (31, 8), (8, 32), (26, 14), (7, 23), (18, 12), (36, 5), (16, 8), (24, 13), (28, 4), (16, 30), (34, 10), (25, 35), (0, 18), (17, 23), (1, 2), (27, 22), (27, 28), (23, 10), (26, 26), (14, 29), (31, 29), (26, 23), (17, 34), (2, 31), (33, 23), (0, 31), (15, 11), (24, 22), (16, 4), (16, 28), (31, 3), (31, 1), (35, 30), (36, 8), (27, 6), (9, 20), (28, 3), (12, 26), (20, 32), (3, 36), (6, 3), (5, 1), (12, 15), (29, 26), (18, 19), (7, 28), (23, 36), (0, 16), (7, 8), (35, 6), (28, 18), (30, 27), (3, 25), (30, 24), (25, 37), (9, 22), (24, 4), (26, 28), (17, 6), (6, 10), (28, 6), (13, 4), (18, 22), (18, 5), (29, 19), (5, 22), (20, 0), (18, 21), (8, 2), (31, 13), (32, 30), (31, 21), (8, 30), (0, 24), (0, 2), (26, 4), (24, 32), (25, 1), (3, 19), (2, 36), (5, 23), (30, 2), (0, 10), (6, 8), (27, 18), (32, 7), (5, 35), (3, 0), (10, 37), (11, 24), (9, 21), (30, 4), (26, 25), (5, 34), (2, 21), (28, 36), (3, 3), (33, 14), (6, 23), (24, 11), (25, 15), (8, 28), (28, 22), (11, 33), (13, 25), (22, 37), (0, 9), (13, 15), (28, 1), (25, 14), (32, 1), (0, 34), (9, 18), (29, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "981240", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (8, 33), (18, 13), (12, 4), (29, 20), (15, 28), (14, 4), (10, 19), (17, 9), (26, 6), (11, 24), (7, 24), (1, 26), (22, 25), (0, 16), (22, 3), (15, 14), (17, 15), (15, 7), (17, 17), (11, 34), (21, 17), (27, 4), (5, 21), (1, 9), (0, 3), (31, 13), (34, 26), (23, 33), (26, 27), (4, 13), (12, 28), (34, 13), (34, 11), (33, 6), (32, 33), (32, 8), (3, 30), (8, 20), (22, 6), (29, 23), (22, 20), (5, 0), (5, 20), (9, 2), (25, 29), (21, 15), (10, 17), (2, 8), (8, 29), (30, 9), (32, 14), (19, 19), (34, 10), (13, 1), (2, 14), (0, 17), (28, 31), (1, 27), (11, 15), (6, 9), (28, 34), (35, 26), (32, 10), (1, 1), (11, 20), (13, 15), (16, 2), (10, 28), (22, 0), (24, 28), (2, 11), (31, 20), (23, 28), (29, 15), (9, 0), (29, 33), (24, 5), (16, 6), (23, 14), (3, 23), (13, 12), (17, 10), (20, 9), (34, 17), (2, 18), (5, 3), (24, 33), (32, 20), (23, 2), (0, 26), (21, 7), (4, 2), (28, 2), (10, 2), (5, 31), (6, 10), (4, 32), (29, 31), (32, 25), (28, 3), (6, 7), (21, 34), (27, 26), (10, 27), (11, 32), (16, 20), (3, 8), (8, 17), (10, 21), (26, 26), (16, 17), (24, 30), (30, 6), (6, 1), (7, 10), (28, 13), (35, 3), (13, 24), (1, 28), (14, 7), (5, 12), (3, 13), (0, 34), (25, 33), (22, 29), (33, 29), (17, 19), (28, 28), (6, 2), (9, 28), (5, 27), (17, 29), (27, 17), (6, 27), (17, 23), (15, 34), (1, 23), (25, 24), (9, 16), (21, 29), (20, 0), (28, 27), (10, 23), (17, 18), (20, 28), (19, 22), (9, 6), (24, 10), (19, 23), (7, 20), (19, 4), (15, 20), (27, 14), (29, 7), (32, 13), (27, 27), (7, 17), (13, 33), (18, 25), (23, 20), (7, 31), (12, 6), (11, 27), (24, 9), (9, 9), (6, 22), (7, 15), (0, 24), (35, 27), (5, 23), (23, 7), (30, 7), (18, 3), (31, 10), (17, 34), (12, 25), (3, 2), (12, 14), (11, 2), (4, 5), (28, 1), (33, 23), (18, 27), (14, 16), (20, 4), (8, 32), (30, 2), (34, 0), (8, 4), (22, 17), (7, 32), (9, 4), (29, 28), (8, 10), (5, 22), (13, 0), (12, 12), (18, 20), (8, 18), (11, 21), (21, 0), (3, 10), (24, 22), (29, 19), (13, 11), (2, 23), (14, 21), (29, 18), (16, 23), (14, 18), (17, 26), (32, 4), (34, 12), (30, 16), (15, 15), (23, 12), (17, 12), (1, 16), (24, 1), (31, 5), (33, 11), (21, 22), (20, 23), (22, 31), (11, 7), (32, 34), (10, 34), (6, 28), (14, 27), (20, 18), (6, 20), (3, 20), (12, 10), (15, 22), (29, 24), (6, 34), (33, 19), (31, 32), (7, 13), (9, 19), (19, 15), (19, 14), (30, 15), (2, 9), (3, 12), (11, 16), (22, 24), (14, 1), (1, 31), (25, 15), (13, 16), (15, 16), (29, 32), (26, 28), (0, 27), (7, 7), (9, 20), (25, 21), (3, 15), (3, 19), (34, 9), (1, 3), (34, 6), (3, 33), (2, 5), (30, 11), (4, 7), (4, 9), (34, 15), (23, 1), (29, 16), (14, 34), (8, 12), (4, 11), (28, 9), (13, 26), (9, 10), (23, 4), (24, 2), (28, 18), (0, 18), (2, 30), (18, 15), (35, 17), (35, 13), (1, 14), (35, 18), (21, 13), (31, 2), (8, 9), (22, 14), (4, 29), (22, 8), (1, 8), (2, 24), (20, 14), (25, 0), (30, 0), (33, 8), (8, 31), (1, 12), (23, 6), (26, 15), (1, 5), (5, 33), (27, 2), (35, 19), (25, 20), (18, 7), (29, 34), (24, 23), (0, 2), (27, 21), (3, 1), (4, 34), (12, 24), (19, 7), (5, 29), (32, 11), (19, 34), (12, 3), (21, 30), (22, 30), (8, 16), (13, 10), (30, 22), (10, 24), (22, 34), (3, 27), (12, 8), (19, 2), (31, 17), (16, 19), (6, 23), (21, 11), (14, 20), (7, 14), (13, 19), (33, 20), (34, 22), (19, 33), (20, 25), (0, 6), (21, 31), (16, 15), (26, 5), (28, 0), (10, 12), (25, 30), (16, 14), (6, 32), (29, 21), (1, 30), (32, 2), (22, 7), (9, 13), (7, 3), (21, 23), (18, 11), (31, 14), (34, 16), (20, 31), (33, 10), (23, 11), (11, 28), (21, 16), (28, 15), (19, 31), (16, 28), (25, 32), (0, 23), (11, 31), (28, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93960", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 4), (3, 21), (10, 3), (28, 27), (8, 24), (27, 16), (7, 3), (0, 19), (14, 12), (22, 14), (12, 14), (30, 0), (13, 0), (4, 10), (11, 26), (18, 15), (21, 15), (32, 24), (16, 17), (21, 27), (10, 15), (17, 11), (3, 6), (31, 22), (1, 15), (20, 29), (18, 10), (30, 12), (0, 26), (30, 18), (25, 10), (25, 29), (12, 26), (26, 3), (31, 5), (26, 0), (26, 7), (29, 12), (27, 26), (26, 28), (3, 10), (16, 4), (12, 24), (17, 3), (4, 7), (0, 12), (5, 7), (11, 23), (26, 29), (26, 5), (4, 12), (26, 6), (14, 3), (3, 26), (22, 30), (9, 7), (20, 1), (10, 0), (13, 12), (33, 6), (28, 22), (32, 22), (32, 1), (6, 12), (1, 25), (24, 8), (10, 18), (18, 23), (21, 26), (28, 3), (2, 5), (11, 16), (15, 24), (15, 19), (2, 7), (32, 9), (10, 9), (29, 13), (10, 30), (29, 19), (29, 23), (17, 6), (15, 3), (10, 14), (9, 20), (2, 1), (23, 27), (29, 8), (13, 16), (11, 3), (25, 23), (30, 20), (5, 12), (0, 5), (11, 30), (23, 29), (18, 28), (13, 13), (6, 22), (27, 10), (26, 14), (4, 3), (16, 3), (4, 26), (10, 21), (26, 23), (33, 5), (24, 12), (31, 25), (25, 21), (4, 16), (31, 20), (30, 13), (26, 2), (31, 1), (10, 13), (0, 6), (20, 17), (0, 22), (32, 10), (29, 20), (0, 4), (7, 17), (21, 11), (3, 30), (21, 3), (10, 23), (13, 6), (17, 18), (15, 11), (5, 21), (8, 26), (14, 30), (6, 10), (8, 30), (31, 6), (7, 6), (2, 26), (12, 5), (19, 23), (8, 20), (21, 14), (25, 4), (14, 4), (12, 3), (5, 15), (12, 19), (29, 24), (0, 30), (2, 11), (13, 24), (20, 7), (12, 29), (7, 16), (33, 21), (33, 11), (17, 24), (27, 9), (5, 0), (4, 18), (26, 26), (0, 7), (6, 1), (28, 23), (29, 5), (20, 30), (11, 22), (22, 28), (20, 24), (32, 25), (32, 11), (1, 28), (14, 17), (25, 14), (21, 23), (24, 19), (30, 15), (2, 24), (27, 18), (8, 21), (4, 24), (33, 26), (32, 27), (19, 30), (16, 25), (2, 15), (17, 10), (27, 14), (13, 27), (25, 17), (0, 28), (18, 12), (15, 13), (6, 29), (24, 28), (18, 30), (31, 11), (18, 7), (20, 2), (20, 25), (18, 25), (17, 29), (27, 20), (3, 28), (12, 23), (13, 20), (4, 1), (0, 29), (20, 14), (30, 9), (16, 23), (20, 18), (5, 18), (32, 26), (11, 7), (23, 19), (10, 29), (24, 2), (12, 1), (29, 22), (11, 9), (2, 12), (9, 10), (18, 4), (5, 3), (21, 12), (26, 21), (2, 22), (0, 13), (4, 23), (6, 2), (15, 16), (1, 18), (13, 11), (15, 10), (1, 21), (8, 7), (2, 18), (2, 13), (27, 1), (3, 7), (30, 5), (15, 22), (5, 17), (28, 18), (31, 7), (9, 25), (28, 11), (19, 2), (19, 12), (15, 9), (8, 27), (25, 6), (25, 25), (20, 4), (28, 4), (2, 10), (2, 20), (25, 11), (27, 30), (32, 18), (6, 26), (1, 29), (9, 30), (13, 25), (19, 14), (27, 19), (10, 28), (27, 15), (18, 6), (33, 27), (22, 23), (3, 4), (2, 9), (24, 0), (24, 18), (24, 21), (4, 22), (33, 19), (30, 24), (18, 24), (17, 25), (19, 16), (2, 21), (14, 11), (7, 25), (5, 10), (3, 27), (16, 15), (10, 24), (8, 23), (28, 8), (23, 10), (8, 5), (3, 25), (24, 15), (17, 21), (32, 23), (20, 28), (7, 19), (25, 13), (5, 28), (17, 22), (23, 9), (16, 22), (15, 4), (21, 4), (21, 20), (28, 29), (32, 28), (12, 21), (6, 30), (3, 8), (16, 28), (22, 19), (4, 27), (32, 12), (32, 19), (29, 16), (15, 28), (33, 24), (14, 2), (33, 28), (14, 25), (6, 6), (10, 22), (9, 16), (19, 7), (13, 29), (0, 21), (17, 26), (19, 22), (8, 10), (28, 10), (12, 27), (20, 3), (23, 20), (29, 17), (1, 19), (27, 29), (5, 27), (18, 27), (14, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "446256", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), 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), (28, 22), (15, 25), (13, 22), (13, 17), (32, 7), (7, 7), (33, 29), (30, 4), (20, 23), (11, 31), (17, 1), (31, 21), (32, 15), (5, 29), (14, 19), (32, 25), (8, 28), (32, 30), (12, 29), (31, 0), (29, 21), (1, 6), (15, 3), (24, 29), (14, 0), (20, 8), (15, 22), (4, 12), (21, 8), (22, 32), (26, 5), (13, 8), (28, 0), (6, 3), (24, 1), (8, 3), (23, 9), (5, 6), (29, 19), (21, 27), (28, 4), (25, 17), (3, 15), (4, 16), (20, 25), (4, 0), (12, 17), (32, 31), (18, 15), (16, 10), (13, 29), (8, 16), (0, 19), (9, 4), (21, 20), (10, 1), (18, 9), (29, 10), (24, 24), (10, 25), (32, 5), (6, 27), (9, 27), (23, 16), (18, 32), (7, 32), (4, 3), (11, 10), (0, 7), (2, 2), (25, 0), (22, 23), (33, 19), (4, 32), (31, 9), (0, 1), (27, 18), (22, 13), (7, 27), (29, 6), (10, 10), (27, 29), (26, 23), (23, 25), (29, 15), (28, 27), (33, 9), (27, 19), (27, 2), (1, 31), (0, 14), (32, 24), (31, 4), (19, 0), (21, 17), (29, 8), (17, 29), (28, 24), (20, 14), (19, 25), (3, 28), (22, 4), (29, 23), (28, 10), (12, 8), (25, 8), (15, 11), (15, 18), (5, 32), (6, 4), (25, 20), (1, 5), (11, 28), (27, 32), (21, 24), (8, 15), (22, 10), (20, 28), (33, 2), (8, 31), (8, 23), (6, 2), (25, 1), (7, 9), (11, 30), (20, 32), (18, 7), (9, 26), (3, 32), (5, 25), (5, 14), (3, 24), (12, 18), (4, 10), (32, 12), (32, 29), (3, 22), (14, 25), (26, 24), (18, 16), (16, 2), (2, 31), (2, 5), (12, 20), (19, 29), (9, 0), (32, 19), (3, 17), (16, 1), (5, 1), (12, 4), (32, 20), (29, 18), (30, 30), (22, 12), (30, 12), (10, 19), (7, 31), (3, 11), (10, 29), (3, 13), (21, 28), (5, 30), (32, 13), (31, 14), (14, 1), (15, 9), (1, 17), (2, 15), (14, 14), (17, 7), (7, 12), (22, 6), (6, 12), (1, 23), (18, 14), (27, 17), (7, 0), (2, 25), (21, 21), (4, 28), (3, 3), (15, 32), (28, 23), (11, 6), (30, 1), (2, 3), (1, 13), (26, 12), (28, 5), (0, 21), (32, 8), (22, 18), (17, 32), (11, 3), (18, 19), (25, 28), (24, 14), (12, 7), (26, 13), (8, 17), (32, 14), (23, 2), (16, 19), (4, 15), (4, 2), (28, 21), (10, 5), (30, 18), (13, 32), (30, 29), (32, 10), (18, 0), (4, 7), (33, 24), (14, 6), (31, 5), (21, 3), (5, 15), (31, 13), (11, 32), (9, 13), (0, 20), (1, 11), (28, 11), (26, 26), (29, 25), (27, 13), (32, 21), (4, 19), (0, 32), (12, 11), (9, 15), (5, 3), (6, 32), (28, 29), (19, 11), (18, 2), (16, 24), (2, 20), (15, 29), (2, 19), (17, 16), (16, 23), (20, 1), (21, 25), (3, 9), (4, 8), (7, 30), (7, 15), (29, 9), (8, 21), (33, 31), (32, 9), (26, 18), (23, 31), (17, 12), (24, 12), (25, 9), (7, 20), (13, 21), (10, 18), (16, 32), (5, 2), (24, 13), (29, 7), (19, 19), (8, 14), (2, 9), (30, 31), (23, 10), (25, 26), (27, 14), (26, 31), (7, 6), (22, 2), (1, 20), (6, 30), (33, 17), (19, 27), (22, 25), (4, 23), (10, 27), (7, 16), (15, 31), (2, 17), (5, 13), (21, 9), (22, 19), (20, 21), (14, 20), (24, 16), (30, 27), (7, 10), (21, 14), (31, 7), (11, 11), (26, 10), (1, 29), (7, 18), (1, 32), (26, 17), (33, 10), (10, 16), (23, 23), (21, 13), (14, 2), (16, 14), (18, 6), (27, 12), (9, 23), (21, 29), (28, 17), (14, 15), (25, 12), (3, 30), (1, 10), (20, 31), (18, 13), (23, 8), (17, 0), (26, 11), (13, 27), (5, 8), (13, 12), (4, 11), (17, 22), (24, 22), (16, 0), (28, 2), (20, 2), (31, 30), (8, 2), (7, 28), (20, 17), (20, 19), (8, 20), (12, 14), (21, 1), (19, 9), (19, 15), (2, 29), (19, 2), (28, 32), (2, 18), (0, 18), (33, 1), (12, 2), (21, 15), (11, 1), (9, 7), (26, 1), (27, 0), (26, 9), (33, 18), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "938088", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), 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), (14, 23), (1, 29), (22, 13), (7, 2), (4, 14), (16, 22), (20, 29), (2, 10), (16, 28), (22, 21), (24, 32), (9, 19), (28, 18), (16, 27), (21, 29), (10, 3), (30, 32), (4, 12), (13, 24), (21, 37), (18, 14), (34, 7), (33, 7), (19, 37), (28, 25), (17, 20), (12, 27), (8, 28), (6, 1), (26, 6), (22, 17), (18, 19), (11, 24), (25, 34), (21, 15), (21, 16), (15, 22), (22, 6), (0, 15), (3, 5), (20, 33), (5, 9), (14, 9), (23, 17), (32, 11), (0, 27), (29, 3), (8, 13), (22, 33), (32, 28), (10, 15), (3, 17), (8, 27), (31, 28), (6, 25), (1, 23), (13, 33), (27, 10), (9, 25), (14, 1), (13, 20), (4, 20), (32, 21), (33, 18), (7, 32), (16, 5), (23, 27), (11, 10), (22, 27), (5, 25), (31, 30), (5, 5), (2, 33), (14, 2), (11, 36), (22, 22), (19, 17), (29, 8), (12, 10), (3, 24), (7, 34), (26, 26), (11, 17), (24, 19), (4, 34), (32, 16), (21, 19), (27, 25), (6, 35), (13, 35), (16, 21), (4, 19), (24, 7), (8, 12), (5, 18), (16, 7), (33, 27), (15, 2), (9, 9), (29, 24), (10, 36), (2, 21), (4, 18), (31, 14), (13, 31), (4, 35), (6, 26), (18, 17), (2, 1), (21, 5), (13, 36), (3, 14), (10, 32), (26, 34), (31, 21), (25, 22), (7, 27), (1, 16), (29, 25), (30, 13), (9, 31), (20, 22), (24, 12), (13, 12), (30, 0), (7, 22), (22, 31), (23, 14), (4, 4), (23, 16), (19, 3), (22, 36), (11, 35), (20, 15), (13, 13), (10, 28), (22, 8), (25, 25), (24, 15), (31, 23), (8, 32), (16, 35), (17, 27), (17, 16), (7, 23), (26, 30), (6, 3), (0, 9), (34, 2), (2, 20), (5, 10), (11, 0), (24, 25), (11, 32), (22, 15), (23, 20), (32, 14), (20, 25), (30, 14), (29, 6), (27, 29), (28, 21), (27, 7), (9, 26), (13, 6), (31, 15), (33, 25), (12, 16), (12, 17), (29, 29), (12, 5), (8, 1), (23, 3), (31, 33), (27, 16), (1, 4), (20, 27), (6, 22), (10, 11), (6, 18), (31, 31), (34, 19), (3, 8), (33, 6), (26, 0), (16, 26), (4, 6), (27, 30), (32, 2), (32, 37), (34, 3), (3, 2), (9, 20), (8, 34), (32, 17), (17, 33), (31, 24), (1, 1), (25, 15), (30, 34), (19, 21), (18, 16), (31, 36), (5, 6), (1, 17), (7, 20), (6, 2), (26, 20), (15, 24), (28, 26), (8, 23), (13, 3), (28, 20), (22, 24), (17, 26), (4, 8), (15, 28), (16, 2), (5, 21), (7, 30), (26, 18), (28, 14), (11, 18), (30, 5), (1, 19), (25, 13), (29, 27), (15, 14), (28, 35), (5, 17), (22, 26), (24, 23), (25, 24), (10, 18), (8, 8), (27, 0), (27, 27), (27, 5), (34, 14), (1, 20), (4, 26), (23, 12), (30, 4), (27, 11), (9, 30), (21, 26), (19, 29), (2, 6), (22, 0), (32, 35), (9, 12), (9, 0), (28, 17), (13, 8), (1, 37), (17, 3), (7, 15), (34, 17), (24, 33), (17, 18), (23, 35), (33, 19), (25, 35), (16, 4), (30, 3), (18, 25), (1, 7), (25, 27), (33, 30), (24, 3), (28, 8), (10, 35), (26, 27), (20, 20), (30, 25), (19, 28), (22, 16), (6, 36), (21, 21), (18, 5), (10, 22), (10, 19), (25, 20), (33, 37), (29, 5), (5, 22), (26, 11), (11, 31), (3, 19), (20, 26), (9, 28), (25, 12), (3, 9), (18, 30), (6, 31), (8, 5), (12, 29), (10, 12), (20, 16), (9, 5), (2, 23), (34, 1), (5, 11), (29, 1), (31, 9), (23, 34), (13, 10), (0, 4), (15, 35), (18, 29), (34, 11), (2, 19), (15, 26), (21, 18), (23, 10), (21, 31), (15, 13), (0, 35), (32, 25), (21, 25), (30, 37), (10, 1), (17, 12), (16, 12), (2, 12), (31, 17), (32, 26), (5, 26), (23, 21), (31, 20), (12, 19), (14, 3), (21, 30), (26, 1), (10, 4), (17, 2), (12, 3), (5, 34), (3, 27), (16, 15), (15, 1), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450870", "dataset": "MATH"}
{"messages": [{"content": "In a 32x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 31), 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), (11, 1), (14, 10), (12, 14), (28, 27), (1, 8), (5, 25), (20, 25), (13, 16), (6, 27), (4, 17), (20, 5), (30, 16), (1, 0), (21, 29), (31, 11), (14, 13), (0, 10), (22, 15), (3, 10), (30, 20), (30, 28), (12, 28), (14, 25), (14, 20), (9, 16), (24, 23), (0, 5), (27, 0), (22, 11), (21, 28), (20, 31), (23, 11), (20, 6), (20, 11), (5, 31), (12, 15), (5, 27), (3, 29), (10, 1), (10, 16), (20, 14), (3, 22), (2, 27), (30, 15), (19, 27), (2, 0), (29, 5), (15, 5), (4, 3), (15, 3), (14, 9), (8, 4), (31, 7), (4, 1), (8, 9), (0, 25), (15, 26), (10, 25), (5, 3), (7, 13), (23, 17), (6, 19), (11, 29), (9, 15), (12, 13), (22, 0), (27, 31), (7, 19), (5, 2), (25, 15), (8, 18), (28, 7), (9, 26), (25, 6), (14, 8), (26, 19), (14, 2), (2, 12), (31, 15), (18, 5), (21, 30), (6, 16), (25, 23), (16, 30), (17, 21), (5, 16), (9, 6), (16, 7), (17, 25), (11, 8), (9, 28), (0, 13), (10, 6), (21, 9), (12, 10), (7, 1), (17, 4), (14, 16), (19, 18), (28, 30), (19, 28), (24, 26), (3, 11), (9, 21), (30, 22), (18, 31), (4, 23), (18, 17), (28, 3), (29, 24), (13, 22), (4, 31), (1, 28), (5, 12), (31, 14), (22, 26), (15, 18), (14, 1), (13, 14), (13, 15), (21, 26), (6, 7), (17, 16), (23, 28), (8, 26), (26, 21), (23, 26), (25, 5), (4, 15), (11, 3), (3, 9), (22, 13), (6, 9), (9, 23), (15, 12), (12, 27), (31, 20), (13, 13), (14, 15), (5, 26), (23, 9), (13, 20), (17, 20), (19, 15), (31, 12), (19, 16), (22, 14), (27, 1), (28, 22), (18, 24), (9, 7), (20, 3), (30, 3), (24, 18), (15, 28), (24, 30), (5, 10), (31, 10), (13, 17), (22, 29), (20, 16), (28, 5), (7, 22), (6, 30), (4, 19), (10, 29), (23, 19), (22, 28), (3, 3), (12, 1), (8, 25), (18, 28), (22, 24), (2, 1), (18, 0), (20, 0), (3, 14), (11, 7), (10, 28), (29, 27), (0, 28), (9, 14), (18, 2), (20, 8), (6, 2), (2, 31), (0, 18), (22, 5), (15, 13), (29, 18), (16, 28), (10, 22), (19, 19), (26, 30), (25, 4), (6, 24), (24, 9), (10, 20), (6, 25), (20, 27), (24, 3), (25, 17), (23, 5), (17, 23), (8, 7), (20, 20), (5, 13), (12, 2), (11, 2), (12, 21), (19, 7), (5, 8), (19, 3), (12, 25), (3, 31), (15, 31), (2, 4), (23, 23), (26, 25), (26, 1), (24, 25), (4, 21), (28, 17), (10, 21), (22, 31), (8, 2), (2, 30), (14, 28), (19, 26), (2, 9), (26, 9), (4, 8), (22, 9), (12, 18), (20, 17), (30, 8), (18, 7), (30, 2), (1, 19), (29, 10), (6, 17), (14, 24), (17, 17), (31, 25), (16, 13), (25, 13), (20, 2), (8, 10), (20, 10), (31, 0), (15, 4), (10, 19), (3, 18), (24, 19), (20, 22), (17, 15), (15, 22), (6, 13), (12, 22), (16, 1), (24, 8), (24, 11), (18, 16), (6, 14), (14, 26), (26, 5), (5, 18), (27, 26), (17, 28), (27, 7), (11, 15), (31, 4), (28, 29), (26, 24), (29, 22), (10, 8), (29, 23), (21, 31), (28, 19), (10, 27), (30, 4), (22, 27), (26, 12), (0, 14), (25, 2), (7, 10), (15, 10), (19, 13), (26, 0), (29, 19), (2, 10), (15, 14), (21, 20), (17, 29), (19, 4), (22, 1), (25, 12), (22, 4), (8, 20), (10, 3), (2, 6), (17, 8), (1, 25), (22, 21), (12, 26), (12, 20), (20, 23), (29, 30), (15, 19), (4, 27), (6, 4), (27, 18), (6, 11), (20, 21), (4, 6), (23, 14), (5, 11), (30, 23), (5, 28), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209664", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), 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), (11, 1), (6, 23), (4, 0), (22, 13), (25, 22), (32, 29), (12, 31), (9, 16), (12, 22), (17, 29), (24, 6), (8, 10), (21, 32), (28, 9), (16, 26), (26, 25), (27, 29), (15, 16), (35, 4), (28, 18), (11, 10), (0, 18), (0, 26), (14, 8), (22, 33), (16, 25), (22, 16), (6, 30), (35, 2), (21, 9), (26, 21), (2, 23), (18, 27), (15, 0), (12, 1), (4, 2), (15, 10), (29, 31), (0, 33), (18, 28), (24, 14), (21, 10), (0, 2), (14, 12), (28, 8), (27, 18), (2, 22), (22, 10), (2, 25), (3, 27), (24, 29), (8, 23), (19, 34), (1, 2), (9, 2), (13, 18), (16, 8), (25, 12), (35, 34), (13, 29), (35, 18), (25, 33), (25, 10), (19, 3), (2, 11), (13, 22), (22, 21), (1, 27), (3, 25), (3, 20), (15, 34), (21, 25), (1, 6), (19, 18), (12, 24), (19, 5), (9, 34), (24, 23), (13, 5), (29, 25), (32, 19), (1, 29), (9, 19), (21, 31), (4, 6), (16, 28), (10, 1), (18, 10), (33, 26), (2, 32), (22, 5), (1, 0), (11, 35), (31, 14), (11, 29), (31, 18), (6, 27), (35, 1), (10, 31), (28, 11), (27, 28), (3, 6), (9, 28), (5, 4), (30, 27), (12, 20), (32, 34), (30, 10), (24, 28), (21, 12), (19, 32), (33, 17), (16, 9), (7, 1), (23, 34), (32, 8), (31, 19), (23, 10), (21, 27), (23, 2), (11, 22), (9, 5), (10, 5), (4, 30), (31, 29), (17, 19), (16, 29), (10, 21), (28, 28), (24, 7), (32, 7), (23, 15), (7, 6), (17, 11), (10, 25), (26, 9), (15, 1), (27, 31), (10, 4), (4, 16), (7, 7), (35, 16), (20, 20), (9, 18), (21, 28), (23, 19), (19, 17), (16, 17), (14, 5), (28, 27), (14, 30), (30, 21), (33, 11), (34, 27), (6, 6), (22, 22), (29, 11), (32, 28), (26, 30), (22, 4), (32, 12), (13, 23), (7, 30), (29, 34), (29, 19), (24, 31), (13, 25), (17, 28), (10, 33), (7, 2), (11, 12), (34, 1), (7, 27), (28, 13), (13, 7), (25, 27), (34, 23), (2, 18), (31, 27), (5, 24), (31, 16), (32, 25), (18, 5), (13, 12), (18, 2), (8, 3), (17, 2), (11, 31), (12, 29), (32, 16), (34, 19), (7, 11), (22, 0), (19, 14), (0, 16), (7, 25), (19, 21), (18, 12), (21, 1), (1, 35), (1, 12), (30, 17), (25, 25), (31, 20), (29, 35), (19, 25), (1, 11), (22, 26), (29, 6), (28, 7), (18, 24), (18, 35), (11, 11), (6, 1), (8, 13), (4, 7), (6, 22), (5, 18), (20, 34), (29, 0), (20, 14), (26, 2), (23, 33), (26, 3), (3, 16), (0, 25), (6, 5), (26, 28), (0, 27), (30, 31), (33, 18), (8, 28), (13, 30), (34, 34), (2, 12), (28, 17), (0, 29), (35, 31), (15, 33), (9, 24), (7, 4), (33, 16), (9, 25), (0, 3), (35, 5), (12, 15), (28, 20), (16, 21), (4, 34), (27, 8), (33, 32), (35, 13), (18, 22), (27, 27), (22, 1), (16, 1), (16, 14), (3, 23), (12, 12), (10, 10), (24, 5), (19, 19), (15, 24), (7, 33), (19, 11), (14, 31), (9, 9), (28, 14), (28, 26), (34, 18), (19, 30), (2, 34), (7, 34), (12, 21), (27, 7), (32, 6), (25, 26), (31, 15), (18, 34), (14, 2), (6, 32), (1, 26), (31, 11), (4, 35), (30, 3), (17, 12), (22, 14), (20, 4), (34, 33), (27, 16), (0, 19), (22, 7), (8, 20), (22, 34), (1, 5), (35, 7), (20, 21), (0, 5), (10, 22), (8, 22), (20, 29), (34, 31), (14, 26), (13, 34), (14, 22), (5, 21), (24, 22), (29, 26), (14, 3), (1, 34), (21, 23), (7, 0), (31, 13), (35, 27), (11, 33), (30, 26), (29, 7), (17, 32), (28, 0), (22, 24), (17, 8), (20, 9), (11, 8), (27, 22), (28, 2), (25, 20), (29, 10), (33, 8), (2, 16), (6, 20), (10, 27), (26, 17), (12, 25), (6, 15), (20, 15), (18, 15), (22, 25), (5, 14), (1, 18), (15, 32), (13, 2), (16, 0), (31, 4), (7, 15), (24, 30), (5, 30), (33, 23), (27, 9), (32, 33), (26, 35), (23, 7), (3, 10), (26, 23), (23, 17), (33, 7), (4, 10), (20, 11), (30, 4), (34, 8), (34, 14), (33, 13), (32, 26), (27, 21), (7, 9), (13, 15), (12, 16), (31, 32), (33, 15), (17, 1), (7, 13), (21, 6), (8, 9), (9, 6), (15, 22), (15, 11), (21, 11), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682320", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 20), (26, 20), (0, 19), (21, 9), (32, 5), (9, 2), (11, 25), (9, 11), (5, 27), (31, 2), (23, 29), (9, 6), (27, 34), (17, 5), (6, 6), (25, 20), (10, 17), (8, 1), (15, 13), (2, 5), (14, 16), (16, 8), (10, 13), (28, 17), (5, 25), (32, 0), (20, 7), (5, 18), (16, 4), (24, 4), (12, 6), (29, 1), (0, 13), (32, 6), (16, 12), (15, 30), (27, 8), (15, 25), (20, 16), (1, 5), (12, 30), (14, 8), (15, 8), (7, 17), (28, 28), (0, 26), (16, 30), (7, 26), (30, 12), (22, 22), (21, 3), (5, 4), (7, 1), (26, 24), (6, 4), (0, 22), (23, 16), (10, 23), (20, 33), (29, 30), (12, 35), (24, 17), (20, 0), (9, 4), (30, 2), (26, 14), (18, 22), (17, 1), (18, 6), (24, 34), (23, 2), (12, 22), (17, 0), (11, 27), (24, 15), (31, 10), (9, 26), (10, 11), (12, 31), (22, 3), (28, 24), (28, 23), (9, 16), (19, 33), (14, 19), (9, 15), (29, 28), (26, 13), (23, 0), (26, 25), (0, 3), (13, 26), (8, 4), (29, 22), (3, 20), (13, 0), (6, 19), (28, 35), (1, 25), (25, 24), (24, 24), (27, 21), (30, 10), (18, 0), (28, 14), (16, 35), (26, 17), (14, 13), (22, 6), (25, 35), (2, 7), (11, 0), (0, 7), (8, 26), (5, 0), (19, 28), (16, 11), (23, 10), (15, 16), (16, 26), (13, 11), (28, 30), (4, 29), (32, 8), (28, 27), (32, 27), (0, 15), (20, 1), (5, 23), (8, 2), (12, 5), (6, 5), (28, 32), (32, 17), (23, 17), (18, 21), (19, 2), (9, 34), (30, 7), (16, 31), (17, 14), (2, 17), (24, 29), (19, 20), (31, 15), (14, 15), (0, 14), (30, 21), (24, 30), (13, 34), (2, 12), (7, 28), (3, 10), (6, 21), (25, 9), (17, 27), (18, 7), (31, 21), (14, 17), (29, 18), (16, 27), (6, 34), (32, 1), (1, 7), (27, 35), (30, 9), (27, 2), (15, 18), (18, 14), (4, 24), (31, 18), (1, 21), (23, 19), (12, 8), (6, 26), (3, 16), (1, 17), (11, 13), (7, 3), (30, 19), (4, 33), (23, 21), (9, 27), (17, 4), (1, 1), (15, 5), (5, 9), (20, 4), (10, 27), (16, 24), (3, 17), (13, 16), (6, 29), (4, 10), (32, 23), (12, 16), (1, 29), (25, 28), (17, 16), (26, 22), (1, 14), (12, 20), (29, 10), (31, 24), (11, 1), (27, 15), (11, 28), (22, 13), (24, 8), (22, 20), (3, 35), (16, 17), (20, 20), (25, 31), (24, 7), (29, 13), (2, 22), (1, 4), (28, 6), (4, 14), (1, 3), (14, 4), (10, 16), (23, 7), (12, 12), (2, 3), (1, 34), (0, 8), (8, 27), (0, 30), (32, 2), (1, 11), (15, 11), (13, 23), (3, 18), (7, 12), (26, 0), (9, 8), (30, 15), (18, 31), (24, 2), (11, 31), (18, 15), (23, 28), (24, 13), (20, 19), (25, 1), (16, 7), (18, 3), (8, 18), (1, 2), (0, 4), (18, 23), (28, 29), (20, 5), (19, 22), (5, 32), (22, 5), (3, 28), (17, 13), (17, 25), (3, 12), (26, 32), (10, 18), (4, 0), (28, 21), (13, 10), (10, 25), (14, 2), (4, 9), (15, 7), (28, 20), (1, 23), (4, 28), (12, 25), (8, 25), (21, 8), (29, 25), (32, 14), (20, 21), (14, 20), (2, 1), (1, 32), (26, 28), (26, 30), (25, 7), (9, 29), (29, 20), (31, 31), (11, 19), (2, 35), (4, 31), (8, 16), (25, 3), (25, 27), (29, 3), (9, 33), (31, 16), (22, 16), (17, 29), (13, 24), (21, 22), (7, 4), (5, 13), (4, 15), (7, 19), (17, 9), (31, 7), (19, 27), (6, 22), (27, 32), (32, 26), (31, 30), (29, 32), (16, 33), (22, 8), (11, 8), (24, 25), (26, 5), (16, 29), (32, 25), (17, 18), (8, 0), (15, 21), (7, 5), (14, 25), (14, 11), (8, 23), (18, 13), (11, 18), (13, 17), (28, 26), (11, 4), (11, 20), (10, 7), (20, 10), (5, 20), (19, 10), (15, 26), (14, 12), (9, 21), (0, 1), (30, 8), (28, 33), (23, 26), (29, 6), (21, 34), (23, 24), (7, 7), (6, 16), (18, 1), (18, 24), (3, 29), (27, 18), (12, 14), (17, 8), (27, 5), (25, 10), (15, 29), (31, 9), (32, 29), (25, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554400", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (8, 31), (22, 15), (4, 4), (20, 33), (9, 16), (22, 27), (16, 9), (25, 25), (28, 21), (18, 28), (1, 4), (16, 38), (11, 5), (34, 31), (36, 28), (31, 30), (8, 25), (20, 12), (22, 8), (12, 24), (34, 17), (19, 29), (9, 23), (12, 19), (35, 23), (33, 8), (8, 4), (16, 12), (24, 37), (35, 27), (15, 34), (21, 18), (13, 29), (29, 0), (0, 28), (28, 10), (18, 20), (36, 0), (1, 15), (21, 25), (2, 1), (1, 24), (24, 2), (33, 37), (30, 18), (22, 10), (29, 34), (6, 22), (14, 14), (29, 27), (15, 22), (21, 7), (0, 23), (13, 1), (15, 1), (25, 26), (35, 38), (21, 26), (0, 15), (12, 9), (10, 27), (37, 15), (1, 34), (22, 37), (25, 4), (29, 26), (5, 21), (26, 24), (31, 21), (37, 33), (23, 12), (27, 32), (13, 22), (18, 14), (2, 8), (35, 24), (24, 5), (35, 26), (33, 30), (35, 17), (13, 6), (3, 12), (36, 21), (17, 2), (9, 18), (22, 17), (35, 16), (23, 1), (2, 29), (15, 27), (2, 23), (14, 29), (29, 24), (20, 0), (14, 7), (38, 24), (2, 6), (21, 23), (32, 22), (6, 32), (26, 16), (15, 32), (12, 23), (17, 20), (24, 3), (37, 26), (20, 5), (20, 23), (24, 4), (12, 22), (25, 15), (1, 26), (13, 12), (27, 6), (24, 6), (34, 30), (14, 22), (37, 10), (7, 19), (7, 20), (23, 38), (32, 15), (6, 11), (37, 21), (33, 24), (24, 0), (33, 31), (2, 25), (16, 13), (11, 35), (5, 32), (7, 37), (10, 15), (38, 7), (32, 3), (34, 37), (15, 36), (19, 25), (26, 26), (36, 24), (19, 11), (21, 35), (22, 22), (25, 30), (18, 12), (32, 12), (35, 14), (4, 33), (14, 16), (36, 9), (2, 14), (23, 21), (2, 12), (1, 21), (27, 38), (13, 27), (8, 16), (15, 7), (16, 27), (29, 23), (10, 22), (33, 1), (18, 10), (12, 33), (32, 20), (10, 8), (4, 6), (29, 10), (21, 2), (19, 5), (36, 1), (5, 4), (9, 7), (29, 15), (9, 4), (24, 22), (9, 31), (38, 14), (36, 14), (33, 19), (9, 30), (15, 30), (7, 9), (9, 37), (13, 21), (19, 6), (19, 28), (9, 8), (6, 27), (10, 34), (7, 13), (35, 18), (38, 25), (34, 11), (12, 1), (32, 19), (6, 7), (21, 8), (16, 16), (30, 4), (27, 22), (38, 32), (23, 0), (23, 11), (6, 35), (28, 20), (10, 5), (24, 8), (37, 37), (20, 4), (18, 9), (26, 12), (19, 4), (13, 11), (32, 5), (24, 26), (36, 26), (38, 27), (4, 24), (13, 23), (35, 11), (3, 38), (8, 11), (21, 9), (26, 18), (16, 23), (4, 29), (14, 28), (8, 38), (24, 12), (5, 36), (34, 26), (0, 12), (6, 20), (2, 15), (21, 37), (5, 2), (17, 19), (24, 30), (1, 36), (15, 35), (23, 26), (12, 29), (37, 27), (1, 22), (5, 12), (33, 20), (33, 11), (29, 7), (38, 2), (5, 30), (38, 17), (1, 30), (13, 14), (38, 9), (6, 15), (4, 17), (34, 29), (26, 25), (17, 18), (25, 20), (18, 18), (14, 37), (7, 1), (33, 17), (7, 8), (24, 35), (13, 28), (4, 35), (35, 12), (25, 8), (2, 38), (22, 16), (17, 22), (21, 12), (15, 28), (14, 31), (21, 17), (18, 1), (5, 10), (17, 7), (28, 28), (34, 1), (24, 7), (32, 25), (11, 14), (17, 8), (21, 36), (24, 9), (3, 20), (20, 19), (19, 20), (2, 35), (0, 10), (26, 7), (38, 1), (6, 28), (17, 25), (26, 28), (24, 19), (38, 35), (19, 1), (0, 38), (32, 0), (0, 35), (3, 19), (30, 10), (9, 5), (10, 6), (6, 24), (23, 2), (3, 11), (34, 13), (23, 37), (27, 33), (9, 20), (35, 10), (36, 35), (18, 29), (37, 6), (25, 18), (16, 7), (33, 12), (11, 16), (6, 8), (22, 33), (14, 17), (16, 25), (35, 3), (34, 3), (12, 30), (12, 35), (8, 37), (24, 14), (3, 25), (32, 16), (19, 22), (1, 25), (36, 23), (38, 0), (0, 16), (11, 6), (14, 26), (38, 5), (2, 26), (19, 13), (6, 0), (23, 33), (0, 33), (5, 14), (18, 36), (11, 30), (23, 8), (8, 15), (8, 29), (32, 26), (21, 21), (30, 19), (29, 36), (12, 38), (9, 14), (23, 18), (5, 3), (19, 9), (38, 34), (28, 17), (13, 26), (28, 26), (9, 22), (19, 30), (32, 35), (7, 17), (31, 9), (23, 35), (5, 38), (32, 33), (18, 15), (29, 13), (38, 4), (17, 34), (2, 21), (9, 25), (14, 30), (36, 29), (5, 37), (35, 1), (15, 25), (14, 13), (30, 16), (34, 22), (20, 20), (11, 8), (25, 13), (12, 18), (16, 34), (15, 37), (15, 21), (2, 7), (37, 31), (14, 32), (26, 3), (16, 11), (20, 27), (3, 5), (6, 26), (36, 2), (27, 21), (30, 0), (17, 32), (19, 15), (27, 24), (23, 22), (14, 0), (30, 34), (0, 17), (1, 7), (7, 29), (16, 29), (30, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18816", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), 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), (29, 10), (18, 27), (20, 20), (28, 19), (1, 6), (1, 4), (22, 20), (23, 27), (16, 29), (7, 4), (14, 15), (3, 35), (30, 22), (27, 2), (25, 22), (8, 7), (31, 29), (20, 13), (13, 2), (10, 7), (11, 10), (14, 31), (27, 3), (23, 18), (23, 16), (21, 29), (17, 21), (7, 25), (20, 28), (27, 8), (28, 27), (8, 9), (29, 20), (5, 18), (7, 14), (18, 33), (29, 32), (12, 2), (22, 16), (29, 3), (11, 8), (6, 35), (11, 5), (16, 16), (14, 32), (0, 19), (1, 30), (4, 21), (8, 11), (19, 32), (12, 4), (17, 2), (13, 9), (31, 9), (19, 5), (28, 17), (15, 13), (9, 20), (8, 20), (13, 19), (21, 35), (5, 20), (6, 4), (26, 16), (3, 16), (13, 15), (12, 27), (1, 12), (13, 0), (5, 3), (2, 7), (27, 24), (10, 29), (4, 18), (21, 5), (23, 17), (3, 9), (23, 15), (17, 32), (22, 24), (14, 12), (28, 23), (14, 20), (11, 15), (7, 2), (23, 32), (14, 25), (29, 15), (13, 8), (10, 16), (13, 27), (24, 4), (22, 4), (22, 34), (0, 14), (25, 1), (9, 31), (3, 6), (27, 17), (14, 23), (22, 17), (11, 14), (30, 19), (21, 2), (0, 15), (4, 35), (9, 1), (21, 7), (10, 25), (11, 3), (5, 30), (27, 30), (29, 2), (13, 24), (13, 22), (4, 5), (24, 32), (11, 17), (7, 26), (4, 6), (0, 28), (28, 28), (25, 16), (24, 0), (23, 24), (20, 34), (30, 7), (9, 22), (3, 23), (12, 26), (30, 12), (28, 3), (15, 24), (21, 28), (16, 26), (26, 3), (25, 17), (1, 27), (19, 17), (4, 3), (4, 2), (5, 5), (17, 4), (24, 7), (16, 8), (7, 24), (20, 25), (21, 12), (8, 14), (8, 0), (14, 5), (31, 33), (10, 33), (25, 19), (16, 14), (7, 28), (22, 23), (12, 5), (28, 11), (15, 6), (11, 35), (27, 1), (21, 22), (25, 18), (14, 0), (22, 26), (24, 25), (24, 3), (17, 35), (4, 24), (30, 2), (5, 16), (9, 7), (15, 7), (15, 29), (11, 20), (15, 34), (7, 9), (18, 2), (11, 27), (18, 18), (4, 15), (18, 31), (6, 33), (18, 20), (21, 14), (29, 23), (8, 8), (12, 6), (8, 4), (25, 35), (16, 2), (4, 31), (30, 24), (13, 17), (12, 13), (24, 27), (9, 2), (8, 19), (5, 34), (9, 4), (27, 28), (21, 26), (7, 11), (1, 17), (6, 26), (23, 13), (16, 18), (22, 8), (24, 10), (8, 33), (19, 1), (16, 4), (3, 18), (30, 34), (17, 10), (12, 8), (19, 8), (25, 21), (14, 11), (18, 21), (5, 35), (13, 3), (23, 5), (31, 4), (20, 12), (26, 6), (31, 5), (15, 9), (15, 19), (12, 35), (10, 15), (25, 14), (13, 28), (6, 17), (5, 24), (27, 4), (16, 19), (12, 10), (26, 12), (11, 4), (3, 3), (6, 23), (12, 32), (7, 30), (18, 11), (29, 8), (19, 11), (8, 15), (11, 11), (6, 25), (31, 27), (13, 14), (11, 0), (4, 9), (14, 33), (28, 9), (16, 0), (1, 13), (23, 35), (5, 17), (26, 7), (20, 32), (6, 32), (31, 25), (1, 33), (2, 3), (11, 13), (28, 5), (18, 13), (30, 11), (3, 13), (13, 7), (17, 31), (24, 11), (19, 0), (8, 25), (5, 2), (27, 5), (4, 13), (3, 19), (18, 23), (17, 6), (21, 31), (2, 8), (22, 27), (27, 11), (15, 3), (1, 34), (21, 33), (2, 34), (29, 6), (11, 9), (26, 17), (17, 13), (11, 31), (25, 9), (24, 17), (23, 14), (15, 10), (20, 7), (24, 20), (20, 19), (6, 27), (10, 5), (15, 17), (27, 18), (9, 33), (11, 1), (9, 12), (17, 29), (17, 8), (3, 22), (2, 2), (30, 21), (3, 2), (18, 15), (23, 12), (18, 32), (24, 28), (27, 6), (31, 18), (19, 7), (11, 23), (12, 23), (29, 21), (18, 26), (12, 21), (6, 5), (24, 34), (23, 25), (29, 30), (8, 28), (13, 33), (29, 33), (14, 6), (1, 15), (28, 34), (19, 25), (0, 20), (20, 2), (19, 22), (16, 5), (13, 20), (23, 26), (9, 24), (15, 1), (27, 21), (6, 11), (16, 25), (23, 28), (6, 8), (23, 6), (2, 6), (4, 16), (19, 27), (6, 13), (19, 10), (22, 10), (26, 1), (16, 13), (22, 3), (6, 24), (5, 25), (10, 30), (3, 12), (30, 3), (25, 0), (21, 25), (4, 7), (30, 8), (23, 23), (28, 22), (15, 27), (10, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "709392", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), 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), (16, 5), (1, 29), (29, 8), (9, 12), (16, 28), (2, 4), (19, 27), (8, 8), (4, 25), (8, 27), (24, 29), (5, 4), (16, 22), (10, 15), (4, 6), (2, 10), (1, 17), (18, 16), (10, 7), (24, 17), (25, 17), (7, 6), (12, 7), (0, 3), (12, 1), (25, 8), (30, 1), (17, 22), (33, 5), (0, 23), (15, 0), (12, 2), (7, 16), (25, 16), (33, 2), (24, 7), (0, 8), (2, 29), (13, 15), (1, 13), (19, 28), (5, 14), (24, 8), (11, 11), (30, 10), (15, 3), (13, 28), (29, 26), (29, 23), (32, 25), (23, 7), (17, 11), (12, 23), (9, 5), (29, 14), (10, 27), (31, 29), (28, 0), (24, 26), (0, 27), (17, 6), (26, 11), (22, 23), (4, 24), (21, 15), (17, 17), (7, 11), (4, 26), (15, 16), (10, 12), (2, 0), (23, 28), (25, 4), (7, 3), (8, 21), (19, 25), (24, 11), (30, 27), (7, 20), (1, 0), (29, 3), (0, 11), (11, 27), (33, 28), (10, 17), (11, 23), (7, 24), (22, 11), (10, 6), (22, 26), (6, 21), (31, 8), (32, 18), (18, 0), (0, 21), (21, 23), (27, 20), (11, 3), (5, 17), (7, 0), (6, 20), (31, 1), (30, 24), (4, 1), (11, 1), (14, 7), (28, 4), (7, 13), (8, 7), (31, 19), (1, 21), (0, 24), (15, 2), (17, 16), (0, 28), (8, 28), (14, 27), (3, 5), (4, 10), (12, 6), (9, 20), (0, 12), (13, 9), (11, 6), (3, 26), (2, 27), (10, 9), (10, 16), (8, 26), (13, 6), (27, 26), (18, 11), (6, 12), (32, 27), (25, 9), (26, 25), (27, 29), (5, 5), (8, 22), (28, 11), (15, 13), (12, 12), (11, 18), (18, 5), (1, 14), (7, 7), (13, 4), (32, 3), (5, 1), (16, 3), (28, 23), (31, 6), (31, 17), (25, 3), (3, 12), (31, 13), (19, 22), (13, 13), (27, 23), (4, 29), (31, 10), (31, 15), (8, 24), (25, 10), (2, 5), (27, 11), (3, 4), (32, 13), (6, 19), (2, 3), (1, 27), (31, 7), (4, 12), (32, 2), (16, 1), (17, 13), (23, 12), (6, 25), (16, 20), (10, 19), (22, 0), (27, 15), (15, 9), (12, 17), (21, 4), (20, 23), (17, 5), (24, 19), (5, 15), (29, 24), (15, 14), (6, 16), (30, 16), (18, 10), (4, 19), (16, 16), (4, 8), (26, 8), (4, 18), (13, 24), (28, 12), (30, 4), (4, 27), (5, 27), (25, 7), (14, 15), (24, 0), (7, 26), (2, 19), (32, 10), (33, 6), (30, 23), (20, 24), (15, 12), (7, 21), (24, 14), (26, 9), (19, 26), (14, 5), (28, 27), (20, 21), (21, 25), (1, 10), (7, 14), (20, 18), (27, 19), (3, 22), (28, 13), (25, 25), (11, 26), (21, 24), (15, 25), (25, 29), (27, 0), (12, 11), (5, 2), (13, 14), (24, 27), (17, 10), (21, 3), (10, 25), (20, 29), (0, 13), (15, 23), (20, 3), (14, 16), (29, 18), (7, 23), (20, 22), (22, 16), (33, 24), (14, 25), (10, 3), (5, 16), (4, 14), (25, 13), (29, 19), (18, 20), (26, 13), (8, 18), (3, 27), (25, 0), (13, 23), (9, 15), (3, 21), (32, 14), (15, 22), (8, 13), (30, 6), (6, 2), (12, 14), (28, 17), (12, 5), (22, 4), (16, 24), (12, 4), (8, 16), (6, 24), (20, 14), (21, 1), (29, 15), (30, 19), (5, 23), (29, 10), (9, 2), (2, 1), (19, 9), (1, 3), (1, 16), (16, 29), (16, 9), (13, 20), (8, 1), (23, 25), (9, 8), (29, 1), (30, 5), (12, 13), (2, 14), (14, 23), (5, 9), (23, 22), (3, 14), (26, 3), (20, 8), (5, 11), (6, 14), (31, 20), (13, 3), (6, 9), (23, 20), (28, 5), (8, 4), (3, 19), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466416", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 14), (2, 21), (2, 2), (21, 10), (20, 25), (29, 1), (23, 6), (4, 19), (8, 21), (12, 4), (0, 8), (28, 2), (22, 26), (2, 20), (31, 0), (2, 28), (19, 12), (11, 19), (30, 22), (23, 30), (10, 2), (22, 27), (22, 10), (10, 21), (11, 8), (6, 12), (0, 3), (17, 12), (11, 21), (15, 15), (25, 14), (11, 24), (31, 8), (29, 6), (12, 29), (33, 14), (29, 16), (32, 12), (6, 23), (27, 29), (12, 10), (28, 26), (11, 4), (29, 12), (6, 25), (15, 9), (3, 25), (29, 13), (28, 8), (18, 25), (11, 17), (14, 19), (19, 3), (8, 28), (23, 17), (17, 19), (27, 12), (10, 11), (30, 17), (13, 0), (5, 3), (12, 7), (12, 12), (25, 2), (0, 7), (6, 7), (9, 23), (27, 3), (5, 23), (19, 25), (34, 6), (9, 12), (25, 30), (26, 28), (11, 7), (18, 26), (12, 27), (11, 32), (23, 18), (7, 3), (12, 16), (20, 12), (0, 31), (31, 20), (3, 13), (30, 3), (10, 13), (10, 5), (28, 20), (29, 25), (2, 10), (17, 22), (2, 24), (31, 11), (15, 2), (1, 3), (26, 17), (12, 2), (18, 19), (6, 28), (29, 31), (1, 19), (33, 4), (25, 19), (29, 27), (32, 5), (0, 12), (2, 12), (9, 27), (24, 32), (4, 12), (33, 3), (25, 16), (17, 31), (20, 10), (18, 7), (19, 23), (11, 9), (15, 18), (18, 32), (5, 8), (10, 0), (31, 9), (13, 21), (27, 0), (29, 24), (3, 28), (22, 30), (17, 5), (0, 29), (7, 6), (1, 31), (31, 12), (25, 27), (25, 20), (28, 19), (5, 0), (31, 30), (22, 31), (16, 22), (32, 8), (29, 32), (28, 11), (31, 17), (28, 0), (13, 31), (21, 4), (32, 15), (2, 5), (12, 13), (20, 27), (12, 5), (26, 3), (7, 31), (17, 28), (9, 31), (14, 26), (0, 25), (24, 7), (5, 6), (3, 30), (30, 5), (18, 9), (28, 10), (9, 1), (7, 27), (13, 17), (0, 13), (1, 29), (2, 25), (19, 20), (1, 4), (30, 10), (21, 29), (4, 20), (21, 23), (0, 4), (28, 31), (2, 22), (28, 24), (16, 8), (34, 16), (3, 8), (28, 28), (15, 16), (5, 7), (33, 0), (27, 9), (30, 31), (30, 27), (6, 18), (1, 22), (13, 2), (15, 24), (15, 0), (1, 18), (4, 15), (20, 8), (2, 30), (26, 7), (8, 6), (17, 32), (2, 11), (8, 4), (31, 10), (31, 3), (11, 30), (31, 29), (17, 15), (19, 2), (26, 22), (21, 7), (17, 14), (32, 2), (31, 1), (4, 0), (2, 26), (32, 6), (11, 27), (32, 1), (25, 24), (8, 24), (9, 14), (14, 14), (4, 6), (13, 15), (16, 11), (10, 4), (11, 28), (6, 17), (18, 18), (21, 16), (34, 12), (25, 29), (31, 21), (22, 11), (4, 4), (1, 1), (24, 13), (12, 17), (24, 10), (4, 8), (16, 5), (3, 10), (14, 0), (17, 29), (0, 23), (21, 8), (17, 10), (22, 28), (32, 28), (7, 14), (16, 27), (16, 14), (29, 14), (9, 13), (12, 3), (26, 5), (13, 28), (33, 23), (24, 18), (23, 8), (2, 8), (14, 8), (19, 15), (1, 28), (22, 20), (5, 14), (20, 5), (1, 7), (17, 21), (18, 13), (16, 21), (9, 0), (20, 4), (29, 20), (29, 18), (26, 26), (13, 11), (7, 13), (24, 25), (5, 11), (15, 31), (34, 4), (1, 21), (10, 29), (9, 21), (25, 15), (14, 29), (1, 9), (3, 22), (19, 26), (7, 7), (3, 6), (25, 10), (10, 16), (6, 11), (20, 14), (19, 21), (4, 9), (20, 32), (15, 11), (24, 24), (13, 27), (16, 7), (18, 3), (18, 14), (31, 31), (2, 13), (5, 30), (33, 28), (16, 12), (31, 19), (26, 10), (21, 9), (34, 7), (30, 9), (7, 26), (4, 5), (23, 2), (15, 27), (23, 7), (19, 18), (14, 27), (12, 22), (2, 31), (26, 19), (0, 15), (24, 28), (16, 20), (0, 11), (18, 12), (32, 18), (31, 2), (30, 4), (27, 1), (5, 17), (22, 12), (16, 4), (30, 1), (4, 3), (14, 15), (26, 0), (5, 19), (25, 6), (29, 0), (32, 14), (7, 29), (20, 22), (14, 17), (19, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (12, 20), (2, 13), (0, 11), (4, 28), (16, 1), (13, 14), (4, 11), (20, 1), (27, 16), (0, 16), (15, 20), (11, 3), (18, 7), (1, 25), (23, 19), (13, 3), (35, 15), (14, 4), (25, 1), (26, 9), (12, 32), (18, 11), (1, 26), (15, 25), (0, 32), (33, 23), (23, 2), (30, 3), (3, 20), (15, 18), (8, 4), (31, 24), (13, 7), (18, 24), (28, 18), (11, 22), (22, 27), (17, 14), (10, 26), (16, 2), (27, 2), (1, 24), (5, 32), (32, 32), (2, 21), (16, 26), (6, 21), (9, 18), (25, 11), (28, 26), (3, 26), (3, 7), (7, 31), (23, 3), (33, 21), (4, 17), (10, 17), (20, 2), (35, 2), (15, 23), (6, 12), (12, 26), (17, 9), (28, 5), (5, 33), (10, 11), (5, 26), (20, 8), (35, 5), (35, 19), (17, 3), (19, 7), (20, 23), (18, 30), (4, 25), (9, 0), (21, 27), (0, 33), (22, 23), (34, 15), (10, 28), (4, 27), (5, 15), (12, 6), (5, 18), (20, 3), (6, 8), (31, 19), (35, 13), (7, 8), (33, 30), (17, 10), (32, 14), (25, 22), (27, 11), (4, 4), (27, 18), (30, 12), (6, 15), (4, 8), (14, 11), (16, 6), (0, 22), (31, 11), (32, 8), (35, 23), (18, 20), (16, 19), (19, 19), (25, 19), (16, 15), (9, 4), (14, 22), (13, 24), (20, 13), (30, 28), (27, 25), (17, 7), (24, 28), (12, 9), (25, 13), (30, 32), (3, 4), (28, 20), (7, 4), (1, 19), (12, 13), (6, 22), (19, 30), (35, 27), (19, 9), (11, 1), (8, 21), (34, 20), (1, 16), (32, 15), (35, 21), (17, 12), (7, 26), (18, 25), (9, 31), (19, 28), (8, 33), (18, 27), (0, 29), (30, 30), (23, 9), (13, 11), (29, 4), (1, 8), (6, 28), (0, 24), (14, 14), (15, 4), (14, 32), (19, 17), (14, 30), (31, 31), (0, 18), (10, 33), (6, 7), (8, 25), (22, 29), (9, 29), (15, 32), (5, 0), (1, 30), (11, 28), (4, 21), (7, 11), (25, 4), (17, 13), (17, 0), (23, 18), (8, 13), (31, 30), (15, 9), (24, 14), (9, 23), (1, 31), (27, 4), (14, 25), (29, 1), (27, 22), (19, 14), (24, 2), (18, 14), (17, 17), (29, 7), (23, 32), (8, 14), (26, 0), (11, 2), (6, 26), (25, 30), (29, 22), (26, 23), (16, 12), (7, 21), (26, 20), (28, 30), (18, 21), (20, 9), (8, 0), (17, 21), (7, 23), (22, 8), (3, 0), (3, 2), (4, 22), (14, 16), (14, 21), (18, 26), (31, 23), (11, 12), (22, 13), (25, 0), (2, 25), (19, 26), (11, 11), (34, 3), (8, 8), (16, 7), (20, 20), (34, 11), (26, 22), (4, 31), (29, 17), (12, 31), (25, 7), (24, 31), (19, 1), (6, 3), (5, 10), (30, 16), (21, 15), (29, 3), (23, 24), (23, 27), (33, 28), (33, 14), (13, 28), (29, 29), (24, 4), (27, 27), (20, 15), (17, 8), (3, 30), (11, 7), (12, 17), (35, 28), (19, 33), (6, 4), (29, 10), (21, 10), (21, 31), (20, 32), (12, 0), (10, 25), (34, 2), (12, 19), (5, 25), (19, 32), (15, 28), (30, 25), (27, 6), (33, 33), (11, 9), (33, 29), (16, 32), (33, 27), (1, 7), (4, 9), (7, 14), (34, 26), (6, 25), (23, 0), (31, 17), (24, 25), (23, 28), (3, 14), (25, 27), (23, 15), (14, 23), (33, 20), (21, 6), (20, 12), (35, 1), (13, 30), (31, 13), (26, 14), (13, 13), (19, 2), (1, 22), (18, 5), (12, 8), (7, 10), (1, 20), (30, 15), (23, 31), (24, 10), (21, 23), (19, 11), (12, 10), (9, 30), (6, 17), (3, 23), (9, 27), (34, 0), (10, 14), (14, 12), (15, 33), (14, 24), (29, 19), (12, 24), (27, 31), (25, 32), (24, 32), (9, 13), (29, 27), (25, 5), (34, 21), (7, 12), (6, 30), (21, 11), (11, 30), (25, 31), (34, 8), (35, 32), (13, 25), (10, 27), (30, 0), (20, 27), (5, 7), (16, 14), (12, 2), (28, 24), (0, 1), (32, 20), (34, 5), (16, 33), (20, 26), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578600", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (3, 1), (4, 15), (10, 6), (30, 34), (34, 7), (0, 20), (25, 12), (9, 30), (12, 24), (37, 1), (36, 32), (33, 20), (20, 26), (12, 9), (25, 23), (20, 11), (35, 3), (14, 35), (26, 20), (0, 24), (28, 21), (5, 9), (16, 6), (20, 9), (37, 4), (33, 14), (5, 3), (12, 11), (15, 9), (36, 6), (26, 33), (31, 5), (14, 0), (14, 18), (30, 11), (9, 22), (33, 31), (34, 2), (0, 3), (19, 23), (29, 9), (29, 0), (23, 13), (8, 21), (7, 9), (3, 19), (30, 25), (6, 24), (5, 31), (36, 33), (24, 20), (14, 22), (12, 22), (4, 0), (23, 18), (28, 7), (11, 35), (32, 15), (28, 30), (13, 7), (14, 26), (35, 20), (10, 5), (2, 0), (19, 2), (5, 32), (5, 21), (30, 24), (12, 20), (1, 17), (9, 33), (16, 17), (29, 30), (22, 26), (31, 19), (29, 11), (30, 5), (18, 33), (14, 29), (33, 10), (10, 2), (26, 26), (31, 15), (5, 20), (15, 25), (14, 31), (7, 10), (33, 0), (35, 22), (10, 27), (18, 3), (20, 1), (15, 17), (33, 2), (35, 5), (26, 15), (20, 33), (22, 16), (37, 14), (5, 30), (2, 23), (21, 16), (4, 25), (23, 6), (1, 18), (11, 26), (32, 4), (19, 18), (24, 14), (23, 0), (37, 27), (20, 22), (16, 35), (8, 11), (25, 27), (3, 30), (23, 24), (12, 5), (23, 15), (24, 10), (3, 7), (15, 26), (17, 18), (18, 31), (4, 12), (19, 15), (27, 17), (37, 21), (21, 8), (11, 20), (33, 5), (34, 31), (13, 32), (16, 31), (17, 6), (3, 6), (31, 11), (0, 19), (7, 16), (23, 34), (35, 33), (35, 10), (2, 1), (4, 6), (30, 32), (20, 19), (27, 15), (21, 3), (14, 13), (34, 29), (31, 7), (16, 28), (11, 22), (23, 31), (14, 16), (14, 11), (36, 2), (13, 33), (34, 4), (7, 34), (32, 18), (8, 13), (8, 3), (2, 27), (3, 32), (6, 5), (1, 11), (8, 24), (2, 35), (36, 1), (7, 29), (4, 35), (13, 25), (6, 1), (10, 14), (35, 26), (5, 15), (15, 27), (18, 36), (29, 23), (25, 34), (16, 22), (28, 26), (12, 13), (33, 26), (22, 11), (26, 19), (33, 11), (10, 15), (24, 15), (5, 4), (1, 36), (28, 19), (15, 28), (20, 28), (22, 8), (27, 26), (19, 3), (30, 27), (34, 14), (2, 30), (19, 20), (11, 31), (10, 26), (25, 13), (29, 22), (7, 0), (24, 2), (11, 32), (34, 16), (14, 19), (18, 13), (6, 17), (20, 17), (15, 34), (16, 19), (1, 1), (36, 13), (33, 8), (28, 9), (28, 8), (37, 3), (1, 25), (30, 17), (37, 0), (20, 20), (4, 4), (12, 31), (19, 7), (19, 31), (37, 33), (1, 19), (35, 17), (0, 35), (25, 8), (11, 36), (23, 27), (29, 26), (5, 19), (3, 34), (30, 28), (9, 6), (12, 23), (28, 11), (32, 2), (6, 13), (35, 0), (9, 34), (5, 10), (31, 31), (1, 21), (24, 31), (8, 1), (15, 16), (35, 24), (6, 7), (26, 1), (31, 30), (24, 26), (5, 24), (3, 21), (32, 28), (30, 15), (24, 8), (33, 30), (28, 2), (17, 23), (32, 20), (17, 20), (32, 16), (36, 21), (0, 15), (20, 27), (6, 22), (33, 29), (28, 5), (19, 30), (11, 19), (19, 19), (17, 36), (6, 16), (5, 5), (27, 3), (10, 28), (17, 14), (17, 32), (28, 33), (29, 29), (6, 31), (33, 19), (17, 16), (36, 11), (13, 18), (22, 1), (15, 35), (18, 34), (26, 27), (9, 31), (11, 30), (18, 14), (3, 36), (1, 30), (19, 27), (21, 32), (20, 15), (22, 0), (28, 29), (24, 13), (9, 9), (13, 36), (24, 28), (10, 18), (21, 24), (25, 29), (36, 0), (30, 18), (26, 28), (22, 29), (30, 6), (13, 9), (34, 11), (27, 18), (21, 14), (3, 2), (9, 3), (7, 12), (29, 14), (16, 9), (0, 31), (12, 16), (26, 12), (27, 5), (15, 20), (4, 19), (14, 5), (21, 12), (15, 2), (14, 28), (1, 15), (25, 16), (5, 36), (35, 18), (3, 25), (26, 5), (24, 18), (18, 18), (23, 23), (9, 20), (14, 25), (9, 11), (21, 31), (21, 18), (3, 31), (5, 18), (30, 2), (14, 34), (4, 26), (27, 6), (32, 19), (14, 7), (7, 6), (29, 12), (34, 36), (34, 22), (23, 19), (13, 27), (8, 19), (28, 28), (35, 25), (8, 28), (26, 16), (6, 26), (18, 19), (32, 17), (0, 33), (37, 8), (31, 35), (10, 34), (9, 27), (36, 7), (15, 24), (2, 28), (0, 32), (28, 0), (10, 33), (22, 24), (2, 32), (37, 6), (14, 1), (35, 34), (16, 27), (22, 5), (26, 14), (19, 17), (15, 36), (25, 26), (33, 24), (16, 23), (12, 36), (1, 23), (11, 1), (7, 4), (24, 1), (16, 32), (22, 21), (15, 31), (12, 10), (3, 18), (19, 0), (27, 36), (5, 16), (23, 17), (16, 14), (9, 5), (31, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "166320", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), 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), (1, 22), (7, 8), (12, 1), (24, 13), (23, 33), (19, 7), (22, 12), (17, 7), (8, 13), (6, 8), (28, 5), (30, 2), (12, 31), (27, 21), (15, 13), (12, 6), (9, 7), (11, 15), (27, 1), (25, 29), (26, 15), (20, 6), (20, 30), (29, 32), (0, 25), (2, 30), (2, 24), (22, 16), (27, 27), (29, 24), (28, 11), (27, 2), (2, 14), (12, 20), (28, 0), (22, 7), (31, 10), (5, 21), (5, 24), (21, 4), (3, 17), (14, 5), (25, 26), (25, 20), (2, 15), (4, 6), (6, 33), (5, 4), (20, 8), (8, 12), (15, 28), (2, 21), (18, 16), (8, 8), (23, 9), (10, 9), (23, 0), (1, 7), (13, 8), (22, 33), (22, 15), (22, 27), (4, 29), (4, 31), (4, 3), (21, 25), (25, 22), (11, 18), (1, 12), (16, 31), (5, 18), (21, 17), (7, 3), (0, 31), (22, 3), (22, 24), (11, 19), (1, 32), (1, 27), (13, 30), (21, 31), (16, 16), (17, 15), (4, 12), (14, 2), (25, 16), (11, 10), (14, 25), (17, 24), (3, 19), (28, 24), (19, 11), (21, 6), (7, 15), (8, 25), (4, 18), (3, 0), (10, 33), (16, 25), (23, 11), (28, 10), (6, 5), (22, 10), (15, 30), (7, 25), (22, 26), (1, 21), (18, 18), (5, 6), (24, 26), (21, 10), (23, 16), (20, 14), (20, 16), (24, 12), (26, 31), (3, 25), (20, 2), (7, 16), (11, 24), (9, 21), (14, 13), (14, 8), (5, 17), (10, 0), (11, 23), (15, 2), (8, 1), (13, 26), (16, 2), (2, 4), (25, 4), (6, 28), (21, 1), (4, 28), (28, 21), (17, 9), (12, 3), (3, 1), (30, 15), (19, 14), (24, 4), (29, 26), (7, 22), (30, 6), (21, 18), (19, 13), (1, 17), (21, 7), (12, 28), (6, 17), (7, 6), (28, 2), (12, 13), (29, 15), (6, 23), (17, 17), (25, 7), (21, 0), (26, 0), (23, 14), (24, 30), (13, 10), (20, 10), (6, 7), (23, 6), (14, 6), (19, 2), (25, 24), (14, 24), (1, 11), (14, 10), (19, 25), (24, 22), (10, 7), (2, 12), (17, 6), (21, 24), (30, 31), (13, 12), (7, 28), (25, 10), (9, 24), (28, 29), (17, 28), (0, 19), (26, 30), (14, 19), (17, 25), (3, 29), (30, 22), (18, 33), (11, 20), (9, 11), (7, 19), (4, 30), (17, 19), (5, 29), (4, 23), (2, 11), (28, 13), (19, 30), (6, 29), (19, 18), (29, 12), (23, 28), (2, 6), (4, 17), (14, 20), (19, 8), (11, 13), (20, 17), (1, 33), (19, 10), (11, 26), (9, 9), (24, 1), (12, 26), (25, 9), (25, 6), (6, 32), (24, 23), (28, 25), (7, 17), (4, 4), (8, 33), (4, 13), (22, 17), (4, 19), (2, 13), (7, 1), (6, 22), (12, 25), (5, 15), (10, 27), (11, 30), (2, 23), (7, 18), (22, 25), (13, 21), (6, 27), (18, 27), (20, 21), (16, 27), (31, 13), (5, 30), (16, 33), (0, 20), (22, 6), (27, 25), (27, 31), (2, 20), (9, 6), (14, 23), (6, 2), (27, 12), (0, 18), (27, 11), (1, 6), (29, 33), (18, 10), (4, 27), (21, 16), (12, 17), (26, 24), (4, 5), (10, 18), (18, 6), (10, 30), (26, 6), (13, 28), (26, 26), (3, 5), (1, 1), (8, 6), (16, 29), (31, 6), (25, 3), (13, 7), (4, 2), (19, 32), (21, 23), (26, 13), (30, 30), (16, 14), (22, 9), (28, 31), (5, 33), (18, 2), (10, 11), (27, 15), (28, 20), (29, 4), (28, 12), (21, 33), (7, 11), (17, 0), (12, 10), (2, 19), (29, 10), (20, 13), (10, 28), (23, 13), (15, 24), (30, 18), (30, 1), (24, 20), (2, 3), (0, 22), (27, 8), (3, 7), (7, 4), (11, 14), (13, 18), (15, 33), (30, 20), (23, 10), (7, 9), (31, 2), (14, 12), (4, 14), (28, 33), (19, 22), (22, 5), (0, 24), (20, 3), (23, 23), (18, 3), (9, 19), (25, 25), (26, 2), (2, 9), (4, 11), (4, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408240", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 35), (13, 33), (38, 7), (30, 8), (15, 30), (19, 17), (11, 6), (26, 1), (23, 4), (2, 8), (22, 19), (37, 0), (17, 9), (21, 22), (38, 32), (38, 11), (1, 31), (36, 11), (33, 29), (29, 0), (26, 16), (6, 8), (25, 31), (23, 0), (34, 7), (30, 26), (20, 30), (36, 19), (7, 37), (16, 32), (30, 32), (35, 19), (31, 24), (10, 11), (9, 24), (29, 16), (28, 6), (21, 16), (22, 31), (1, 33), (11, 21), (21, 33), (28, 33), (30, 0), (6, 23), (25, 34), (3, 4), (18, 10), (22, 22), (32, 27), (2, 9), (11, 26), (7, 30), (8, 35), (3, 6), (25, 25), (36, 8), (30, 5), (3, 28), (8, 24), (18, 19), (8, 10), (12, 24), (35, 11), (31, 8), (21, 30), (31, 11), (30, 1), (17, 22), (27, 37), (18, 27), (16, 37), (33, 6), (19, 11), (28, 20), (20, 17), (11, 14), (21, 32), 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17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726720", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 28), (24, 20), (31, 18), (25, 23), (36, 23), (29, 36), (10, 13), (13, 11), (24, 34), (12, 17), (8, 37), (29, 22), (25, 1), (8, 35), (32, 18), (6, 34), (20, 9), (17, 1), (17, 29), (7, 25), (25, 7), (31, 7), (25, 14), (12, 4), (24, 37), (22, 32), (33, 17), (27, 7), (14, 19), (27, 22), (22, 23), (23, 37), (28, 7), (35, 4), (10, 17), (32, 36), (7, 23), (35, 30), (18, 20), (0, 18), (33, 24), (9, 2), (26, 0), (24, 23), (29, 20), (4, 16), (28, 9), (17, 34), (22, 3), (9, 22), (17, 33), (19, 20), (8, 8), (27, 28), (12, 20), (32, 34), (14, 18), (13, 17), (30, 3), (25, 21), (31, 11), (29, 33), (13, 7), (29, 7), (30, 12), (3, 6), (6, 29), (2, 29), (10, 2), (16, 19), (14, 31), (23, 36), (18, 0), (22, 1), (0, 21), (27, 24), (24, 24), (1, 27), 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17), (10, 27), (24, 13), (19, 17), (2, 17), (25, 25), (27, 32), (14, 14), (0, 9), (3, 27), (36, 2), (17, 12), (11, 30), (33, 12), (16, 28), (30, 37), (14, 7), (36, 8), (13, 5), (29, 2), (33, 31), (18, 25), (4, 23), (33, 15), (33, 8), (27, 37), (11, 5), (12, 36), (23, 30), (4, 27), (9, 26), (3, 17), (29, 26), (7, 4), (0, 26), (15, 9), (19, 16), (22, 30), (26, 1), (25, 26), (31, 27), (32, 28), (21, 23), (10, 36), (19, 24), (9, 21), (18, 10), (27, 31), (28, 5), (10, 14), (33, 9), (14, 20), (3, 0), (29, 0), (32, 20), (13, 8), (35, 0), (24, 6), (18, 7), (26, 15), (11, 4), (24, 16), (3, 2), (21, 30), (11, 28), (19, 25), (13, 10), (2, 9), (9, 11), (33, 18), (35, 12), (9, 15), (6, 10), (13, 1), (11, 22), (18, 2), (31, 0), (0, 36), (18, 11), (2, 31), (6, 20), (8, 33), (25, 24), (0, 35), (35, 35), (8, 24), (3, 34), (25, 29), (1, 36), (32, 13), (30, 17), (31, 10), (12, 10), (21, 24), (32, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816480", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (37, 25), (24, 33), (19, 26), (16, 7), (9, 0), (10, 34), (20, 28), (7, 10), (7, 22), (7, 34), (3, 13), (3, 30), (37, 24), (25, 6), (0, 11), (29, 9), (7, 17), (15, 1), (11, 13), (9, 18), (16, 28), (32, 14), (37, 13), (23, 11), (10, 17), (6, 11), (15, 25), (7, 20), (4, 32), (20, 11), (31, 30), (4, 6), (14, 17), (6, 32), (8, 14), (32, 7), (17, 7), (14, 28), (1, 16), (12, 35), (23, 0), (12, 11), (29, 14), (9, 28), (13, 5), (15, 22), (34, 36), (11, 16), (5, 10), (15, 17), (32, 30), (11, 19), (17, 5), (30, 19), (1, 24), (17, 35), (12, 33), (19, 23), (19, 12), (34, 4), (8, 22), (25, 16), (2, 1), (27, 32), (28, 15), (17, 25), (15, 6), (6, 4), (17, 3), (25, 1), (36, 15), (4, 7), (30, 2), (25, 7), (34, 11), (8, 9), (17, 13), (23, 15), (18, 1), (4, 16), (34, 9), (3, 16), (12, 19), (31, 36), (6, 28), (0, 28), (25, 3), (36, 9), (15, 24), (32, 10), (36, 6), (23, 28), (15, 4), (33, 27), (1, 13), (27, 5), (26, 2), (7, 3), (36, 28), (11, 10), (7, 21), (6, 26), (19, 14), (22, 19), (34, 6), (11, 9), (3, 29), (35, 18), (9, 10), (17, 21), (1, 28), (29, 16), (26, 10), (22, 1), (5, 26), (21, 31), (6, 1), (1, 4), (3, 4), (4, 31), (21, 13), (22, 36), (34, 28), (23, 9), (11, 5), (18, 34), (33, 5), (23, 35), (12, 6), (18, 16), (8, 24), (23, 4), (5, 32), (3, 33), (0, 35), (6, 19), (3, 25), (12, 12), (22, 33), (24, 28), (21, 16), (14, 19), (25, 8), (26, 4), (20, 23), (6, 10), (27, 15), (23, 16), (5, 16), (16, 16), (23, 34), (23, 26), (22, 2), (32, 34), (7, 26), (2, 12), (28, 34), (29, 36), (23, 17), (35, 28), (1, 22), (14, 10), (30, 14), (18, 10), (13, 16), (27, 11), (28, 13), (22, 24), (10, 1), (31, 20), (36, 29), (6, 35), (24, 3), (12, 22), (14, 11), (5, 35), (21, 14), (24, 30), (3, 7), (20, 8), (35, 29), (33, 0), (2, 29), (23, 36), (14, 29), (18, 27), (27, 12), (23, 24), (32, 26), (17, 15), (22, 29), (25, 18), (11, 12), (37, 19), (1, 34), (27, 1), (11, 31), (21, 9), (4, 0), (35, 30), (12, 36), (13, 11), (3, 24), (2, 21), (25, 34), (25, 31), (31, 23), (28, 3), (14, 0), (33, 23), (13, 31), (29, 30), (32, 33), (6, 27), (19, 0), (27, 21), (14, 26), (10, 9), (3, 35), (16, 20), (10, 4), (13, 21), (26, 1), (26, 13), (4, 35), (5, 34), (6, 16), (35, 21), (8, 25), (32, 20), (23, 22), (6, 24), (14, 5), (5, 25), (5, 33), (10, 35), (9, 25), (34, 19), (3, 20), (32, 3), (30, 26), (1, 1), (29, 29), (9, 9), (7, 15), (29, 1), (37, 26), (12, 34), (28, 27), (17, 6), (36, 34), (1, 0), (25, 30), (23, 2), (3, 27), (31, 9), (9, 34), (37, 18), (5, 31), (37, 30), (13, 15), (17, 16), (32, 35), (12, 3), (3, 9), (24, 16), (17, 26), (17, 0), (0, 16), (8, 19), (21, 4), (30, 3), (23, 8), (8, 0), (21, 2), (36, 35), (18, 7), (11, 24), (13, 8), (25, 20), (23, 21), (21, 6), (6, 2), (11, 18), (10, 12), (11, 27), (9, 2), (24, 8), (9, 21), (30, 0), (31, 26), (24, 9), (24, 19), (3, 10), (17, 32), (21, 7), (2, 35), (32, 24), (12, 20), (10, 15), (4, 25), (28, 0), (0, 30), (26, 35), (25, 5), (12, 16), (9, 13), (7, 18), (37, 20), (29, 2), (2, 3), (9, 6), (31, 34), (19, 22), (4, 36), (34, 5), (36, 36), (36, 33), (7, 33), (26, 16), (11, 3), (16, 26), (18, 19), (12, 5), (16, 33), (16, 36), (25, 33), (25, 4), (26, 19), (11, 2), (9, 32), (32, 19), (5, 27), (3, 22), (20, 14), (2, 7), (4, 19), (29, 32), (7, 29), (8, 4), (26, 20), (10, 10), (24, 1), (34, 2), (15, 33), (3, 32), (27, 26), (2, 22), (35, 15), (21, 28), (37, 28), (15, 13), (34, 7), (15, 16), (31, 1), (4, 5), (10, 22), (30, 15), (21, 3), (5, 8), (33, 25), (14, 36), (8, 2), (19, 19), (29, 19), (20, 20), (0, 12), (9, 29), (28, 8), (28, 21), (33, 30), (16, 15), (13, 18), (6, 5), (18, 2), (10, 21), (12, 0), (30, 27), (16, 14), (26, 17), (8, 8), (27, 22), (21, 35), (31, 11), (11, 17), (18, 0), (27, 30), (24, 26), (4, 12), (32, 32), (19, 11), (13, 26), (1, 32), (21, 23), (31, 28), (25, 10), (32, 27), (8, 30), (3, 36), (15, 19), (32, 36), (15, 30), (24, 7), (33, 14), (7, 7), (11, 7), (32, 18), (5, 19), (25, 21), (35, 33), (20, 33), (12, 25), (12, 15), (20, 6), (36, 26), (23, 3), (35, 11), (12, 26), (11, 32), (15, 28), (34, 3), (6, 8), (2, 8), (7, 4), (5, 22), (16, 10), (3, 11), (23, 29), (22, 0), (19, 33), (24, 18), (20, 30), (23, 19), (17, 30), (28, 26), (7, 35), (29, 22), (17, 4), (36, 1), (24, 25), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728640", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 33), (7, 23), (3, 0), (14, 29), (27, 14), (32, 4), (4, 31), (24, 15), (11, 16), (24, 20), (11, 18), (30, 9), (9, 6), (13, 24), (21, 4), (16, 14), (13, 29), (20, 30), (1, 7), (22, 20), (3, 13), (22, 19), (21, 0), (3, 27), (9, 1), (13, 11), (31, 23), (13, 22), (20, 18), (16, 9), (6, 29), (21, 13), (13, 27), (19, 15), (6, 18), (31, 31), (27, 12), (30, 34), (16, 19), (7, 15), (11, 7), (28, 23), (22, 16), (32, 31), (26, 14), (28, 28), (17, 34), (31, 21), (14, 34), (24, 22), (12, 26), (27, 19), (5, 33), (23, 28), (12, 17), (22, 31), (1, 25), (16, 10), (31, 33), (7, 25), (32, 10), (25, 14), (20, 12), (8, 3), (20, 2), (0, 6), (24, 24), (12, 5), (20, 20), (20, 21), (27, 13), (19, 8), (7, 8), (15, 20), (27, 33), (15, 29), (2, 24), (24, 5), (29, 3), (0, 29), (2, 25), (16, 30), (13, 10), (20, 24), (2, 13), (3, 3), (9, 32), (6, 11), (31, 18), (11, 4), (14, 3), (29, 9), (11, 20), (28, 4), (15, 2), (16, 32), (8, 33), (14, 18), (28, 29), (27, 16), (18, 11), (28, 26), (32, 8), (13, 4), (28, 10), (1, 27), (25, 0), (32, 26), (2, 27), (4, 0), (5, 13), (9, 31), (17, 9), (2, 23), (4, 7), (26, 18), (31, 12), (8, 26), (8, 1), (2, 28), (27, 34), (6, 10), (7, 13), (30, 6), (11, 1), (0, 3), (12, 12), (15, 18), (26, 17), (8, 9), (18, 4), (9, 0), (26, 31), (23, 27), (17, 33), (22, 10), (28, 1), (5, 0), (16, 2), (26, 5), (5, 26), (22, 32), (23, 33), (3, 4), (5, 7), (6, 20), (23, 12), (7, 4), (23, 19), (11, 14), (28, 35), (32, 19), (1, 15), (17, 27), (27, 23), (2, 21), (17, 18), (1, 8), (8, 15), (9, 2), (25, 12), (1, 32), (16, 31), (14, 8), (30, 26), (29, 15), (14, 31), (18, 9), (22, 30), (15, 21), (30, 32), (10, 11), (28, 6), (18, 34), (31, 24), (15, 24), (13, 28), (26, 22), (22, 2), (16, 5), (17, 0), (32, 9), (29, 12), (9, 30), (32, 22), (28, 13), (29, 2), (9, 22), (21, 17), (24, 16), (19, 23), (18, 33), (14, 27), (12, 6), (27, 29), (19, 30), (3, 28), (31, 9), (29, 29), (13, 19), (20, 1), (19, 21), (13, 23), (26, 15), (3, 7), (28, 18), (31, 29), (1, 12), (5, 3), (29, 17), (6, 8), (31, 27), (13, 31), (31, 19), (14, 25), (4, 3), (12, 9), (19, 13), (17, 26), (4, 35), (7, 32), (21, 8), (12, 2), (14, 19), (25, 23), (18, 30), (2, 14), (28, 30), (20, 15), (18, 25), (26, 0), (8, 10), (13, 1), (3, 29), (16, 18), (21, 26), (13, 20), (18, 3), (25, 10), (5, 11), (24, 2), (30, 33), (24, 0), (0, 18), (25, 5), (1, 29), (15, 32), (20, 4), (1, 13), (18, 14), (5, 6), (10, 20), (11, 15), (19, 27), (18, 28), (1, 26), (10, 34), (14, 2), (18, 32), (11, 22), (9, 18), (1, 21), (13, 32), (20, 11), (15, 16), (5, 28), (6, 13), (16, 7), (23, 25), (32, 27), (14, 32), (22, 24), (28, 20), (31, 26), (25, 21), (10, 15), (11, 11), (24, 34), (15, 3), (19, 9), (5, 8), (28, 33), (7, 22), (5, 21), (14, 30), (23, 18), (7, 5), (30, 10), (28, 0), (9, 8), (30, 16), (2, 4), (23, 13), (7, 34), (25, 33), (9, 20), (0, 23), (32, 23), (27, 7), (27, 24), (1, 16), (24, 13), (27, 9), (29, 10), (7, 16), (8, 11), (32, 15), (8, 21), (18, 1), (1, 24), (11, 6), (2, 18), (32, 17), (5, 20), (27, 11), (32, 6), (27, 32), (8, 35), (7, 30), (21, 5), (21, 19), (17, 29), (23, 22), (8, 25), (15, 19), (19, 10), (0, 32), (26, 23), (32, 33), (32, 25), (23, 29), (13, 3), (4, 1), (25, 31), (20, 31), (17, 10), (16, 4), (3, 21), (14, 11), (3, 19), (25, 28), (15, 13), (28, 2), (24, 10), (31, 25), (25, 24), (10, 3), (22, 14), (23, 11), (22, 18), (7, 9), (10, 29), (25, 27), (26, 13), (11, 30), (2, 16), (6, 6), (8, 0), (16, 0), (11, 3), (1, 34), (12, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "846720", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (18, 30), (20, 26), (9, 14), (2, 13), (12, 9), (4, 20), (31, 21), (30, 12), (9, 18), (0, 25), (28, 12), (20, 11), (29, 20), (12, 5), (30, 33), (5, 28), (12, 27), (22, 25), (6, 21), (23, 3), (16, 11), (27, 14), (20, 13), (11, 29), (1, 14), (32, 23), (18, 6), (31, 32), (32, 24), (28, 8), (7, 8), (2, 26), (16, 4), (23, 13), (18, 20), (4, 3), (7, 17), (5, 14), (9, 20), (18, 29), (6, 1), (21, 0), (3, 3), (15, 18), (26, 4), (11, 33), (23, 27), (31, 15), (7, 31), (15, 13), (28, 22), (17, 24), (28, 25), (3, 27), (11, 7), (6, 13), (24, 11), (16, 18), (18, 31), (0, 28), (3, 1), (24, 21), (7, 16), (20, 0), (31, 19), (24, 32), (20, 31), (0, 24), (22, 10), (22, 29), (13, 18), (19, 33), (9, 16), (11, 3), (11, 4), (12, 11), (7, 21), (28, 7), (20, 12), (5, 3), (22, 4), (25, 1), (25, 28), (21, 19), (31, 14), (24, 16), (24, 23), (0, 33), (21, 13), (7, 3), (28, 4), (14, 13), (28, 33), (19, 32), (3, 12), (20, 10), (32, 5), (0, 13), (22, 12), (16, 14), (25, 8), (13, 15), (15, 5), (10, 30), (5, 34), (2, 33), (7, 28), (12, 21), (24, 28), (11, 34), (7, 25), (30, 26), (24, 25), (22, 33), (32, 30), (19, 5), (6, 29), (5, 15), (26, 13), (5, 6), (24, 13), (0, 2), (29, 1), (32, 34), (4, 15), (8, 15), (28, 18), (4, 31), (15, 25), (15, 31), (20, 20), (12, 30), (22, 18), (3, 18), (31, 8), (25, 25), (31, 0), (19, 0), (26, 14), (0, 15), (6, 17), (1, 1), (16, 34), (29, 18), (1, 29), (8, 27), (0, 34), (18, 14), (17, 3), (6, 26), (32, 19), (13, 19), (28, 15), (26, 23), (15, 6), (6, 7), (26, 2), (29, 15), (14, 2), (0, 30), (10, 17), (25, 29), (17, 2), (13, 20), (14, 16), (15, 17), (9, 12), (27, 4), (12, 24), (6, 10), (2, 14), (29, 7), (19, 15), (2, 21), (10, 28), (29, 6), (7, 33), (28, 29), (21, 5), (17, 6), (15, 22), (10, 2), (28, 11), (32, 3), (28, 27), (10, 21), (33, 16), (27, 16), (14, 26), (19, 13), (4, 5), (28, 17), (6, 30), (13, 31), (1, 26), (23, 8), (10, 26), (33, 27), (16, 9), (14, 10), (6, 8), (27, 30), (22, 14), (4, 7), (26, 21), (22, 5), (28, 24), (8, 8), (27, 12), (14, 12), (0, 10), (25, 24), (11, 22), (30, 25), (7, 4), (32, 25), (15, 24), (28, 31), (14, 27), (4, 0), (32, 29), (9, 26), (26, 22), (23, 0), (33, 7), (9, 33), (7, 15), (14, 3), (14, 29), (26, 1), (18, 27), (6, 9), (27, 18), (13, 16), (24, 15), (23, 1), (6, 2), (3, 24), (14, 23), (8, 26), (20, 22), (10, 1), (23, 20), (28, 32), (1, 15), (32, 26), (31, 26), (22, 20), (20, 1), (24, 9), (11, 20), (27, 24), (23, 28), (3, 13), (28, 6), (5, 17), (10, 22), (22, 21), (23, 24), (10, 23), (27, 21), (31, 6), (25, 4), (5, 11), (33, 4), (2, 20), (16, 2), (10, 6), (25, 14), (30, 10), (9, 27), (14, 18), (14, 17), (25, 34), (28, 9), (7, 10), (26, 28), (22, 17), (26, 17), (13, 11), (10, 19), (4, 23), (17, 30), (14, 14), (29, 9), (9, 3), (20, 6), (18, 11), (31, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "779130", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 30), (6, 16), (0, 12), (29, 11), (3, 31), (22, 17), (14, 21), (25, 8), (17, 4), (27, 9), (8, 7), (5, 6), (15, 12), (16, 9), (28, 20), (4, 33), (17, 3), (4, 16), (6, 11), (26, 17), (26, 19), (19, 26), (25, 7), (28, 24), (21, 22), (28, 17), (0, 9), (2, 31), (22, 9), (16, 25), (5, 17), (15, 30), (28, 19), (18, 0), (19, 32), (25, 15), (9, 5), (24, 16), (10, 26), (3, 16), (10, 29), (29, 17), (6, 31), (7, 16), (1, 27), (26, 11), (10, 20), (4, 8), (24, 22), (31, 31), (22, 30), (8, 14), (8, 28), (11, 0), (17, 8), (0, 10), (15, 26), (7, 30), (15, 33), (26, 0), (18, 30), (18, 3), (19, 2), (2, 15), (22, 22), (13, 29), (27, 20), (14, 15), (2, 5), (11, 8), (7, 1), (21, 8), (20, 5), (23, 9), (26, 3), (29, 2), (13, 17), (25, 17), (21, 30), (22, 19), (31, 30), (19, 9), (18, 2), (10, 7), (17, 26), (17, 16), (13, 4), (9, 30), (9, 21), (29, 6), (0, 28), (19, 31), (11, 10), (7, 27), (26, 8), (28, 12), (28, 3), (13, 33), (6, 26), (21, 5), (20, 3), (10, 25), (24, 21), (0, 27), (1, 16), (21, 29), (8, 1), (6, 33), (13, 7), (5, 30), (3, 32), (2, 19), (15, 2), (17, 2), (31, 22), (17, 6), (30, 17), (2, 22), (0, 4), (12, 13), (3, 28), (15, 16), (22, 33), (20, 6), (30, 1), (1, 29), (13, 0), (30, 15), (31, 16), (12, 27), (6, 23), (9, 16), (6, 12), (24, 24), (17, 17), (24, 19), (24, 14), (15, 18), (27, 10), (7, 29), (6, 19), (31, 13), (24, 15), (22, 6), (25, 25), (11, 30), (5, 11), (10, 31), (11, 12), (31, 14), (19, 23), (3, 11), (27, 6), (17, 24), (21, 21), (9, 11), (7, 7), (22, 25), (23, 4), (10, 10), (2, 2), (27, 0), (24, 13), (15, 9), (23, 6), (13, 5), (4, 13), (21, 32), (14, 23), (23, 12), (10, 17), (11, 5), (2, 27), (5, 3), (1, 2), (6, 1), (30, 19), (23, 24), (19, 3), (4, 14), (14, 5), (22, 3), (31, 12), (12, 5), (7, 12), (13, 22), (2, 6), (6, 25), (27, 4), (13, 21), (18, 11), (9, 32), (12, 1), (22, 8), (21, 2), (0, 26), (2, 26), (26, 1), (29, 32), (1, 28), (6, 9), (4, 15), (26, 7), (21, 1), (5, 19), (31, 10), (13, 26), (5, 14), (30, 7), (30, 29), (25, 0), (19, 8), (20, 21), (15, 19), (30, 25), (0, 31), (1, 31), (16, 0), (22, 24), (12, 15), (24, 27), (2, 29), (16, 26), (25, 30), (31, 29), (0, 15), (31, 21), (16, 1), (6, 15), (22, 10), (4, 9), (2, 1), (17, 33), (1, 21), (18, 17), (27, 25), (10, 18), (9, 20), (18, 8), (28, 10), (12, 3), (29, 24), (3, 12), (1, 24), (3, 21), (5, 20), (28, 32), (2, 13), (23, 30), (7, 25), (27, 5), (4, 10), (19, 21), (7, 14), (27, 22), (31, 26), (5, 32), (3, 27), (2, 28), (9, 29), (1, 17), (8, 20), (6, 3), (23, 18), (11, 14), (9, 7), (8, 0), (25, 33), (20, 2), (30, 22), (17, 27), (9, 31), (3, 17), (26, 9), (16, 10), (13, 12), (7, 3), (31, 6), (3, 24), (21, 17), (8, 22), (3, 9), (29, 3), (19, 11), (27, 2), (26, 30), (16, 20), (18, 21), (8, 13), (13, 3), (24, 11), (14, 20), (31, 8), (4, 19), (1, 6), (24, 6), (21, 13), (6, 18), (13, 32), (14, 25), (31, 0), (24, 29), (0, 29), (4, 18), (4, 28), (5, 10), (11, 3), (3, 5), (23, 7), (10, 28), (23, 32), (15, 23), (21, 6), (27, 33), (16, 3), (8, 19), (15, 21), (10, 30), (7, 0), (26, 18), (24, 1), (31, 3), (11, 9), (24, 26), (24, 20), (29, 13), (17, 13), (6, 24), (1, 14), (26, 20), (9, 27), (22, 12), (3, 8), (0, 11), (4, 24), (1, 12), (4, 20), (25, 14), (6, 2), (25, 29), (20, 0), (12, 11), (26, 32), (0, 13), (16, 8), (11, 1), (28, 29), (23, 29), (18, 19), (14, 19), (19, 17), (17, 25), (28, 11), (11, 29), (8, 9), (17, 7), (29, 15), (12, 21), (13, 25), (27, 14), (18, 7), (9, 8), (29, 16), (6, 29), (4, 22), (31, 5), (25, 18), (23, 22), (6, 22), (9, 19), (28, 1), (12, 19), (20, 31), (1, 10), (22, 21), (5, 9), (13, 10), (9, 25), (28, 13), (29, 31), (27, 8), (31, 28), (2, 18), (23, 0), (19, 5), (17, 9), (30, 33), (29, 4), (0, 2), (9, 18), (22, 32), (18, 16), (5, 7), (20, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "932320", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 9), (29, 4), (24, 12), (36, 15), (30, 11), (16, 16), (29, 19), (20, 11), (32, 18), (17, 17), (25, 29), (17, 13), (9, 16), (7, 9), (13, 10), (4, 12), (23, 25), (4, 21), (8, 11), (20, 30), (34, 23), (0, 1), (7, 18), (4, 25), (28, 14), (21, 21), (24, 13), (17, 12), (12, 0), (33, 21), (2, 8), (13, 3), (29, 20), (16, 25), (33, 24), (26, 19), (3, 5), (25, 7), (33, 6), (15, 4), (6, 29), (24, 18), (9, 6), (24, 1), (12, 20), (1, 13), (27, 22), (35, 1), (36, 10), (15, 27), (16, 12), (7, 8), (11, 0), (33, 4), (27, 19), (20, 23), (2, 27), (20, 12), (16, 19), (4, 0), (11, 13), (15, 21), (20, 26), (0, 23), (30, 26), (26, 0), (36, 29), (33, 5), (4, 9), (14, 13), (8, 5), (21, 3), (38, 2), (35, 6), (21, 9), (38, 12), (30, 24), (3, 0), (22, 22), (31, 6), (4, 22), (34, 0), (1, 15), (17, 28), (13, 1), (31, 19), (18, 29), (13, 14), (0, 26), (32, 8), (28, 18), (22, 12), (16, 27), (0, 29), (3, 18), (14, 5), (7, 27), (35, 29), (3, 3), (32, 3), (29, 25), (32, 4), (38, 18), (37, 18), (32, 21), (23, 30), (31, 27), (19, 14), (24, 5), (17, 9), (1, 5), (18, 17), (15, 1), (0, 24), (21, 14), (8, 4), (7, 7), (4, 13), (3, 6), (20, 13), (4, 8), (8, 16), (0, 3), (7, 11), (1, 4), (10, 0), (31, 21), (6, 25), (25, 0), (15, 6), (16, 3), (31, 30), (20, 5), (34, 25), (31, 14), (17, 2), (15, 13), (9, 9), (8, 25), (31, 11), (1, 9), (32, 1), (21, 10), (11, 21), (0, 2), (2, 28), (21, 25), (4, 23), (14, 27), (32, 16), (15, 18), (1, 29), (12, 13), (20, 27), (12, 11), (4, 18), (8, 3), (1, 30), (27, 8), (24, 9), (28, 23), (10, 7), (9, 4), (9, 25), (16, 15), (7, 2), (22, 9), (27, 21), (17, 15), (12, 5), (24, 21), (0, 8), (11, 1), (26, 11), (28, 29), (31, 22), (11, 25), (1, 25), (3, 12), (36, 30), (15, 22), (7, 13), (7, 21), (25, 26), (25, 25), (5, 18), (16, 5), (37, 14), (6, 21), (11, 14), (32, 24), (21, 18), (2, 29), (25, 23), (18, 8), (34, 8), (25, 14), (0, 28), (6, 6), (15, 28), (31, 18), (19, 1), (30, 25), (37, 30), (18, 14), (20, 8), (28, 24), (7, 17), (28, 28), (21, 2), (2, 7), (2, 0), (4, 14), (0, 6), (24, 19), (25, 13), (4, 30), (32, 22), (19, 27), (25, 8), (21, 1), (16, 6), (28, 8), (2, 1), (32, 11), (17, 4), (30, 4), (10, 23), (32, 29), (35, 12), (20, 4), (36, 24), (0, 9), (35, 24), (4, 27), (14, 17), (22, 10), (11, 18), (23, 11), (35, 0), (19, 26), (10, 14), (13, 21), (10, 3), (21, 17), (20, 22), (11, 16), (15, 7), (11, 23), (18, 10), (9, 24), (27, 11), (25, 10), (31, 29), (17, 3), (38, 13), (26, 18), (37, 20), (35, 4), (18, 1), (13, 5), (31, 1), (35, 3), (5, 3), (5, 15), (34, 27), (32, 30), (16, 23), (27, 20), (30, 7), (35, 8), (30, 15), (0, 22), (13, 8), (15, 17), (17, 6), (29, 10), (31, 17), (31, 24), (28, 26), (14, 10), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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), (28, 10), (29, 24), (25, 6), (25, 37), (3, 6), (10, 3), (0, 25), (28, 1), (14, 38), (23, 3), (17, 15), (26, 35), (21, 25), (26, 7), (21, 29), (8, 32), (7, 27), (7, 19), (17, 18), (30, 6), (20, 29), (7, 25), (10, 12), (9, 8), (13, 6), (12, 28), (11, 14), (28, 2), (26, 25), (16, 28), (9, 14), (25, 2), (13, 30), (9, 33), (25, 20), (23, 1), (2, 30), (19, 16), (12, 37), (22, 9), (10, 38), (10, 31), (17, 34), (8, 12), (2, 22), (21, 17), (2, 33), (20, 22), (24, 4), (18, 0), (3, 8), (10, 8), (4, 7), (29, 16), (0, 3), (3, 28), (17, 10), (10, 34), (5, 26), (25, 26), (12, 29), (25, 4), (7, 2), (1, 24), (23, 34), (28, 12), (17, 5), (27, 31), (29, 5), (1, 4), (24, 36), (11, 34), (16, 10), (24, 20), (28, 3), (20, 13), (21, 24), (14, 18), (19, 23), (2, 21), (3, 9), (16, 1), (6, 33), (4, 13), (12, 19), (16, 0), (9, 34), (17, 37), (8, 13), (5, 8), (21, 9), (13, 18), (20, 10), (8, 14), (2, 5), (29, 32), (3, 2), (28, 26), (1, 31), (19, 15), (17, 35), (15, 10), (2, 20), (9, 3), (0, 15), (7, 35), (2, 24), (25, 31), (0, 31), (21, 27), (24, 7), (5, 2), (0, 34), (24, 26), (10, 29), (26, 0), (6, 12), (27, 30), (20, 16), (16, 29), (7, 33), (3, 7), (5, 37), (22, 11), (27, 36), (23, 36), (11, 33), (9, 28), (13, 5), (14, 13), (23, 16), (0, 9), (3, 12), (15, 37), (24, 30), (6, 1), (15, 25), (5, 20), (25, 13), (19, 24), (11, 11), (30, 10), (14, 33), (3, 35), (20, 1), (20, 37), (18, 8), (7, 7), (14, 24), (0, 20), (27, 35), (26, 27), (4, 4), (9, 36), (27, 2), (23, 31), (27, 34), (1, 3), (4, 9), (28, 11), (29, 30), (28, 5), (9, 37), (28, 16), (24, 27), (6, 7), (5, 10), (2, 34), (20, 26), (15, 16), (6, 18), (5, 30), (15, 32), (26, 2), (15, 12), (5, 17), (22, 20), (3, 14), (26, 16), (15, 35), (0, 8), (15, 34), (21, 36), (30, 22), (11, 25), (16, 35), (2, 2), (12, 13), (12, 14), (4, 16), (24, 31), (22, 28), (12, 0), (13, 25), (8, 8), (4, 8), (2, 8), (3, 15), (7, 12), (6, 20), (16, 37), (24, 24), (27, 18), (16, 4), (28, 31), (1, 34), (20, 31), (17, 6), (20, 36), (23, 5), (24, 13), (21, 7), (9, 38), (1, 35), (6, 27), (14, 22), (13, 28), (3, 34), (6, 0), (23, 2), (10, 35), (1, 10), (1, 36), (12, 6), (25, 3), (18, 3), (29, 28), (10, 2), (13, 20), (18, 13), (18, 24), (7, 10), (25, 32), (18, 11), (7, 13), (15, 36), (1, 0), (30, 0), (20, 19), (27, 22), (16, 21), (26, 38), (2, 12), (0, 7), (4, 0), (25, 19), (7, 3), (10, 16), (13, 4), (13, 1), (24, 37), (25, 25), (13, 12), (9, 15), (16, 3), (20, 18), (1, 30), (13, 19), (3, 10), (27, 37), (11, 3), (22, 22), (11, 10), (5, 31), (21, 5), (12, 12), (25, 8), (24, 18), (4, 35), (11, 17), (12, 17), (17, 13), (24, 2), (25, 38), (3, 37), (18, 12), (15, 17), (21, 13), (14, 19), (17, 28), (16, 19), (16, 2), (15, 6), (30, 15), (28, 20), (23, 14), (14, 8), (24, 5), (29, 17), (13, 15), (27, 14), (10, 24), (8, 30), (5, 15), (25, 10), (0, 17), (30, 24), (18, 10), (28, 8), (4, 20), (26, 21), (26, 1), (3, 27), (23, 0), (18, 37), (4, 29), (22, 32), (6, 38), (11, 0), (12, 3), (12, 10), (1, 23), (28, 35), (3, 36), (3, 3), (23, 13), (10, 26), (26, 32), (16, 26), (21, 22), (10, 0), (17, 25), (21, 32), (15, 29), (24, 32), (7, 9), (21, 35), (29, 7), (13, 24), (3, 32), (25, 5), (28, 17), (10, 5), (29, 6), (2, 37), (30, 16), (16, 12), (26, 28), (19, 21), (28, 21), (15, 20), (17, 16), (7, 1), (13, 0), (5, 27), (28, 9), (17, 36), (8, 26), (20, 12), (12, 18), (5, 14), (10, 10), (20, 8), (15, 5), (11, 18), (16, 5), (14, 5), (23, 22), (9, 12), (12, 31), (2, 32), (0, 2), (11, 5), (1, 12), (17, 29), (16, 24), (30, 12), (10, 20), (21, 28), (14, 23), (0, 26), (21, 38), (22, 3), (14, 17), (30, 23), (12, 27), (4, 5), (2, 19), (26, 8), (15, 28), (30, 3), (28, 13), (21, 30), (10, 13), (22, 24), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514605", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 29), (24, 3), (36, 13), (25, 11), (20, 16), (37, 3), (34, 33), (17, 25), (19, 16), (29, 18), (18, 0), (7, 18), (35, 4), (26, 32), (26, 7), (32, 12), (3, 10), (36, 27), (21, 14), (34, 27), (6, 17), (3, 28), (3, 22), (1, 2), (20, 12), (26, 28), (19, 5), (32, 16), (23, 9), (35, 13), (15, 8), (6, 19), (31, 2), (8, 25), (32, 26), (18, 18), (26, 30), (32, 4), (11, 12), (16, 16), (12, 4), (30, 24), (20, 32), (25, 10), (32, 34), (14, 5), (16, 15), (24, 20), (33, 16), (7, 13), (12, 27), (23, 25), (0, 14), (4, 20), (12, 22), (6, 2), (1, 16), (17, 22), (32, 10), (3, 23), (19, 13), (35, 6), (3, 17), (22, 13), (30, 33), (7, 31), (0, 34), (24, 4), (16, 4), (11, 17), (7, 29), (21, 12), (17, 27), (37, 32), (7, 23), (9, 0), (35, 3), (31, 30), (7, 25), (18, 15), (25, 20), (25, 34), (21, 33), (11, 30), (1, 10), (16, 19), (14, 2), (31, 4), (28, 5), (16, 14), (34, 28), (23, 16), (34, 19), (27, 20), (5, 1), (17, 1), (11, 9), (14, 33), (36, 18), (6, 9), (4, 9), (19, 10), (25, 6), (13, 4), (19, 15), (14, 21), (8, 19), (10, 7), (18, 8), (29, 11), (27, 28), (37, 0), (31, 29), (1, 13), (33, 14), (28, 22), (28, 20), (5, 7), (25, 28), (29, 6), (15, 6), (15, 17), (19, 8), (16, 32), (25, 16), (8, 33), (9, 8), (33, 18), (5, 11), (27, 27), (30, 19), (7, 15), (19, 7), (30, 31), (9, 5), (15, 19), (35, 10), (36, 17), (20, 9), (5, 14), (8, 17), (8, 3), (12, 23), (21, 20), (28, 32), (34, 11), (17, 16), (3, 11), (26, 34), (22, 9), (31, 5), (4, 1), (10, 9), (4, 31), (26, 5), (11, 7), (0, 23), (12, 19), (26, 11), (11, 24), (33, 29), (17, 18), (15, 14), (10, 28), (26, 10), (6, 22), (24, 27), (9, 20), (5, 10), (34, 30), (28, 34), (2, 15), (29, 33), (11, 26), (2, 22), (37, 5), (34, 9), (37, 19), (10, 21), (9, 18), (2, 24), (27, 32), (18, 12), (27, 4), (3, 24), (32, 5), (27, 17), (19, 31), (15, 0), (4, 24), (29, 7), (13, 3), (20, 29), (22, 0), (37, 8), (2, 34), (15, 5), (22, 23), (18, 17), (32, 21), (18, 11), (15, 1), (17, 21), (18, 4), (27, 9), (6, 13), (25, 26), (30, 5), (9, 21), (36, 15), (27, 34), (9, 17), (32, 18), (34, 13), (0, 29), (24, 16), (18, 3), (12, 30), (35, 18), (9, 11), (3, 29), (16, 30), (23, 26), (14, 30), (0, 4), (18, 1), (28, 21), (22, 18), (7, 22), (13, 0), (35, 7), (11, 1), (35, 5), (13, 29), (9, 9), (26, 20), (20, 13), (33, 1), (31, 31), (20, 21), (25, 32), (0, 10), (19, 14), (4, 16), (28, 19), (29, 3), (33, 9), (11, 23), (5, 24), (2, 0), (8, 10), (0, 32), (36, 22), (13, 34), (0, 30), (4, 22), (18, 24), (18, 31), (30, 30), (25, 0), (8, 21), (22, 6), (15, 25), (0, 26), (37, 10), (36, 29), (23, 14), (17, 5), (36, 24), (1, 18), (26, 16), (2, 5), (21, 25), (16, 24), (8, 26), (16, 8), (9, 25), (24, 24), (23, 31), (31, 17), (3, 21), (37, 22), (3, 31), (20, 30), (6, 8), (22, 19), (0, 22), (11, 16), (27, 26), (36, 32), (32, 0), (18, 7), (13, 7), (2, 23), (24, 29), (8, 9), (23, 3), (20, 23), (8, 16), (37, 28), (16, 13), (20, 18), (29, 2), (10, 11), (10, 4), (5, 3), (29, 29), (7, 32), (21, 6), (2, 10), (9, 28), (13, 33), (5, 22), (3, 12), (1, 0), (6, 26), (16, 2), (0, 12), (3, 25), (25, 3), (16, 34), (23, 32), (8, 8), (35, 31), (22, 33), (5, 30), (15, 18), (13, 15), (3, 14), (13, 21), (37, 1), (20, 28), (27, 14), (8, 5), (22, 30), (1, 30), (35, 0), (1, 8), (29, 1), (33, 17), (21, 22), (14, 16), (34, 25), (12, 11), (30, 9), (33, 5), (15, 2), (33, 27), (13, 11), (8, 20), (11, 28), (12, 34), (23, 4), (3, 19), (1, 21), (19, 29), (36, 30), (12, 13), (8, 28), (32, 24), (37, 17), (36, 20), (0, 17), (29, 15), (5, 18), (6, 23), (36, 33), (11, 34), (36, 10), (34, 29), (4, 15), (24, 18), (10, 0), (35, 12), (8, 14), (2, 28), (29, 28), (13, 12), (33, 15), (36, 0), (12, 2), (22, 20), (17, 4), (28, 25), (13, 6), (33, 22), (25, 21), (4, 21), (13, 10), (18, 16), (9, 34), (37, 12), (8, 7), (21, 4), (26, 15), (13, 30), (8, 18), (7, 17), (24, 14), (28, 30), (4, 11), (18, 29), (32, 2), (37, 9), (26, 12), (10, 14), (21, 10), (9, 10), (31, 19), (35, 17), (31, 13), (3, 16), (16, 6), (13, 16), (36, 31), (17, 10), (22, 16), (17, 12), (21, 24), (6, 4), (30, 0), (25, 22), (1, 33), (16, 31), (36, 14), (34, 34), (36, 3), (6, 21), (3, 5), (6, 14), (8, 4), (25, 18), (13, 18), (3, 9), (29, 34), (0, 16), (13, 19), (34, 1), (8, 1), (18, 6), (5, 8), (20, 25), (4, 28), (32, 15), (19, 17), (33, 28), (29, 10), (18, 25), (30, 12), (6, 20), (25, 25), (17, 19), (20, 8), (10, 12), (19, 9), (5, 25), (0, 9), (14, 29), (9, 3), (15, 30), (19, 27), (22, 14), (33, 8), (21, 34), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "933120", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 34), (20, 31), (28, 37), (2, 2), (18, 15), (10, 12), (24, 34), (1, 28), (2, 28), (18, 31), (14, 17), (23, 38), (34, 20), (26, 19), (28, 9), (13, 24), (22, 21), (2, 11), (20, 15), (4, 13), (4, 38), (33, 10), (2, 0), (17, 30), (34, 14), (11, 34), (18, 8), (24, 17), (23, 26), (34, 26), (13, 19), (16, 6), (22, 17), (3, 9), (33, 37), (29, 4), (14, 14), (31, 13), (6, 24), (5, 18), (14, 25), (7, 24), (31, 8), (10, 21), (32, 2), (35, 28), (22, 35), (13, 16), (20, 38), (32, 10), (29, 34), (9, 2), (10, 30), (27, 33), (22, 37), (12, 14), (18, 12), (30, 26), (15, 9), (23, 18), (32, 23), (19, 11), (4, 33), (20, 19), (34, 5), (24, 33), (16, 16), (21, 13), (3, 36), (20, 1), (7, 19), (20, 33), (13, 22), (29, 7), (2, 38), (0, 36), (34, 29), (33, 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2), (34, 11), (3, 18), (32, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "584064", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 22), (1, 19), (30, 8), (27, 28), (30, 1), (2, 33), (27, 9), (22, 5), (8, 23), (22, 19), (3, 8), (22, 7), (3, 12), (22, 35), (31, 1), (17, 33), (19, 1), (2, 3), (25, 21), (6, 3), (4, 27), (18, 7), (6, 14), (18, 18), (6, 9), (10, 20), (29, 10), (9, 28), (17, 34), (4, 17), (14, 3), (5, 7), (28, 8), (24, 3), (4, 28), (12, 23), (7, 0), (0, 24), (18, 8), (21, 31), (3, 30), (26, 28), (24, 26), (18, 36), (25, 27), (7, 8), (29, 31), (11, 4), (26, 5), (3, 35), (30, 37), (22, 4), (18, 21), (4, 13), (10, 9), (10, 26), (30, 34), (34, 7), (28, 21), (10, 27), (12, 9), (26, 8), (27, 4), (14, 31), (12, 11), (15, 36), (22, 18), (0, 31), (11, 23), (9, 32), (9, 14), (15, 4), (22, 27), (0, 14), (29, 9), (27, 0), (29, 29), (17, 23), (18, 9), (18, 17), (0, 15), (18, 37), (27, 15), (34, 10), (9, 36), (8, 18), (27, 20), (9, 16), (11, 18), (32, 28), (26, 2), (15, 18), (31, 10), (0, 25), (15, 11), (28, 26), (19, 10), (8, 3), (22, 14), (25, 28), (20, 6), (17, 12), (27, 29), (24, 34), (13, 13), (8, 27), (17, 24), (20, 23), (34, 36), (16, 21), (2, 21), (28, 37), (8, 30), (3, 7), (19, 2), (31, 33), (28, 24), (16, 9), (0, 3), (4, 12), (14, 0), (22, 24), (17, 11), (1, 7), (31, 7), (10, 25), (20, 10), (10, 23), (33, 22), (4, 35), (1, 33), (5, 24), (19, 34), (12, 3), (10, 14), (18, 24), (28, 22), (2, 5), (10, 31), (20, 35), (6, 8), (29, 25), (25, 17), (6, 26), (13, 34), (16, 22), (5, 1), (19, 3), (25, 9), (28, 29), (21, 37), (32, 7), (3, 27), (4, 23), (1, 22), (33, 18), (8, 5), (19, 5), (13, 19), (13, 2), (21, 2), (18, 34), (12, 26), (28, 7), (3, 17), (10, 10), (30, 3), (26, 35), (24, 1), (21, 21), (8, 1), (25, 7), (3, 18), (34, 20), (11, 3), (1, 20), (22, 13), (32, 23), (4, 25), (30, 18), (21, 14), (14, 11), (9, 33), (25, 26), (10, 21), (19, 35), (11, 6), (27, 22), (6, 19), (26, 25), (31, 17), (14, 14), (6, 31), (24, 32), (6, 21), (8, 17), (27, 5), (9, 22), (16, 3), (20, 15), (17, 14), (22, 20), (32, 0), (0, 29), (30, 17), (6, 2), (3, 22), (27, 26), (8, 0), (31, 2), (13, 32), (1, 11), (25, 18), (3, 29), (24, 27), (19, 17), (4, 1), (20, 18), (2, 34), (26, 22), (2, 4), (3, 25), (25, 24), (17, 5), (16, 30), (5, 3), (17, 7), (14, 7), (3, 28), (1, 29), (34, 4), (23, 33), (4, 0), (14, 28), (22, 17), (32, 24), (5, 25), (20, 29), (29, 21), (16, 18), (4, 29), (28, 16), (9, 13), (6, 20), (18, 30), (21, 28), (5, 37), (20, 30), (17, 3), (13, 20), (2, 20), (24, 14), (20, 34), (13, 18), (10, 8), (33, 24), (13, 30), (29, 20), (2, 22), (1, 37), (8, 2), (29, 26), (13, 36), (5, 15), (32, 17), (11, 25), (19, 7), (19, 4), (11, 15), (6, 25), (2, 36), (33, 12), (1, 9), (2, 17), (15, 10), (17, 32), (34, 0), (7, 36), (8, 7), (14, 33), (21, 36), (28, 11), (18, 19), (2, 13), (24, 21), (13, 21), (10, 35), (29, 6), (28, 36), (19, 32), (1, 27), (0, 19), (2, 35), (19, 11), (25, 33), (9, 18), (30, 6), (17, 13), (28, 5), (32, 2), (0, 5), (31, 29), (15, 13), (14, 19), (34, 26), (29, 24), (34, 3), (25, 15), (21, 24), (13, 11), (14, 12), (1, 1), (30, 23), (10, 33), (9, 17), (19, 31), (12, 22), (12, 5), (5, 28), (15, 1), (34, 23), (33, 26), (30, 24), (16, 2), (9, 15), (28, 19), (24, 7), (12, 17), (21, 4), (13, 28), (2, 2), (12, 30), (25, 0), (1, 26), (4, 14), (21, 20), (12, 19), (18, 6), (26, 26), (20, 2), (0, 18), (1, 2), (0, 37), (1, 28), (4, 31), (24, 22), (5, 17), (0, 33), (5, 22), (11, 37), (24, 16), (0, 35), (2, 15), (26, 17), (19, 15), (31, 9), (32, 19), (5, 18), (8, 12), (24, 20), (24, 11), (20, 9), (8, 4), (5, 10), (29, 13), (1, 17), (2, 10), (5, 36), (33, 17), (3, 21), (2, 11), (14, 30), (5, 23), (21, 8), (15, 27), (32, 26), (3, 31), (24, 9), (30, 32), (19, 16), (34, 28), (12, 4), (30, 12), (20, 32), (27, 36), (16, 15), (15, 31), (2, 31), (32, 10), (22, 25), (3, 23), (20, 14), (32, 1), (17, 27), (17, 0), (1, 30), (28, 13), (2, 26), (13, 15), (34, 14), (32, 6), (3, 5), (34, 2), (11, 32), (10, 24), (12, 21), (29, 0), (11, 9), (1, 25), (26, 27), (21, 5), (29, 22), (32, 5), (1, 21), (24, 24), (29, 15), (33, 19), (7, 24), (19, 13), (2, 37), (27, 18), (5, 11), (6, 12), (13, 16), (34, 16), (28, 1), (20, 36), (13, 6), (13, 9), (28, 18), (16, 25), (0, 6), (20, 1), (32, 33), (28, 12), (28, 32), (30, 11), (26, 34), (3, 34), (13, 23), (23, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10080", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 1), (28, 8), (16, 30), (4, 9), (6, 2), (4, 20), (8, 19), (6, 19), (16, 33), (27, 31), (34, 32), (34, 0), (12, 0), (15, 31), (7, 8), (14, 4), (8, 14), (2, 16), (17, 12), (15, 4), (5, 19), (29, 18), (32, 9), (33, 26), (13, 5), (26, 13), (7, 9), (34, 7), (5, 13), (7, 22), (17, 5), (13, 34), (24, 18), (28, 19), (21, 33), (33, 19), (35, 19), (30, 17), (22, 0), (22, 3), (7, 27), (14, 6), (0, 33), (11, 20), (11, 2), (19, 30), (15, 9), (5, 1), (1, 31), (18, 31), (33, 17), (14, 1), (21, 17), (10, 7), (10, 10), (21, 22), (20, 1), (28, 11), (0, 5), (21, 26), (6, 4), (24, 13), (1, 6), (4, 11), (32, 25), (5, 8), (31, 5), (7, 17), (10, 26), (1, 24), (27, 21), (25, 3), (0, 18), (24, 16), (34, 3), (0, 10), (32, 5), (9, 17), (11, 13), (15, 5), (33, 12), (10, 4), (2, 22), (31, 30), (33, 21), (2, 27), (25, 34), (22, 22), (35, 26), (31, 2), (29, 21), (24, 15), (14, 23), (3, 14), (23, 3), (30, 24), (22, 2), (34, 11), (19, 0), (1, 34), (15, 17), (7, 23), (3, 27), (10, 13), (5, 21), (25, 33), (32, 19), (23, 4), (33, 14), (13, 26), (20, 29), (13, 18), (15, 21), (4, 2), (20, 23), (14, 27), (17, 2), (22, 31), (29, 3), (3, 32), (36, 30), (20, 12), (11, 29), (28, 6), (36, 3), (17, 11), (22, 17), (13, 12), (32, 10), (19, 15), (7, 15), (25, 0), (32, 7), (25, 27), (24, 3), (2, 23), (17, 22), (3, 25), (31, 21), (10, 8), (16, 22), (35, 7), (36, 5), (16, 4), (9, 21), (35, 32), (28, 2), (8, 28), (34, 24), (28, 0), (35, 34), (13, 32), (36, 10), (16, 10), (26, 33), (0, 7), (18, 3), (0, 13), (3, 23), (3, 13), (33, 25), (25, 32), (1, 11), (17, 18), (23, 15), (14, 31), (1, 1), (34, 26), (0, 6), (32, 33), (8, 13), (20, 14), (31, 14), (16, 0), (9, 23), (17, 30), (1, 5), (33, 27), (24, 10), (22, 24), (25, 28), (16, 25), (17, 25), (35, 6), (31, 1), (17, 26), (12, 30), (5, 12), (25, 8), (24, 29), (0, 26), (15, 25), (21, 4), (6, 22), (27, 5), (17, 29), (10, 33), (19, 22), (30, 12), (5, 22), (21, 19), (1, 16), (36, 2), (32, 30), (30, 4), (26, 22), (29, 22), (16, 12), (17, 19), (19, 24), (18, 26), (26, 19), (33, 3), (11, 23), (24, 11), (19, 8), (13, 3), (1, 3), (32, 17), (19, 33), (14, 21), (16, 32), (31, 19), (7, 29), (3, 2), (21, 13), (23, 31), (6, 17), (13, 1), (9, 5), (18, 5), (6, 30), (27, 18), (7, 21), (26, 34), (3, 17), (15, 23), (2, 2), (5, 7), (3, 4), (6, 23), (35, 24), (32, 26), (31, 26), (11, 5), (33, 29), (35, 25), (11, 6), (18, 12), (20, 13), (22, 6), (27, 25), (10, 5), (14, 14), (28, 9), (7, 30), (19, 1), (6, 14), (31, 29), (3, 26), (21, 29), (25, 20), (14, 10), (31, 22), (22, 32), (21, 6), (24, 7), (34, 34), (29, 20), (14, 20), (30, 25), (15, 18), (1, 7), (21, 14), (10, 31), (25, 4), (13, 22), (36, 7), (34, 23), (21, 2), (32, 28), (9, 6), (20, 8), (15, 24), (20, 3), (30, 28), (24, 30), (27, 27), (32, 29), (29, 32), (12, 23), (26, 14), (10, 1), (7, 32), (11, 33), (27, 3), (26, 30), (18, 0), (19, 20), (22, 21), (17, 3), (4, 8), (21, 16), (24, 9), (4, 7), (24, 24), (24, 21), (5, 18), (23, 14), (30, 1), (36, 26), (28, 33), (26, 28), (26, 0), (18, 4), (21, 7), (22, 34), (11, 30), (23, 1), (22, 18), (12, 22), (16, 27), (24, 0), (16, 31), (10, 21), (5, 6), (15, 8), (24, 4), (1, 12), (17, 23), (10, 9), (35, 13), (33, 13), (35, 9), (14, 29), (17, 9), (15, 15), (15, 19), (6, 32), (9, 1), (14, 24), (6, 5), (35, 1), (20, 32), (22, 19), (5, 5), (21, 24), (26, 15), (11, 27), (16, 2), (34, 13), (23, 26), (35, 33), (8, 30), (32, 22), (36, 21), (3, 1), (11, 15), (22, 16), (31, 16), (23, 12), (18, 8), (13, 19), (36, 29), (26, 27), (1, 26), (27, 13), (35, 27), (26, 4), (26, 16), (19, 27), (30, 5), (27, 4), (35, 11), (30, 23), (14, 5), (21, 23), (33, 34), (20, 28), (30, 21), (36, 14), (19, 2), (2, 6), (21, 10), (3, 30), (3, 20), (13, 13), (35, 17), (20, 20), (23, 6), (18, 11), (3, 11), (19, 10), (33, 18), (7, 33), (6, 13), (25, 13), (5, 20), (8, 4), (1, 29), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "696555", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), 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), (15, 38), (15, 13), (28, 28), (4, 6), (9, 28), (26, 25), (7, 17), (30, 11), (14, 17), (12, 35), (25, 37), (6, 33), (4, 18), (28, 5), (13, 3), (24, 13), (29, 20), (18, 7), (9, 37), (15, 16), (6, 20), (18, 31), (22, 3), (24, 6), (10, 30), (16, 11), (12, 28), (8, 6), (11, 10), (28, 18), (30, 8), (19, 18), (22, 34), (30, 19), (4, 33), (5, 9), (16, 9), (10, 4), (14, 37), (18, 27), (20, 19), (13, 16), (17, 25), (31, 5), (27, 27), (31, 26), (30, 33), (19, 16), (17, 23), (15, 37), (12, 1), (24, 8), (0, 24), (28, 29), (28, 22), (24, 4), (1, 1), (13, 20), (15, 10), (0, 35), (0, 38), (10, 3), (31, 8), (23, 0), (19, 11), (2, 7), (29, 26), (28, 6), (19, 1), (7, 15), (3, 10), (27, 17), (9, 19), (4, 31), (22, 29), (31, 10), (5, 16), (8, 15), (0, 31), (16, 26), (4, 17), (2, 15), (16, 28), (18, 23), (23, 19), (13, 1), (28, 34), (27, 31), (26, 32), (26, 9), (23, 11), (29, 12), (24, 34), (0, 18), (10, 7), (4, 10), (7, 6), (9, 12), (14, 24), (23, 15), (7, 23), (29, 24), (4, 32), (0, 1), (21, 11), (21, 23), (2, 14), (7, 9), (1, 31), (31, 0), (13, 8), (29, 22), (31, 35), (14, 5), (4, 38), (28, 37), (26, 37), (6, 22), (2, 38), (8, 26), (23, 35), (24, 27), (10, 14), (27, 1), (16, 5), (1, 27), (0, 26), (29, 38), (2, 22), (10, 10), (17, 19), (22, 37), (9, 3), (16, 35), (9, 16), (4, 14), (5, 36), (23, 22), (25, 3), (17, 3), (5, 38), (16, 4), (16, 33), (4, 15), (28, 9), (21, 18), (3, 16), (15, 3), (20, 28), (0, 27), (10, 29), (9, 22), (25, 36), (25, 16), (19, 8), (16, 29), (15, 29), (5, 35), (11, 17), (24, 21), (0, 28), (2, 26), (23, 30), (8, 7), (12, 22), (27, 23), (22, 15), (2, 9), (21, 12), (7, 29), (18, 28), (18, 22), (13, 28), (19, 10), (2, 37), (1, 34), (25, 35), (2, 17), (14, 18), (12, 13), (25, 5), (31, 30), (6, 28), (0, 17), (13, 13), (8, 18), (4, 20), (7, 35), (2, 2), (14, 35), (6, 12), (10, 0), (3, 15), (8, 10), (1, 5), (17, 12), (9, 20), (22, 13), (26, 21), (9, 31), (11, 4), (19, 20), (10, 26), (27, 29), (31, 24), (11, 37), (11, 28), (14, 36), (23, 27), (19, 24), (30, 17), (4, 2), (2, 6), (3, 11), (12, 37), (15, 14), (22, 25), (5, 21), (0, 34), (3, 30), (26, 1), (5, 17), (6, 21), (3, 22), (7, 24), (6, 37), (0, 5), (8, 22), (12, 21), (30, 35), (31, 20), (2, 10), (15, 9), (27, 5), (18, 24), (20, 36), (31, 6), (6, 29), (22, 12), (31, 12), (27, 20), (28, 23), (21, 38), (10, 1), (17, 16), (22, 7), (4, 25), (0, 8), (30, 34), (22, 22), (25, 13), (26, 28), (17, 13), (18, 16), (0, 23), (29, 29), (27, 26), (24, 22), (25, 28), (26, 5), (23, 14), (17, 37), (12, 23), (22, 5), (21, 31), (21, 17), (13, 35), (20, 34), (27, 30), (2, 31), (6, 27), (3, 28), (25, 27), (21, 22), (21, 2), (23, 38), (21, 3), (26, 38), (10, 20), (5, 25), (30, 2), (1, 19), (15, 36), (9, 14), (11, 35), (7, 12), (7, 8), (15, 15), (1, 12), (20, 23), (25, 1), (6, 30), (18, 9), (4, 24), (16, 31), (3, 3), (10, 35), (25, 17), (13, 7), (7, 0), (13, 6), (21, 34), (8, 3), (18, 30), (9, 9), (9, 4), (22, 35), (1, 10), (20, 33), (25, 25), (0, 19), (19, 29), (25, 38), (13, 21), (7, 19), (16, 23), (23, 37), (3, 24), (4, 35), (14, 15), (27, 18), (7, 1), (13, 31), (23, 4), (4, 28), (28, 24), (11, 27), (10, 17), (5, 14), (19, 7), (4, 1), (13, 32), (9, 34), (5, 23), (2, 8), (6, 32), (26, 20), (3, 7), (31, 37)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "583200", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), 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), (14, 29), (25, 28), (21, 7), (32, 9), (7, 20), (4, 19), (22, 25), (7, 16), (19, 16), (21, 6), (23, 12), (26, 7), (1, 3), (9, 22), (8, 0), (11, 27), (11, 4), (11, 8), (0, 17), (13, 14), (4, 17), (5, 4), (0, 29), (22, 3), (25, 8), (15, 3), (16, 23), (3, 19), (1, 13), (8, 24), (21, 16), (15, 17), (9, 10), (0, 9), (21, 27), (23, 1), (7, 7), (24, 8), (14, 19), (3, 9), (21, 28), (17, 20), (22, 12), (14, 0), (19, 7), (1, 15), (32, 8), (22, 29), (7, 19), (20, 0), (10, 13), (24, 4), (14, 3), (29, 17), (20, 28), (20, 23), (10, 1), (13, 21), (31, 8), (11, 28), (2, 10), (8, 22), (21, 0), (33, 29), (19, 20), (12, 25), (29, 24), (28, 13), (23, 22), (29, 21), (12, 8), (32, 7), (7, 26), (12, 14), (7, 11), (10, 20), (27, 20), (19, 17), (20, 19), (30, 16), (15, 15), (25, 4), (34, 12), (14, 4), (22, 18), (23, 26), (27, 11), (13, 22), (27, 1), (22, 28), (8, 23), (16, 7), (5, 21), (3, 10), (12, 29), (34, 8), (5, 16), (10, 7), (23, 0), (16, 19), (17, 19), (5, 0), (2, 14), (18, 7), (1, 23), (21, 5), (34, 21), (4, 20), (13, 17), (18, 11), (8, 25), (20, 8), (16, 4), (32, 12), (34, 22), (25, 14), (32, 20), (2, 1), (18, 19), (6, 2), (20, 11), (12, 0), (20, 4), (19, 28), (33, 18), (12, 26), (29, 19), (6, 1), (31, 22), (23, 20), (23, 17), (24, 24), (7, 12), (16, 17), (25, 22), (28, 22), (9, 20), (5, 26), (12, 12), (7, 25), (8, 8), (28, 23), (3, 18), (29, 29), (22, 11), (34, 3), (26, 28), (34, 18), (23, 11), (25, 3), (24, 9), (19, 25), (18, 17), (22, 20), (10, 5), (8, 3), (33, 15), (31, 7), (25, 16), (15, 18), (13, 11), (5, 10), (21, 13), (0, 27), (3, 4), (13, 3), (29, 4), (29, 14), (13, 19), (18, 12), (4, 27), (11, 18), (14, 10), (10, 28), (11, 14), (25, 19), (28, 8), (9, 16), (27, 0), (21, 25), (13, 13), (10, 8), (24, 18), (32, 5), (20, 21), (8, 28), (33, 26), (0, 13), (0, 23), (32, 26), (24, 10), (18, 15), (7, 1), (3, 3), (33, 25), (28, 19), (29, 26), (29, 6), (13, 26), (33, 0), (16, 6), (31, 13), (30, 25), (9, 6), (25, 10), (28, 5), (10, 25), (33, 17), (9, 1), (5, 7), (5, 28), (15, 21), (32, 3), (1, 28), (26, 6), (15, 29), (17, 14), (10, 11), (29, 3), (5, 25), (8, 14), (8, 4), (28, 29), (13, 28), (33, 6), (1, 27), (29, 18), (34, 11), (24, 27), (15, 10), (21, 4), (2, 2), (0, 19), (19, 11), (17, 7), (32, 25), (29, 10), (14, 1), (27, 17), (5, 18), (26, 2), (21, 20), (13, 4), (22, 16), (26, 25), (28, 28), (12, 28), (17, 22), (26, 13), (11, 15), (17, 10), (32, 10), (30, 6), (9, 8), (6, 9), (12, 19), (12, 23), (13, 12), (6, 14), (20, 6), (1, 1), (33, 4), (6, 21), (10, 23), (32, 28), (34, 23), (17, 12), (2, 4), (31, 20), (34, 20), (17, 5), (3, 7), (19, 13), (31, 24), (23, 7), (18, 22), (10, 21), (12, 10), (32, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1680", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 28), (0, 22), (19, 16), (4, 21), (10, 29), (32, 29), (1, 6), (31, 4), (3, 30), (6, 5), (19, 8), (27, 1), (26, 2), (29, 17), (16, 17), (8, 2), (10, 10), (19, 15), (17, 2), (16, 5), (0, 20), (21, 26), (23, 13), (22, 26), (13, 4), (1, 17), (0, 8), (24, 17), (5, 4), (27, 25), (0, 2), (4, 18), (4, 28), (22, 11), (3, 27), (3, 14), (11, 15), (23, 25), (26, 14), (4, 30), (15, 1), (4, 20), (14, 22), (9, 2), (24, 12), (19, 7), (31, 2), (2, 24), (22, 25), (14, 26), (25, 10), (25, 0), (27, 19), (11, 27), (19, 28), (11, 3), (27, 10), (27, 21), (4, 11), (6, 24), (28, 15), (0, 13), (6, 19), (18, 2), (17, 1), (22, 15), (27, 4), (26, 18), (5, 16), (5, 7), (31, 22), (6, 10), (26, 8), (16, 2), (29, 18), (14, 29), (5, 6), (6, 4), (20, 20), (6, 7), (24, 21), (4, 19), (3, 21), (19, 23), (15, 2), (14, 9), (17, 9), (5, 10), (19, 20), (11, 10), (23, 22), (15, 14), (29, 8), (17, 23), (3, 6), (32, 17), (23, 16), (15, 10), (28, 11), (16, 30), (32, 13), (30, 0), (15, 28), (1, 16), (18, 24), (7, 15), (9, 28), (4, 24), (26, 15), (3, 2), (31, 19), (10, 28), (18, 22), (20, 2), (7, 1), (32, 5), (8, 18), (18, 4), (19, 30), (28, 18), (2, 5), (22, 7), (12, 4), (14, 21), (28, 10), (25, 11), (20, 14), (30, 13), (32, 1), (16, 15), (24, 14), (20, 27), (31, 16), (7, 20), (1, 8), (0, 3), (2, 28), (28, 24), (23, 2), (8, 15), (19, 17), (23, 19), (24, 4), (27, 30), (28, 3), (23, 15), (32, 9), (10, 0), (17, 17), (22, 3), (8, 5), (25, 30), (24, 8), (11, 19), (22, 24), (29, 28), (14, 18), (6, 6), (11, 28), (25, 9), (12, 22), (5, 2), (31, 20), (13, 21), (4, 25), (16, 14), (31, 15), (24, 9), (25, 5), (28, 27), (25, 16), (3, 28), (10, 2), (24, 10), (14, 23), (5, 17), (24, 23), (5, 19), (0, 29), (1, 7), (21, 24), (8, 26), (25, 25), (24, 18), (7, 5), (30, 15), (17, 10), (27, 14), (5, 5), (32, 3), (4, 13), (10, 8), (15, 12), (7, 26), (8, 28), (18, 26), (4, 29), (18, 18), (14, 7), (26, 0), (26, 13), (25, 14), (21, 28), (10, 6), (4, 2), (8, 10), (20, 8), (11, 22), (1, 18), (8, 6), (19, 10), (18, 5), (18, 17), (11, 9), (13, 3), (17, 5), (12, 29), (29, 10), (3, 24), (30, 27), (6, 21), (25, 20), (0, 10), (0, 11), (29, 26), (9, 24), (21, 9), (3, 8), (5, 29), (11, 16), (26, 1), (28, 9), (2, 25), (8, 11), (19, 12), (8, 16), (30, 11), (16, 23), (29, 3), (22, 10), (0, 9), (2, 23), (13, 20), (26, 6), (8, 30), (28, 5), (29, 21), (19, 24), (6, 17), (23, 18), (12, 0), (9, 20), (10, 12), (4, 17), (26, 23), (7, 12), (2, 26), (8, 27), (1, 24), (20, 6), (9, 12), (9, 1), (15, 11), (20, 3), (30, 10), (18, 23), (7, 4), (28, 7), (21, 25), (2, 0), (15, 9), (18, 0), (8, 12), (0, 5), (18, 13), (10, 26), (16, 1), (15, 23), (2, 1), (25, 27), (10, 14), (1, 5), (22, 0), (24, 25), (30, 23), (16, 10), (20, 15), (18, 9), (29, 30), (30, 19), (12, 21), (20, 25), (4, 23), (13, 11), (3, 9), (9, 17), (16, 29), (16, 0), (15, 6), (1, 10), (9, 19), (9, 7), (4, 8), (11, 21), (20, 9), (10, 7), (3, 7), (27, 9), (22, 5), (23, 27), (31, 5), (22, 14), (25, 22), (30, 14), (1, 12), (11, 1), (22, 8), (8, 29), (7, 13), (6, 28), (12, 10), (3, 20), (31, 29), (7, 24), (28, 1), (20, 11), (20, 23), (13, 5), (5, 24), (29, 6), (31, 11), (1, 20), (27, 0), (11, 14), (31, 12), (20, 5), (2, 12), (18, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978432", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), 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), (14, 1), (17, 17), (16, 8), (30, 18), (7, 24), (7, 27), (23, 14), (0, 29), (31, 0), (30, 11), (19, 23), (20, 26), (28, 36), (22, 7), (25, 7), (22, 28), (27, 34), (30, 19), (6, 28), (25, 26), (14, 20), (7, 18), (0, 10), (28, 30), (12, 30), (25, 8), (13, 35), (14, 22), (28, 17), (0, 5), (18, 35), (13, 30), (31, 11), (7, 33), (16, 31), (2, 12), (23, 19), (30, 4), (19, 30), (14, 13), (29, 6), (5, 7), (5, 29), (6, 4), (16, 16), (24, 29), (16, 19), (8, 12), (1, 30), (13, 12), (24, 23), (23, 21), (25, 27), (27, 23), (17, 21), (30, 32), (25, 9), (19, 8), (0, 1), (31, 34), (1, 33), (9, 7), (14, 5), (1, 23), (18, 34), (19, 29), (24, 7), (31, 35), (26, 33), (22, 24), (28, 14), (25, 29), (5, 1), (12, 25), (22, 35), (24, 10), (10, 14), (27, 31), (26, 11), (9, 6), (8, 20), (17, 29), (17, 18), (27, 36), (12, 3), (31, 29), (26, 12), (26, 27), (3, 2), (30, 9), (25, 18), (26, 0), (28, 15), (19, 22), (27, 20), (18, 3), (21, 9), (12, 7), (4, 28), (5, 36), (11, 28), (0, 4), (14, 29), (31, 24), (8, 34), (31, 17), (23, 30), (30, 20), (14, 31), (14, 23), (18, 20), (17, 5), (25, 5), (0, 17), (15, 20), (10, 0), (22, 13), (6, 30), (26, 36), (7, 31), (21, 4), (15, 12), (15, 31), (16, 24), (23, 33), (18, 24), (5, 3), (1, 28), (28, 11), (20, 17), (10, 4), (26, 1), (12, 12), (16, 15), (12, 10), (13, 3), (19, 19), (9, 26), (11, 26), (11, 1), (1, 14), (21, 29), (4, 0), (23, 25), (23, 36), (15, 17), (11, 16), (24, 20), (15, 37), (17, 13), (17, 30), (26, 25), (31, 8), (20, 15), (10, 13), (7, 22), (21, 8), (17, 31), (16, 34), (15, 18), (30, 14), (1, 34), (0, 20), (11, 31), (3, 16), (18, 12), (3, 19), (31, 12), (19, 26), (28, 29), (13, 9), (19, 10), (9, 28), (7, 9), (21, 28), (18, 23), (28, 4), (8, 15), (2, 20), (13, 21), (16, 27), (13, 1), (1, 31), (7, 12), (6, 11), (18, 1), (30, 35), (12, 4), (10, 10), (19, 12), (30, 12), (22, 3), (22, 14), (15, 13), (26, 20), (17, 26), (25, 19), (21, 31), (30, 3), (25, 6), (25, 15), (16, 26), (10, 16), (1, 25), (9, 19), (11, 29), (24, 3), (25, 22), (8, 2), (7, 25), (0, 33), (4, 24), (1, 5), (26, 2), (5, 21), (29, 28), (13, 5), (30, 8), (8, 13), (31, 25), (27, 2), (11, 7), (23, 22), (8, 24), (1, 27), (11, 37), (2, 3), (6, 7), (10, 21), (30, 34), (13, 17), (30, 15), (5, 2), (10, 7), (16, 4), (18, 8), (18, 2), (8, 25), (20, 29), (21, 7), (21, 3), (24, 25), (7, 1), (14, 7), (30, 17), (11, 35), (29, 3), (26, 21), (13, 32), (13, 37), (5, 14), (26, 23), (29, 2), (18, 27), (17, 20), (7, 30), (9, 13), (6, 2), (21, 35), (5, 32), (2, 33), (21, 5), (8, 28), (7, 3), (26, 3), (22, 6), (13, 14), (19, 9), (12, 6), (16, 36), (25, 16), (4, 34), (11, 3), (6, 16), (30, 5), (12, 28), (12, 15), (21, 18), (1, 36), (13, 26), (11, 24), (4, 25), (28, 21), (6, 8), (2, 15), (29, 32), (17, 2), (18, 26), (9, 3), (25, 25), (30, 10), (25, 24), (9, 17), (25, 14), (2, 4), (3, 34), (11, 36), (23, 31), (15, 33), (13, 23), (23, 13), (31, 19), (5, 15), (29, 17), (6, 37), (22, 17), (17, 9), (21, 14), (28, 12), (24, 14), (4, 11), (12, 16), (15, 8), (12, 19), (4, 36), (28, 18), (2, 17), (0, 9), (5, 33), (4, 33), (27, 15), (7, 8), (20, 31), (21, 30), (20, 22), (22, 32), (22, 18), (20, 34), (18, 19), (1, 26), (10, 23), (19, 31), (9, 0), (19, 15), (21, 22), (1, 8), (23, 6), (16, 5), (30, 2), (11, 6), (17, 16), (3, 17), (17, 10), (21, 2), (14, 10), (27, 1), (19, 36), (24, 31), (2, 5), (0, 23), (3, 24), (31, 2), (9, 23), (15, 15), (13, 16), (25, 20), (11, 5), (0, 3), (25, 3), (19, 13), (24, 35), (12, 17), (24, 1), (14, 16), (24, 4), (3, 4), (16, 10), (0, 35), (1, 13), (11, 25), (0, 13), (28, 19), (13, 10), (28, 37), (16, 12), (27, 5), (15, 35), (3, 18), (28, 3), (12, 34), (2, 10), (1, 12), (24, 15), (2, 30), (16, 9), (12, 33), (15, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373248", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 32), (3, 1), (2, 12), (7, 2), (17, 34), (18, 7), (16, 9), (13, 33), (17, 26), (13, 24), (24, 36), (26, 20), (12, 35), (23, 35), (23, 16), (17, 30), (9, 7), (19, 36), (28, 30), (3, 12), (9, 24), (21, 18), (4, 14), (0, 13), (12, 19), (23, 3), (20, 10), (20, 35), (18, 9), (28, 15), (25, 22), (4, 22), (1, 37), (13, 35), (24, 0), (15, 10), (9, 37), (23, 14), (12, 1), (3, 33), (0, 23), (25, 31), (6, 1), (2, 21), (13, 8), (27, 19), (23, 37), (27, 31), (6, 4), (3, 22), (20, 37), (27, 15), (12, 30), (3, 32), (18, 19), (17, 9), (21, 14), (3, 31), (31, 11), (3, 10), (29, 20), (27, 2), (22, 30), (0, 1), (6, 0), (31, 21), (31, 0), (5, 14), (16, 19), (20, 32), (23, 10), (26, 37), (3, 24), (27, 17), (12, 26), (29, 18), (24, 29), (15, 16), (18, 5), (12, 25), (21, 15), (31, 27), (10, 27), (7, 17), (22, 7), (30, 9), (5, 2), (15, 36), (15, 19), (16, 14), (0, 14), (23, 17), (8, 29), (6, 16), (5, 4), (19, 25), (0, 19), (18, 34), (10, 12), (11, 17), (16, 37), (2, 29), (5, 23), (12, 7), (8, 33), (26, 28), (13, 6), (24, 28), (1, 10), (17, 7), (30, 21), (9, 8), (12, 13), (21, 11), (7, 29), (15, 17), (6, 9), (14, 8), (3, 0), (26, 2), (12, 31), (4, 17), (15, 32), (14, 24), (23, 2), (13, 26), (12, 10), (14, 22), (2, 34), (11, 33), (27, 23), (8, 36), (9, 1), (18, 26), (31, 29), (27, 34), (3, 2), (16, 36), (5, 15), (9, 3), (19, 2), (0, 27), (31, 10), (18, 18), (13, 22), (11, 19), (26, 14), (8, 23), (23, 12), (14, 31), (2, 0), (21, 32), (7, 30), (17, 21), (17, 10), (25, 29), (20, 13), (13, 25), (10, 22), (3, 16), (5, 33), (11, 10), (17, 31), (16, 34), (13, 1), (17, 16), (1, 4), (2, 23), (15, 14), (29, 19), (15, 12), (11, 3), (25, 33), (9, 4), (9, 26), (5, 5), (17, 18), (5, 13), (30, 19), (18, 11), (25, 24), (23, 19), (31, 34), (19, 13), (20, 4), (9, 29), (19, 5), (30, 22), (23, 9), (12, 6), (10, 11), (0, 31), (18, 27), (16, 7), (18, 32), (31, 14), (4, 31), (24, 15), (9, 31), (0, 30), (19, 29), (13, 23), (8, 0), (8, 13), (5, 9), (12, 15), (27, 0), (3, 13), (30, 7), (7, 26), (11, 32), (5, 37), (23, 13), (0, 21), (31, 16), (11, 24), (14, 13), (18, 12), (30, 35), (12, 33), (28, 11), (20, 1), (27, 9), (29, 28), (25, 12), (23, 1), (23, 8), (14, 2), (29, 16), (27, 7), (12, 21), (25, 26), (4, 8), (14, 23), (28, 8), (24, 20), (19, 18), (1, 11), (23, 23), (4, 5), (6, 32), (22, 0), (15, 23), (28, 10), (24, 1), (23, 34), (30, 20), (8, 25), (4, 23), (22, 11), (28, 27), (5, 20), (3, 9), (9, 9), (24, 14), (28, 16), (5, 12), (19, 11), (3, 26), (28, 17), (9, 6), (7, 11), (3, 4), (14, 26), (20, 15), (18, 24), (20, 28), (14, 28), (2, 15), (29, 21), (13, 28), (18, 22), (3, 23), (11, 29), (27, 16), (1, 29), (26, 13), (24, 13), (29, 32), (8, 7), (8, 20), (6, 22), (0, 37), (12, 37), (1, 30), (15, 2), (11, 31), (14, 4), (3, 6), (1, 14), (30, 27), (8, 14), (9, 21), (15, 15), (23, 11), (16, 3), (11, 13), (5, 24), (17, 1), (18, 2), (2, 26), (24, 32), (26, 15), (27, 35), (14, 35), (8, 22), (30, 18), (10, 28), (11, 7), (30, 17), (6, 21), (24, 3), (13, 13), (29, 31), (4, 30), (26, 8), (30, 30), (16, 33), (0, 4), (4, 20), (14, 15), (26, 0), (21, 21), (21, 20), (17, 5), (12, 20), (20, 24), (26, 9), (30, 36), (25, 13), (15, 37), (22, 33), (23, 22), (2, 18), (11, 12), (31, 33), (22, 12), (23, 15), (19, 23), (20, 31), (5, 30), (3, 17), (1, 8), (24, 9), (18, 13), (14, 34), (31, 2), (26, 21), (18, 36), (11, 28), (23, 28), (9, 27), (4, 33), (17, 17), (10, 20), (17, 20), (27, 37), (18, 37), (14, 6), (11, 0), (25, 21), (7, 37), (20, 6), (4, 28), (7, 18), (8, 6), (28, 32), (19, 12), (9, 16), (24, 19), (11, 18), (16, 24), (21, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487458", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 3), (14, 9), (8, 9), (27, 10), (21, 23), (14, 19), (12, 27), (30, 11), (30, 14), (29, 29), (2, 2), (14, 14), (28, 18), (19, 10), (3, 31), (29, 13), (30, 21), (17, 9), (1, 14), (4, 25), (13, 28), (9, 17), (0, 29), (22, 11), (18, 12), (14, 13), (28, 17), (10, 29), (27, 27), (4, 22), (18, 29), (0, 8), (9, 16), (0, 6), (18, 0), (17, 6), (10, 30), (26, 15), (12, 10), (6, 29), (17, 11), (19, 22), (10, 26), (19, 19), (19, 7), (17, 22), (17, 5), (1, 9), (26, 12), (1, 11), (7, 5), (14, 0), (14, 29), (13, 23), (26, 3), (8, 5), (28, 26), (10, 19), (9, 13), (26, 2), (12, 29), (1, 29), (6, 21), (1, 30), (11, 15), (5, 0), (24, 21), (26, 10), (0, 4), (12, 0), (24, 18), (21, 26), (8, 27), (21, 11), (17, 2), (23, 15), (8, 19), (1, 19), (8, 14), (29, 16), (13, 16), (11, 12), (16, 30), (29, 3), (25, 4), (15, 17), (22, 31), (21, 10), (6, 3), (17, 23), (9, 21), (13, 1), (22, 19), (28, 20), (9, 7), (23, 6), (10, 6), (24, 11), (16, 13), (25, 31), (8, 24), (22, 16), (6, 19), (28, 5), (6, 27), (28, 14), (10, 7), (2, 13), (7, 22), (22, 6), (13, 15), (16, 12), (27, 22), (24, 13), (30, 15), (2, 14), (17, 12), (22, 1), (0, 16), (20, 26), (1, 18), (28, 27), (23, 1), (28, 13), (3, 11), (10, 23), (0, 10), (5, 26), (24, 29), (2, 7), (21, 0), (12, 19), (13, 14), (24, 0), (15, 27), (26, 19), (30, 1), (25, 25), (20, 27), (25, 11), (15, 18), (7, 10), (9, 25), (19, 6), (10, 28), (28, 1), (21, 18), (3, 0), (29, 17), (15, 4), (14, 25), (18, 31), (27, 29), (4, 2), (30, 28), (30, 23), (7, 1), (8, 20), (15, 8), (27, 28), (4, 19), (19, 26), (26, 5), (3, 26), (3, 8), (16, 15), (18, 27), (17, 14), (9, 23), (5, 8), (5, 22), (11, 13), (19, 15), (20, 2), (28, 21), (6, 1), (3, 2), (26, 9), (21, 20), (25, 5), (3, 30), (8, 0), (14, 1), (26, 16), (10, 31), (22, 2), (5, 23), (16, 9), (23, 5), (8, 23), (16, 4), (17, 0), (9, 14), (1, 26), (17, 27), (23, 16), (25, 2), (6, 5), (29, 1), (4, 5), (23, 10), (27, 31), (26, 14), (25, 20), (5, 1), (9, 28), (29, 24), (20, 17), (20, 18), (12, 7), (23, 12), (9, 20), (1, 28), (7, 11), (20, 5), (12, 31), (15, 11), (16, 28), (6, 2), (4, 24), (9, 26), (15, 19), (29, 15), (4, 27), (8, 17), (11, 10), (18, 24), (11, 27), (9, 4), (19, 18), (20, 3), (14, 16), (13, 3), (0, 14), (15, 12), (6, 18), (11, 3), (12, 28), (27, 13), (1, 17), (4, 12), (30, 8), (28, 25), (4, 13), (22, 29), (28, 11), (14, 23), (9, 11), (22, 5), (23, 25), (21, 30), (5, 12), (21, 24), (28, 3), (15, 25), (14, 5), (20, 30), (6, 24), (30, 29), (9, 0), (30, 9), (9, 6), (8, 22), (3, 18), (12, 17), (15, 28), (10, 4), (20, 7), (29, 31), (0, 27), (7, 0), (9, 2), (7, 27), (30, 26), (7, 6), (30, 13), (15, 1), (18, 25), (8, 18), (20, 10), (30, 24), (20, 29), (11, 16), (12, 23), (4, 23), (6, 12), (19, 23), (16, 8), (3, 7), (8, 30), (8, 12), (28, 9), (18, 1), (9, 31), (6, 22), (23, 30), (4, 18), (15, 20), (10, 1), (5, 30), (0, 17), (29, 23), (19, 5), (19, 28), (23, 29), (19, 25), (1, 10), (18, 13), (13, 18), (15, 9), (3, 3), (16, 10), (10, 20), (21, 27), (3, 27), (12, 21), (11, 9), (12, 15), (1, 0), (25, 3), (17, 24), (20, 15), (1, 23), (7, 23), (24, 20), (19, 2), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992340", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), 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), (9, 17), (4, 5), (16, 34), (10, 11), (25, 30), (5, 8), (17, 16), (38, 23), (18, 23), (22, 12), (28, 11), (16, 30), (25, 25), (5, 34), (37, 15), (32, 15), (20, 0), (13, 29), (7, 23), (24, 0), (13, 22), (9, 33), (9, 22), (11, 26), (4, 19), (13, 15), (24, 22), (29, 25), (9, 13), (34, 17), (23, 27), (11, 14), (18, 16), (23, 28), (14, 5), (37, 31), (13, 11), (30, 24), (17, 34), (38, 6), (20, 11), (33, 22), (23, 10), (33, 2), (11, 13), (29, 13), (5, 26), (25, 0), (12, 6), (2, 11), (18, 20), (9, 21), (7, 30), (4, 6), (29, 22), (10, 25), (9, 32), (35, 12), (25, 18), (18, 7), (38, 18), (15, 4), (0, 6), (10, 32), (5, 4), (24, 5), (13, 8), (12, 14), (30, 8), (8, 22), (25, 19), (2, 27), (35, 14), (29, 6), (10, 26), (30, 22), (4, 18), (4, 10), (11, 12), (9, 15), (26, 9), (33, 23), (20, 8), (25, 23), (27, 13), (15, 34), (26, 5), (16, 23), (23, 21), (16, 11), (19, 22), (36, 23), (29, 14), (37, 0), (22, 14), (1, 2), (0, 28), (20, 9), (2, 21), (4, 24), (11, 5), (35, 20), (7, 29), (0, 12), (30, 25), (0, 26), (24, 28), (33, 27), (22, 10), (9, 12), (32, 17), (31, 3), (27, 29), (17, 24), (27, 0), (2, 20), (22, 29), (19, 33), (20, 30), (32, 23), (3, 33), (35, 10), (30, 17), (0, 25), (23, 0), (3, 30), (31, 20), (26, 21), (9, 10), (21, 17), (16, 15), (37, 20), (35, 22), (1, 15), (31, 29), (22, 3), (29, 32), (31, 2), (17, 30), (1, 12), (5, 3), (26, 25), (17, 33), (2, 33), (32, 28), (21, 6), (9, 0), (31, 4), (15, 22), (28, 22), (17, 25), (27, 10), (4, 12), (30, 31), (0, 21), (1, 27), (2, 30), (17, 9), (32, 29), (35, 29), (9, 3), (23, 8), (18, 13), (2, 15), (16, 32), (3, 32), (35, 15), (29, 15), (13, 17), (9, 9), (16, 20), (2, 32), (37, 17), (5, 6), (21, 14), (12, 34), (7, 20), (24, 13), (35, 21), (13, 14), (6, 8), (6, 24), (35, 33), (36, 16), (11, 19), (18, 12), (15, 16), (34, 5), (31, 25), (18, 34), (23, 7), (10, 21), (25, 15), (6, 11), (29, 16), (23, 3), (15, 9), (6, 6), (17, 18), (24, 1), (8, 4), (27, 7), (23, 13), (11, 22), (26, 2), (21, 19), (17, 19), (2, 7), (7, 14), (4, 1), (14, 31), (20, 1), (25, 12), (15, 24), (38, 15), (38, 8), (29, 31), (27, 30), (31, 7), (28, 26), (5, 16), (19, 0), (27, 34), (3, 23), (3, 0), (33, 25), (5, 32), (32, 18), (28, 29), (4, 28), (6, 31), (10, 28), (11, 23), (4, 3), (18, 29), (38, 11), (1, 5), (7, 10), (17, 8), (1, 32), (16, 31), (5, 24), (10, 12), (8, 2), (0, 4), (22, 0), (15, 25), (3, 17), (28, 1), (36, 9), (1, 8), (8, 33), (2, 8), (3, 18), (36, 5), (30, 14), (14, 1), (16, 3), (29, 28), (12, 16), (36, 15), (12, 11), (8, 21), (27, 33), (1, 14), (12, 9), (30, 12), (24, 33), (6, 21), (35, 16), (15, 11), (14, 17), (30, 15), (21, 31), (20, 15), (28, 16), (14, 25), (5, 7), (21, 33), (27, 17), (23, 11), (8, 19), (37, 19), (17, 17), (23, 1), (14, 20), (35, 18), (24, 26), (1, 10), (35, 28), (33, 11), (30, 29), (20, 3), (20, 4), (33, 1), (14, 13), (31, 23), (33, 6), (3, 2), (11, 10), (22, 22), (36, 14), (8, 18), (34, 6), (18, 30), (28, 3), (25, 7), (12, 31), (14, 30), (20, 18), (0, 33), (12, 28), (14, 12), (33, 18), (15, 28), (8, 3), (37, 29), (8, 7), (26, 3), (22, 20), (20, 32), (34, 13), (13, 10), (11, 9), (30, 19), (9, 16), (26, 15), (8, 29), (23, 30), (23, 16), (21, 22), (22, 23), (5, 33), (38, 25), (24, 18), (6, 34), (34, 30), (35, 11), (10, 2), (3, 26), (34, 4), (16, 24), (10, 29), (1, 30), (20, 20), (26, 16), (7, 9), (10, 30), (23, 22), (23, 15), (31, 34), (33, 17), (28, 12), (21, 10), (7, 11), (25, 27), (32, 27), (11, 25), (4, 7), (25, 20), (4, 23), (32, 6), (15, 33), (36, 0), (3, 15), (24, 24), (16, 16), (26, 6), (8, 9), (11, 6), (0, 27), (3, 29), (22, 32), (19, 20), (30, 3), (24, 2), (19, 10), (21, 5), (29, 26), (7, 17), (0, 10), (18, 19), (11, 4), (12, 18), (24, 21), (5, 9), (32, 16), (18, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562590", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 27), (6, 19), (21, 12), (20, 21), (14, 20), (6, 22), (14, 30), (37, 3), (35, 15), (34, 24), (2, 12), (17, 15), (30, 30), (23, 3), (17, 30), (34, 13), (6, 11), (13, 13), (35, 16), (10, 6), (21, 7), (22, 30), (5, 28), (5, 23), (4, 15), (4, 26), (30, 13), (0, 29), (21, 9), (30, 14), (21, 4), (9, 19), (6, 13), (23, 17), (22, 3), (9, 4), (11, 22), (12, 22), (26, 11), (14, 18), (8, 10), (16, 1), (30, 7), (21, 14), (17, 1), (12, 21), (31, 8), (20, 29), (7, 4), (12, 16), (35, 2), (0, 6), (29, 18), (24, 8), (12, 6), (17, 25), (28, 28), (8, 11), (3, 22), (34, 12), (7, 7), (6, 10), (23, 10), (27, 12), (22, 28), (14, 5), (5, 7), (18, 9), (14, 11), (26, 27), (10, 28), (24, 9), (2, 14), (6, 6), (30, 15), (21, 16), (17, 24), (3, 20), (2, 4), (36, 6), (36, 12), (32, 14), (37, 8), (1, 16), (28, 3), (20, 24), (16, 2), (13, 19), (6, 29), (32, 17), (24, 19), (23, 4), (11, 11), (0, 25), (24, 2), (33, 5), (5, 26), (18, 29), (22, 14), (18, 6), (35, 6), (3, 2), (19, 7), (3, 23), (8, 12), (7, 6), (26, 21), (23, 6), (17, 27), (35, 7), (35, 1), (12, 19), (14, 24), (2, 8), (20, 2), (22, 9), (15, 13), (11, 19), (19, 29), (11, 7), (36, 29), (28, 26), (24, 20), (22, 8), (2, 15), (17, 12), (20, 15), (27, 28), (18, 23), (9, 17), (31, 5), (3, 29), (22, 20), (29, 26), (12, 1), (8, 13), (37, 5), (19, 6), (21, 17), (5, 30), (0, 21), (15, 25), (11, 30), (19, 19), (27, 25), (15, 23), (34, 17), (11, 25), (4, 0), (33, 15), (14, 14), (2, 9), (14, 6), (25, 13), (36, 7), (23, 30), (2, 2), (30, 8), (18, 14), (0, 20), (8, 1), (15, 22), (36, 10), (18, 10), (12, 13), (8, 22), (6, 17), (7, 26), (22, 1), (25, 20), (13, 28), (34, 29), (21, 22), (34, 19), (21, 28), (22, 4), (12, 2), (15, 28), (33, 8), (31, 26), (3, 27), (2, 20), (36, 5), (5, 13), (7, 19), (8, 16), (34, 15), (4, 4), (9, 5), (11, 6), (4, 8), (35, 4), (24, 23), (7, 14), (27, 30), (1, 24), (8, 21), (24, 3), (19, 27), (24, 18), (9, 1), (20, 20), (7, 11), (0, 16), (5, 17), (32, 7), (1, 2), (29, 30), (7, 2), (29, 19), (33, 16), (5, 4), (1, 26), (4, 5), (33, 11), (3, 17), (36, 3), (35, 10), (6, 25), (33, 6), (23, 26), (26, 0), (18, 18), (30, 26), (13, 7), (32, 1), (24, 12), (36, 2), (32, 11), (36, 25), (10, 19), (26, 28), (27, 21), (32, 5), (31, 17), (7, 24), (10, 8), (36, 0), (29, 16), (34, 26), (24, 28), (27, 11), (17, 0), (13, 6), (29, 7), (27, 6), (8, 6), (6, 5), (36, 27), (13, 25), (27, 15), (27, 19), (28, 27), (18, 26), (13, 21), (26, 7), (0, 24), (11, 20), (9, 28), (23, 12), (32, 25), (9, 11), (3, 25), (2, 23), (14, 1), (20, 3), (3, 12), (23, 19), (6, 24), (20, 1), (19, 17), (3, 11), (4, 30), (0, 27), (18, 12), (27, 4), (19, 28), (7, 27), (23, 8), (15, 5), (32, 6), (11, 29), (7, 20), (35, 12), (29, 12), (2, 18), (12, 5), (30, 17), (18, 7), (35, 23), (26, 14), (18, 13), (14, 16), (10, 21), (28, 13), (9, 26), (9, 27), (3, 5), (28, 30), (37, 13), (24, 15), (29, 27), (26, 1), (33, 30), (23, 29), (13, 22), (10, 14), (34, 27), (14, 21), (15, 17), (23, 15), (17, 14), (31, 23), (3, 13), (15, 19), (32, 4), (36, 16), (14, 9), (35, 30), (33, 22), (25, 3), (18, 8), (18, 2), (9, 8), (16, 14), (4, 19), (28, 14), (6, 4), (12, 17), (16, 19), (6, 14), (19, 2), (22, 16), (34, 5), (20, 7), (4, 24), (31, 7), (25, 30), (30, 2), (29, 8), (28, 12), (30, 5), (9, 10), (33, 0), (27, 1), (28, 18), (20, 23), (16, 21), (18, 22), (2, 3), (10, 7), (28, 9), (6, 0), (16, 7), (29, 24), (25, 21), (8, 25), (32, 18), (20, 6), (22, 6), (37, 24), (30, 19), (19, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35424", "dataset": "MATH"}
{"messages": [{"content": "In a 32x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 31), 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), (23, 21), (15, 28), (16, 10), (23, 18), (10, 24), (22, 24), (1, 12), (28, 26), (19, 18), (20, 6), (11, 1), (3, 9), (30, 25), (30, 3), (6, 7), (27, 15), (23, 12), (22, 4), (31, 9), (6, 24), (0, 10), (11, 2), (13, 27), (1, 21), (8, 27), (3, 31), (0, 18), (15, 20), (15, 11), (9, 17), (21, 25), (14, 24), (28, 2), (17, 8), (3, 22), (18, 15), (21, 20), (5, 14), (22, 25), (20, 3), (3, 5), (19, 0), (23, 10), (13, 11), (25, 7), (1, 3), (9, 3), (6, 30), (31, 26), (14, 25), (22, 6), (16, 3), (8, 11), (22, 16), (5, 0), (11, 19), (17, 3), (27, 18), (8, 21), (31, 5), (12, 3), (30, 0), (9, 4), (1, 5), (25, 14), (2, 6), (24, 7), (0, 26), (18, 13), (4, 23), (23, 9), (21, 14), (3, 1), (10, 18), (27, 30), (24, 18), (25, 20), (0, 23), (24, 6), (21, 28), (8, 16), (12, 29), (19, 15), (17, 4), (14, 21), (13, 19), (7, 18), (8, 7), (26, 26), (31, 17), (24, 0), (10, 19), (27, 3), (10, 8), (10, 21), (14, 22), (20, 12), (7, 19), (0, 8), (11, 15), (19, 6), (27, 5), (30, 7), (1, 16), (17, 23), (14, 6), (19, 14), (26, 4), (31, 27), (24, 19), (24, 14), (21, 0), (16, 23), (18, 18), (30, 2), (2, 23), (15, 21), (20, 25), (19, 16), (9, 21), (0, 4), (12, 19), (13, 3), (15, 5), (21, 18), (24, 20), (18, 30), (29, 7), (16, 31), (15, 15), (7, 3), (30, 5), (31, 6), (21, 13), (14, 4), (17, 16), (5, 10), (26, 27), (13, 17), (29, 19), (1, 10), (24, 11), (9, 16), (25, 31), (13, 22), (12, 14), (31, 2), (7, 26), (3, 0), (11, 5), (13, 2), (13, 25), (28, 27), (23, 26), (10, 7), (5, 18), (19, 1), (4, 20), (3, 15), (17, 19), (0, 22), (15, 14), (28, 12), (28, 17), (16, 26), (23, 8), (17, 28), (18, 22), (12, 21), (17, 26), (16, 17), (24, 1), (11, 16), (29, 30), (21, 31), (7, 12), (2, 10), (19, 4), (6, 26), (5, 2), (10, 16), (19, 8), (30, 8), (16, 1), (24, 27), (4, 27), (27, 6), (9, 22), (8, 8), (5, 17), (19, 29), (29, 17), (3, 20), (27, 28), (28, 21), (12, 24), (7, 7), (6, 5), (29, 15), (27, 2), (30, 24), (3, 26), (4, 24), (0, 15), (29, 4), (31, 20), (11, 12), (18, 28), (26, 22), (29, 22), (27, 24), (5, 15), (18, 3), (1, 1), (16, 22), (23, 6), (3, 14), (22, 26), (18, 4), (16, 27), (6, 6), (21, 2), (26, 10), (23, 5), (23, 7), (16, 29), (12, 6), (24, 15), (22, 28), (9, 5), (31, 29), (2, 21), (26, 20), (15, 13), (17, 0), (5, 16), (21, 6), (0, 17), (15, 24), (5, 3), (20, 16), (20, 13), (23, 19), (9, 20), (3, 16), (24, 9), (17, 17), (15, 22), (15, 25), (30, 4), (7, 30), (3, 23), (6, 22), (10, 6), (18, 8), (4, 18), (14, 10), (2, 4), (19, 23), (29, 28), (14, 11), (10, 11), (26, 7), (7, 24), (9, 30), (13, 13), (20, 17), (15, 18), (19, 9), (3, 6), (16, 19), (13, 30), (9, 23), (6, 14), (11, 18), (26, 1), (21, 29), (19, 7), (22, 2), (22, 7), (21, 15), (20, 20), (9, 31), (23, 1), (2, 15), (26, 0), (0, 30), (29, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "942400", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), 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), (6, 27), (10, 9), (30, 36), (18, 6), (20, 32), (14, 1), (22, 17), (2, 22), (16, 11), (18, 17), (11, 3), (1, 28), (27, 19), (4, 27), (2, 28), (24, 17), (21, 20), (21, 5), (31, 6), (27, 28), (29, 13), (27, 5), (9, 21), (32, 7), (30, 21), (3, 32), (21, 15), (27, 14), (6, 28), (32, 20), (6, 21), (15, 19), (2, 27), (10, 0), (7, 13), (10, 6), (1, 4), (29, 35), (10, 4), (21, 6), (20, 14), (20, 20), (27, 31), (15, 23), (5, 20), (17, 32), (17, 12), (14, 27), (4, 15), (21, 36), (9, 20), (30, 5), (14, 7), (21, 4), (15, 28), (12, 6), (25, 32), (24, 6), (32, 15), (16, 33), (17, 3), (18, 5), (4, 21), (27, 3), (22, 2), (13, 29), (18, 26), (2, 32), (13, 0), (21, 30), (15, 8), (2, 35), (18, 7), (16, 17), (29, 8), (24, 13), (8, 7), (26, 34), (23, 16), (14, 20), (22, 31), (26, 21), (24, 10), (32, 34), (1, 26), (29, 14), (26, 32), (6, 6), (20, 27), (32, 10), (28, 29), (24, 5), (7, 3), (8, 8), (5, 29), (17, 11), (22, 27), (8, 23), (27, 16), (13, 2), (2, 26), (23, 18), (8, 26), (25, 29), (13, 34), (24, 32), (32, 24), (3, 12), (2, 33), (27, 24), (18, 3), (12, 11), (3, 28), (4, 11), (18, 15), (11, 10), (9, 12), (28, 18), (28, 7), (6, 8), (22, 3), (14, 15), (18, 29), (14, 5), (17, 9), (10, 30), (31, 32), (7, 24), (10, 5), (12, 14), (6, 16), (11, 13), (19, 10), (1, 22), (18, 4), (0, 22), (28, 24), (25, 20), (30, 18), (13, 37), (7, 1), (8, 16), (17, 10), (2, 30), (6, 1), (13, 9), (9, 24), (16, 5), (5, 26), (9, 22), (26, 37), (12, 13), (24, 11), (21, 14), (23, 7), (8, 18), (18, 11), (15, 16), (19, 26), (5, 37), (27, 23), (15, 34), (7, 2), (25, 37), (31, 27), (22, 6), (20, 6), (24, 16), (17, 18), (14, 12), (32, 6), (18, 27), (21, 31), (14, 36), (1, 23), (10, 19), (20, 26), (15, 9), (18, 16), (12, 34), (4, 5), (8, 6), (0, 23), (18, 10), (5, 36), (27, 36), (8, 31), (28, 30), (6, 22), (19, 23), (6, 13), (9, 32), (15, 1), (23, 8), (7, 11), (0, 26), (22, 34), (16, 18), (16, 6), (8, 9), (31, 31), (19, 0), (3, 13), (4, 18), (15, 24), (23, 27), (2, 37), (22, 30), (15, 21), (16, 0), (17, 24), (17, 4), (17, 5), (13, 4), (1, 30), (9, 36), (10, 18), (13, 19), (15, 27), (24, 1), (22, 1), (26, 20), (13, 30), (16, 22), (11, 24), (10, 20), (16, 3), (17, 33), (19, 7), (7, 9), (10, 26), (19, 31), (25, 0), (26, 0), (14, 17), (14, 9), (5, 0), (28, 17), (29, 10), (23, 37), (26, 10), (29, 33), (12, 19), (29, 26), (0, 7), (5, 3), (7, 32), (4, 1), (22, 0), (23, 34), (25, 27), (26, 6), (30, 30), (16, 28), (25, 9), (31, 33), (12, 28), (5, 31), (25, 18), (9, 5), (22, 23), (23, 26), (22, 19), (10, 24), (17, 26), (12, 0), (9, 33), (20, 23), (4, 37), (9, 15), (27, 7), (8, 29), (18, 34), (30, 35), (0, 4), (9, 19), (16, 34), (32, 0), (4, 8), (26, 25), (16, 29), (30, 19), (0, 31), (3, 17), (12, 12), (14, 2), (7, 12), (25, 4), (8, 14), (20, 37), (15, 33), (6, 33), (28, 27), (31, 20), (32, 3), (12, 7), (9, 29), (29, 21), (23, 24), (31, 11), (31, 29), (30, 24), (28, 32), (11, 28), (27, 0), (28, 20), (25, 34), (16, 35), (23, 0), (15, 18), (4, 13), (3, 24), (14, 25), (28, 21), (23, 1), (11, 21), (4, 9), (32, 2), (12, 29), (20, 9), (13, 24), (0, 6), (8, 33), (29, 6), (19, 21), (0, 18), (25, 10), (10, 16), (30, 15), (26, 17), (10, 11), (29, 27), (18, 30), (9, 0), (7, 7), (1, 14), (32, 11), (5, 17), (19, 32), (6, 37), (23, 15), (13, 10), (17, 6), (15, 22), (2, 34), (2, 15), (15, 25), (23, 5), (6, 19), (3, 35), (1, 9), (22, 11), (25, 16), (30, 29), (11, 23), (30, 6), (18, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431200", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), 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), (29, 10), (13, 25), (4, 4), (23, 2), (0, 28), (30, 16), (24, 22), (33, 17), (9, 5), (23, 22), (28, 6), (21, 4), (15, 26), (19, 8), (24, 0), (21, 8), (13, 24), (19, 29), (11, 16), (12, 0), (16, 24), (33, 13), (28, 16), (32, 13), (29, 3), (17, 9), (32, 21), (3, 16), (21, 12), (15, 2), (0, 13), (7, 9), (10, 24), (13, 12), (8, 26), (25, 26), (4, 6), (7, 19), (18, 4), (26, 17), (28, 8), (23, 1), (0, 27), (9, 25), (32, 16), (26, 16), (21, 10), (22, 7), (6, 29), (19, 0), (19, 26), (10, 12), (8, 9), (8, 18), (31, 18), (34, 16), (25, 27), (7, 27), (35, 1), (21, 18), (0, 15), (31, 5), (11, 5), (32, 27), (26, 15), (32, 18), (22, 14), (16, 25), (3, 20), (5, 24), (1, 27), (6, 26), (30, 15), (9, 24), (17, 18), (17, 5), (23, 13), (14, 20), (2, 11), (3, 14), (9, 6), (24, 15), (5, 2), (25, 4), (32, 14), (8, 1), (23, 11), (33, 26), (15, 0), (7, 21), (26, 6), (3, 12), (3, 27), (15, 15), (6, 28), (16, 19), (19, 18), (17, 1), (22, 19), (6, 4), (25, 6), (25, 0), (27, 18), (9, 18), (29, 2), (29, 29), (16, 11), (22, 5), (24, 10), (2, 5), (29, 18), (33, 4), (15, 23), (25, 21), (7, 16), (7, 12), (31, 20), (6, 23), (22, 25), (32, 29), (20, 13), (16, 23), (30, 14), (21, 5), (13, 9), (17, 2), (12, 1), (29, 14), (0, 1), (27, 15), (16, 28), (0, 8), (31, 9), (18, 27), (17, 3), (21, 23), (5, 8), (8, 10), (26, 4), (13, 22), (1, 29), (0, 14), (9, 8), (23, 27), (13, 13), (11, 2), (19, 9), (23, 26), (32, 9), (34, 27), (26, 20), (33, 7), (16, 27), (26, 13), (14, 17), (20, 9), (33, 16), (10, 28), (35, 0), (20, 1), (23, 20), (6, 24), (13, 16), (14, 1), (2, 27), (9, 2), (11, 8), (3, 6), (32, 22), (10, 27), (25, 2), (21, 13), (27, 21), (8, 29), (9, 16), (34, 26), (34, 25), (28, 29), (1, 17), (32, 12), (5, 1), (13, 14), (4, 14), (31, 27), (18, 11), (6, 25), (27, 0), (5, 21), (33, 10), (9, 23), (33, 28), (5, 28), (8, 14), (4, 8), (20, 24), (28, 13), (32, 10), (30, 12), (24, 24), (8, 20), (29, 13), (16, 2), (6, 18), (14, 22), (35, 9), (13, 17), (14, 8), (8, 22), (18, 29), (30, 11), (4, 10), (26, 24), (6, 14), (18, 7), (0, 23), (13, 18), (2, 7), (17, 15), (28, 5), (27, 23), (26, 0), (0, 17), (20, 7), (17, 16), (16, 26), (17, 10), (1, 11), (28, 24), (17, 13), (24, 17), (32, 5), (19, 15), (25, 12), (4, 27), (31, 22), (33, 15), (35, 16), (23, 0), (30, 13), (5, 4), (23, 18), (29, 27), (6, 6), (3, 25), (22, 17), (9, 7), (9, 27), (27, 14), (12, 7), (26, 22), (35, 17), (27, 11), (13, 5), (23, 12), (13, 23), (1, 16), (28, 21), (7, 6), (21, 1), (16, 18), (12, 17), (35, 8), (11, 17), (24, 27), (18, 16), (21, 7), (31, 24), (33, 20), (19, 21), (1, 5), (19, 13), (12, 8), (22, 18), (2, 0), (26, 23), (12, 22), (8, 27), (11, 4), (9, 1), (5, 14), (26, 26), (24, 4), (10, 3), (1, 9), (31, 1), (5, 26), (12, 15), (7, 20), (23, 21), (30, 9), (25, 24), (18, 1), (9, 29), (4, 22), (3, 19), (31, 10), (14, 2), (18, 0), (26, 10), (28, 11), (20, 20), (34, 29), (16, 16), (17, 0), (32, 24), (25, 8), (24, 1), (23, 29), (15, 25), (8, 0), (31, 19), (32, 6), (34, 6), (24, 3), (23, 8), (32, 8), (10, 0), (25, 1), (3, 1), (14, 3), (25, 29), (6, 16), (19, 7), (34, 13), (9, 14), (12, 12), (14, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825552", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 36), (10, 30), (22, 8), (36, 33), (11, 9), (26, 17), (23, 25), (18, 1), (4, 33), (18, 30), (4, 18), (20, 23), (19, 0), (20, 24), (27, 1), (10, 22), (0, 3), (27, 30), (12, 13), (23, 17), (30, 36), (33, 19), (13, 1), (16, 33), (36, 26), (21, 10), (29, 15), (30, 16), (33, 4), (15, 34), (23, 15), (33, 18), (23, 2), (29, 8), (22, 29), (16, 30), (21, 31), (2, 22), (33, 12), (12, 19), (34, 21), (22, 11), (33, 37), (28, 26), (11, 18), (8, 24), (4, 0), (36, 15), (22, 21), (23, 9), (27, 35), (19, 18), (8, 16), (22, 23), (10, 21), (18, 13), (5, 17), (32, 13), (12, 18), (26, 31), (0, 23), (1, 21), (7, 9), (19, 24), (0, 32), (5, 35), (31, 20), (36, 1), (33, 26), (1, 35), (2, 30), (24, 15), (29, 28), (8, 0), (18, 7), (34, 1), (4, 35), (35, 1), (3, 32), (21, 13), (24, 0), (7, 32), (36, 18), (21, 5), (29, 23), (31, 29), (6, 16), (35, 16), (2, 35), (0, 29), (30, 20), (17, 8), (4, 5), (17, 25), (28, 16), (12, 32), (16, 0), (21, 3), (36, 22), (14, 20), (21, 19), (2, 5), (5, 10), (25, 19), (10, 2), (23, 6), (29, 35), (31, 28), (23, 11), (18, 12), (13, 15), (24, 24), (10, 18), (6, 20), (14, 24), (3, 34), (22, 15), (16, 29), (21, 34), (9, 12), (19, 37), (16, 24), (9, 30), (25, 37), (28, 6), (25, 30), (14, 36), (17, 10), (18, 28), (33, 16), (7, 25), (20, 2), (28, 1), (4, 28), (0, 14), (21, 6), (8, 15), (9, 3), (24, 26), (33, 27), (8, 12), (34, 30), (0, 37), (8, 22), (18, 18), (1, 30), (3, 0), (26, 26), (30, 0), (4, 11), (3, 1), (22, 14), (27, 34), (22, 34), (35, 4), (8, 34), (31, 9), (27, 9), (13, 18), (36, 31), (29, 25), (4, 19), (23, 23), (34, 14), (8, 3), (20, 5), (21, 9), (8, 20), (8, 26), (12, 7), (29, 32), (34, 26), (32, 6), (33, 6), (17, 27), (35, 0), (35, 12), (13, 14), (23, 28), (18, 14), (3, 19), (0, 6), (24, 8), (27, 11), (34, 20), (10, 24), (31, 15), (7, 10), (30, 5), (1, 15), (26, 24), (9, 6), (32, 32), (19, 6), (1, 7), (20, 12), (30, 26), (13, 24), (34, 12), (6, 3), (34, 27), (19, 33), (34, 5), (18, 5), (10, 8), (8, 36), (26, 19), (30, 1), (22, 26), (18, 27), (14, 15), (25, 16), (12, 26), (25, 35), (12, 29), (36, 19), (35, 24), (3, 6), (2, 37), (6, 1), (1, 24), (11, 17), (36, 24), (4, 4), (20, 29), (4, 8), (30, 22), (16, 21), (27, 26), (24, 23), (20, 32), (13, 9), (23, 19), (14, 8), (4, 31), (0, 36), (26, 27), (9, 34), (1, 18), (26, 20), (17, 5), (15, 26), (17, 11), (7, 28), (14, 30), (6, 31), (33, 20), (1, 16), (7, 5), (4, 29), (24, 22), (5, 0), (5, 19), (10, 26), (0, 31), (10, 13), (30, 3), (27, 6), (3, 20), (28, 23), (20, 26), (18, 24), (22, 31), (34, 3), (7, 3), (23, 35), (32, 28), (6, 8), (8, 6), (0, 25), (31, 17), (9, 33), (22, 3), (21, 33), (2, 20), (3, 12), (36, 8), (3, 3), (16, 10), (12, 6), (21, 29), (24, 12), (23, 24), (11, 23), (6, 0), (33, 21), (13, 30), (34, 8), (8, 21), (18, 22), (32, 15), (19, 1), (15, 13), (34, 11), (1, 8), (34, 16), (8, 28), (23, 31), (0, 26), (35, 22), (30, 9), (9, 23), (22, 6), (3, 22), (15, 27), (29, 29), (7, 4), (35, 28), (17, 1), (21, 21), (10, 34), (33, 2), (33, 29), (10, 16), (29, 33), (23, 36), (16, 13), (8, 13), (7, 35), (7, 11), (3, 4), (5, 20), (24, 36), (17, 15), (14, 13), (33, 13), (17, 33), (35, 3), (4, 37), (23, 0), (13, 25), (22, 5), (12, 23), (28, 31), (26, 1), (5, 28), (32, 22), (15, 11), (13, 28), (9, 14), (19, 17), (27, 17), (20, 31), (14, 27), (31, 34), (21, 11), (9, 35), (31, 33), (16, 16), (31, 37), (30, 7), (8, 27), (27, 28), (10, 28), (9, 26), (12, 10), (35, 8), (31, 5), (36, 7), (4, 9), (23, 29), (35, 36), (17, 31), (32, 36), (22, 4), (33, 33), (13, 5), (35, 2), (36, 2), (35, 30), (6, 6), (4, 6), (15, 12), (33, 0), (12, 24), (0, 21), (12, 22), (3, 14), (33, 24), (33, 17), (31, 32), (18, 37), (19, 26), (20, 27), (27, 8), (14, 14), (1, 6), (3, 13), (31, 19), (4, 15), (30, 27), (33, 14), (36, 3), (22, 19), (16, 3), (22, 20), (27, 36), (30, 24), (25, 6), (3, 9), (6, 13), (33, 3), (11, 33), (5, 16), (11, 22), (35, 27), (31, 26), (0, 24), (32, 1), (34, 36), (31, 24), (36, 28), (1, 0), (15, 18), (9, 10), (13, 22), (2, 8), (9, 5), (2, 33), (25, 36), (26, 21), (34, 19), (16, 32), (12, 33), (15, 33), (21, 18), (19, 7), (27, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972162", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (36, 32), (14, 17), (1, 23), (13, 31), (33, 7), (15, 29), (26, 3), (37, 18), (15, 2), (2, 2), (12, 10), (38, 9), (15, 3), (9, 19), (8, 18), (27, 29), (7, 0), (13, 21), (14, 25), (19, 20), (14, 26), (10, 13), (33, 6), (30, 16), (9, 24), (26, 31), (36, 2), (20, 1), (37, 24), (25, 18), (28, 22), (36, 11), (34, 26), (18, 22), (26, 34), (3, 21), (35, 13), (18, 1), (16, 3), (19, 16), (8, 19), (0, 8), (34, 30), (11, 0), (34, 16), (29, 14), (33, 30), (18, 32), (10, 17), (4, 21), (32, 29), (27, 26), (14, 23), (0, 13), (32, 25), (19, 31), (15, 15), (26, 12), (7, 2), (17, 11), (35, 22), (5, 32), (28, 8), (23, 2), (11, 21), (0, 4), (17, 24), (30, 14), (4, 12), (28, 13), (19, 18), (38, 33), (22, 32), (6, 2), (14, 2), (32, 31), (13, 22), (31, 31), (33, 27), (2, 7), (31, 12), (10, 29), (26, 8), (37, 16), (0, 17), (38, 19), (6, 3), (20, 13), (8, 15), (20, 9), (22, 9), (8, 12), (2, 3), (0, 33), (13, 30), (7, 17), (16, 29), (37, 33), (37, 31), (31, 20), (29, 2), (13, 34), (21, 26), (23, 3), (15, 28), (29, 32), (18, 25), (4, 34), (20, 6), (24, 22), (27, 33), (26, 22), (2, 16), (11, 2), (11, 6), (24, 1), (22, 3), (35, 6), (22, 29), (18, 28), (4, 18), (31, 24), (32, 16), (2, 20), (0, 19), (17, 3), (11, 10), (20, 22), (4, 16), (13, 17), (2, 25), (23, 24), (9, 25), (27, 20), (10, 27), (7, 24), (14, 24), (12, 7), (15, 16), (7, 19), (10, 10), (32, 26), (2, 34), (18, 8), (5, 14), (32, 24), (21, 33), (9, 12), (13, 6), (33, 26), (18, 17), (18, 23), (11, 31), (20, 28), (7, 3), (22, 30), (31, 8), (35, 4), (29, 27), (8, 21), (8, 20), (4, 13), (20, 26), (3, 27), (6, 34), (25, 19), (22, 16), (16, 26), (10, 24), (35, 21), (1, 27), (11, 13), (10, 3), (20, 30), (10, 25), (32, 8), (15, 24), (37, 22), (4, 11), (17, 6), (28, 33), (15, 27), (23, 27), (36, 17), (7, 10), (20, 23), (38, 18), (35, 34), (11, 29), (19, 8), (4, 29), (20, 5), (3, 0), (16, 31), (13, 18), (4, 7), (30, 2), (1, 10), (27, 7), (32, 14), (9, 11), (36, 18), (28, 30), (1, 4), (19, 27), (4, 0), (2, 32), (27, 0), (6, 21), (38, 13), (29, 15), (24, 13), (35, 24), (32, 9), (28, 26), (17, 8), (14, 18), (25, 31), (25, 7), (15, 19), (23, 16), (22, 11), (17, 7), (14, 14), (19, 21), (36, 29), (0, 22), (8, 33), (0, 1), (33, 13), (8, 34), (7, 16), (26, 30), (24, 25), (5, 11), (12, 1), (30, 7), (9, 26), (5, 25), (2, 29), (14, 31), (26, 24), (23, 12), (24, 15), (37, 17), (22, 22), (32, 22), (10, 31), (31, 28), (27, 34), (2, 22), (4, 22), (36, 30), (18, 31), (3, 13), (4, 14), (18, 29), (35, 11), (12, 27), (22, 28), (5, 10), (14, 5), (5, 22), (5, 23), (0, 2), (26, 4), (17, 5), (29, 29), (22, 7), (6, 22), (30, 5), (23, 33), (30, 22), (34, 7), (23, 22), (14, 9), (27, 11), (1, 3), (18, 30), (35, 9), (27, 17), (12, 2), (29, 10), (15, 30), (24, 29), (30, 25), (19, 25), (16, 14), (15, 34), (5, 27), (17, 12), (7, 31), (19, 13), (24, 11), (26, 10), (8, 2), (25, 6), (5, 3), (18, 11), (34, 9), (31, 11), (4, 6), (25, 24), (20, 0), (38, 25), (34, 15), (28, 4), (7, 8), (31, 32), (7, 30), (8, 10), (33, 16), (8, 11), (32, 18), (12, 5), (11, 23), (14, 28), (19, 10), (23, 28), (16, 1), (2, 15), (35, 30), (13, 19), (1, 2), (33, 12), (29, 20), (31, 5), (35, 7), (3, 22), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208800", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (18, 15), (7, 18), (19, 30), (3, 3), (21, 14), (1, 34), (19, 2), (16, 7), (7, 21), (14, 26), (12, 34), (18, 25), (20, 9), (25, 14), (4, 11), (21, 18), (6, 4), (0, 16), (24, 14), (17, 35), (0, 7), (3, 1), (29, 0), (26, 23), (25, 19), (15, 19), (28, 7), (0, 4), (27, 15), (10, 24), (8, 17), (12, 10), (6, 26), (14, 27), (24, 21), (24, 24), (8, 24), (2, 11), (20, 30), (13, 28), (27, 5), (7, 19), (21, 21), (30, 31), (22, 28), (24, 8), (23, 7), (16, 2), (11, 17), (25, 37), (17, 19), (16, 4), (8, 28), (28, 30), (29, 21), (15, 37), (8, 12), (11, 6), (9, 17), (14, 1), (0, 20), (26, 5), (1, 7), (15, 14), (25, 28), (4, 13), (1, 4), (14, 16), (18, 31), (8, 23), (18, 23), (6, 34), (17, 26), (15, 23), (3, 4), (22, 8), (20, 20), (0, 21), (30, 2), (1, 28), (3, 35), (16, 28), (22, 17), (12, 32), (21, 26), (15, 7), (4, 1), (23, 3), (11, 13), (22, 23), (3, 24), (27, 32), (30, 34), (13, 14), (15, 20), (24, 12), (1, 20), (0, 18), (12, 11), (0, 12), (17, 0), (2, 4), (15, 4), (18, 1), (30, 20), (6, 35), (19, 8), (22, 3), (26, 33), (21, 36), (30, 33), (10, 23), (4, 26), (10, 6), (15, 17), (7, 30), (11, 22), (27, 17), (1, 11), (30, 22), (5, 37), (3, 33), (2, 20), (28, 20), (22, 29), (28, 32), (13, 27), (17, 10), (26, 22), (18, 13), (3, 27), (21, 8), (11, 37), (16, 19), (30, 9), (11, 11), (5, 3), (25, 3), (22, 6), (13, 34), (12, 20), (6, 23), (6, 3), (23, 31), (7, 31), (20, 13), (9, 1), (13, 3), (20, 19), (29, 26), (13, 13), (30, 12), (4, 12), (14, 9), (9, 28), (1, 26), (8, 20), (9, 5), (17, 33), (25, 5), (9, 33), (9, 35), (1, 21), (22, 9), (15, 15), (30, 15), (24, 22), (18, 35), (22, 33), (29, 5), (23, 8), (8, 30), (10, 20), (27, 11), (16, 13), (1, 31), (21, 16), (30, 14), (16, 26), (19, 15), (14, 33), (8, 26), (22, 12), (9, 21), (7, 36), (1, 0), (21, 25), (7, 29), (6, 7), (24, 33), (28, 5), (7, 12), (24, 2), (5, 2), (21, 23), (2, 18), (3, 13), (22, 2), (22, 4), (22, 37), (10, 13), (26, 7), (6, 1), (24, 13), (8, 27), (4, 5), (26, 11), (12, 15), (4, 9), (29, 12), (8, 29), (13, 24), (12, 6), (6, 30), (22, 14), (10, 14), (3, 32), (30, 35), (5, 33), (5, 15), (20, 7), (10, 16), (7, 24), (29, 3), (28, 11), (29, 8), (30, 29), (9, 7), (23, 29), (27, 2), (16, 8), (14, 5), (5, 22), (14, 18), (26, 15), (28, 3), (19, 1), (1, 15), (8, 13), (19, 29), (14, 13), (15, 3), (29, 34), (2, 0), (24, 6), (10, 26), (3, 18), (4, 30), (23, 35), (6, 8), (0, 10), (15, 6), (21, 29), (20, 25), (3, 10), (9, 13), (19, 5), (28, 17), (18, 10), (0, 9), (8, 34), (21, 2), (26, 18), (19, 34), (8, 25), (24, 26), (18, 16), (26, 10), (9, 22), (18, 12), (5, 34), (7, 23), (4, 10), (14, 23), (29, 30), (29, 25), (10, 2), (17, 15), (13, 4), (22, 1), (6, 21), (27, 25), (13, 36), (24, 23), (27, 29), (13, 31), (3, 28), (7, 25), (15, 35), (11, 35), (5, 6), (8, 36), (0, 26), (25, 23), (29, 32), (9, 36), (22, 26), (0, 32), (26, 31), (22, 20), (5, 27), (10, 12), (27, 14), (17, 28), (16, 25), (16, 33), (8, 21), (5, 13), (14, 17), (9, 16), (9, 29), (7, 9), (0, 31), (23, 11), (2, 1), (13, 33), (2, 21), (22, 19), (1, 18), (24, 35), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "457968", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 31), (28, 4), (33, 16), (3, 28), (20, 5), (12, 21), (36, 20), (7, 30), (34, 8), (19, 21), (10, 17), (13, 2), (18, 5), (32, 24), (24, 2), (31, 29), (4, 1), (32, 11), (0, 15), (34, 31), (23, 29), (36, 16), (35, 30), (18, 19), (10, 32), (36, 1), (2, 11), (0, 29), (23, 31), (22, 2), (29, 22), (34, 12), (14, 31), (36, 9), (23, 2), (8, 18), (19, 13), (23, 28), (13, 10), (14, 32), (30, 4), (13, 27), (26, 18), (3, 21), (30, 2), (3, 15), (27, 0), (24, 25), (6, 5), (20, 12), (4, 6), (33, 3), (34, 16), (31, 4), (3, 22), (32, 23), (5, 0), (5, 16), (5, 31), (8, 13), (19, 27), (23, 17), (6, 19), (5, 29), (30, 19), (34, 6), (27, 7), (37, 24), (21, 3), (5, 15), (13, 12), (21, 27), (7, 22), (14, 16), (12, 0), (25, 8), (6, 18), (6, 10), (0, 24), (14, 14), (31, 21), (34, 32), (26, 1), (33, 18), (0, 20), (19, 12), (32, 19), (16, 28), (27, 25), (35, 17), (18, 10), (34, 9), (37, 22), (13, 15), (34, 5), (30, 14), (18, 8), (4, 12), (7, 20), (22, 23), (1, 21), (31, 19), (28, 20), (24, 26), (26, 3), (25, 3), (37, 16), (27, 9), (4, 21), (37, 7), (2, 16), (2, 5), (31, 1), (13, 23), (10, 10), (28, 10), (11, 16), (24, 3), (34, 15), (13, 31), (28, 12), (12, 10), (18, 9), (29, 12), (12, 9), (24, 16), (9, 16), (11, 5), (5, 19), (1, 30), (21, 21), (5, 2), (36, 23), (31, 10), (17, 4), (33, 17), (20, 29), (30, 13), (19, 31), (23, 0), (18, 24), (14, 30), (26, 32), (32, 16), (7, 18), (34, 13), (11, 9), (36, 27), (9, 2), (32, 31), (12, 3), (7, 31), (0, 28), (13, 0), (35, 28), (37, 6), (35, 23), (0, 23), (9, 24), (28, 15), (25, 21), (36, 22), (7, 8), (18, 26), (25, 32), (12, 26), (24, 19), (1, 28), (36, 19), (13, 26), (11, 15), (11, 27), (16, 29), (35, 32), (8, 2), (20, 24), (3, 29), (9, 12), (3, 31), (11, 23), (3, 2), (17, 27), (31, 12), (35, 10), (23, 8), (31, 31), (30, 25), (8, 20), (34, 11), (30, 30), (8, 17), (16, 8), (19, 17), (17, 15), (14, 22), (32, 25), (11, 13), (34, 23), (37, 10), (8, 27), (8, 1), (16, 27), (6, 3), (35, 18), (8, 14), (28, 0), (13, 16), (35, 26), (1, 16), (14, 23), (16, 24), (5, 10), (0, 31), (4, 30), (5, 8), (2, 8), (7, 16), (30, 18), (16, 21), (11, 12), (3, 12), (27, 23), (10, 12), (11, 30), (1, 8), (16, 22), (33, 11), (32, 15), (18, 4), (3, 10), (35, 9), (25, 4), (14, 9), (11, 25), (12, 6), (25, 18), (5, 25), (25, 13), (28, 31), (29, 2), (22, 29), (14, 26), (18, 14), (23, 20), (24, 7), (35, 8), (2, 18), (15, 13), (6, 20), (15, 10), (9, 8), (6, 21), (2, 29), (27, 6), (11, 7), (23, 11), (26, 6), (12, 16), (11, 19), (7, 11), (8, 21), (30, 27), (8, 0), (2, 6), (8, 26), (15, 30), (16, 1), (9, 31), (10, 9), (24, 22), (23, 16), (14, 21), (7, 15), (5, 5), (9, 10), (21, 31), (2, 7), (32, 28), (15, 21), (1, 5), (5, 17), (37, 1), (14, 2), (28, 28), (23, 14), (1, 23), (31, 17), (4, 26), (26, 27), (20, 17), (6, 1), (21, 6), (19, 25), (4, 28), (25, 12), (20, 30), (3, 14), (8, 25), (24, 20), (25, 22), (6, 25), (4, 20), (19, 24), (23, 18), (20, 4), (29, 20), (23, 26), (26, 8), (1, 0), (24, 14), (2, 31), (17, 2), (18, 2), (4, 14), (30, 17), (28, 26), (5, 13), (16, 2), (22, 22), (35, 1), (3, 27), (5, 11), (10, 6), (24, 24), (17, 29), (18, 28), (37, 4), (34, 21), (2, 21), (34, 17), (6, 24), (22, 30), (15, 28), (1, 7), (35, 21), (13, 29), (12, 22), (37, 27), (24, 23), (5, 26), (36, 21), (33, 10), (12, 11), (11, 18), (5, 21), (12, 7), (11, 4), (0, 25), (3, 17), (7, 25), (6, 4), (19, 9), (32, 30), (9, 11), (22, 25), (8, 11), (29, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552960", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 24), (7, 30), (17, 4), (6, 14), (24, 16), (17, 3), (16, 8), (27, 17), (14, 33), (23, 9), (14, 1), (15, 28), (8, 1), (8, 28), (2, 20), (11, 15), (9, 4), (6, 9), (26, 19), (22, 13), (17, 5), (20, 9), (7, 33), (0, 35), (16, 18), (3, 8), (10, 6), (29, 3), (3, 5), (27, 24), (25, 11), (7, 5), (20, 26), (26, 25), (22, 7), (26, 6), (30, 9), (15, 31), (8, 19), (10, 17), (19, 6), (6, 5), (19, 14), (9, 13), (1, 6), (6, 7), (26, 5), (12, 14), (10, 19), (27, 32), (27, 10), (21, 26), (6, 34), (12, 9), (30, 20), (0, 34), (19, 12), (9, 22), (19, 15), (25, 31), (3, 14), (27, 27), (8, 30), (20, 33), (30, 4), (24, 3), (24, 20), (8, 2), (5, 1), (27, 9), (3, 35), (16, 3), (9, 14), (13, 23), (30, 24), (21, 29), (6, 10), (16, 14), (18, 15), (28, 8), (17, 19), (27, 26), (0, 13), (6, 28), (13, 35), (2, 28), (11, 4), (11, 19), (25, 10), (12, 12), (13, 27), (9, 12), (18, 20), (26, 15), (27, 31), (6, 29), (19, 0), (16, 27), (29, 33), (13, 5), (8, 18), (18, 1), (18, 0), (22, 16), (5, 28), (18, 2), (1, 33), (9, 5), (21, 32), (9, 18), (1, 26), (24, 9), (14, 22), (4, 32), (13, 20), (0, 2), (25, 2), (20, 11), (26, 2), (21, 7), (4, 15), (23, 15), (24, 22), (13, 7), (22, 10), (29, 30), (23, 11), (2, 21), (29, 4), (12, 28), (8, 24), (17, 16), (16, 35), (28, 30), (7, 26), (19, 8), (12, 17), (25, 0), (7, 10), (21, 28), (5, 33), (0, 20), (21, 33), (3, 27), (27, 8), (0, 11), (1, 14), (11, 31), (18, 4), (13, 13), (11, 14), (2, 4), (11, 13), (7, 9), (28, 21), (24, 4), (21, 20), (4, 28), (25, 21), (11, 35), (27, 14), (8, 0), (1, 10), (6, 30), (2, 13), (8, 16), (21, 13), (28, 6), (30, 25), (9, 23), (26, 32), (30, 15), (5, 30), (29, 16), (17, 17), (28, 20), (9, 27), (15, 9), (9, 24), (23, 7), (8, 10), (9, 10), (5, 10), (11, 18), (19, 24), (20, 15), (26, 18), (16, 7), (15, 1), (24, 0), (4, 10), (9, 30), (3, 3), (20, 18), (25, 4), (17, 20), (15, 6), (28, 19), (1, 25), (2, 18), (14, 0), (18, 16), (15, 17), (21, 3), (26, 9), (10, 32), (8, 7), (28, 28), (24, 25), (16, 0), (6, 31), (26, 28), (28, 13), (30, 8), (12, 27), (12, 4), (0, 8), (25, 34), (26, 3), (11, 16), (13, 22), (10, 13), (19, 18), (10, 9), (15, 16), (14, 7), (10, 8), (0, 24), (16, 22), (15, 25), (17, 33), (13, 21), (12, 26), (18, 18), (2, 24), (26, 24), (23, 31), (13, 18), (24, 35), (21, 2), (11, 6), (2, 3), (3, 2), (6, 3), (3, 23), (11, 32), (6, 4), (11, 2), (26, 10), (25, 8), (27, 20), (14, 30), (22, 15), (17, 28), (27, 21), (5, 5), (23, 22), (24, 10), (22, 19), (0, 10), (28, 35), (14, 12), (11, 5), (14, 35), (20, 32), (27, 6), (3, 29), (14, 28), (4, 13), (21, 21), (5, 29), (22, 24), (23, 26), (1, 34), (5, 9), (3, 4), (7, 6), (15, 13), (12, 2), (28, 12), (19, 35), (4, 23), (28, 5), (24, 29), (14, 10), (22, 3), (9, 3), (11, 8), (28, 33), (17, 18), (29, 21), (22, 20), (19, 31), (23, 16), (18, 27), (17, 10), (27, 18), (14, 23), (28, 3), (7, 1), (5, 15), (15, 30), (4, 14), (14, 4), (18, 19), (29, 9), (5, 24), (14, 31), (17, 34), (14, 17), (12, 24), (5, 4), (15, 15), (4, 7), (23, 6), (7, 21), (19, 2), (29, 31), (13, 33), (7, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "138348", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 32), (18, 28), (15, 12), (28, 21), (34, 9), (24, 17), (34, 16), (4, 29), (32, 17), (20, 9), (0, 9), (6, 30), (18, 1), (6, 1), (31, 24), (26, 31), (5, 32), (28, 6), (17, 23), (7, 4), (27, 11), (15, 2), (31, 27), (2, 33), (8, 11), (2, 37), (27, 16), (20, 20), (22, 25), (24, 29), (21, 5), (17, 12), (24, 11), (26, 27), (21, 24), (14, 26), (6, 0), (29, 7), (25, 0), (14, 15), (24, 4), (3, 28), (12, 13), (10, 19), (9, 8), (33, 7), (19, 0), (8, 23), (17, 20), (33, 14), (13, 25), (6, 4), (32, 28), (15, 33), (19, 2), (6, 26), (29, 11), (19, 21), (23, 22), (1, 25), (7, 34), (31, 34), (19, 34), (23, 37), (31, 13), (26, 16), (15, 0), (3, 4), (17, 25), (12, 12), (24, 32), (5, 27), (15, 29), (33, 37), (0, 27), (26, 1), (3, 17), (20, 0), (31, 23), (8, 19), (25, 23), (4, 7), (14, 23), (18, 10), (11, 33), (15, 7), (8, 13), (9, 15), (1, 29), (22, 22), (4, 24), (17, 3), (30, 29), (12, 5), (2, 28), (27, 17), (21, 31), (16, 1), (3, 3), (13, 8), (22, 33), (5, 36), (30, 24), (23, 3), (8, 30), (7, 28), (2, 36), (18, 24), (18, 32), (18, 3), (14, 24), (34, 17), (3, 10), (2, 22), (18, 23), (29, 5), (32, 16), (13, 9), (17, 8), (14, 4), (35, 2), (5, 8), (18, 8), (33, 31), (28, 12), (3, 35), (10, 30), (25, 1), (31, 37), (13, 16), (22, 32), (0, 19), (16, 31), (20, 10), (33, 25), (12, 31), (9, 13), (23, 6), (26, 9), (30, 0), (17, 13), (28, 8), (9, 17), (4, 13), (2, 1), (6, 2), (30, 34), (19, 37), (35, 23), (2, 0), (12, 14), (7, 17), (31, 12), (20, 23), (6, 5), (2, 29), (12, 18), (8, 7), (10, 23), (32, 25), (9, 19), (23, 20), (2, 13), (15, 27), (8, 28), (26, 7), (30, 30), (27, 32), (20, 21), (3, 9), (5, 15), (19, 33), (32, 21), (3, 32), (35, 30), (12, 1), (23, 12), (12, 33), (5, 37), (17, 15), (14, 31), (24, 34), (30, 31), (13, 34), (11, 20), (16, 5), (27, 0), (33, 11), (0, 10), (32, 23), (18, 4), (9, 16), (31, 20), (22, 28), (28, 19), (21, 15), (14, 14), (24, 25), (31, 31), (33, 35), (10, 6), (9, 28), (15, 16), (2, 4), (0, 3), (13, 28), (15, 25), (0, 5), (8, 29), (23, 31), (23, 16), (17, 34), (29, 3), (2, 9), (25, 36), (11, 23), (18, 19), (35, 7), (35, 4), (31, 25), (17, 4), (28, 7), (15, 14), (11, 17), (20, 37), (15, 3), (29, 36), (15, 17), (8, 37), (28, 36), (31, 17), (15, 24), (18, 35), (14, 20), (0, 21), (23, 17), (32, 30), (5, 6), (33, 18), (14, 7), (25, 29), (34, 8), (3, 6), (30, 26), (18, 16), (10, 34), (13, 27), (10, 10), (12, 28), (12, 30), (16, 35), (21, 4), (10, 12), (20, 22), (17, 1), (0, 15), (12, 9), (27, 21), (23, 7), (33, 2), (30, 15), (3, 37), (7, 32), (35, 12), (3, 22), (12, 2), (0, 35), (1, 19), (11, 1), (2, 5), (23, 1), (15, 21), (25, 2), (27, 3), (26, 12), (0, 25), (35, 35), (1, 4), (5, 1), (16, 2), (1, 16), (22, 24), (22, 29), (15, 13), (21, 29), (2, 14), (19, 11), (21, 2), (33, 15), (13, 0), (17, 32), (20, 18), (14, 21), (0, 28), (28, 18), (22, 34), (30, 17), (14, 29), (25, 30), (35, 16), (34, 25), (20, 36), (24, 37), (32, 33), (28, 14), (4, 17), (1, 23), (30, 32), (7, 16), (14, 25), (9, 4), (26, 22), (22, 20), (25, 24), (31, 16), (2, 20), (19, 15), (28, 13), (16, 13), (10, 2), (19, 6), (9, 34), (27, 23), (5, 20), (29, 26), (35, 18), (32, 36), (0, 8), (33, 16), (13, 33), (24, 23), (7, 25), (30, 37), (17, 31), (28, 31), (18, 34), (7, 36), (21, 28), (11, 36), (2, 34), (34, 27), (18, 12), (2, 6), (28, 27), (25, 7), (31, 3), (15, 5), (8, 34), (9, 0), (17, 35), (28, 25), (23, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887040", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), 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), (7, 15), (27, 22), (12, 13), (11, 0), (6, 3), (18, 26), (28, 29), (21, 14), (23, 1), (10, 21), (1, 15), (16, 33), (0, 24), (16, 18), (7, 8), (21, 0), (17, 4), (23, 14), (19, 29), (25, 8), (22, 25), (8, 9), (27, 29), (6, 11), (18, 6), (14, 2), (24, 14), (21, 20), (11, 22), (12, 2), (9, 22), (6, 30), (6, 7), (8, 3), (19, 27), (14, 16), (9, 23), (25, 1), (15, 29), (19, 14), (24, 31), (16, 10), (26, 10), (27, 19), (13, 19), (22, 32), (29, 30), (5, 27), (3, 13), (8, 19), (23, 18), (10, 11), (13, 12), (21, 32), (6, 22), (23, 7), (8, 22), (29, 4), (24, 11), (10, 31), (20, 31), (2, 11), (8, 14), (22, 16), (3, 25), (22, 19), (2, 9), (3, 3), (13, 5), (9, 20), (8, 10), (0, 23), (11, 6), (4, 12), (18, 9), (21, 16), (4, 24), (9, 26), (11, 18), (27, 9), (7, 2), (28, 7), (22, 33), (22, 6), (4, 17), (27, 6), (5, 33), (13, 28), (9, 1), (25, 9), (26, 27), (13, 0), (18, 20), (25, 0), (7, 7), (18, 16), (23, 16), (13, 17), (6, 0), (0, 20), (15, 14), (0, 6), (24, 6), (5, 21), (25, 29), (18, 22), (12, 20), (8, 25), (23, 23), (27, 4), (27, 11), (12, 30), (0, 5), (8, 20), (0, 9), (26, 31), (22, 18), (8, 32), (6, 18), (13, 1), (15, 5), (16, 17), (14, 11), (9, 16), (1, 31), (8, 33), (0, 11), (18, 17), (4, 20), (13, 24), (2, 32), (16, 22), (9, 6), (18, 13), (24, 10), (19, 33), (10, 28), (10, 23), (24, 16), (10, 30), (14, 7), (21, 25), (23, 29), (16, 4), (26, 3), (4, 4), (14, 13), (6, 2), (3, 4), (23, 28), (7, 27), (19, 1), (3, 27), (27, 25), (17, 31), (0, 14), (3, 9), (17, 27), (16, 26), (22, 29), (24, 27), (25, 21), (19, 32), (27, 2), (1, 5), (10, 2), (10, 27), (14, 8), (17, 12), (21, 31), (2, 8), (22, 27), (19, 15), (16, 27), (26, 33), (16, 28), (28, 1), (29, 20), (9, 15), (10, 26), (13, 13), (16, 19), (22, 11), (23, 21), (18, 15), (0, 12), (25, 11), (21, 23), (27, 14), (4, 16), (20, 11), (10, 5), (17, 5), (20, 1), (4, 15), (16, 24), (12, 28), (27, 20), (10, 17), (19, 6), (25, 20), (11, 9), (8, 24), (26, 22), (19, 16), (24, 17), (9, 9), (19, 31), (29, 2), (20, 32), (27, 5), (12, 6), (28, 5), (8, 16), (2, 0), (24, 29), (21, 10), (24, 8), (8, 5), (21, 15), (22, 2), (3, 17), (14, 12), (9, 33), (12, 25), (21, 6), (20, 14), (6, 32), (18, 29), (3, 11), (3, 2), (12, 3), (22, 30), (23, 5), (25, 5), (26, 20), (8, 29), (23, 20), (8, 0), (19, 24), (21, 22), (4, 11), (0, 3), (1, 13), (11, 19), (9, 27), (26, 9), (28, 8), (28, 6), (8, 27), (25, 18), (17, 30), (12, 8), (29, 19), (9, 21), (11, 7), (22, 13), (1, 26), (1, 23), (26, 11), (20, 17), (10, 8), (29, 13), (10, 24), (14, 18), (3, 7), (19, 2), (17, 11), (14, 25), (23, 3), (17, 17), (27, 15), (9, 8), (14, 6), (13, 29), (4, 8), (28, 17), (1, 8), (25, 25), (18, 32), (15, 23), (28, 10), (1, 16), (15, 11), (17, 16), (25, 13), (6, 10), (28, 15), (10, 29), (0, 7), (19, 13), (7, 32), (18, 18), (5, 1), (4, 33), (2, 21), (19, 8), (15, 6), (2, 17), (17, 9), (26, 2), (11, 31), (13, 32), (14, 14), (5, 17), (21, 30), (17, 32), (5, 19), (11, 17), (28, 20), (17, 15), (4, 21), (18, 23), (20, 0), (0, 16), (19, 9), (11, 25), (18, 2), (29, 10), (23, 17), (2, 14), (21, 27), (26, 5), (13, 26), (26, 13), (19, 3), (9, 5), (17, 13), (11, 14), (0, 18), (29, 1), (9, 30), (2, 31), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591300", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (35, 28), (17, 7), (19, 31), (2, 30), (34, 15), (3, 11), (16, 6), (11, 5), (31, 3), (29, 8), (11, 12), (30, 16), (24, 18), (14, 28), (0, 17), (36, 13), (33, 16), (12, 21), (8, 9), (15, 4), (32, 4), (7, 24), (31, 6), (21, 17), (16, 14), (32, 15), (37, 12), (25, 1), (9, 28), (7, 12), (7, 30), (19, 27), (12, 15), (17, 14), (15, 22), (14, 7), (37, 7), (21, 32), (8, 20), (33, 11), (25, 17), (9, 16), (38, 12), (7, 28), (23, 27), (7, 11), (6, 19), (16, 10), (0, 22), (3, 13), (19, 33), (30, 30), (27, 34), (31, 0), (21, 27), (31, 7), (23, 19), (12, 34), (37, 29), (30, 9), (35, 31), (5, 14), (11, 8), (4, 22), (8, 18), (10, 17), (11, 23), (25, 19), (1, 0), (34, 31), (7, 9), (1, 28), (29, 1), (17, 23), (19, 23), (12, 30), (5, 7), (14, 17), (7, 14), (38, 1), (6, 22), (27, 8), (25, 16), (33, 25), (6, 13), (26, 20), (19, 29), (7, 21), (5, 34), (7, 20), (10, 23), (19, 22), (23, 24), (10, 9), (33, 10), (25, 3), (37, 20), (18, 29), (12, 27), (33, 5), (35, 14), (32, 30), (28, 19), (12, 2), (23, 18), (13, 23), (26, 33), (3, 6), (15, 18), (9, 21), (21, 34), (34, 2), (15, 7), (15, 20), (2, 29), (20, 8), (26, 13), (35, 9), (17, 21), (17, 10), (21, 21), (25, 26), (9, 17), (34, 33), (28, 30), (29, 5), (19, 13), (21, 16), (38, 14), (28, 14), (31, 13), (0, 9), (35, 26), (38, 17), (4, 12), (9, 29), (36, 10), (3, 33), (3, 8), (22, 29), (4, 33), (17, 28), (17, 34), (19, 3), (22, 12), (7, 31), (25, 12), (22, 24), (36, 6), (7, 8), (8, 5), (7, 13), (17, 12), (0, 21), (26, 19), (7, 33), (9, 27), (37, 23), (27, 29), (2, 18), (16, 25), (22, 34), (12, 18), (22, 16), (36, 23), (38, 29), (1, 6), (3, 12), (26, 0), (36, 19), (37, 21), (31, 25), (11, 26), (9, 12), (28, 1), (17, 22), (28, 24), (0, 33), (11, 7), (18, 32), (10, 20), (21, 7), (7, 7), (23, 3), (8, 26), (10, 33), (11, 27), (17, 9), (29, 23), (35, 8), (26, 9), (19, 17), (9, 6), (38, 25), (4, 10), (24, 29), (1, 25), (5, 0), (21, 9), (12, 13), (22, 30), (27, 0), (10, 30), (3, 26), (35, 7), (10, 29), (15, 26), (20, 21), (22, 19), (33, 8), (12, 12), (33, 24), (22, 14), (28, 7), (6, 26), (6, 4), (6, 20), (5, 29), (2, 24), (8, 11), (36, 8), (31, 28), (27, 12), (14, 30), (17, 6), (23, 17), (23, 11), (23, 7), (34, 16), (8, 0), (28, 15), (35, 13), (1, 19), (22, 26), (9, 31), (13, 33), (6, 11), (30, 33), (8, 29), (21, 24), (16, 30), (26, 30), (36, 25), (4, 11), (24, 28), (18, 2), (31, 9), (3, 9), (21, 25), (13, 13), (35, 16), (32, 33), (19, 2), (33, 4), (29, 3), (35, 5), (26, 27), (3, 15), (10, 12), (34, 1), (22, 27), (4, 30), (1, 16), (18, 25), (12, 14), (31, 1), (10, 14), (14, 20), (20, 11), (7, 18), (23, 9), (24, 6), (20, 19), (15, 5), (16, 22), (1, 2), (8, 14), (0, 8), (17, 30), (36, 14), (19, 5), (5, 21), (18, 20), (20, 24), (19, 19), (2, 28), (10, 7), (37, 11), (3, 18), (10, 22), (12, 0), (20, 34), (28, 6), (0, 20), (22, 28), (14, 23), (13, 22), (18, 14), (22, 33), (14, 24), (14, 1), (38, 22), (4, 0), (17, 17), (27, 33), (36, 27), (37, 17), (21, 33), (11, 0), (8, 4), (27, 16), (36, 33), (5, 31), (36, 31), (25, 5), (29, 0), (30, 0), (5, 24), (0, 6), (8, 6), (38, 13), (25, 0), (30, 18), (1, 23), (14, 27), (23, 33), (7, 15), (28, 22), (30, 27), (24, 7), (0, 4), (7, 27), (0, 31), (38, 33), (19, 21), (24, 23), (34, 5), (20, 17), (26, 26), (37, 2), (31, 15), (18, 19), (16, 34), (37, 28), (8, 22), (3, 34), (24, 2), (17, 0), (26, 2), (32, 28), (3, 7), (8, 30), (33, 17), (27, 24), (6, 16), (22, 1), (33, 22), (7, 10), (13, 9), (19, 8), (20, 31), (9, 22), (10, 15), (33, 7), (11, 3), (31, 27), (21, 20), (16, 9), (2, 6), (3, 30), (35, 30), (0, 13), (38, 9), (19, 24), (12, 11), (22, 2), (24, 11), (11, 1), (24, 26), (36, 16), (13, 24), (17, 18), (25, 15), (34, 20), (20, 23), (1, 31), (27, 27), (2, 14), (6, 25), (11, 10), (28, 26), (25, 23), (15, 23), (25, 34), (26, 14), (5, 11), (15, 6), (1, 13), (20, 30), (15, 9), (6, 0), (1, 29), (26, 12), (10, 34), (24, 33), (26, 6), (20, 9), (32, 9), (5, 9), (10, 26), (18, 33), (18, 17), (29, 26), (15, 0), (8, 7), (26, 17), (17, 19), (0, 24), (9, 18), (29, 19), (7, 32), (5, 5), (1, 27), (11, 30), (37, 24), (23, 23), (2, 20), (7, 34), (35, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "967200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), 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), (31, 8), (14, 26), (23, 26), (4, 12), (20, 9), (13, 18), (15, 9), (6, 22), (18, 17), (22, 30), (3, 4), (23, 9), (9, 15), (16, 25), (24, 2), (10, 9), (16, 15), (13, 1), (17, 5), (9, 21), (3, 15), (7, 19), (3, 17), (30, 7), (16, 1), (2, 21), (4, 14), (18, 23), (24, 12), (15, 25), (21, 29), (8, 7), (4, 2), (1, 25), (13, 27), (17, 29), (28, 1), (21, 1), (10, 17), (19, 9), (13, 9), (14, 5), (3, 6), (17, 27), (21, 16), (24, 13), (5, 4), (18, 31), (18, 6), (2, 1), (20, 23), (31, 12), (11, 16), (29, 27), (30, 30), (0, 3), (18, 12), (27, 10), (22, 19), (21, 26), (32, 16), (7, 13), (25, 4), (8, 14), (5, 10), (22, 13), (7, 29), (13, 12), (17, 6), (9, 13), (2, 28), (17, 17), (26, 3), (30, 4), (5, 9), (29, 18), (15, 5), (2, 5), (1, 14), (18, 7), (0, 6), (23, 12), (31, 18), (26, 29), (29, 16), (3, 13), (28, 17), (12, 16), (6, 28), (0, 1), (20, 4), (13, 23), (16, 19), (27, 17), (9, 19), (4, 13), (7, 8), (22, 7), (8, 2), (10, 0), (5, 16), (15, 23), (29, 31), (29, 19), (0, 17), (27, 11), (5, 25), (24, 14), (10, 13), (17, 19), (21, 15), (12, 30), (24, 15), (10, 29), (23, 0), (20, 29), (12, 27), (11, 13), (4, 17), (17, 26), (10, 20), (27, 29), (19, 3), (19, 7), (31, 28), (25, 30), (15, 12), (20, 14), (27, 31), (0, 28), (11, 17), (30, 24), (11, 7), (21, 8), (31, 6), (32, 5), (15, 6), (9, 22), (11, 18), (30, 14), (24, 21), (23, 14), (31, 29), (19, 15), (17, 3), (12, 9), (15, 14), (30, 22), (13, 14), (25, 31), (20, 11), (27, 5), (23, 18), (9, 23), (23, 8), (8, 16), (0, 12), (17, 11), (20, 8), (1, 20), (5, 20), (6, 11), (5, 17), (12, 1), (21, 2), (5, 18), (14, 4), (23, 13), (2, 13), (8, 0), (32, 17), (24, 25), (26, 28), (30, 25), (5, 26), (1, 29), (16, 4), (26, 2), (31, 21), (17, 9), (8, 30), (9, 18), (23, 17), (17, 23), (1, 27), (8, 24), (30, 19), (14, 21), (7, 16), (1, 3), (22, 11), (13, 6), (12, 31), (6, 26), (19, 22), (27, 14), (10, 24), (32, 11), (28, 18), (14, 6), (1, 17), (16, 5), (15, 15), (24, 7), (22, 17), (30, 31), (25, 7), (22, 5), (3, 23), (27, 8), (32, 10), (28, 30), (30, 12), (16, 0), (6, 29), (1, 7), (28, 6), (6, 14), (32, 20), (15, 10), (2, 7), (32, 6), (31, 24), (6, 23), (29, 13), (19, 2), (19, 29), (14, 14), (20, 1), (16, 21), (10, 19), (15, 19), (8, 10), (29, 5), (3, 14), (6, 21), (32, 14), (23, 19), (0, 30), (13, 17), (0, 10), (19, 12), (2, 2), (29, 28), (17, 20), (20, 16), (24, 5), (0, 13), (13, 26), (11, 0), (32, 12), (24, 22), (16, 14), (27, 0), (2, 27), (17, 12), (26, 7), (6, 15), (15, 4), (9, 17), (20, 21), (29, 25), (9, 6), (18, 29), (29, 2), (8, 20), (9, 5), (25, 17), (4, 7), (0, 22), (9, 14), (20, 27), (13, 29), (25, 5), (14, 16), (24, 29), (27, 4), (18, 18), (10, 12), (16, 6), (26, 10), (26, 8), (2, 14), (5, 7), (19, 11), (13, 16), (4, 23), (11, 19), (3, 28), (24, 27), (24, 6), (23, 22), (14, 12), (25, 13), (29, 8), (24, 23), (23, 25), (8, 28), (5, 15), (29, 7), (23, 30), (8, 18), (28, 20), (32, 18), (7, 21), (18, 26), (10, 15), (29, 22), (13, 2), (14, 24), (12, 29), (8, 27), (4, 21), (9, 2), (7, 18), (28, 4), (24, 24), (7, 25), (0, 9), (11, 8), (10, 21), (15, 24), (21, 28), (30, 16), (4, 28), (1, 31), (28, 3), (6, 0), (9, 16), (15, 11), (16, 10), (12, 19), (22, 23), (32, 0), (28, 23), (3, 2), (26, 1), (8, 1), (11, 6), (10, 7), (5, 23), (32, 3), (19, 24), (15, 1), (13, 5), (7, 3), (8, 22), (9, 7), (15, 27), (13, 20), (25, 18), (23, 10), (21, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863082", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 3), (26, 20), (22, 14), (29, 3), (16, 6), (27, 30), (13, 4), (13, 14), (27, 25), (31, 12), (24, 10), (23, 7), (15, 22), (0, 16), (29, 11), (28, 6), (1, 16), (7, 6), (21, 28), (21, 10), (19, 16), (1, 4), (18, 24), (21, 23), (2, 8), (19, 11), (23, 23), (14, 20), (26, 29), (30, 1), (15, 6), (6, 16), (25, 18), (9, 18), (23, 21), (23, 2), (27, 21), (2, 2), (27, 29), (0, 20), (5, 14), (10, 14), (5, 6), (11, 30), (27, 28), (14, 8), (16, 27), (10, 6), (20, 11), (24, 25), (7, 30), (28, 24), (17, 9), (13, 21), (22, 27), (28, 9), (14, 0), (12, 13), (7, 3), (10, 1), (4, 30), (7, 28), (29, 2), (5, 12), (6, 11), (22, 28), (0, 21), (14, 3), (2, 3), (29, 5), (12, 16), (17, 16), (30, 5), (31, 10), (0, 31), (14, 19), (13, 24), (4, 31), (27, 18), (18, 18), (24, 19), (21, 30), (26, 4), (28, 28), (1, 25), (1, 5), (19, 0), (14, 17), (0, 18), (8, 7), (25, 12), (4, 22), (9, 22), (30, 24), (16, 4), (17, 21), (20, 28), (24, 4), (23, 19), (15, 9), (26, 16), (30, 30), (21, 29), (0, 4), (13, 8), (30, 31), (12, 12), (31, 4), (21, 8), (3, 29), (24, 2), (15, 10), (1, 28), (6, 18), (7, 26), (4, 8), (26, 11), (18, 10), (10, 27), (22, 7), (6, 19), (4, 21), (26, 14), (28, 21), (10, 24), (16, 32), (5, 3), (17, 4), (11, 7), (18, 26), (15, 11), (24, 22), (12, 28), (13, 31), (15, 32), (19, 10), (23, 32), (2, 15), (30, 3), (7, 31), (15, 13), (26, 2), (16, 2), (18, 7), (3, 3), (21, 3), (28, 7), (19, 1), (12, 20), (4, 1), (5, 10), (19, 25), (21, 19), (10, 13), (19, 30), (20, 6), (9, 5), (20, 9), (26, 22), (7, 12), (18, 22), (3, 7), (23, 30), (21, 0), (22, 26), (12, 27), (17, 18), (30, 20), (0, 30), (19, 23), (27, 27), (1, 31), (25, 3), (2, 10), (21, 20), (31, 29), (13, 19), (6, 17), (11, 26), (8, 30), (23, 6), (23, 3), (25, 21), (26, 15), (9, 21), (28, 14), (25, 19), (25, 25), (1, 11), (6, 6), (20, 15), (9, 15), (11, 32), (16, 5), (20, 27), (18, 21), (8, 31), (7, 21), (23, 20), (10, 5), (24, 0), (12, 23), (10, 15), (7, 1), (8, 32), (5, 29), (7, 4), (28, 23), (30, 21), (3, 0), (16, 18), (27, 7), (1, 12), (22, 23), (19, 3), (22, 30), (7, 0), (20, 17), (2, 0), (6, 21), (20, 24), (11, 21), (19, 28), (11, 1), (2, 18), (9, 3), (13, 29), (18, 20), (1, 32), (17, 30), (27, 17), (20, 13), (19, 15), (28, 11), (28, 26), (18, 12), (29, 23), (31, 16), (29, 7), (19, 14), (0, 1), (30, 26), (5, 28), (23, 29), (28, 12), (4, 19), (29, 25), (4, 18), (6, 1), (16, 22), (18, 15), (10, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736938", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 27), (4, 11), (21, 8), (20, 36), (22, 25), (28, 25), (6, 9), (10, 0), (34, 16), (10, 9), (26, 19), (8, 16), (20, 23), (14, 20), (21, 26), (27, 36), (35, 6), (27, 0), (15, 8), (35, 22), (27, 16), (0, 21), (22, 14), (19, 10), (10, 28), (19, 27), (0, 2), (33, 8), (9, 15), (14, 22), (22, 20), (16, 5), (16, 20), (8, 19), (5, 32), (1, 17), (33, 29), (24, 16), (0, 30), (32, 26), (17, 2), (21, 36), (29, 14), (23, 20), (6, 33), (30, 6), (7, 32), (29, 34), (11, 18), (21, 20), (31, 7), (27, 5), (25, 1), (29, 20), (24, 27), (1, 26), (0, 3), (12, 13), (16, 36), (31, 16), (9, 22), (33, 3), (11, 22), (31, 24), (16, 32), (9, 16), (18, 5), (4, 5), (26, 35), (27, 25), (8, 18), (11, 2), (13, 2), (15, 17), (20, 28), (34, 9), (12, 26), (7, 30), (27, 22), (2, 4), (27, 27), (8, 2), (21, 13), (17, 13), (7, 29), (25, 25), (6, 23), (5, 18), (11, 8), (28, 2), (4, 26), (3, 18), (0, 17), (33, 15), (24, 25), (23, 31), (34, 15), (18, 19), (13, 34), (6, 10), (2, 20), (35, 21), (7, 5), (25, 3), (28, 11), (1, 32), (11, 16), (35, 32), (4, 28), (26, 2), (1, 24), (13, 20), (29, 30), (27, 23), (27, 1), (5, 25), (5, 14), (17, 34), (13, 10), (5, 35), (32, 2), (7, 6), (23, 17), (14, 24), (27, 19), (29, 2), (1, 2), (7, 36), (0, 27), (11, 9), (8, 36), (13, 6), (3, 8), (10, 27), (26, 5), (8, 4), (18, 33), (9, 21), (16, 15), (19, 32), (4, 31), (34, 20), (6, 2), (3, 13), (22, 33), (13, 19), (20, 18), (35, 28), (22, 18), (32, 35), (4, 8), (4, 33), (18, 21), (18, 26), (5, 13), (10, 1), (25, 18), (15, 12), (35, 9), (3, 9), (9, 36), (16, 27), (30, 20), (13, 33), (35, 27), (9, 12), (32, 5), (14, 31), (31, 23), (35, 17), (14, 14), (29, 28), (17, 11), (0, 1), (9, 7), (33, 21), (0, 26), (22, 6), (32, 6), (23, 9), (9, 32), (1, 21), (22, 19), (11, 6), (31, 14), (15, 14), (27, 34), (19, 28), (17, 21), (30, 2), (4, 32), (23, 35), (31, 4), (20, 9), (18, 36), (2, 22), (11, 13), (25, 33), (23, 33), (32, 3), (28, 12), (34, 7), (14, 9), (27, 18), (23, 32), (22, 10), (19, 16), (33, 6), (16, 16), (34, 31), (10, 30), (23, 36), (4, 6), (11, 1), (0, 36), (9, 9), (23, 15), (0, 28), (26, 32), (7, 31), (0, 22), (7, 24), (25, 26), (29, 27), (33, 33), (12, 36), (16, 30), (22, 7), (14, 29), (34, 26), (35, 30), (12, 18), (16, 11), (10, 13), (23, 24), (26, 4), (25, 35), (16, 26), (18, 29), (6, 28), (26, 33), (6, 26), (7, 16), (19, 24), (35, 0), (15, 36), (35, 26), (0, 34), (10, 26), (20, 33), (35, 20), (11, 7), (33, 16), (0, 16), (8, 5), (25, 10), (19, 6), (17, 35), (12, 12), (13, 31), (8, 30), (28, 26), (18, 12), (2, 28), (3, 0), (30, 34), (28, 5), (5, 2), (1, 35), (30, 9), (25, 5), (18, 31), (31, 10), (4, 10), (23, 28), (17, 9), (11, 19), (18, 27), (3, 1), (20, 17), (26, 6), (18, 32), (5, 19), (10, 20), (18, 28), (34, 29), (5, 16), (27, 35), (9, 4), (18, 17), (24, 2), (16, 29), (32, 27), (20, 15), (20, 2), (13, 32), (4, 27), (20, 21), (4, 35), (28, 13), (33, 32), (4, 3), (26, 31), (27, 15), (18, 25), (14, 21), (19, 11), (25, 6), (9, 11), (6, 29), (16, 13), (19, 21), (32, 21), (15, 20), (11, 34), (7, 2), (29, 32), (31, 34), (21, 9), (5, 33), (20, 13), (32, 25), (1, 29), (24, 33), (12, 0), (16, 31), (26, 7), (4, 20), (10, 33), (0, 24), (13, 1), (29, 36), (33, 12), (22, 23), (6, 20), (19, 23), (24, 21), (19, 12), (35, 13), (8, 32), (16, 33), (7, 23), (26, 12), (2, 29), (3, 19), (15, 15), (21, 14), (4, 29), (9, 0), (0, 15), (1, 6), (7, 26), (7, 27), (24, 35), (12, 33), (9, 1), (34, 17), (12, 19), (2, 21), (27, 21), (26, 29), (31, 3), (7, 17), (14, 5), (24, 9), (0, 10), (3, 6), (30, 11), (21, 34), (15, 11), (13, 11), (18, 22), (28, 21), (33, 18), (12, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888576", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 17), (15, 26), (4, 0), (28, 23), (19, 1), (2, 17), (29, 15), (19, 10), (2, 25), (5, 22), (10, 19), (28, 19), (33, 17), (4, 14), (16, 15), (11, 15), (8, 24), (8, 19), (35, 7), (2, 22), (0, 23), (20, 5), (15, 8), (24, 12), (14, 1), (28, 22), (13, 1), (36, 13), (21, 26), (11, 25), (13, 9), (16, 29), (12, 15), (21, 11), (18, 25), (15, 20), (15, 11), (29, 8), (28, 7), (31, 18), (24, 14), (22, 19), (18, 18), (24, 18), (17, 2), (32, 2), (27, 22), (7, 26), (35, 5), (9, 12), (11, 22), (4, 11), (28, 16), (16, 2), (19, 17), (18, 17), (7, 7), (18, 19), (8, 15), (24, 28), (21, 14), (31, 25), (11, 13), (16, 28), (35, 20), (22, 12), (3, 10), (9, 18), (4, 15), (6, 3), (8, 2), (22, 26), (16, 7), (3, 8), (20, 27), (19, 5), (35, 18), (22, 4), (27, 10), (5, 4), (16, 12), (29, 17), (10, 5), (6, 24), (33, 12), (36, 15), (36, 2), (28, 3), (6, 19), (36, 16), (15, 1), (3, 25), (10, 7), (37, 5), (1, 22), (36, 17), (3, 9), (36, 14), (26, 12), (22, 27), (23, 25), (27, 16), (13, 20), (19, 9), (34, 1), (16, 14), (14, 27), (28, 17), (18, 29), (4, 19), (20, 0), (6, 7), (32, 11), (19, 21), (9, 10), (5, 17), (3, 19), (28, 15), (11, 17), (0, 27), (22, 25), (30, 12), (10, 11), (1, 19), (15, 15), (31, 3), (34, 26), (30, 20), (17, 3), (24, 16), (6, 4), (27, 1), (27, 23), (5, 15), (2, 26), (31, 6), (31, 21), (25, 23), (29, 19), (20, 12), (29, 2), (32, 22), (36, 25), (32, 17), (9, 15), (5, 18), (10, 17), (35, 24), (5, 2), (37, 18), (24, 1), (28, 10), (29, 5), (32, 29), (19, 19), (7, 1), (13, 13), (33, 3), (30, 24), (30, 6), (25, 18), (25, 22), (8, 12), (5, 8), (24, 21), (34, 21), (37, 26), (31, 13), (17, 13), (13, 17), (9, 2), (26, 7), (1, 3), (14, 8), (26, 28), (25, 9), (37, 7), (31, 11), (14, 7), (2, 20), (18, 15), (13, 24), (4, 2), (20, 15), (2, 19), (29, 12), (11, 16), (22, 7), (0, 13), (24, 22), (36, 22), (6, 22), (12, 9), (24, 5), (17, 11), (20, 2), (36, 4), (31, 28), (31, 1), (25, 25), (18, 11), (15, 28), (37, 14), (10, 0), (1, 27), (7, 21), (20, 18), (25, 26), (34, 25), (21, 19), (14, 22), (5, 26), (17, 7), (31, 26), (31, 2), (25, 7), (22, 24), (5, 5), (23, 4), (10, 4), (15, 2), (26, 13), (37, 12), (9, 5), (7, 27), (35, 16), (17, 12), (1, 26), (20, 7), (8, 3), (28, 25), (36, 12), (11, 26), (14, 28), (0, 14), (6, 2), (19, 29), (10, 20), (34, 15), (22, 29), (7, 16), (26, 10), (10, 23), (27, 29), (23, 19), (13, 23), (23, 10), (9, 14), (14, 25), (28, 8), (1, 6), (8, 18), (27, 25), (20, 16), (22, 9), (18, 12), (29, 22), (36, 18), (24, 15), (33, 14), (26, 1), (13, 15), (37, 0), (32, 14), (27, 5), (19, 2), (24, 2), (7, 22), (24, 9), (16, 23), (7, 8), (9, 24), (8, 29), (27, 2), (15, 6), (21, 15), (30, 18), (22, 18), (23, 0), (33, 16), (25, 16), (31, 27), (35, 27), (36, 11), (36, 3), (24, 27), (16, 1), (12, 24), (6, 18), (35, 17), (22, 3), (11, 23), (32, 5), (28, 9), (34, 4), (34, 11), (31, 14), (25, 6), (13, 27), (0, 5), (16, 17), (25, 13), (5, 12), (1, 0), (5, 24), (8, 11), (13, 19), (34, 14), (14, 21), (21, 21), (5, 19), (3, 14), (23, 5), (5, 20), (30, 15), (25, 17), (5, 6), (35, 29), (2, 12), (11, 20), (35, 22), (14, 12), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72000", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 7), (21, 22), (23, 33), (11, 15), (23, 23), (13, 7), (25, 3), (28, 1), (5, 27), (3, 22), (14, 13), (2, 3), (7, 24), (27, 22), (26, 16), (9, 19), (23, 13), (19, 16), (16, 13), (14, 5), (6, 8), (9, 22), (18, 23), (17, 14), (27, 32), (23, 3), (4, 33), (1, 16), (29, 7), (6, 32), (7, 10), (26, 0), (21, 10), (1, 18), (4, 31), (8, 5), (7, 0), (25, 11), (3, 19), (18, 27), (26, 24), (4, 23), (15, 6), (1, 23), (25, 34), (20, 5), (12, 34), (15, 28), (19, 23), (4, 21), (26, 30), (11, 19), (19, 0), (29, 32), (27, 11), (27, 28), (27, 7), (11, 7), (1, 22), (27, 20), (25, 9), (1, 19), (20, 6), (8, 25), (29, 31), (8, 1), (0, 9), (11, 13), (21, 5), (21, 6), (28, 16), (22, 6), (28, 17), (16, 14), (11, 33), (2, 19), (21, 21), (9, 23), (19, 31), (11, 27), (26, 13), (25, 21), (10, 5), (19, 21), (1, 34), (11, 23), (2, 29), (12, 8), (14, 1), (18, 0), (24, 25), (20, 29), (15, 29), (23, 17), (16, 5), (5, 7), (24, 23), (0, 30), (4, 17), (22, 28), (3, 16), (11, 25), (4, 10), (24, 22), (19, 26), (10, 11), (19, 5), (8, 23), (5, 22), (2, 25), (12, 20), (9, 15), (24, 17), (12, 19), (14, 2), (16, 15), (22, 27), (23, 0), (4, 18), (8, 24), (17, 32), (20, 22), (18, 25), (28, 15), (4, 15), (1, 28), (9, 2), (21, 23), (29, 34), (3, 7), (27, 29), (7, 2), (6, 14), (28, 34), (7, 1), (13, 31), (3, 3), (5, 10), (0, 12), (14, 32), (29, 17), (25, 12), (9, 16), (26, 6), (4, 22), (27, 23), (13, 12), (21, 34), (20, 17), (19, 1), (23, 30), (5, 32), (2, 34), (10, 25), (7, 34), (21, 33), (6, 7), (5, 8), (23, 5), (14, 26), (28, 27), (24, 12), (7, 4), (16, 33), (10, 6), (14, 3), (12, 1), (12, 32), (5, 35), (28, 4), (29, 3), (28, 26), (17, 17), (12, 6), (5, 26), (26, 10), (6, 13), (23, 27), (28, 10), (2, 23), (25, 33), (4, 1), (27, 8), (8, 9), (29, 22), (6, 3), (25, 7), (20, 13), (19, 13), (8, 33), (7, 20), (5, 6), (12, 26), (23, 19), (0, 22), (29, 5), (0, 20), (17, 2), (12, 27), (0, 32), (2, 14), (19, 18), (7, 5), (9, 3), (11, 5), (8, 12), (12, 11), (19, 2), (9, 27), (21, 17), (21, 35), (15, 24), (28, 20), (0, 18), (3, 31), (1, 27), (10, 17), (25, 25), (4, 3), (17, 26), (8, 6), (18, 31), (0, 11), (22, 29), (23, 26), (0, 17), (1, 2), (1, 31), (10, 33), (16, 6), (6, 12), (19, 3), (23, 9), (14, 6), (0, 7), (21, 31), (27, 17), (20, 4), (11, 29), (9, 30), (18, 10), (21, 30), (17, 16), (6, 0), (19, 11), (10, 16), (21, 15), (9, 6), (20, 19), (11, 17), (14, 17), (11, 8), (7, 25), (15, 18), (18, 24), (2, 24), (13, 20), (12, 22), (13, 23), (19, 32), (20, 2), (4, 16), (21, 0), (12, 9), (5, 12), (4, 8), (5, 34), (24, 29), (15, 11), (23, 4), (18, 26), (8, 29), (3, 17), (4, 26), (2, 20), (24, 5), (28, 28), (13, 17), (15, 3), (1, 5), (11, 0), (21, 16), (6, 2), (14, 27), (17, 13), (27, 12), (13, 22), (26, 20), (23, 22), (29, 14), (21, 11), (23, 11), (2, 21), (21, 7), (6, 25), (9, 26), (4, 24), (27, 2), (6, 22), (2, 31), (29, 28), (14, 12), (13, 28), (13, 33), (9, 31), (3, 13), (25, 15), (16, 19), (29, 15), (2, 27), (12, 2), (11, 31), (0, 16), (22, 35), (22, 19), (2, 26), (23, 15), (3, 33), (12, 18), (3, 30), (23, 31), (12, 15), (20, 11), (26, 29), (24, 7), (5, 23), (16, 8), (27, 26), (3, 1), (1, 14), (16, 7), (9, 0), (14, 31), (2, 22), (1, 9), (15, 0), (19, 29), (7, 18), (26, 23), (4, 34), (13, 30), (13, 10), (8, 15), (1, 30), (2, 35), (0, 5), (6, 27), (8, 20), (17, 4), (8, 11), (6, 26), (7, 3), (29, 25), (25, 17), (2, 1), (7, 12), (8, 30), (7, 14), (9, 4), (6, 9), (22, 2), (17, 21), (28, 8), (26, 5), (9, 12), (15, 34), (10, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752328", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (7, 9), (19, 24), (34, 31), (11, 18), (34, 32), (2, 22), (11, 30), (12, 7), (25, 7), (27, 22), (26, 32), (24, 10), (7, 4), (9, 17), (16, 17), (0, 2), (5, 22), (28, 10), (16, 3), (31, 21), (10, 8), (26, 31), (4, 28), (18, 18), (8, 24), (4, 14), (37, 17), (1, 22), (21, 10), (25, 29), (19, 1), (30, 2), (34, 4), (28, 21), (22, 23), (29, 20), (3, 14), (20, 18), (15, 20), (3, 15), (37, 31), (34, 23), (8, 2), (32, 18), (35, 21), (22, 20), (1, 16), (9, 13), (37, 14), (2, 13), (18, 31), (7, 28), (0, 7), (8, 30), (0, 24), (33, 15), (17, 14), (34, 19), (21, 12), (29, 32), (22, 12), (4, 15), (32, 29), (34, 14), (11, 11), (29, 25), (15, 8), (15, 18), (19, 32), (37, 7), (22, 19), (14, 24), (36, 19), (32, 22), (35, 32), (33, 6), (30, 17), (25, 3), (1, 4), (14, 22), (35, 4), (23, 16), (9, 27), (27, 11), (26, 1), (12, 5), (21, 1), (21, 22), (8, 3), (28, 3), (5, 1), (4, 13), (32, 7), (0, 1), (29, 16), (7, 22), (8, 11), (3, 7), (24, 29), (21, 25), (22, 4), (32, 19), (32, 28), (1, 19), (17, 25), (26, 28), (5, 18), (21, 18), (4, 3), (2, 2), (2, 17), (30, 16), (4, 12), (23, 15), (20, 29), (10, 11), (10, 16), (36, 12), (28, 19), (29, 9), (9, 30), (2, 0), (33, 13), (23, 19), (27, 20), (3, 18), (0, 3), (37, 6), (0, 5), (33, 21), (6, 2), (13, 21), (34, 2), (37, 28), (14, 29), (16, 12), (10, 14), (31, 6), (34, 0), (10, 7), (16, 1), (8, 17), (4, 11), (17, 17), (21, 23), (32, 30), (11, 8), (24, 23), (21, 2), (4, 20), (4, 30), (2, 14), (35, 6), (19, 31), (23, 10), (21, 27), (1, 20), (29, 23), (35, 23), (1, 27), (18, 8), (36, 5), (33, 23), (30, 15), (13, 3), (3, 29), (36, 4), (22, 7), (28, 6), (2, 19), (35, 24), (34, 24), (33, 30), (11, 27), (7, 13), (7, 6), (5, 23), (11, 32), (24, 12), (36, 24), (4, 24), (37, 4), (33, 10), (28, 4), (12, 32), (33, 5), (14, 17), (23, 32), (27, 16), (7, 23), (17, 7), (35, 19), (31, 25), (18, 30), (31, 11), (32, 10), (29, 2), (24, 19), (28, 18), (35, 16), (25, 23), (31, 10), (5, 26), (10, 13), (29, 13), (22, 27), (9, 10), (20, 21), (30, 9), (0, 9), (5, 7), (15, 30), (16, 13), (20, 15), (16, 25), (4, 10), (21, 28), (13, 12), (34, 25), (20, 1), (15, 22), (16, 14), (13, 22), (5, 24), (23, 0), (3, 17), (13, 17), (30, 32), (12, 31), (9, 18), (36, 0), (11, 0), (8, 15), (34, 21), (7, 26), (31, 8), (15, 0), (5, 13), (37, 26), (1, 2), (13, 30), (3, 31), (5, 25), (4, 0), (20, 30), (37, 25), (2, 29), (6, 3), (26, 24), (33, 25), (19, 15), (26, 19), (12, 6), (29, 28), (26, 21), (33, 3), (21, 6), (13, 16), (37, 12), (22, 8), (6, 19), (15, 14), (19, 18), (31, 32), (26, 4), (21, 3), (16, 27), (18, 22), (7, 3), (4, 31), (30, 12), (5, 16), (34, 6), (8, 25), (17, 20), (6, 31), (26, 14), (37, 9), (17, 30), (14, 9), (4, 7), (17, 31), (33, 29), (30, 10), (2, 10), (18, 6), (19, 19), (28, 5), (8, 7), (30, 5), (13, 7), (22, 11), (13, 31), (19, 12), (10, 26), (6, 27), (37, 2), (30, 28), (29, 31), (6, 11), (14, 11), (15, 11), (32, 25), (0, 11), (2, 28), (26, 6), (25, 19), (25, 26), (15, 3), (27, 12), (15, 19), (2, 24), (32, 21), (33, 19), (30, 25), (15, 17), (6, 5), (31, 22), (23, 8), (30, 24), (19, 0), (27, 10), (16, 10), (3, 20), (4, 26), (6, 12), (19, 25), (24, 24), (1, 28), (12, 1), (21, 19), (22, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680064", "dataset": "MATH"}
{"messages": [{"content": "In a 38x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 12), (10, 23), (33, 20), (26, 9), (33, 30), (24, 27), (0, 22), (17, 29), (33, 27), (35, 18), (31, 29), (19, 18), (13, 29), (2, 30), (32, 3), (14, 19), (37, 22), (28, 2), (30, 2), (7, 4), (24, 5), (22, 29), (36, 20), (25, 7), (35, 16), (28, 21), (24, 25), (35, 9), (6, 3), (14, 12), (9, 7), (4, 7), (9, 22), (0, 16), (29, 4), (23, 9), (31, 4), (20, 1), (20, 7), (27, 18), (21, 17), (8, 30), (30, 9), (31, 6), (32, 28), (11, 8), (9, 11), (33, 8), (16, 21), (12, 26), (14, 16), (35, 7), (25, 28), (7, 17), (5, 4), (5, 20), (28, 14), (8, 12), (9, 2), (17, 22), (11, 5), (2, 8), (29, 24), (25, 23), (32, 19), (32, 26), (1, 22), (26, 5), (11, 14), (34, 9), (8, 20), (9, 4), (25, 8), (28, 31), (15, 29), (14, 15), (18, 12), (28, 9), (12, 23), (37, 16), (12, 14), (14, 5), (1, 17), (11, 17), (11, 19), (33, 2), (14, 13), (9, 6), (35, 21), (34, 16), (27, 3), (27, 31), (6, 5), (14, 26), (28, 5), (28, 19), (0, 24), (33, 31), (2, 18), (29, 20), (33, 17), (34, 10), (5, 26), (35, 23), (10, 18), (20, 31), (34, 20), (18, 18), (0, 28), (0, 17), (32, 30), (33, 25), (11, 18), (28, 11), (5, 27), (35, 8), (23, 16), (16, 9), (19, 22), (4, 21), (30, 11), (0, 9), (16, 30), (6, 20), (12, 25), (13, 18), (10, 5), (3, 7), (4, 14), (13, 25), (23, 21), (17, 14), (2, 19), (20, 22), (7, 3), (7, 24), (13, 12), (18, 14), (23, 1), (6, 29), (28, 28), (6, 31), (12, 12), (20, 20), (14, 18), (36, 0), (31, 24), (0, 18), (21, 5), (5, 22), (7, 31), (17, 17), (34, 0), (21, 24), (21, 16), (28, 0), (18, 2), (1, 0), (27, 10), (10, 19), (13, 4), (23, 7), (19, 14), (16, 20), (34, 4), (15, 24), (28, 12), (14, 31), (10, 10), (30, 1), (34, 6), (8, 4), (32, 21), (18, 8), (4, 26), (10, 7), (19, 0), (30, 18), (3, 10), (25, 2), (31, 15), (10, 27), (7, 23), (37, 12), (13, 23), (8, 1), (4, 19), (13, 9), (36, 15), (28, 29), (13, 8), (32, 9), (13, 21), (20, 5), (18, 10), (19, 16), (13, 19), (23, 25), (8, 23), (9, 14), (12, 1), (24, 6), (14, 0), (15, 28), (14, 14), (37, 4), (22, 6), (3, 17), (19, 8), (15, 2), (10, 22), (27, 11), (17, 20), (37, 23), (23, 19), (13, 28), (29, 22), (19, 11), (2, 25), (27, 4), (33, 21), (16, 15), (15, 19), (0, 4), (5, 3), (20, 11), (34, 12), (17, 13), (23, 0), (31, 13), (13, 20), (37, 14), (23, 24), (24, 7), (12, 7), (33, 28), (10, 16), (0, 8), (9, 1), (36, 9), (33, 10), (24, 19), (34, 7), (1, 29), (16, 27), (26, 12), (2, 27), (6, 11), (30, 20), (37, 9), (2, 17), (21, 4), (7, 19), (18, 16), (10, 28), (8, 26), (29, 14), (36, 11), (18, 9), (36, 26), (18, 0), (36, 1), (31, 23), (26, 14), (2, 24), (25, 30), (34, 24), (8, 13), (24, 13), (16, 0), (3, 8), (32, 24), (5, 31), (27, 13), (4, 23), (7, 10), (15, 23), (18, 7), (1, 4), (25, 5), (13, 24), (4, 1), (1, 2), (4, 3), (1, 9), (12, 9), (4, 27), (15, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "918896", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (20, 24), (13, 22), (8, 23), (31, 19), (10, 35), (0, 29), (13, 20), (32, 21), (18, 11), (25, 22), (4, 23), (23, 18), (31, 33), (24, 14), (5, 15), (27, 35), (1, 12), (29, 8), (0, 4), (19, 20), (3, 26), (14, 6), (34, 17), (29, 34), (1, 14), (18, 17), (9, 3), (2, 24), (28, 22), (25, 2), (15, 24), (4, 15), (8, 3), (34, 20), (23, 13), (1, 32), (24, 19), (30, 11), (20, 4), (28, 18), (10, 36), (31, 2), (22, 19), (19, 36), (17, 0), (33, 18), (14, 22), (21, 27), (12, 29), (27, 22), (33, 23), (17, 11), (16, 3), (23, 5), (22, 2), (13, 17), (29, 35), (5, 29), (5, 33), (23, 17), (33, 7), (6, 6), (5, 16), (22, 4), (16, 24), (25, 31), (32, 6), (13, 18), (19, 35), (30, 8), (12, 5), (22, 33), (13, 21), (27, 32), (10, 19), (18, 36), (4, 9), (30, 2), (32, 14), (21, 5), (34, 31), (3, 10), (22, 0), (22, 11), (3, 23), (15, 26), (14, 3), (30, 7), (18, 12), (26, 2), (34, 4), (7, 12), (29, 29), (8, 8), (26, 14), (31, 18), (33, 24), (12, 24), (30, 26), (9, 11), (10, 21), (9, 17), (33, 34), (19, 33), (23, 3), (14, 4), (10, 14), (15, 18), (1, 9), (16, 7), (8, 18), (21, 25), (17, 13), (2, 21), (18, 23), (17, 32), (20, 3), (9, 19), (11, 5), (17, 25), (24, 11), (24, 12), (27, 9), (28, 24), (12, 0), (2, 18), (12, 26), (6, 19), (5, 36), (30, 29), (3, 8), (0, 9), (14, 30), (28, 13), (24, 5), (1, 6), (4, 6), (33, 2), (29, 10), (34, 0), (8, 22), (25, 27), (19, 25), (11, 0), (18, 2), (8, 12), (18, 19), (11, 34), (2, 0), (18, 27), (27, 5), (23, 10), (23, 27), (0, 7), (6, 4), (34, 34), (24, 23), (28, 31), (13, 12), (12, 19), (28, 9), (10, 30), (16, 17), (32, 1), (34, 23), (15, 1), (29, 3), (20, 7), (16, 29), (33, 19), (17, 3), (8, 21), (33, 11), (3, 2), (26, 19), (32, 31), (27, 3), (27, 28), (22, 8), (10, 23), (16, 18), (20, 1), (29, 16), (10, 5), (11, 35), (29, 7), (12, 25), (3, 19), (12, 31), (0, 11), (1, 35), (14, 24), (3, 36), (19, 22), (15, 9), (7, 7), (17, 1), (13, 33), (18, 13), (5, 32), (20, 20), (32, 25), (12, 21), (22, 3), (7, 33), (34, 13), (29, 31), (6, 8), (5, 21), (26, 16), (24, 16), (32, 9), (5, 24), (7, 1), (0, 2), (12, 11), (6, 18), (31, 22), (27, 12), (17, 8), (14, 10), (30, 3), (18, 32), (10, 24), (14, 15), (7, 3), (23, 21), (14, 27), (11, 2), (22, 23), (12, 10), (25, 25), (14, 11), (29, 36), (15, 16), (32, 8), (13, 16), (10, 28), (20, 12), (25, 21), (32, 15), (11, 13), (3, 27), (26, 15), (1, 17), (12, 3), (11, 24), (3, 1), (13, 30), (16, 19), (9, 12), (9, 26), (31, 1), (25, 3), (12, 28), (21, 8), (25, 14), (28, 4), (33, 15), (19, 9), (26, 29), (7, 4), (30, 20), (29, 20), (5, 27), (26, 6), (21, 1), (11, 29), (3, 33), (12, 7), (1, 25), (8, 36), (8, 16), (8, 24), (22, 27), (3, 3), (9, 30), (19, 14), (24, 32), (10, 17), (9, 15), (20, 34), (11, 11), (18, 30), (21, 32), (3, 31), (15, 4), (24, 9), (0, 15), (12, 33), (21, 21), (23, 4), (21, 28), (28, 3), (12, 30), (0, 12), (6, 17), (25, 5), (10, 6), (28, 21), (5, 34), (24, 29), (32, 3), (24, 21), (3, 11), (0, 28), (6, 25), (26, 12), (8, 28), (21, 20), (16, 36), (14, 31), (18, 28), (30, 32), (4, 8), (9, 20), (31, 26), (33, 27), (3, 14), (9, 25), (24, 31), (12, 36), (9, 34), (10, 29), (15, 35), (33, 26), (34, 1), (15, 33), (9, 10), (3, 13), (17, 36), (19, 1), (13, 31), (17, 20), (3, 18), (32, 22), (14, 5), (12, 6), (26, 1), (19, 17), (3, 12), (14, 35), (25, 28), (5, 35), (21, 10), (33, 0), (14, 20), (2, 6), (22, 30), (9, 1), (12, 16), (15, 13), (30, 4), (23, 36), (31, 35), (33, 21), (34, 30), (15, 36), (34, 19), (25, 13), (5, 12), (8, 13), (15, 21), (10, 3), (31, 4), (33, 20), (25, 35), (22, 17), (15, 34), (6, 7), (6, 9), (27, 6), (22, 16), (4, 7), (0, 27), (28, 15), (26, 34), (8, 29), (0, 3), (26, 5), (22, 15), (2, 11), (28, 26), (17, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "694212", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (32, 13), (30, 14), (2, 17), (23, 3), (35, 9), (32, 19), (9, 0), (30, 3), (21, 12), (19, 28), (22, 22), (16, 2), (33, 16), (22, 0), (21, 5), (26, 9), (24, 32), (22, 15), (13, 10), (8, 2), (23, 26), (11, 8), (2, 24), (30, 27), (18, 19), (2, 23), (5, 28), (8, 31), (21, 0), (16, 4), (17, 9), (29, 20), (20, 24), (3, 30), (2, 12), (36, 18), (5, 16), (19, 10), (9, 13), (22, 13), (6, 29), (33, 28), (0, 1), (17, 27), (16, 28), (16, 6), (31, 7), (28, 18), (22, 33), (17, 16), (1, 25), (6, 10), (25, 21), (28, 6), (13, 33), (29, 11), (34, 20), (26, 31), (37, 27), (5, 25), (15, 17), (34, 28), (35, 6), (38, 30), (30, 9), (1, 11), (33, 26), (30, 19), (37, 25), (1, 23), (11, 26), (38, 23), (35, 1), (9, 24), (2, 33), (11, 5), (30, 29), (13, 0), (25, 33), (2, 3), (25, 13), (36, 28), (3, 25), (38, 7), (26, 3), (13, 23), (18, 21), (38, 16), (36, 10), (20, 21), (13, 16), (30, 15), (23, 22), (27, 15), (4, 8), (19, 8), (10, 20), (11, 0), (12, 28), (19, 14), (1, 17), (9, 10), (25, 15), (7, 6), (15, 9), (0, 21), (4, 31), (5, 31), (3, 26), (27, 21), (3, 27), (24, 30), (1, 5), (4, 0), (13, 5), (17, 5), (0, 9), (22, 27), (25, 6), (19, 9), (23, 11), (18, 28), (14, 1), (35, 25), (25, 29), (14, 13), (5, 29), (23, 16), (13, 18), (32, 24), (8, 8), (8, 30), (32, 27), (11, 11), (22, 10), (18, 8), (30, 20), (36, 16), (2, 19), (6, 19), (35, 15), (24, 14), (11, 3), (15, 18), (8, 27), (23, 24), (27, 13), (33, 33), (2, 18), (37, 13), (15, 32), (15, 29), (0, 33), (34, 24), (14, 19), (27, 32), (31, 4), (21, 27), (36, 25), (31, 24), (34, 13), (12, 19), (35, 28), (11, 21), (1, 3), (14, 32), (8, 12), (30, 24), (7, 21), (11, 18), (21, 7), (24, 19), (38, 4), (35, 12), (38, 29), (23, 29), (22, 9), (7, 2), (0, 17), (23, 20), (9, 30), (36, 7), (20, 18), (1, 30), (12, 24), (34, 15), (15, 11), (22, 25), (10, 15), (16, 13), (7, 4), (20, 7), (19, 19), (16, 27), (3, 33), (25, 22), (19, 3), (11, 17), (10, 16), (23, 15), (3, 21), (6, 11), (29, 7), (12, 14), (21, 30), (29, 33), (0, 3), (36, 19), (29, 26), (10, 25), (35, 10), (23, 32), (3, 4), (28, 1), (32, 12), (10, 31), (15, 24), (12, 30), (27, 17), (23, 25), (5, 24), (12, 8), (17, 8), (21, 22), (34, 27), (29, 16), (25, 9), (7, 0), (32, 2), (10, 26), (13, 2), (26, 28), (26, 29), (35, 22), (34, 8), (16, 33), (26, 2), (5, 5), (14, 8), (12, 18), (22, 12), (27, 29), (14, 22), (29, 24), (29, 14), (21, 32), (23, 23), (26, 1), (7, 8), (20, 1), (10, 9), (31, 6), (37, 28), (34, 3), (22, 11), (16, 3), (0, 25), (24, 24), (24, 16), (9, 21), (32, 23), (34, 7), (37, 31), (5, 11), (30, 0), (8, 28), (25, 25), (9, 28), (4, 9), (21, 8), (15, 15), (8, 20), (16, 5), (29, 0), (19, 29), (35, 18), (28, 3), (0, 5), (17, 33), (36, 1), (9, 7), (6, 8), (21, 16), (12, 11), (8, 5), (30, 28), (32, 10), (16, 10), (2, 31), (30, 6), (38, 12), (29, 5), (27, 11), (20, 9), (6, 20), (21, 17), (5, 30), (4, 13), (15, 22), (3, 20), (10, 22), (29, 32), (21, 21), (1, 24), (34, 11), (8, 9), (9, 23), (18, 26), (18, 10), (29, 29), (20, 0), (0, 30), (6, 30), (13, 14), (28, 30), (35, 16), (17, 4), (34, 25), (6, 6), (8, 25), (14, 33), (38, 1), (20, 8), (3, 12), (8, 29), (36, 11), (27, 33), (19, 22), (18, 9), (34, 0), (36, 12), (2, 30), (15, 0), (11, 33), (20, 6), (21, 9), (16, 8), (10, 5), (31, 3), (17, 29), (9, 4), (34, 6), (7, 28), (14, 16), (27, 8), (34, 18), (32, 5), (2, 25), (25, 7), (38, 19), (18, 12), (9, 14), (28, 33), (18, 29), (9, 9), (12, 21), (20, 22), (25, 4), (12, 15), (7, 5), (10, 1), (22, 18), (23, 28), (4, 29), (8, 23), (4, 24), (16, 9), (18, 15), (3, 24), (7, 29), (4, 6), (37, 20), (21, 19), (33, 19), (29, 21), (7, 22), (28, 12), (25, 2), (5, 13), (32, 30), (31, 15), (32, 14), (14, 7), (1, 20), (18, 23), (38, 0), (5, 26), (10, 6), (36, 6), (12, 17), (0, 20), (5, 9), (25, 10), (16, 21), (0, 19), (38, 31), (37, 2), (34, 9), (35, 20), (9, 15), (31, 33), (35, 29), (6, 26), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547128", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), 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), (25, 11), (24, 16), (3, 29), (7, 27), (14, 15), (2, 25), (4, 26), (3, 13), (15, 28), (22, 0), (31, 17), (26, 14), (12, 1), (18, 15), (27, 3), (16, 5), (30, 5), (13, 17), (15, 6), (17, 15), (11, 16), (12, 20), (0, 19), (22, 19), (11, 22), (24, 12), (19, 2), (31, 26), (24, 9), (0, 1), (30, 23), (16, 15), (18, 24), (13, 26), (10, 21), (31, 10), (4, 10), (7, 30), (11, 3), (4, 30), (4, 4), (9, 22), (21, 10), (15, 8), (23, 21), (15, 31), (28, 5), (2, 26), (26, 5), (4, 18), (8, 14), (22, 31), (4, 9), (22, 18), (12, 17), (26, 21), (22, 6), (0, 22), (23, 10), (12, 31), (28, 29), (0, 14), (16, 18), (9, 26), (30, 18), (6, 11), (12, 4), (28, 0), (6, 24), (30, 17), (0, 28), (3, 20), (2, 27), (28, 27), (32, 16), (1, 2), (21, 2), (9, 30), (25, 18), (29, 26), (8, 8), (7, 18), (29, 23), (26, 3), (1, 7), (0, 31), (19, 28), (14, 25), (28, 23), (25, 9), (20, 0), (6, 20), (15, 18), (7, 22), (19, 30), (26, 24), (10, 22), (7, 2), (21, 25), (8, 24), (15, 2), (15, 11), (27, 21), (17, 9), (7, 3), (2, 28), (27, 22), (9, 0), (30, 26), (30, 22), (3, 27), (18, 20), (18, 3), (22, 15), (5, 10), (6, 0), (10, 29), (19, 8), (2, 21), (11, 13), (8, 5), (5, 27), (12, 3), (8, 18), (29, 14), (20, 7), (21, 26), (11, 12), (18, 10), (13, 10), (17, 18), (32, 28), (26, 2), (15, 4), (24, 28), (26, 6), (19, 5), (5, 16), (32, 2), (3, 17), (24, 29), (29, 5), (25, 3), (7, 28), (31, 3), (27, 10), (4, 12), (31, 1), (27, 15), (27, 24), (7, 6), (26, 12), (26, 8), (18, 28), (17, 23), (32, 30), (8, 20), (18, 27), (22, 22), (6, 13), (27, 17), (22, 9), (30, 4), (32, 19), (6, 25), (16, 2), (14, 17), (3, 25), (14, 13), (15, 13), (0, 10), (13, 28), (23, 18), (26, 0), (19, 18), (6, 3), (5, 18), (9, 3), (5, 29), (13, 14), (10, 6), (16, 25), (23, 12), (8, 19), (29, 30), (32, 10), (8, 17), (31, 9), (11, 26), (9, 14), (11, 25), (27, 14), (14, 21), (24, 14), (1, 17), (9, 21), (7, 26), (14, 12), (6, 30), (21, 9), (1, 12), (23, 24), (23, 28), (4, 7), (6, 29), (8, 9), (30, 16), (22, 1), (28, 16), (8, 10), (31, 30), (20, 26), (11, 20), (32, 0), (29, 3), (25, 20), (8, 12), (4, 5), (19, 6), (31, 21), (22, 8), (6, 16), (6, 9), (4, 0), (5, 9), (2, 8), (1, 9), (8, 23), (13, 15), (18, 22), (9, 7), (4, 28), (30, 27), (17, 22), (11, 1), (4, 13), (23, 14), (31, 25), (24, 25), (10, 19), (11, 31), (0, 4), (13, 22), (7, 9), (24, 21), (14, 23), (10, 17), (23, 25), (21, 6), (19, 25), (29, 20), (11, 15), (30, 28), (29, 27), (23, 27), (11, 6), (1, 24), (29, 24), (21, 12), (18, 25), (25, 4), (16, 31), (28, 22), (7, 5), (32, 3), (12, 25), (15, 17), (10, 13), (20, 6), (21, 8), (4, 29), (5, 24), (3, 24), (8, 30), (16, 11), (31, 8), (23, 8), (18, 21), (18, 16), (18, 18), (22, 17), (28, 12), (14, 2), (19, 10), (15, 20), (8, 26), (7, 14), (25, 30), (18, 11), (18, 14), (13, 16), (14, 10), (0, 11), (7, 1), (25, 0), (25, 16), (0, 15), (22, 29), (30, 21), (0, 29), (21, 24), (17, 17), (21, 11), (16, 30), (18, 1), (29, 18), (25, 25), (5, 21), (22, 16), (3, 26), (17, 31), (20, 11), (30, 11), (31, 22), (12, 29), (4, 22), (30, 9), (28, 19), (7, 13), (17, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339120", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (20, 17), (0, 23), (14, 29), (17, 8), (11, 0), (32, 28), (27, 17), (26, 14), (7, 21), (3, 21), (16, 15), (7, 14), (3, 35), (6, 24), (19, 30), (34, 27), (26, 1), (27, 18), (23, 30), (24, 27), (29, 17), (28, 0), (1, 2), (24, 33), (31, 17), (3, 17), (21, 29), (21, 31), (5, 22), (26, 8), (13, 30), (9, 14), (17, 34), (17, 17), (29, 23), (32, 7), (26, 23), (9, 29), (7, 3), (20, 22), (11, 5), (19, 34), (30, 31), (8, 17), (34, 8), (22, 1), (31, 28), (3, 15), (33, 24), (27, 23), (32, 8), (34, 30), (5, 2), (18, 31), (14, 16), (23, 11), (7, 13), (2, 21), (29, 18), (24, 23), (14, 28), (8, 4), (13, 5), (19, 19), (31, 20), (28, 24), (6, 23), (3, 32), (2, 13), (10, 27), (24, 18), (5, 15), (15, 22), (2, 1), (15, 3), (31, 31), (5, 36), (22, 7), (6, 15), (6, 30), (12, 22), (20, 30), (18, 3), (34, 26), (6, 2), (10, 18), (28, 9), (0, 11), (32, 9), (21, 5), (33, 0), (4, 23), (12, 30), (1, 35), (9, 35), (32, 30), (5, 33), (13, 28), (5, 18), (16, 23), (20, 7), (10, 15), (11, 25), (4, 26), (9, 15), (5, 26), (22, 35), (29, 35), (3, 6), (25, 11), (4, 34), (1, 20), (2, 2), (15, 20), (29, 7), (28, 28), (15, 27), (16, 19), (29, 9), (16, 3), (19, 0), (34, 28), (11, 23), (8, 33), (20, 16), (25, 12), (27, 6), (17, 16), (10, 12), (9, 23), (25, 25), (25, 15), (9, 25), (34, 24), (33, 21), (28, 2), (18, 2), (19, 7), (7, 29), (19, 6), (10, 36), (8, 29), (32, 16), (31, 27), (22, 33), (10, 8), (7, 35), (26, 18), (26, 4), (2, 15), (15, 23), (12, 21), (8, 8), (30, 36), (0, 5), (14, 18), (22, 30), (1, 32), (11, 34), (6, 13), (18, 4), (24, 6), (3, 9), (0, 6), (9, 10), (8, 26), (30, 35), (27, 7), (31, 0), (32, 19), (4, 22), (13, 25), (9, 9), (26, 33), (13, 1), (26, 10), (5, 13), (2, 27), (31, 9), (19, 1), (5, 9), (19, 27), (29, 24), (11, 11), (3, 22), (16, 4), (18, 28), (13, 34), (20, 0), (2, 16), (14, 4), (10, 21), (10, 22), (15, 1), (13, 18), (12, 10), (22, 18), (14, 17), (10, 3), (29, 29), (31, 4), (31, 25), (2, 28), (25, 2), (32, 22), (33, 3), (12, 29), (18, 17), (27, 16), (9, 16), (29, 36), (1, 33), (2, 9), (6, 25), (34, 22), (34, 5), (31, 21), (13, 22), (3, 23), (15, 6), (27, 26), (30, 3), (30, 4), (28, 11), (21, 14), (31, 3), (22, 11), (34, 13), (20, 12), (19, 28), (6, 11), (11, 8), (33, 2), (14, 31), (26, 11), (3, 31), (16, 22), (1, 22), (29, 33), (19, 31), (34, 7), (28, 10), (3, 0), (26, 27), (7, 34), (3, 16), (9, 3), (9, 12), (22, 6), (13, 10), (20, 36), (31, 10), (17, 36), (5, 11), (33, 20), (12, 26), (4, 16), (12, 31), (34, 16), (26, 35), (2, 20), (6, 28), (23, 25), (7, 1), (5, 35), (22, 9), (9, 17), (25, 26), (15, 21), (12, 2), (25, 34), (19, 13), (31, 26), (11, 33), (17, 20), (18, 16), (23, 36), (1, 9), (24, 9), (29, 1), (20, 5), (29, 25), (26, 28), (4, 4), (34, 12), (34, 3), (25, 10), (28, 18), (33, 18), (6, 22), (31, 8), (7, 10), (6, 32), (25, 20), (9, 1), (10, 17), (34, 10), (20, 26), (9, 13), (22, 36), (10, 13), (2, 25), (25, 0), (1, 34), (24, 7), (14, 24), (11, 9), (0, 31), (10, 19), (12, 23), (27, 11), (1, 17), (3, 13), (27, 29), (16, 12), (4, 20), (11, 26), (6, 36), (13, 4), (12, 33), (7, 26), (13, 27), (19, 33), (29, 14), (3, 5), (8, 9), (27, 36), (19, 22), (16, 10), (9, 0), (20, 25), (2, 11), (19, 2), (24, 17), (4, 12), (32, 31), (26, 36), (29, 20), (25, 4), (10, 5), (16, 8), (30, 22), (22, 5), (5, 7), (27, 15), (6, 18), (28, 13), (2, 18), (11, 10), (11, 2), (25, 23), (22, 13), (13, 36), (1, 29), (13, 6), (34, 17), (28, 20), (13, 31), (14, 7), (33, 26), (1, 13), (32, 17), (21, 16), (7, 11), (14, 12), (25, 5), (17, 26), (3, 26), (4, 29), (21, 13), (5, 19), (6, 4), (25, 9), (28, 29), (11, 30), (16, 26), (2, 33), (7, 18), (7, 17), (33, 14), (16, 36), (21, 17), (31, 14), (26, 25), (7, 7), (9, 27), (12, 14), (28, 19), (29, 10), (18, 6), (21, 4), (27, 19), (15, 12), (7, 19), (30, 18), (8, 1), (23, 21), (33, 16), (14, 32), (10, 9), (7, 27), (17, 6), (4, 36), (0, 10), (6, 6), (1, 31), (26, 26), (32, 23), (20, 2), (17, 18), (22, 31), (32, 11), (3, 18), (22, 34), (21, 7), (1, 16), (14, 10), (1, 23), (9, 18), (27, 32), (25, 29), (7, 15), (34, 21), (12, 28), (3, 14), (7, 6), (15, 18), (0, 13), (2, 32), (22, 19), (11, 1), (26, 29), (2, 24), (29, 12), (31, 5), (25, 3), (5, 10), (19, 12), (16, 14), (2, 29), (31, 1), (33, 27), (14, 33), (12, 19), (21, 0), (15, 31), (5, 30), (28, 1), (29, 32), (26, 3), (24, 2), (15, 16), (25, 14), (11, 29), (23, 2), (12, 0), (10, 24), (27, 10), (3, 30), (32, 32), (30, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "207900", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 10), (3, 21), (18, 20), (2, 32), (16, 31), (24, 24), (18, 7), (10, 11), (27, 17), (12, 28), (5, 3), (25, 6), (27, 2), (8, 3), (9, 2), (24, 2), (27, 33), (11, 37), (2, 23), (22, 13), (15, 28), (11, 8), (16, 33), (13, 13), (16, 16), (2, 7), (18, 12), (18, 19), (21, 29), (4, 10), (5, 35), (25, 26), (9, 27), (24, 14), (7, 29), (9, 37), (16, 36), (2, 5), (12, 15), (24, 18), (4, 36), (17, 33), (21, 21), (27, 22), (29, 36), (2, 27), (19, 14), (26, 15), (6, 4), (1, 26), (18, 34), (10, 16), (0, 22), (8, 8), (6, 26), (17, 4), (7, 1), (6, 30), (9, 7), (1, 8), (19, 36), (24, 17), (0, 19), (1, 34), (28, 13), (7, 13), (26, 37), (23, 1), (25, 31), (2, 14), (3, 8), (5, 7), (2, 24), (20, 20), (25, 13), (27, 5), (20, 31), (29, 26), (23, 8), (29, 16), (2, 8), (2, 22), (26, 29), (15, 22), (7, 23), (22, 16), (23, 27), (16, 35), (5, 20), (23, 15), (14, 23), (26, 13), (16, 7), (24, 36), (29, 18), (12, 34), (7, 32), (0, 27), (6, 35), (1, 14), (26, 35), (19, 24), (10, 35), (29, 22), (5, 33), (11, 31), (11, 13), (14, 29), (16, 15), (24, 16), (26, 23), (10, 27), (12, 37), (8, 27), (16, 8), (0, 32), (14, 16), (14, 33), (13, 16), (8, 18), (21, 4), (1, 30), (2, 0), (0, 15), (0, 31), (13, 9), (28, 29), (7, 7), (12, 22), (3, 10), (3, 22), (18, 1), (3, 7), (22, 10), (29, 34), (22, 1), (10, 9), (9, 25), (28, 27), (29, 35), (19, 28), (5, 24), (21, 15), (13, 3), (3, 16), (20, 16), (7, 22), (21, 0), (24, 12), (10, 25), (28, 9), (13, 19), (9, 0), (16, 6), (24, 23), (17, 35), (25, 1), (27, 1), (11, 34), (16, 0), (11, 3), (10, 18), (23, 30), (9, 32), (17, 16), (20, 25), (19, 26), (24, 34), (17, 27), (17, 0), (10, 3), (27, 15), (18, 16), (17, 34), (14, 4), (15, 13), (14, 2), (29, 25), (10, 34), (2, 6), (9, 24), (5, 10), (9, 13), (16, 1), (17, 28), (11, 6), (9, 17), (16, 19), (23, 35), (23, 33), (26, 8), (15, 0), (14, 3), (23, 12), (13, 37), (17, 29), (24, 9), (18, 0), (20, 15), (22, 36), (23, 10), (6, 17), (26, 27), (8, 23), (12, 9), (0, 18), (28, 24), (4, 5), (6, 14), (7, 8), (18, 15), (6, 19), (13, 12), (5, 23), (22, 29), (26, 32), (14, 17), (8, 1), (4, 22), (24, 32), (10, 15), (2, 33), (4, 24), (27, 8), (25, 15), (19, 21), (6, 21), (4, 21), (23, 26), (23, 2), (28, 19), (25, 29), (8, 32), (21, 24), (10, 14), (29, 33), (14, 26), (19, 16), (12, 23), (1, 22), (22, 37), (6, 33), (27, 0), (2, 9), (13, 32), (7, 37), (0, 23), (6, 24), (29, 30), (25, 12), (1, 7), (2, 25), (27, 10), (27, 34), (12, 17), (11, 17), (29, 29), (23, 4), (4, 6), (25, 9), (17, 8), (17, 25), (3, 30), (5, 26), (11, 23), (3, 27), (25, 14), (27, 37), (20, 14), (8, 13), (11, 16), (9, 35), (27, 26), (13, 24), (8, 2), (19, 11), (10, 26), (19, 19), (19, 3), (2, 3), (22, 6), (21, 22), (8, 19), (22, 11), (5, 17), (17, 18), (11, 1), (19, 7), (27, 6), (9, 21), (6, 34), (16, 12), (13, 4), (26, 34), (16, 3), (9, 1), (19, 0), (18, 13), (1, 11), (14, 8), (11, 20), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "605784", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 1), (28, 20), (22, 18), (18, 32), (0, 19), (19, 2), (2, 5), (20, 5), (33, 10), (14, 16), (4, 7), (11, 37), (11, 31), (32, 17), (23, 26), (36, 21), (24, 32), (7, 24), (25, 34), (22, 10), (24, 5), (26, 5), (12, 36), (37, 13), (27, 18), (36, 17), (21, 14), (25, 33), (0, 11), (12, 0), (14, 14), (18, 20), (3, 32), (14, 23), (17, 8), (31, 32), (35, 11), (9, 3), (9, 29), (29, 7), (12, 3), (26, 22), (29, 5), (27, 7), (12, 15), (4, 18), (27, 27), (19, 3), (3, 17), (29, 13), (26, 38), (17, 38), (3, 28), (5, 22), (9, 38), (34, 36), (15, 2), (20, 34), (34, 4), (27, 2), (29, 17), (28, 28), (29, 30), (15, 30), (17, 34), (1, 17), (26, 31), (38, 34), (33, 11), (37, 22), (21, 17), (18, 3), (15, 6), (30, 34), (27, 31), (16, 12), (20, 35), (26, 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33), (14, 2), (14, 9), (24, 12), (5, 13), (7, 25), (29, 19), (0, 29), (35, 13), (8, 31), (15, 22), (3, 31), (25, 5), (12, 16), (17, 31), (14, 26), (38, 14), (23, 12), (0, 3), (6, 18), (14, 30), (19, 12), (10, 12), (11, 29), (36, 0), (35, 21), (1, 30), (6, 30), (11, 13), (15, 12), (34, 8), (19, 37), (15, 4), (11, 14), (3, 33), (28, 34), (35, 30), (30, 16), (38, 23), (29, 4), (3, 21), (28, 17), (10, 0), (4, 21), (2, 30), (18, 15), (24, 21), (37, 3), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874800", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 27), (12, 29), (33, 30), (7, 8), (15, 0), (16, 2), (35, 8), (11, 26), (21, 4), (9, 6), (9, 16), (14, 22), (15, 29), (30, 30), (12, 2), (36, 19), (31, 7), (28, 6), (7, 17), (16, 5), (20, 29), (21, 22), (33, 15), (24, 4), (23, 28), (2, 23), (31, 23), (4, 13), (21, 30), (12, 15), (4, 24), (19, 16), (24, 7), (27, 25), (36, 12), (24, 14), (22, 9), (36, 4), (20, 14), (8, 17), (20, 8), (35, 27), (29, 10), (20, 22), (1, 14), (21, 17), (34, 13), (6, 14), (8, 26), (36, 25), (29, 0), (8, 29), (34, 28), (2, 19), (35, 1), (26, 6), (6, 3), (26, 1), (23, 0), (21, 2), (10, 17), (20, 18), (8, 12), (18, 7), (11, 30), (13, 6), (17, 22), (7, 11), (17, 17), (26, 3), (32, 12), (14, 4), (36, 18), (35, 20), (29, 13), (29, 2), (26, 15), (11, 17), (1, 9), (14, 7), (33, 0), (7, 15), (30, 21), (11, 23), (13, 17), (13, 19), (0, 4), (14, 17), (1, 5), (16, 15), (10, 31), (24, 26), (19, 8), (10, 28), (30, 22), (31, 22), (35, 5), (21, 26), (18, 2), (8, 16), (7, 31), (17, 15), (15, 17), (2, 7), (17, 11), (12, 13), (22, 29), (18, 29), (21, 8), (13, 14), (31, 21), (8, 3), (35, 31), (32, 16), (33, 8), (20, 30), (11, 7), (13, 20), (14, 9), (21, 23), (31, 0), (17, 29), (33, 10), (29, 11), (10, 24), (26, 4), (12, 18), (28, 26), (32, 19), (31, 31), (29, 21), (26, 20), (5, 7), (32, 5), (6, 5), (27, 21), (18, 31), (24, 2), (25, 32), (28, 25), (14, 1), (15, 12), (11, 1), (1, 28), (15, 11), (28, 4), (30, 20), (3, 11), (4, 15), (36, 14), (18, 12), (22, 11), (19, 13), (25, 16), (13, 22), (30, 23), (23, 10), (1, 25), (1, 31), (25, 29), (20, 16), (13, 7), (7, 26), (19, 23), (8, 0), (11, 20), (24, 15), (1, 3), (13, 5), (31, 8), (24, 9), (6, 32), (36, 21), (16, 11), (34, 6), (3, 14), (20, 24), (2, 17), (11, 15), (34, 11), (11, 6), (20, 23), (28, 16), (12, 26), (34, 29), (0, 9), (19, 25), (13, 18), (15, 20), (18, 6), (7, 27), (1, 2), (1, 12), (31, 3), (12, 32), (5, 3), (9, 12), (14, 11), (29, 8), (5, 9), (30, 29), (19, 17), (35, 14), (21, 15), (9, 27), (3, 24), (36, 31), (11, 3), (18, 18), (25, 23), (34, 16), (18, 14), (3, 27), (7, 28), (35, 11), (6, 27), (15, 27), (3, 12), (21, 10), (4, 9), (18, 4), (14, 14), (35, 22), (14, 26), (11, 24), (27, 27), (10, 3), (5, 29), (28, 32), (33, 14), (0, 19), (0, 32), (1, 29), (24, 11), (23, 15), (34, 21), (2, 16), (2, 2), (28, 8), (5, 6), (21, 20), (13, 23), (34, 15), (7, 25), (2, 21), (29, 30), (8, 19), (19, 2), (30, 28), (6, 7), (7, 4), (35, 17), (20, 12), (19, 5), (5, 25), (3, 22), (4, 1), (25, 19), (2, 3), (0, 5), (22, 27), (31, 9), (12, 4), (25, 30), (16, 19), (13, 12), (29, 20), (10, 14), (8, 9), (33, 9), (26, 0), (7, 9), (36, 13), (29, 26), (30, 27), (33, 1), (34, 27), (11, 4), (14, 12), (12, 30), (10, 30), (7, 21), (32, 23), (2, 20), (16, 25), (14, 2), (22, 19), (32, 25), (24, 21), (27, 26), (7, 7), (3, 30), (17, 14), (35, 25), (8, 5), (15, 13), (9, 14), (0, 15), (23, 5), (25, 3), (0, 24), (6, 18), (16, 20), (2, 18), (34, 2), (18, 23), (16, 32), (17, 12), (14, 21), (17, 1), (34, 4), (16, 7), (30, 15), (29, 17), (3, 21), (8, 27), (20, 21), (7, 13), (9, 22), (35, 10), (32, 17), (1, 20), (6, 29), (0, 3), (29, 6), (11, 8), (22, 26), (3, 17), (33, 28), (35, 6), (21, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82224", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 5), (5, 27), (12, 20), (25, 33), (7, 22), (22, 9), (25, 8), (26, 23), (20, 23), (17, 13), (5, 4), (17, 33), (9, 27), (3, 16), (24, 18), (16, 18), (0, 22), (6, 1), (22, 23), (0, 33), (28, 16), (3, 2), (5, 12), (5, 29), (9, 6), (11, 30), (28, 8), (2, 27), (8, 15), (0, 31), (22, 27), (11, 14), (26, 29), (2, 33), (5, 30), (21, 0), (27, 0), (22, 25), (18, 6), (23, 6), (19, 2), (9, 4), (12, 10), (14, 9), (0, 11), (26, 1), (2, 11), (21, 19), (23, 12), (1, 27), (1, 21), (11, 15), (12, 19), (21, 6), (23, 20), (10, 26), (10, 29), (21, 4), (24, 9), (17, 0), (1, 2), (17, 27), (12, 12), (11, 32), (29, 6), (8, 0), (14, 15), (21, 32), (14, 4), (10, 16), (7, 16), (26, 2), (15, 28), (26, 28), (8, 34), (4, 23), (29, 28), (15, 17), (29, 10), (29, 8), (18, 8), (19, 27), (0, 9), (12, 14), (23, 24), (26, 22), (7, 26), (7, 21), (11, 0), (20, 14), (29, 0), (27, 31), (14, 17), (5, 32), (29, 17), (9, 10), (16, 16), (18, 22), (11, 1), (28, 20), (16, 13), (14, 24), (2, 7), (10, 20), (14, 10), (10, 22), (23, 34), (5, 5), (21, 21), (26, 4), (28, 26), (4, 4), (23, 30), (20, 7), (11, 11), (13, 20), (3, 27), (13, 31), (1, 10), (13, 7), (15, 3), (12, 21), (20, 22), (8, 25), (12, 4), (2, 29), (0, 8), (3, 25), (4, 29), (12, 30), (22, 17), (20, 5), (28, 17), (17, 7), (23, 17), (13, 23), (23, 21), (0, 26), (21, 8), (23, 1), (27, 8), (21, 18), (18, 2), (12, 31), (13, 4), (9, 8), (11, 7), (28, 15), (16, 24), (4, 0), (11, 9), (17, 1), (7, 30), (8, 22), (21, 1), (29, 9), (14, 14), (24, 10), (27, 25), (7, 25), (2, 3), (13, 22), (1, 1), (4, 16), (1, 0), (20, 21), (20, 6), (28, 6), (17, 12), (23, 15), (9, 20), (12, 16), (20, 15), (21, 25), (1, 3), (12, 2), (23, 10), (4, 6), (10, 11), (27, 26), (22, 16), (24, 3), (5, 8), (13, 1), (19, 29), (10, 18), (16, 27), (10, 32), (23, 2), (6, 9), (22, 30), (25, 14), (7, 18), (5, 24), (24, 28), (19, 9), (11, 25), (19, 22), (5, 16), (19, 34), (6, 30), (27, 24), (26, 11), (29, 32), (9, 13), (28, 22), (22, 14), (10, 0), (28, 12), (24, 8), (5, 34), (23, 22), (21, 34), (21, 9), (25, 27), (26, 20), (22, 7), (22, 6), (12, 32), (19, 1), (26, 15), (9, 11), (2, 16), (25, 29), (1, 11), (2, 19), (21, 22), (22, 24), (15, 23), (2, 24), (22, 11), (12, 28), (29, 27), (11, 10), (28, 29), (18, 11), (24, 32), (22, 20), (5, 33), (22, 28), (16, 8), (3, 15), (25, 32), (19, 30), (21, 17), (10, 10), (5, 11), (12, 24), (15, 4), (6, 34), (13, 15), (7, 6), (16, 23), (6, 28), (28, 30), (10, 17), (3, 8), (10, 27), (8, 30), (21, 23), (7, 11), (14, 5), (7, 28), (27, 9), (14, 34), (24, 25), (24, 2), (28, 23), (24, 1), (1, 23), (17, 4), (26, 8), (13, 12), (14, 8), (15, 33), (6, 10), (20, 1), (9, 34), (1, 5), (27, 23), (6, 24), (29, 21), (12, 5), (13, 26), (7, 17), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "692016", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 6), (7, 13), (31, 12), (16, 14), (19, 27), (12, 21), (9, 5), (23, 18), (7, 30), (1, 2), (27, 10), (26, 19), (21, 18), (31, 25), (3, 4), (8, 6), (23, 5), (1, 26), (26, 5), (1, 15), (24, 29), (22, 18), (7, 25), (3, 19), (7, 31), (9, 11), (27, 26), (16, 24), (20, 18), (25, 24), (22, 21), (8, 10), (2, 15), (26, 16), (4, 22), (29, 1), (4, 16), (28, 28), (31, 1), (22, 32), (7, 20), (13, 6), (30, 20), (15, 12), (1, 11), (15, 4), (16, 10), (23, 15), (26, 21), (31, 7), (12, 24), (1, 17), (23, 11), (17, 9), (22, 25), (5, 1), (13, 14), (22, 4), (5, 9), (5, 10), (14, 10), (1, 4), (11, 28), (9, 18), (26, 27), (16, 28), (13, 13), (27, 12), (30, 17), (24, 22), (8, 12), (17, 31), (28, 16), (0, 6), (25, 14), (31, 5), (22, 24), (18, 9), (11, 23), (23, 7), (28, 25), (30, 16), (29, 14), (7, 8), (19, 11), (4, 7), (26, 1), (20, 7), (27, 18), (28, 31), (10, 23), (23, 27), (28, 0), (6, 19), (3, 9), (10, 0), (10, 22), (16, 8), (31, 22), (5, 0), (20, 31), (12, 22), (19, 20), (15, 1), (21, 23), (27, 5), (28, 17), (9, 15), (5, 6), (24, 6), (27, 21), (5, 11), (19, 5), (23, 29), (18, 13), (11, 16), (2, 31), (17, 25), (4, 12), (19, 19), (20, 5), (24, 26), (25, 28), (5, 30), (25, 25), (12, 3), (31, 29), (26, 29), (26, 6), (20, 20), (4, 4), (8, 17), (20, 30), (19, 3), (1, 20), (16, 9), (2, 1), (10, 12), (4, 10), (2, 17), (25, 0), (30, 3), (21, 29), (1, 27), (26, 11), (1, 0), (17, 17), (8, 16), (31, 27), (22, 22), (8, 3), (2, 16), (5, 31), (7, 27), (7, 10), (18, 25), (25, 6), (25, 8), (2, 14), (3, 7), (17, 10), (2, 0), (28, 4), (22, 13), (23, 20), (0, 25), (16, 3), (2, 8), (25, 32), (23, 14), (23, 1), (3, 11), (8, 0), (19, 17), (22, 23), (10, 14), (7, 4), (3, 32), (5, 4), (0, 19), (28, 23), (10, 28), (29, 4), (9, 31), (17, 12), (21, 32), (22, 14), (13, 27), (10, 17), (26, 15), (12, 4), (9, 4), (10, 29), (5, 12), (21, 8), (17, 21), (31, 14), (12, 29), (10, 8), (7, 1), (6, 6), (23, 2), (29, 5), (6, 7), (10, 13), (17, 27), (6, 1), (14, 26), (0, 9), (8, 4), (23, 12), (6, 29), (14, 0), (9, 30), (2, 25), (27, 7), (16, 23), (22, 3), (0, 31), (18, 27), (26, 28), (19, 16), (10, 1), (11, 10), (28, 9), (15, 10), (3, 6), (15, 30), (17, 28), (24, 3), (7, 32), (27, 14), (31, 3), (7, 23), (6, 10), (31, 20), (6, 23), (3, 29), (28, 5), (13, 7), (18, 8), (29, 6), (1, 31), (30, 27), (22, 2), (8, 5), (4, 15), (20, 19), (28, 14), (20, 2), (29, 2), (20, 25), (4, 17), (19, 0), (26, 13), (15, 23), (16, 1), (1, 9), (9, 1), (3, 12), (24, 14), (12, 15), (17, 0), (16, 25), (26, 17), (13, 18), (14, 3), (11, 11), (14, 11), (12, 0), (6, 17), (21, 24), (31, 23), (0, 27), (4, 9), (6, 30), (12, 16), (24, 4), (2, 2), (23, 8), (15, 7), (28, 32), (7, 9), (15, 24), (30, 0), (9, 9), (28, 29), (18, 16), (30, 5), (14, 4), (23, 25), (31, 17), (5, 27), (29, 21), (18, 29), (9, 16), (18, 3), (13, 8), (26, 2), (3, 27), (1, 12), (16, 27), (1, 14), (3, 31), (31, 26), (31, 8), (10, 2), (27, 9), (25, 23), (1, 1), (12, 20), (11, 19), (22, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993168", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), 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), (26, 24), (32, 29), (32, 38), (14, 31), (15, 12), (2, 35), (24, 21), (21, 38), (30, 38), (33, 20), (10, 15), (11, 34), (36, 15), (9, 27), (27, 5), (6, 28), (11, 32), (11, 17), (9, 23), (9, 5), (15, 37), (13, 17), (14, 19), (16, 6), (22, 31), (10, 13), (24, 19), (20, 19), (29, 22), (6, 38), (29, 17), (26, 23), (30, 35), (23, 23), (17, 14), (4, 27), (16, 3), (12, 17), (28, 36), (5, 14), (8, 34), (6, 31), (28, 33), (19, 15), (33, 22), (6, 19), (5, 25), (7, 37), (18, 38), (10, 2), (27, 6), (30, 3), (9, 31), (10, 3), (29, 18), (12, 10), (26, 20), (16, 10), (5, 19), (27, 4), (18, 22), (25, 14), (33, 36), (27, 23), (2, 4), (22, 28), (36, 6), (11, 36), (27, 9), (14, 0), (29, 23), (11, 12), (3, 14), (4, 13), (12, 33), (30, 22), (8, 13), (27, 27), (15, 38), (16, 4), (24, 23), (32, 7), (32, 0), (9, 34), (27, 11), (4, 19), (5, 2), (22, 11), (23, 15), (23, 16), (15, 17), (32, 19), (12, 11), (22, 32), (27, 29), (25, 31), (22, 19), (25, 1), (7, 7), (18, 10), (27, 12), (30, 15), (23, 36), (34, 7), (25, 32), (14, 26), (2, 38), (8, 8), (5, 11), (21, 27), (35, 8), (6, 4), (24, 30), (6, 23), (25, 36), (15, 11), (30, 24), (36, 7), (20, 16), (4, 24), (2, 37), (0, 37), (34, 13), (8, 5), (26, 3), (8, 9), (33, 35), (26, 32), (28, 6), (26, 17), (10, 11), (3, 28), (3, 5), (11, 15), (33, 38), (19, 30), (18, 28), (27, 17), (21, 25), (9, 9), (11, 7), (27, 33), (25, 25), (4, 37), (8, 21), (26, 33), (4, 30), (3, 36), (13, 25), (1, 16), (28, 12), (20, 15), (8, 18), (23, 32), (8, 28), (3, 29), (4, 0), (20, 32), (36, 25), (5, 4), (18, 31), (28, 37), (26, 38), (30, 17), (8, 15), (25, 27), (20, 24), (6, 9), (12, 28), (34, 14), (36, 21), (16, 26), (3, 23), (22, 0), (27, 38), (7, 18), (0, 3), (2, 20), (7, 27), (36, 23), (24, 7), (14, 3), (0, 22), (28, 11), (17, 2), (18, 24), (11, 21), (20, 27), (36, 2), (20, 6), (8, 30), (1, 38), (28, 20), (25, 19), (12, 12), (11, 5), (28, 26), (20, 22), (36, 31), (25, 33), (10, 33), (2, 12), (25, 9), (24, 25), (34, 27), (4, 35), (36, 30), (6, 0), (10, 8), (2, 14), (14, 25), (25, 4), (3, 12), (29, 38), (34, 2), (33, 34), (27, 0), (12, 7), (26, 2), (35, 28), (23, 30), (3, 35), (8, 7), (14, 29), (16, 37), (15, 18), (24, 11), (34, 16), (6, 30), (2, 22), (2, 18), (0, 15), (16, 8), (4, 21), (27, 10), (0, 13), (6, 32), (0, 30), (30, 30), (11, 13), (32, 6), (3, 25), (28, 29), (29, 29), (21, 5), (28, 30), (33, 32), (17, 32), (30, 37), (7, 29), (36, 19), (27, 2), (18, 19), (35, 15), (30, 6), (11, 22), (23, 19), (6, 27), (3, 33), (3, 31), (26, 11), (30, 28), (2, 19), (8, 6), (0, 14), (0, 10), (17, 11), (31, 22), (22, 2), (23, 21), (35, 21), (15, 6), (7, 19), (23, 31), (15, 25), (18, 33), (11, 28), (31, 16), (10, 14), (15, 8), (31, 24), (29, 19), (11, 38), (35, 12), (33, 37), (6, 13), (20, 5), (0, 23), (27, 14), (22, 26), (18, 8), (27, 3), (13, 2), (1, 30), (16, 15), (4, 29), (33, 1), (29, 7), (23, 1), (11, 24), (22, 23), (19, 23), (2, 31), (22, 4), (29, 14), (21, 33), (14, 23), (5, 32), (26, 0), (26, 19), (20, 21), (11, 8), (22, 25), (10, 5), (4, 28), (2, 2), (12, 26), (28, 14), (36, 9), (22, 1), (8, 36), (15, 0), (23, 22), (24, 10), (8, 23), (17, 30), (23, 18), (13, 4), (20, 33), (8, 22), (23, 5), (22, 13), (29, 16), (31, 20), (12, 19), (8, 11), (32, 26), (13, 16), (9, 2), (31, 21), (0, 4), (9, 13), (27, 18), (31, 0), (13, 29), (27, 37), (32, 3), (33, 30), (19, 1), (30, 11), (5, 33), (11, 31), (35, 14), (20, 29), (36, 32), (34, 0), (10, 18), (28, 34), (23, 34), (17, 8), (16, 7), (10, 30), (21, 15), (14, 21), (28, 1), (33, 17), (36, 11), (18, 2), (19, 2), (25, 10), (31, 30), (30, 2), (23, 13), (16, 27), (7, 20), (6, 24), (32, 22), (34, 34), (5, 30), (19, 12), (16, 32), (0, 11), (8, 32), (6, 37), (12, 20), (18, 20), (18, 35), (21, 16), (31, 27), (16, 33), (4, 10), (4, 22), (3, 10), (3, 11), (35, 34), (10, 35), (6, 1), (20, 28), (22, 29), (28, 21), (28, 2), (0, 17), (18, 34), (3, 1), (35, 13), (19, 38), (34, 1), (7, 26), (12, 24), (1, 14), (14, 20), (7, 31), (26, 13), (19, 19), (33, 7), (8, 31), (9, 30), (30, 26), (10, 1), (24, 16), (29, 31), (31, 3), (22, 38), (32, 24), (28, 19), (35, 37), (9, 33), (18, 27), (28, 18), (15, 19), (26, 28), (31, 17), (27, 24), (25, 34), (24, 28), (2, 6), (12, 37), (32, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "438624", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 23), (9, 6), (18, 20), (1, 1), (32, 6), (12, 10), (17, 25), (2, 34), (8, 7), (20, 24), (31, 3), (29, 10), (13, 31), (27, 16), (21, 4), (0, 32), (20, 36), (32, 35), (33, 32), (17, 33), (34, 15), (36, 27), (13, 19), (35, 36), (16, 10), (2, 21), (24, 11), (5, 32), (22, 23), (2, 9), (32, 16), (37, 10), (37, 26), (35, 7), (15, 31), (38, 31), (12, 6), (34, 22), (23, 35), (26, 12), (0, 34), (0, 13), (11, 28), (36, 35), (11, 24), (32, 8), (6, 13), (0, 2), (6, 21), (27, 17), (33, 14), (5, 9), (3, 22), (29, 28), (30, 27), (4, 29), (6, 31), (8, 1), (25, 3), (32, 19), (23, 19), (7, 11), (5, 7), (37, 11), (13, 22), (2, 29), (21, 26), (36, 14), (19, 23), (35, 0), (6, 22), (27, 25), (33, 27), (31, 31), (32, 21), (6, 2), (14, 23), (35, 8), (22, 26), (30, 13), (33, 29), (30, 32), (7, 19), (8, 23), (30, 36), (36, 23), (8, 0), (29, 22), (22, 14), (34, 10), (2, 28), (3, 13), (33, 30), (11, 1), (23, 36), (27, 4), (32, 24), (36, 36), (9, 9), (24, 16), (8, 10), (28, 14), (11, 18), (0, 7), (21, 25), (32, 32), (5, 28), (17, 24), (7, 18), (19, 4), (32, 15), (34, 29), (6, 27), (28, 31), (31, 34), (2, 5), (32, 12), (5, 31), (24, 25), (1, 32), (9, 32), (24, 8), (2, 6), (8, 26), (12, 17), (26, 11), (22, 36), (20, 13), (3, 32), (9, 1), (15, 33), (17, 16), (5, 14), (16, 27), (35, 10), (19, 26), (7, 34), (33, 4), (33, 6), (34, 3), (32, 9), (3, 31), (35, 13), (12, 30), (22, 6), (4, 34), (3, 4), (20, 4), (7, 14), (22, 0), (21, 6), (16, 8), (38, 30), (18, 4), (29, 30), (4, 25), (18, 16), (4, 26), (12, 36), (4, 0), (14, 30), (27, 3), (20, 31), (5, 19), (14, 19), (12, 28), (0, 23), (20, 21), (4, 22), (21, 13), (16, 32), (37, 7), (3, 29), (24, 5), (5, 2), (25, 36), (3, 5), (30, 17), (30, 19), (23, 33), (6, 14), (12, 22), (6, 3), (3, 10), (16, 18), (26, 14), (3, 21), (11, 16), (28, 11), (31, 11), (7, 31), (25, 17), (35, 26), (7, 10), (35, 34), (27, 30), (31, 5), (37, 36), (9, 12), (38, 15), (20, 26), (1, 29), (14, 35), (33, 36), (10, 20), (4, 12), (18, 12), (13, 17), (37, 25), (10, 3), (19, 28), (29, 27), (13, 32), (38, 7), (19, 6), (3, 20), (17, 0), (35, 22), (21, 14), (16, 12), (32, 33), (21, 9), (16, 2), (4, 5), (24, 30), (35, 27), (38, 2), (25, 19), (37, 9), (16, 19), (12, 29), (2, 14), (15, 14), (23, 28), (30, 34), (21, 23), (18, 22), (6, 29), (0, 24), (10, 24), (22, 25), (26, 17), (32, 36), (1, 20), (22, 33), (15, 19), (2, 31), (10, 30), (26, 3), (32, 10), (0, 5), (27, 32), (11, 15), (20, 11), (6, 23), (37, 5), (38, 25), (29, 4), (10, 0), (0, 6), (1, 10), (25, 5), (34, 19), (0, 8), (26, 19), (6, 7), (16, 22), (24, 21), (33, 26), (28, 2), (31, 28), (34, 23), (16, 30), (0, 30), (8, 16), (24, 4), (10, 7), (21, 17), (13, 2), (2, 24), (17, 1), (1, 16), (11, 17), (6, 26), (32, 1), (3, 33), (19, 3), (1, 8), (25, 6), (13, 21), (24, 34), (20, 7), (21, 36), (18, 32), (23, 9), (11, 8), (22, 16), (19, 17), (0, 14), (31, 0), (1, 3), (31, 25), (13, 28), (14, 4), (30, 7), (37, 31), (21, 31), (9, 5), (8, 25), (15, 20), (9, 15), (26, 7), (11, 20), (19, 21), (8, 20), (20, 14), (11, 19), (17, 31), (8, 19), (2, 22), (23, 8), (38, 26), (8, 34), (30, 9), (13, 16), (2, 30), (20, 27), (35, 12), (2, 25), (17, 13), (15, 5), (26, 0), (12, 4), (2, 4), (30, 20), (17, 20), (14, 10), (14, 29), (2, 10), (5, 30), (5, 4), (21, 33), (2, 1), (33, 28), (14, 6), (34, 18), (0, 22), (19, 11), (5, 12), (34, 11), (33, 0), (5, 25), (24, 18), (21, 8), (12, 23), (18, 2), (10, 19), (5, 26), (1, 35), (30, 33), (17, 15), (20, 20), (5, 3), (9, 23), (0, 12), (5, 5), (1, 15), (26, 9), (31, 30), (33, 10), (0, 19), (19, 19), (31, 22), (35, 16), (17, 11), (22, 28), (19, 10), (15, 17), (16, 1), (20, 22), (32, 14), (29, 7), (8, 13), (33, 11), (6, 17), (33, 22), (17, 22), (26, 25), (12, 9), (15, 23), (19, 29), (7, 26), (9, 0), (5, 10), (34, 25), (7, 33), (11, 9), (0, 4), (8, 4), (15, 1), (32, 2), (13, 34), (36, 33), (17, 8), (26, 6), (8, 28), (19, 7), (29, 26), (22, 32), (33, 19), (7, 24), (21, 0), (30, 0), (15, 13), (33, 7), (9, 3), (13, 15), (31, 2), (19, 32), (34, 17), (6, 36), (19, 16), (36, 31), (29, 14), (25, 2), (19, 24), (9, 22), (20, 34), (5, 35), (25, 26), (38, 3), (14, 11), (8, 32), (2, 33), (26, 1), (36, 2), (6, 10), (23, 5), (29, 24), (31, 20), (27, 9), (16, 24), (12, 32), (3, 3), (29, 13), (6, 35), (30, 28), (38, 1), (38, 20), (38, 13), (35, 2), (4, 32), (2, 16), (3, 18), (23, 32), (10, 4), (30, 22), (5, 18), (17, 4), (26, 22), (38, 10), (33, 12), (9, 7), (9, 21), (33, 8), (7, 28), (12, 25), (3, 27), (10, 32), (16, 26), (27, 35), (1, 28), (35, 3), (17, 29), (4, 2), (21, 11), (27, 19), (11, 33), (9, 16), (1, 5), (31, 1), (11, 22), (10, 9), (23, 34), (29, 34), (16, 23), (7, 15), (24, 22), (30, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649032", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 5), (4, 25), (24, 6), (0, 8), (6, 1), (17, 20), (9, 1), (20, 18), (14, 15), (12, 4), (21, 6), (1, 5), (12, 16), (13, 24), (33, 21), (22, 22), (1, 18), (18, 13), (20, 20), (4, 18), (12, 26), (13, 16), (8, 13), (5, 7), (33, 18), (27, 6), (2, 19), (11, 21), (26, 11), (30, 17), (1, 16), (32, 7), (31, 14), (6, 7), (27, 1), (27, 29), (13, 17), (5, 21), (0, 24), (23, 26), (27, 15), (20, 5), (10, 21), (25, 23), (10, 20), (32, 10), (2, 16), (11, 14), (32, 2), (16, 27), (29, 14), (2, 11), (7, 18), (2, 24), (24, 26), (21, 1), (5, 3), (3, 8), (7, 29), (21, 8), (4, 20), (34, 2), (21, 12), (6, 5), (26, 17), (8, 3), (19, 18), (11, 12), (30, 11), (11, 24), (1, 29), (12, 28), (20, 9), (34, 12), (13, 28), (24, 12), (20, 16), (17, 19), (23, 25), (18, 19), (28, 13), (28, 5), (25, 7), (16, 16), (4, 14), (33, 3), (6, 27), (34, 16), (9, 4), (28, 27), (29, 4), (8, 10), (32, 29), (24, 27), (2, 21), (8, 17), (18, 12), (18, 17), (17, 27), (19, 1), (22, 3), (13, 15), (6, 29), (13, 20), (28, 19), (25, 29), (31, 22), (26, 8), (21, 22), (33, 9), (30, 29), (33, 28), (33, 16), (5, 17), (4, 5), (29, 0), (14, 9), (24, 15), (14, 3), (0, 1), (26, 27), (7, 12), (8, 22), (10, 19), (3, 27), (10, 16), (0, 17), (25, 24), (9, 25), (22, 21), (4, 28), (1, 3), (11, 5), (7, 20), (34, 18), (22, 5), (10, 29), (17, 6), (20, 19), (0, 20), (25, 28), (28, 11), (12, 24), (32, 1), (8, 29), (32, 3), (17, 18), (16, 6), (30, 25), (27, 19), (33, 8), (20, 21), (11, 6), (21, 25), (10, 10), (22, 11), (12, 9), (4, 17), (22, 24), (7, 9), (11, 10), (2, 25), (34, 15), (31, 28), (11, 19), (14, 2), (5, 12), (2, 17), (2, 27), (20, 4), (26, 3), (15, 25), (12, 19), (2, 2), (17, 0), (3, 13), (23, 17), (25, 6), (6, 6), (25, 13), (4, 27), (18, 4), (4, 8), (23, 8), (5, 8), (21, 24), (5, 26), (28, 26), (16, 21), (19, 15), (7, 2), (29, 12), (29, 6), (12, 8), (29, 20), (29, 3), (18, 20), (8, 21), (16, 20), (18, 29), (9, 3), (4, 16), (21, 10), (9, 18), (18, 1), (3, 17), (2, 14), (32, 23), (27, 7), (2, 1), (14, 7), (5, 15), (14, 0), (18, 21), (23, 4), (15, 1), (17, 23), (6, 26), (8, 1), (32, 12), (16, 26), (20, 24), (29, 22), (15, 0), (1, 17), (8, 15), (34, 4), (7, 5), (1, 14), (24, 3), (31, 21), (15, 20), (25, 2), (14, 10), (17, 13), (22, 20), (17, 14), (9, 6), (7, 8), (16, 29), (0, 29), (6, 9), (29, 5), (27, 0), (24, 29), (14, 24), (5, 11), (23, 3), (31, 17), (2, 4), (1, 4), (17, 21), (25, 14), (6, 3), (10, 14), (34, 22), (22, 19), (10, 25), (25, 5), (7, 15), (18, 23), (22, 8), (18, 14), (23, 10), (12, 20), (26, 23), (20, 12), (32, 0), (0, 2), (20, 10), (21, 21), (16, 8), (29, 9), (15, 14), (13, 12), (8, 8), (21, 9), (15, 11), (15, 8), (31, 9), (14, 18), (9, 20), (26, 21), (31, 3), (14, 17), (31, 5), (16, 4), (28, 3), (25, 8), (9, 19), (5, 23), (28, 15), (11, 3), (30, 16), (24, 24), (1, 21), (19, 20), (19, 0), (25, 11), (30, 3), (34, 10), (3, 19), (20, 28), (23, 21), (19, 8), (16, 7), (5, 0), (15, 18), (5, 2), (7, 13), (34, 1), (2, 9), (33, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "945100", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 28), (0, 15), (0, 16), (11, 18), (20, 26), (16, 10), (15, 25), (25, 0), (9, 27), (23, 28), (14, 5), (23, 19), (22, 26), (8, 20), (29, 26), (11, 19), (14, 19), (14, 20), (21, 4), (23, 4), (17, 16), (1, 12), (18, 21), (3, 15), (3, 17), (15, 14), (29, 13), (17, 10), (8, 8), (13, 2), (20, 16), (29, 29), (5, 5), (2, 23), (15, 23), (8, 1), (8, 10), (18, 23), (18, 25), (18, 2), (26, 20), (4, 14), (25, 5), (20, 29), (9, 31), (25, 28), (26, 15), (14, 18), (14, 24), (7, 22), (9, 4), (24, 20), (10, 14), (17, 20), (8, 12), (17, 23), (8, 13), (6, 9), (9, 15), (3, 18), (13, 10), (15, 22), (29, 12), (12, 24), (3, 7), (21, 23), (30, 0), (10, 19), (1, 11), (8, 11), (13, 7), (20, 23), (18, 8), (3, 29), (3, 6), (30, 16), (19, 5), (9, 3), (1, 4), (17, 24), (21, 11), (10, 2), (18, 12), (12, 0), (11, 27), (29, 8), (7, 31), (27, 16), (12, 7), (9, 0), (30, 18), (9, 19), (13, 17), (21, 27), (11, 21), (12, 28), (6, 21), (2, 5), (3, 24), (1, 31), (15, 11), (16, 30), (22, 18), (24, 10), (30, 19), (24, 17), (13, 13), (11, 3), (19, 18), (13, 12), (17, 25), (20, 5), (2, 2), (4, 4), (27, 25), (1, 18), (4, 18), (20, 8), (23, 23), (3, 14), (30, 7), (15, 27), (12, 31), (27, 3), (23, 18), (25, 11), (4, 30), (16, 27), (7, 24), (24, 6), (25, 4), (8, 24), (7, 5), (11, 29), (28, 6), (5, 24), (23, 31), (21, 24), (20, 9), (5, 13), (6, 31), (28, 2), (24, 11), (10, 16), (17, 15), (26, 22), (27, 29), (17, 5), (5, 25), (4, 10), (0, 30), (13, 15), (7, 3), (27, 31), (8, 7), (14, 31), (18, 19), (12, 8), (13, 29), (12, 10), (7, 25), (3, 13), (16, 7), (10, 17), (30, 6), (15, 16), (26, 25), (30, 14), (5, 27), (2, 0), (9, 13), (4, 2), (28, 8), (11, 24), (12, 19), (18, 22), (26, 0), (18, 16), (29, 9), (3, 31), (11, 30), (30, 4), (3, 1), (22, 17), (5, 26), (27, 12), (5, 23), (15, 8), (7, 15), (13, 19), (12, 15), (5, 21), (26, 18), (19, 20), (10, 21), (21, 18), (7, 27), (25, 26), (15, 15), (22, 6), (29, 4), (13, 4), (21, 17), (12, 13), (27, 8), (22, 13), (13, 8), (0, 2), (6, 28), (28, 11), (12, 14), (10, 27), (23, 25), (22, 24), (26, 29), (14, 0), (10, 3), (16, 2), (29, 10), (26, 24), (15, 20), (18, 26), (4, 28), (16, 5), (18, 13), (7, 18), (3, 0), (21, 25), (12, 23), (7, 2), (1, 19), (9, 6), (24, 7), (25, 16), (21, 3), (9, 21), (10, 22), (27, 27), (25, 6), (6, 15), (8, 5), (1, 22), (25, 8), (28, 9), (6, 26), (22, 30), (25, 24), (12, 25), (11, 20), (26, 10), (1, 16), (14, 6), (20, 25), (26, 7), (17, 28), (0, 20), (0, 7), (16, 9), (2, 29), (23, 5), (7, 0), (26, 27), (29, 27), (24, 16), (19, 30), (30, 13), (3, 22), (27, 15), (5, 14), (7, 7), (18, 30), (22, 27), (22, 12), (17, 27), (18, 14), (20, 4), (25, 13), (5, 31), (15, 0), (13, 14), (27, 5), (28, 17), (19, 27), (9, 20), (27, 6), (19, 6), (21, 10), (4, 16), (4, 15), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "784728", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), 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), (28, 8), (9, 8), (26, 16), (34, 2), (29, 11), (35, 7), (20, 9), (3, 11), (16, 23), (4, 11), (10, 0), (36, 1), (15, 14), (32, 2), (19, 23), (2, 7), (19, 11), (31, 19), (30, 25), (37, 25), (30, 17), (10, 18), (13, 17), (13, 25), (20, 7), (37, 15), (23, 18), (34, 10), (31, 14), (2, 22), (7, 23), (2, 5), (29, 12), (32, 8), (21, 26), (7, 10), (23, 6), (8, 25), (12, 24), (13, 29), (1, 25), (15, 12), (2, 17), (17, 28), (30, 9), (24, 7), (28, 10), (14, 28), (17, 1), (3, 27), (11, 22), (12, 16), (26, 10), (12, 21), (9, 23), (27, 7), (8, 23), (23, 23), (17, 8), (10, 26), (11, 17), (14, 25), (0, 20), (10, 24), (30, 16), (17, 21), (11, 1), (17, 7), (34, 19), (12, 5), (13, 13), (17, 12), (21, 6), (37, 18), (8, 15), (18, 9), (23, 10), (8, 26), (20, 18), (11, 15), (24, 29), (19, 19), (4, 5), (32, 11), (9, 4), (14, 27), (11, 20), (22, 12), (10, 19), (8, 24), (22, 13), (20, 11), (21, 2), (7, 13), (2, 18), (34, 23), (1, 1), (13, 18), (20, 25), (17, 13), (17, 24), (3, 21), (23, 12), (30, 10), (18, 12), (4, 15), (25, 3), (13, 22), (11, 29), (23, 22), (10, 15), (0, 15), (9, 18), (33, 27), (36, 11), (0, 14), (10, 27), (26, 19), (37, 14), (18, 16), (35, 16), (5, 13), (16, 5), (33, 29), (30, 24), (8, 17), (26, 4), (5, 7), (28, 9), (35, 26), (25, 6), (24, 25), (28, 7), (19, 28), (23, 5), (22, 5), (19, 8), (2, 21), (6, 18), (24, 21), (19, 26), (9, 28), (6, 27), (4, 18), (10, 16), (29, 3), (14, 26), (17, 19), (4, 10), (37, 23), (28, 20), (20, 23), (3, 26), (36, 27), (5, 0), (28, 26), (11, 9), (10, 14), (8, 7), (6, 1), (33, 9), (32, 3), (0, 2), (37, 3), (29, 1), (30, 0), (23, 20), (13, 12), (8, 22), (22, 10), (22, 29), (16, 16), (2, 15), (27, 19), (5, 25), (21, 8), (8, 13), (26, 17), (15, 20), (18, 3), (8, 10), (3, 8), (35, 4), (17, 27), (33, 2), (13, 26), (12, 12), (16, 8), (35, 11), (30, 23), (9, 3), (32, 24), (9, 16), (30, 3), (22, 22), (18, 4), (33, 16), (32, 19), (35, 1), (5, 3), (37, 19), (3, 9), (23, 0), (13, 11), (18, 29), (6, 17), (4, 8), (37, 8), (13, 3), (1, 12), (29, 26), (9, 17), (34, 5), (0, 19), (0, 1), (18, 23), (6, 14), (14, 8), (25, 7), (34, 26), (30, 15), (33, 14), (3, 28), (29, 19), (3, 29), (21, 16), (17, 29), (13, 5), (16, 3), (9, 29), (21, 3), (22, 17), (1, 6), (22, 7), (20, 0), (4, 27), (4, 7), (30, 1), (5, 11), (34, 8), (6, 10), (34, 7), (10, 7), (6, 15), (15, 22), (24, 3), (31, 27), (23, 9), (22, 27), (21, 21), (12, 2), (28, 15), (30, 27), (4, 12), (35, 2), (8, 3), (33, 13), (31, 8), (4, 4), (24, 14), (26, 7), (32, 9), (23, 16), (9, 7), (20, 29), (3, 17), (10, 28), (35, 0), (32, 29), (1, 10), (2, 27), (16, 14), (18, 1), (9, 21), (35, 23), (6, 2), (0, 12), (10, 1), (17, 11), (31, 18), (13, 16), (4, 2), (34, 13), (31, 5), (33, 6), (10, 17), (16, 27), (28, 5), (0, 29), (34, 4), (18, 20), (29, 7), (22, 24), (20, 2), (31, 23), (15, 23), (21, 27), (29, 28), (20, 24), (0, 13), (3, 25), (18, 6), (13, 9), (22, 21), (12, 3), (6, 23), (9, 27), (32, 15), (24, 9), (15, 2), (25, 12), (5, 19), (7, 17), (28, 18), (8, 29), (23, 11), (8, 14), (22, 25), (7, 25), (37, 24), (11, 28), (12, 9), (29, 9), (26, 1), (30, 11), (10, 22), (24, 11), (14, 16), (24, 27), (1, 2), (32, 0), (18, 8), (19, 2), (1, 16), (2, 2), (36, 18), (6, 3), (24, 2), (14, 6), (19, 14), (12, 11), (36, 28), (27, 29), (29, 15), (33, 10), (2, 13), (37, 12), (13, 21), (0, 8), (14, 3), (27, 13), (27, 6), (28, 6), (26, 20), (6, 22), (31, 20), (25, 19), (18, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680310", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 19), (15, 18), (16, 2), (24, 15), (35, 27), (7, 17), (25, 1), (30, 12), (15, 1), (15, 27), (24, 23), (26, 26), (10, 31), (10, 12), (17, 26), (7, 0), (3, 22), (11, 19), (0, 25), (2, 7), (0, 28), (25, 25), (32, 21), (32, 0), (4, 9), (33, 17), (14, 0), (1, 23), (35, 17), (31, 12), (5, 12), (26, 16), (17, 1), (15, 9), (19, 20), (16, 6), (35, 12), (19, 15), (7, 26), (20, 1), (26, 4), (25, 11), (2, 28), (6, 4), (1, 27), (22, 28), (25, 31), (8, 2), (28, 29), (10, 10), (3, 18), (21, 2), (10, 16), (12, 31), (7, 24), (30, 4), (2, 3), (29, 2), (17, 30), (1, 13), (32, 8), (25, 15), (3, 20), (22, 20), (15, 14), (6, 7), (24, 0), (3, 24), (33, 19), (25, 0), (26, 19), (6, 16), (34, 24), (12, 0), (3, 3), (9, 23), (1, 24), (2, 6), (4, 12), (1, 21), (33, 20), (7, 15), (11, 12), (30, 25), (18, 1), (27, 27), (15, 12), (25, 7), (28, 28), (23, 6), (29, 3), (31, 8), (23, 4), (9, 2), (18, 21), (13, 30), (29, 8), (13, 13), (21, 1), (11, 31), (24, 8), (14, 20), (21, 17), (0, 14), (11, 2), (34, 13), (29, 15), (13, 31), (6, 28), (12, 5), (16, 21), (8, 0), (18, 25), (22, 12), (15, 0), (23, 27), (30, 7), (35, 23), (15, 29), (18, 3), (26, 27), (1, 12), (15, 5), (26, 7), (27, 4), (35, 0), (16, 11), (8, 26), (26, 31), (26, 24), (31, 1), (14, 26), (22, 24), (18, 10), (22, 19), (6, 20), (17, 7), (28, 16), (24, 19), (8, 3), (19, 3), (2, 15), (12, 15), (20, 31), (31, 25), (35, 10), (0, 6), (31, 5), (3, 27), (25, 29), (33, 16), (6, 6), (3, 4), (32, 15), (2, 0), (4, 2), (17, 3), (14, 28), (11, 11), (15, 23), (32, 18), (0, 15), (24, 18), (29, 17), (21, 3), (25, 12), (9, 13), (12, 23), (6, 14), (4, 4), (27, 17), (31, 23), (9, 7), (16, 26), (2, 16), (11, 17), (2, 17), (23, 1), (4, 17), (29, 20), (6, 25), (18, 6), (0, 31), (19, 28), (5, 11), (23, 15), (17, 29), (22, 4), (23, 16), (21, 9), (27, 26), (10, 24), (31, 2), (32, 20), (21, 28), (32, 5), (11, 6), (29, 27), (3, 23), (4, 27), (15, 19), (27, 31), (23, 25), (24, 10), (20, 14), (15, 24), (2, 18), (10, 7), (13, 18), (21, 12), (24, 20), (14, 18), (22, 31), (29, 25), (27, 30), (13, 11), (10, 19), (12, 3), (22, 21), (7, 27), (23, 21), (3, 31), (13, 15), (6, 24), (29, 26), (30, 20), (12, 11), (29, 29), (35, 22), (12, 30), (16, 7), (28, 5), (25, 8), (29, 24), (21, 18), (19, 2), (35, 9), (18, 15), (10, 30), (8, 28), (6, 13), (27, 21), (26, 6), (9, 1), (31, 31), (24, 22), (34, 20), (27, 2), (31, 10), (10, 13), (33, 8), (32, 26), (30, 27), (6, 26), (30, 19), (2, 29), (9, 30), (16, 16), (13, 24), (32, 28), (17, 4), (14, 31), (28, 31), (29, 4), (28, 27), (32, 22), (32, 19), (6, 10), (0, 16), (3, 13), (26, 11), (9, 8), (4, 3), (34, 4), (5, 24), (33, 9), (2, 20), (26, 18), (21, 22), (7, 2), (25, 16), (7, 7), (6, 22), (12, 17), (24, 7), (32, 3), (7, 28), (0, 1), (18, 14), (30, 16), (2, 11), (5, 4), (24, 11), (11, 15), (16, 20), (27, 8), (9, 17), (19, 31), (5, 2), (17, 8), (19, 23), (6, 5), (22, 0), (4, 1), (23, 7), (33, 5), (30, 31), (4, 14), (32, 10), (33, 24), (30, 5), (28, 10), (15, 26), (16, 13), (34, 29), (25, 2), (26, 30), (33, 14), (13, 26), (5, 9), (7, 12), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22638", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), 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), (7, 7), (3, 21), (20, 12), (13, 33), (6, 0), (10, 28), (3, 32), (2, 21), (18, 26), (28, 29), (26, 29), (24, 6), (0, 7), (2, 1), (30, 26), (13, 14), (15, 21), (26, 15), (14, 32), (2, 24), (10, 24), (29, 25), (12, 22), (6, 14), (4, 29), (30, 30), (14, 2), (5, 1), (25, 0), (30, 28), (25, 27), (0, 15), (11, 2), (7, 24), (31, 23), (27, 7), (22, 7), (15, 17), (6, 30), (6, 10), (28, 15), (0, 30), (30, 8), (2, 23), (15, 18), (19, 1), (21, 7), (1, 26), (9, 14), (17, 25), (5, 5), (19, 31), (16, 23), (30, 17), (9, 23), (27, 8), (5, 27), (28, 24), (5, 8), (13, 7), (14, 25), (12, 33), (11, 22), (17, 4), (20, 32), (24, 11), (22, 27), (29, 31), (29, 5), (3, 7), (7, 9), (16, 21), (23, 30), (7, 35), (31, 21), (5, 23), (10, 0), (12, 28), (20, 34), (17, 32), (21, 19), (30, 24), (20, 30), (13, 1), (12, 1), (15, 10), (23, 10), (9, 26), (29, 33), (13, 4), (6, 6), (29, 15), (31, 5), (29, 4), (24, 3), (3, 24), (21, 2), (8, 25), (6, 15), (12, 12), (31, 20), (29, 6), (8, 14), (0, 1), (2, 16), (7, 15), (2, 34), (14, 20), (4, 34), (26, 28), (22, 6), (8, 24), (11, 13), (19, 0), (17, 6), (14, 34), (11, 26), (21, 3), (24, 16), (10, 23), (18, 30), (16, 28), (6, 20), (13, 12), (23, 22), (8, 31), (9, 2), (13, 6), (11, 25), (22, 5), (30, 21), (14, 30), (12, 31), (6, 4), (15, 23), (10, 6), (13, 31), (5, 33), (8, 12), (1, 4), (0, 4), (9, 10), (25, 32), (1, 5), (4, 0), (28, 7), (21, 23), (1, 20), (3, 30), (30, 13), (18, 19), (28, 22), (6, 3), (0, 21), (16, 1), (0, 14), (17, 13), (5, 3), (20, 3), (20, 15), (26, 3), (24, 23), (28, 4), (2, 27), (31, 16), (21, 21), (10, 31), (27, 31), (18, 17), (20, 0), (12, 15), (22, 8), (15, 35), (12, 26), (5, 13), (12, 21), (31, 33), (1, 6), (19, 24), (18, 8), (27, 23), (7, 28), (7, 4), (8, 34), (11, 20), (8, 9), (5, 24), (14, 35), (23, 24), (6, 12), (28, 12), (26, 0), (8, 33), (0, 18), (13, 32), (7, 30), (13, 24), (2, 18), (15, 24), (17, 3), (19, 14), (6, 29), (21, 27), (1, 12), (18, 12), (0, 24), (31, 14), (16, 13), (7, 16), (12, 14), (20, 10), (17, 35), (5, 14), (5, 12), (20, 19), (23, 18), (2, 28), (13, 5), (29, 30), (0, 25), (27, 22), (24, 33), (9, 34), (31, 27), (15, 0), (21, 12), (25, 34), (20, 1), (28, 1), (31, 11), (2, 32), (0, 10), (4, 30), (13, 18), (30, 23), (15, 26), (1, 33), (29, 11), (23, 11), (1, 3), (14, 3), (14, 28), (12, 32), (6, 33), (1, 23), (9, 31), (17, 23), (25, 23), (19, 34), (13, 9), (7, 33), (4, 22), (3, 26), (15, 8), (23, 28), (16, 5), (9, 3), (13, 0), (26, 25), (2, 26), (10, 21), (25, 9), (0, 11), (28, 9), (27, 25), (23, 23), (26, 31), (18, 32), (22, 4), (20, 31), (28, 28), (15, 32), (2, 14), (24, 25), (11, 27), (22, 12), (3, 10), (29, 12), (22, 23), (1, 18), (2, 13), (28, 16), (3, 18), (1, 30), (28, 3), (6, 24), (20, 8), (30, 10), (21, 29), (13, 16), (27, 9), (24, 17), (8, 13), (10, 2), (2, 8), (14, 17), (26, 17), (24, 4), (24, 1), (19, 27), (19, 2), (0, 5), (31, 3), (24, 28), (25, 10), (12, 9), (0, 27), (22, 25), (29, 1), (20, 20), (29, 8), (9, 25), (31, 30), (27, 4), (21, 13), (19, 17), (26, 34), (13, 25), (1, 2), (18, 0), (14, 27), (17, 26), (23, 12), (1, 16), (22, 20), (31, 6), (23, 17), (4, 6), (27, 27), (2, 35), (21, 4), (27, 32), (3, 2), (14, 13), (9, 8), (27, 24), (16, 30), (30, 25), (13, 17), (4, 24), (11, 9), (19, 4), (18, 2), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "611604", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 29), (25, 16), (11, 13), (23, 33), (9, 30), (28, 15), (18, 10), (35, 10), (4, 6), (31, 20), (32, 6), (23, 25), (9, 32), (12, 19), (28, 27), (19, 8), (18, 22), (28, 14), (23, 12), (26, 26), (0, 1), (18, 28), (9, 13), (9, 10), (24, 6), (6, 1), (7, 18), (6, 12), (13, 30), (19, 19), (17, 23), (3, 6), (34, 14), (29, 26), (9, 17), (8, 19), (2, 4), (32, 27), (14, 23), (30, 34), (33, 5), (36, 13), (33, 7), (15, 20), (0, 18), (17, 12), (14, 34), (7, 10), (28, 26), (8, 20), (16, 18), (13, 25), (18, 20), (3, 1), (0, 20), (28, 0), (3, 26), (14, 4), (11, 29), (12, 23), (35, 15), (31, 5), (22, 31), (1, 33), (26, 13), (5, 19), (5, 14), (33, 4), (27, 22), (19, 11), (24, 31), (10, 20), (18, 19), (25, 30), (12, 11), (26, 32), (20, 2), (11, 8), (5, 23), (33, 32), (27, 27), (3, 17), (35, 31), (11, 0), (14, 6), (21, 34), (25, 5), (15, 29), (22, 6), (27, 12), (1, 22), (14, 30), (31, 28), (18, 15), (18, 18), (1, 12), (36, 2), (34, 27), (4, 26), (1, 5), (4, 33), (6, 22), (12, 13), (31, 16), (8, 15), (30, 2), (20, 7), (4, 8), (26, 22), (34, 26), (22, 14), (16, 15), (15, 13), (21, 3), (25, 25), (32, 25), (16, 28), (35, 20), (22, 20), (23, 27), (16, 29), (12, 2), (31, 0), (22, 25), (17, 20), (26, 10), (19, 15), (7, 25), (5, 33), (6, 26), (5, 16), (22, 10), (27, 11), (36, 0), (33, 19), (21, 28), (31, 26), (27, 1), (20, 23), (13, 7), (10, 16), (14, 20), (0, 2), (3, 16), (30, 20), (17, 9), (6, 23), (10, 32), (34, 19), (7, 19), (36, 29), (22, 29), (9, 26), (23, 5), (27, 28), (16, 16), (14, 7), (27, 13), (33, 14), (0, 29), (31, 21), (11, 26), (36, 22), (16, 0), (18, 4), (36, 1), (22, 21), (11, 24), (5, 31), (31, 22), (30, 4), (8, 1), (21, 12), (35, 18), (13, 33), (5, 13), (6, 2), (4, 23), (25, 11), (31, 18), (4, 5), (27, 10), (29, 8), (7, 1), (1, 1), (4, 24), (27, 34), (0, 32), (3, 27), (16, 30), (3, 33), (20, 11), (18, 33), (0, 16), (36, 32), (17, 19), (1, 21), (28, 33), (17, 11), (15, 14), (31, 27), (11, 10), (26, 34), (6, 34), (29, 13), (17, 24), (27, 15), (35, 21), (0, 24), (29, 28), (27, 24), (3, 28), (7, 2), (19, 28), (17, 10), (16, 26), (32, 20), (29, 33), (28, 18), (33, 26), (26, 18), (8, 12), (6, 3), (14, 25), (2, 2), (27, 23), (22, 16), (8, 32), (19, 1), (29, 29), (20, 20), (10, 3), (2, 27), (14, 33), (1, 32), (35, 27), (26, 7), (16, 21), (24, 8), (32, 8), (30, 23), (2, 34), (26, 0), (30, 14), (4, 32), (36, 19), (9, 1), (9, 15), (6, 24), (36, 25), (1, 2), (0, 23), (12, 26), (22, 18), (18, 2), (11, 17), (11, 15), (32, 33), (0, 14), (17, 27), (30, 30), (33, 25), (29, 32), (1, 24), (31, 30), (17, 8), (27, 19), (20, 14), (15, 32), (19, 10), (13, 6), (28, 25), (22, 2), (23, 28), (22, 24), (1, 23), (5, 28), (27, 14), (16, 32), (19, 12), (28, 5), (20, 28), (2, 13), (25, 28), (11, 2), (28, 31), (18, 3), (25, 21), (24, 17), (36, 33), (17, 17), (19, 2), (27, 6), (22, 8), (16, 19), (35, 33), (11, 3), (22, 1), (16, 12), (28, 20), (22, 17), (12, 12), (28, 11), (24, 19), (23, 23), (10, 24), (6, 25), (30, 28), (6, 29), (7, 8), (5, 10), (18, 26), (21, 32), (15, 23), (20, 13), (24, 20), (18, 0), (34, 7), (18, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146376", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), 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), (29, 2), (9, 24), (5, 32), (1, 1), (26, 22), (28, 14), (24, 13), (10, 2), (11, 34), (0, 11), (3, 17), (15, 12), (27, 18), (2, 8), (9, 34), (14, 20), (5, 24), (29, 26), (25, 14), (8, 15), (5, 33), (10, 19), (30, 28), (33, 14), (14, 6), (14, 30), (20, 13), (32, 10), (36, 17), (10, 33), (18, 10), (9, 29), (20, 6), (8, 4), (27, 7), (24, 8), (24, 6), (6, 22), (22, 2), (7, 33), (20, 26), (34, 7), (31, 29), (27, 4), (24, 33), (9, 27), (17, 9), (14, 15), (26, 5), (9, 4), (7, 19), (11, 6), (22, 28), (4, 32), (16, 8), (2, 33), (25, 18), (3, 1), (28, 7), (19, 17), (22, 29), (35, 34), (33, 9), (25, 12), (25, 32), (26, 34), (6, 20), (23, 24), (29, 4), (24, 20), (5, 21), (32, 9), (29, 9), (8, 19), (5, 15), (31, 10), (23, 2), (31, 23), (19, 9), (14, 22), (4, 24), (7, 28), (3, 11), (36, 8), (18, 2), (30, 22), (23, 20), (17, 18), (27, 21), (32, 13), (36, 20), (3, 7), (12, 19), (28, 9), (29, 24), (28, 26), (4, 14), (32, 27), (32, 14), (30, 20), (25, 13), (19, 34), (5, 16), (6, 9), (7, 5), (14, 5), (24, 9), (35, 21), (25, 16), (30, 8), (28, 25), (16, 1), (6, 5), (19, 3), (25, 8), (20, 21), (35, 11), (30, 12), (3, 22), (27, 33), (12, 18), (14, 27), (19, 23), (31, 8), (10, 17), (33, 8), (3, 18), (14, 18), (33, 17), (13, 16), (23, 18), (11, 28), (13, 13), (27, 14), (32, 2), (22, 17), (3, 16), (12, 27), (32, 23), (1, 16), (17, 6), (4, 27), (12, 12), (0, 17), (19, 21), (1, 15), (33, 0), (33, 33), (24, 17), (17, 15), (17, 8), (19, 29), (18, 12), (36, 23), (20, 28), (7, 25), (15, 34), (33, 27), (32, 18), (28, 16), (19, 30), (27, 19), (10, 31), (22, 13), (10, 22), (35, 30), (13, 34), (35, 29), (13, 11), (9, 19), (36, 2), (6, 25), (22, 1), (8, 12), (9, 12), (5, 7), (18, 29), (17, 3), (11, 4), (35, 4), (2, 5), (4, 22), (20, 31), (6, 2), (25, 24), (16, 3), (9, 10), (15, 18), (20, 7), (21, 4), (5, 26), (13, 18), (29, 13), (3, 8), (11, 13), (12, 13), (34, 11), (32, 5), (26, 19), (12, 7), (5, 31), (1, 29), (31, 24), (36, 31), (36, 29), (1, 17), (18, 26), (3, 34), (0, 32), (30, 9), (16, 11), (18, 14), (11, 12), (9, 28), (32, 12), (25, 15), (21, 15), (4, 10), (33, 12), (17, 29), (3, 28), (14, 14), (27, 23), (0, 14), (12, 16), (28, 0), (8, 26), (34, 8), (34, 33), (14, 24), (26, 28), (19, 0), (30, 34), (29, 18), (23, 9), (18, 13), (36, 32), (22, 19), (1, 0), (20, 34), (19, 11), (24, 18), (4, 11), (7, 15), (16, 26), (26, 32), (28, 34), (2, 34), (16, 7), (7, 30), (17, 34), (35, 14), (16, 19), (13, 17), (2, 31), (7, 0), (28, 23), (1, 21), (29, 28), (27, 12), (35, 13), (6, 15), (36, 18), (12, 1), (5, 17), (27, 22), (23, 12), (13, 10), (33, 7), (15, 32), (14, 2), (25, 11), (21, 19), (17, 30), (32, 24), (2, 32), (18, 17), (6, 11), (12, 4), (11, 20), (21, 18), (28, 5), (15, 9), (3, 21), (26, 29), (28, 3), (33, 13), (34, 27), (1, 34), (36, 4), (33, 15), (13, 32), (12, 22), (34, 17), (3, 6), (1, 9), (1, 19), (27, 10), (10, 16), (4, 3), (27, 20), (11, 2), (6, 27), (13, 3), (16, 30), (19, 16), (17, 32), (27, 32), (24, 29), (13, 25), (23, 8), (4, 33), (3, 5), (17, 28), (17, 13), (29, 11), (21, 20), (21, 3), (15, 3), (24, 16), (18, 6), (6, 29), (34, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "327600", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 28), (0, 21), (32, 22), (23, 17), (4, 17), (14, 21), (8, 19), (16, 17), (26, 20), (13, 16), (18, 18), (12, 10), (30, 26), (17, 0), (3, 11), (27, 13), (2, 9), (32, 14), (28, 5), (13, 2), (34, 20), (4, 1), (3, 10), (28, 21), (25, 17), (16, 32), (6, 1), (21, 29), (20, 3), (26, 7), (15, 8), (14, 1), (2, 24), (29, 17), (22, 0), (25, 29), (11, 23), (7, 15), (14, 26), (8, 8), (7, 13), (20, 18), (26, 29), (22, 23), (19, 22), (2, 16), (1, 9), (24, 20), (5, 17), (20, 9), (26, 9), (24, 27), (29, 27), (6, 31), (2, 18), (24, 13), (24, 11), (31, 4), (2, 12), (16, 10), (34, 6), (2, 29), (5, 24), (6, 10), (32, 16), (13, 28), (3, 17), (26, 11), (25, 32), (28, 7), (34, 26), (34, 12), (33, 11), (16, 11), (9, 3), (29, 26), (25, 0), (5, 31), (18, 12), (27, 3), (15, 0), (15, 24), (2, 22), (19, 7), (11, 21), (3, 21), (25, 13), (12, 27), (20, 23), (32, 21), (24, 4), (13, 23), (5, 27), (8, 5), (29, 25), (14, 8), (4, 3), (9, 21), (8, 27), (21, 15), (10, 26), (17, 5), (20, 30), (7, 24), (3, 13), (31, 6), (22, 10), (1, 28), (3, 3), (11, 3), (31, 18), (15, 29), (32, 27), (29, 18), (11, 31), (23, 25), (30, 22), (11, 7), (10, 0), (21, 16), (3, 8), (33, 24), (14, 3), (31, 20), (22, 9), (31, 31), (29, 1), (27, 22), (32, 20), (34, 5), (8, 25), (29, 11), (21, 24), (14, 25), (10, 19), (34, 31), (13, 9), (26, 0), (24, 2), (14, 18), (1, 2), (33, 3), (12, 32), (15, 10), (33, 25), (2, 25), (21, 5), (34, 2), (15, 7), (0, 20), (21, 18), (33, 13), (7, 26), (11, 4), (16, 23), (12, 20), (32, 10), (22, 12), (25, 7), (13, 26), (7, 1), (19, 0), (15, 26), (9, 29), (3, 29), (6, 9), (32, 9), (22, 14), (16, 2), (16, 31), (29, 15), (26, 18), (13, 19), (2, 8), (17, 7), (8, 24), (22, 26), (21, 21), (3, 15), (21, 4), (9, 19), (15, 1), (30, 12), (28, 16), (18, 25), (10, 2), (4, 29), (7, 0), (33, 4), (23, 9), (25, 4), (7, 28), (10, 25), (11, 6), (22, 3), (19, 3), (22, 29), (15, 21), (10, 28), (12, 9), (3, 22), (27, 27), (13, 29), (25, 19), (34, 15), (8, 2), (13, 24), (0, 18), (7, 12), (33, 20), (15, 20), (22, 27), (10, 10), (5, 12), (2, 4), (31, 21), (2, 2), (4, 24), (18, 31), (6, 21), (1, 3), (27, 20), (14, 9), (6, 3), (1, 26), (31, 5), (12, 21), (18, 21), (25, 24), (5, 25), (28, 11), (34, 30), (3, 20), (27, 5), (21, 10), (19, 26), (16, 1), (27, 23), (21, 17), (30, 15), (14, 0), (10, 23), (17, 30), (24, 24), (19, 21), (9, 5), (24, 1), (8, 11), (28, 18), (15, 27), (1, 20), (10, 30), (21, 26), (32, 0), (34, 22), (17, 9), (34, 16), (3, 5), (3, 12), (22, 31), (29, 16), (24, 28), (24, 9), (34, 0), (17, 10), (13, 6), (25, 30), (14, 7), (7, 25), (9, 15), (22, 25), (27, 14), (11, 17), (14, 27), (21, 28), (23, 28), (17, 19), (15, 13), (2, 14), (33, 6), (0, 24), (2, 0), (28, 29), (20, 31), (5, 9), (18, 24), (31, 23), (19, 8), (5, 1), (34, 3), (13, 0), (34, 14), (20, 32), (28, 4), (0, 27), (21, 0), (4, 11), (18, 26), (30, 21), (1, 4), (31, 7), (29, 2), (20, 11), (22, 24), (2, 28), (16, 14), (8, 30), (7, 5), (15, 2), (31, 0), (27, 24), (6, 5), (10, 21), (26, 14), (0, 23), (22, 7), (8, 32), (22, 16), (21, 20), (10, 3), (16, 27), (18, 22), (18, 27), (34, 19), (13, 32), (20, 6), (9, 6), (6, 7), (17, 23), (17, 2), (25, 8), (8, 9), (10, 8), (31, 15), (14, 15), (9, 18), (9, 17), (30, 30), (9, 12), (8, 22), (31, 17), (15, 31), (27, 32), (20, 4), (30, 7), (24, 19), (2, 21), (30, 17), (20, 10), (31, 13), (10, 22), (25, 10), (1, 15), (7, 6), (16, 15), (32, 18), (19, 9), (17, 16), (16, 18), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940896", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (13, 22), (6, 28), (12, 21), (23, 19), (25, 27), (13, 1), (13, 2), (22, 27), (18, 26), (4, 25), (16, 26), (4, 16), (23, 22), (2, 20), (3, 10), (23, 4), (11, 13), (36, 4), (27, 18), (24, 1), (16, 11), (29, 7), (28, 20), (15, 3), (31, 3), (8, 2), (13, 10), (6, 10), (4, 10), (8, 28), (28, 24), (36, 19), (25, 19), (29, 28), (19, 12), (26, 5), (8, 19), (24, 13), (34, 18), (28, 19), (11, 17), (14, 3), (19, 23), (15, 20), (4, 20), (20, 19), (21, 18), (1, 17), (27, 25), (22, 20), (1, 20), (28, 8), (12, 22), (1, 22), (17, 27), (4, 6), (17, 28), (20, 4), (23, 26), (19, 16), (17, 2), (27, 17), (3, 4), (21, 23), (7, 21), (6, 0), (24, 28), (1, 5), (2, 25), (21, 0), (19, 10), (9, 20), (30, 18), (8, 16), (35, 3), (16, 23), (19, 27), (3, 24), (30, 28), (22, 25), (31, 2), (16, 28), (34, 3), (21, 25), (15, 5), (5, 19), (33, 7), (13, 4), (17, 14), (12, 5), (32, 3), (1, 1), (8, 27), (28, 23), (13, 25), (26, 4), (27, 8), (28, 13), (15, 10), (34, 12), (22, 29), (7, 1), (26, 10), (35, 4), (14, 13), (4, 22), (6, 3), (29, 6), (4, 29), (11, 12), (19, 29), (17, 4), (34, 8), (4, 18), (33, 2), (3, 5), (15, 9), (10, 3), (0, 9), (34, 9), (0, 23), (32, 18), (34, 10), (6, 25), (26, 16), (28, 12), (5, 24), (17, 9), (28, 29), (26, 26), (32, 25), (9, 29), (7, 7), (0, 29), (35, 13), (9, 15), (31, 20), (26, 13), (20, 1), (14, 6), (1, 0), (17, 6), (8, 4), (21, 3), (12, 16), (12, 12), (31, 28), (8, 14), (29, 10), (8, 1), (3, 20), (14, 11), (7, 8), (24, 20), (17, 16), (20, 9), (29, 24), (21, 7), (19, 24), (32, 6), (32, 11), (14, 24), (33, 27), (26, 25), (2, 18), (5, 28), (11, 28), (5, 2), (33, 12), (11, 24), (7, 4), (32, 24), (29, 18), (25, 7), (24, 10), (7, 25), (33, 6), (35, 29), (5, 8), (24, 5), (2, 12), (36, 22), (16, 18), (10, 4), (34, 19), (36, 21), (15, 18), (18, 2), (30, 24), (16, 14), (2, 7), (32, 9), (6, 7), (9, 8), (31, 23), (9, 11), (30, 1), (32, 23), (6, 9), (3, 16), (25, 21), (0, 13), (10, 29), (5, 1), (6, 22), (14, 22), (16, 24), (13, 21), (33, 25), (34, 27), (24, 15), (22, 10), (23, 29), (19, 18), (30, 22), (25, 4), (0, 6), (10, 21), (2, 8), (33, 23), (4, 1), (28, 25), (22, 6), (27, 16), (1, 8), (16, 22), (19, 2), (22, 7), (32, 0), (14, 15), (23, 24), (9, 17), (17, 15), (30, 0), (20, 26), (19, 11), (29, 3), (2, 10), (8, 25), (7, 22), (14, 7), (23, 14), (25, 5), (3, 23), (25, 26), (10, 5), (5, 21), (9, 18), (8, 9), (20, 27), (9, 22), (9, 23), (22, 14), (31, 0), (8, 13), (11, 2), (19, 19), (36, 2), (1, 19), (10, 24), (35, 6), (24, 9), (23, 25), (0, 19), (5, 20), (4, 14), (34, 2), (16, 21), (17, 19), (11, 15), (14, 5), (3, 1), (8, 10), (5, 29), (31, 25), (10, 27), (5, 5), (7, 12), (27, 13), (5, 7), (16, 6), (31, 9), (3, 8), (22, 4), (32, 15), (19, 6), (9, 25), (24, 3), (13, 16), (22, 5), (23, 10), (18, 24), (20, 21), (12, 11), (24, 7), (36, 27), (33, 20), (26, 6), (36, 6), (9, 1), (23, 15), (26, 24), (25, 0), (11, 20), (28, 16), (33, 16), (15, 21), (23, 6), (4, 23), (0, 17), (2, 5), (12, 24), (7, 26), (27, 11), (0, 26), (16, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62370", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), 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), (25, 26), (18, 18), (10, 28), (20, 7), (30, 16), (17, 24), (21, 2), (20, 30), (1, 10), (26, 8), (12, 25), (14, 12), (17, 0), (27, 15), (27, 18), (20, 18), (33, 26), (19, 16), (38, 26), (27, 29), (28, 1), (20, 34), (17, 21), (29, 4), (22, 29), (10, 12), (0, 34), (25, 30), (13, 6), (4, 14), (6, 33), (30, 22), (33, 29), (6, 1), (13, 4), (31, 31), (19, 8), (15, 13), (28, 33), (6, 25), (32, 28), (31, 20), (0, 17), (15, 7), (5, 18), (15, 3), (33, 14), (37, 17), (28, 6), (35, 6), (2, 11), (38, 32), (26, 25), (12, 20), (4, 10), (9, 7), (8, 31), (32, 25), (36, 24), (4, 4), (22, 34), (24, 10), (6, 0), (13, 9), (38, 20), (19, 10), (38, 5), (28, 10), (24, 33), (9, 4), (21, 7), (32, 8), (21, 13), (30, 15), (31, 1), (35, 22), (1, 31), (33, 11), (7, 33), (0, 9), (9, 29), (0, 22), (34, 22), (3, 10), (29, 10), (29, 12), (19, 31), (11, 4), (26, 30), (34, 2), (21, 1), (22, 32), (21, 21), (36, 10), (14, 11), (23, 12), (37, 15), (29, 25), (8, 29), (3, 5), (27, 16), (1, 24), (7, 26), (34, 33), (8, 12), (37, 20), (19, 3), (24, 12), (8, 8), (32, 19), (26, 15), (1, 17), (18, 7), (7, 13), (13, 30), (19, 15), (22, 24), (30, 33), (22, 7), (32, 1), (20, 25), (35, 21), (22, 15), (14, 2), (38, 21), (34, 31), (11, 9), (6, 11), (33, 32), (27, 13), (7, 8), (8, 3), (19, 14), (35, 18), (14, 10), (18, 13), (14, 24), (8, 32), (20, 22), (23, 13), (21, 11), (3, 7), (29, 24), (38, 30), (19, 23), (26, 7), (7, 32), (7, 23), (1, 1), (29, 13), (9, 34), (28, 12), (26, 19), (15, 17), (30, 26), (25, 9), (12, 26), (32, 16), (9, 2), (18, 6), (31, 22), (32, 6), (3, 2), (36, 30), (16, 34), (21, 12), (11, 25), (15, 25), (27, 24), (9, 18), (13, 24), (18, 19), (1, 33), (10, 27), (20, 21), (25, 12), (6, 18), (24, 15), (8, 11), (33, 3), (1, 34), (25, 11), (27, 17), (37, 19), (4, 1), (17, 7), (31, 13), (15, 22), (37, 28), (35, 16), (38, 1), (32, 32), (15, 5), (3, 31), (33, 10), (19, 7), (16, 27), (22, 10), (20, 16), (4, 28), (21, 20), (31, 15), (16, 2), (6, 14), (4, 12), (8, 4), (26, 26), (6, 26), (11, 31), (32, 4), (31, 9), (31, 32), (21, 32), (26, 27), (3, 15), (26, 16), (32, 30), (24, 11), (33, 4), (9, 27), (12, 31), (9, 25), (29, 23), (16, 32), (22, 9), (12, 24), (35, 1), (0, 5), (10, 15), (32, 17), (4, 8), (27, 19), (22, 31), (24, 18), (20, 0), (18, 28), (28, 20), (0, 7), (10, 30), (35, 14), (4, 23), (28, 21), (26, 1), (26, 13), (0, 6), (13, 17), (7, 15), (32, 26), (7, 27), (23, 21), (17, 11), (19, 5), (6, 19), (34, 8), (6, 27), (35, 33), (37, 31), (22, 14), (11, 16), (38, 13), (32, 10), (35, 30), (25, 5), (0, 11), (30, 7), (38, 12), (31, 2), (15, 26), (2, 2), (38, 15), (12, 16), (0, 19), (6, 10), (8, 9), (16, 23), (21, 23), (32, 7), (23, 17), (38, 29), (8, 34), (11, 0), (24, 14), (20, 15), (30, 1), (38, 22), (36, 4), (0, 14), (4, 22), (11, 11), (14, 33), (5, 15), (4, 29), (1, 12), (32, 3), (9, 15), (5, 33), (30, 31), (7, 14), (21, 19), (10, 24), (31, 23), (20, 3), (7, 21), (20, 14), (2, 18), (32, 5), (14, 21), (13, 32), (13, 26), (11, 23), (4, 30), (32, 29), (34, 12), (29, 1), (2, 1), (1, 8), (4, 16), (10, 4), (9, 21), (25, 18), (19, 28), (12, 28), (15, 31), (3, 0), (23, 34), (2, 22), (6, 13), (28, 23), (21, 18), (15, 33), (0, 25), (23, 22), (28, 18), (32, 31), (4, 6), (20, 31), (24, 30), (9, 14), (1, 0), (17, 30), (33, 22), (31, 18), (1, 5), (28, 34), (20, 24), (27, 14), (25, 20), (5, 13), (13, 13), (18, 25), (27, 33), (26, 2), (25, 31), (10, 19), (29, 30), (15, 23), (12, 32), (32, 12), (26, 22), (3, 17), (33, 7), (20, 32), (32, 15), (37, 29), (34, 18), (27, 20), (3, 23), (25, 32), (33, 19), (3, 1), (6, 16), (15, 14), (34, 10), (5, 7), (32, 18), (5, 24), (9, 32), (8, 18), (7, 2), (24, 28), (12, 10), (3, 13), (35, 31), (16, 0), (3, 30), (17, 10), (31, 30), (11, 17), (28, 8), (31, 29), (11, 27), (28, 25), (25, 2), (16, 6), (22, 18), (26, 5), (30, 30), (26, 11), (19, 19), (1, 26), (15, 1), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "955152", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 28), (8, 6), (29, 25), (18, 23), (19, 1), (6, 3), (23, 2), (31, 18), (3, 15), (16, 3), (7, 0), (26, 29), (6, 13), (30, 13), (11, 14), (11, 29), (3, 10), (21, 17), (15, 2), (12, 25), (29, 21), (15, 29), (19, 24), (28, 28), (18, 20), (18, 28), (23, 22), (12, 4), (18, 21), (15, 20), (18, 29), (11, 24), (16, 22), (6, 14), (8, 13), (26, 13), (25, 20), (1, 6), (25, 5), (14, 28), (31, 14), (3, 16), (3, 3), (11, 21), (29, 27), (9, 19), (13, 29), (31, 2), (15, 12), (22, 26), (10, 0), (10, 19), (9, 23), (7, 23), (19, 8), (5, 16), (14, 10), (30, 25), (8, 10), (9, 30), (6, 1), (12, 30), (10, 2), (3, 8), (16, 7), (31, 9), (22, 14), (20, 24), (27, 25), (27, 3), (23, 24), (26, 21), (30, 7), (27, 7), (1, 16), (15, 16), (15, 13), (9, 9), (3, 2), (0, 16), (15, 3), (22, 29), (26, 14), (27, 18), (17, 14), (21, 11), (24, 14), (24, 8), (15, 28), (8, 27), (23, 29), (17, 22), (8, 16), (26, 19), (12, 13), (15, 18), (0, 29), (9, 18), (5, 24), (31, 6), (30, 16), (9, 20), (26, 3), (7, 12), (29, 15), (30, 8), (24, 15), (21, 22), (29, 2), (19, 25), (5, 27), (30, 20), (6, 11), (4, 6), (2, 6), (16, 8), (18, 9), (9, 17), (27, 29), (27, 12), (31, 5), (9, 6), (4, 7), (18, 12), (11, 2), (9, 8), (27, 20), (14, 19), (20, 12), (0, 11), (28, 25), (7, 11), (8, 23), (22, 15), (4, 5), (2, 5), (14, 30), (14, 18), (9, 16), (22, 0), (21, 7), (5, 2), (23, 20), (23, 30), (17, 7), (16, 27), (29, 14), (10, 13), (29, 26), (24, 6), (27, 22), (24, 0), (12, 29), (5, 9), (25, 26), (20, 28), (19, 10), (10, 9), (10, 3), (24, 16), (7, 14), (24, 26), (3, 14), (11, 9), (1, 4), (16, 30), (22, 24), (0, 27), (27, 14), (9, 24), (0, 20), (10, 1), (17, 12), (27, 5), (7, 26), (27, 2), (30, 6), (1, 15), (31, 1), (15, 23), (6, 6), (17, 1), (19, 14), (13, 13), (12, 17), (12, 26), (27, 8), (30, 30), (16, 24), (6, 0), (17, 13), (9, 0), (23, 21), (5, 5), (24, 11), (18, 25), (16, 10), (10, 30), (10, 17), (9, 25), (25, 29), (20, 8), (27, 17), (23, 19), (30, 11), (4, 18), (18, 24), (0, 8), (28, 27), (16, 2), (24, 20), (4, 3), (10, 4), (28, 29), (23, 7), (12, 5), (7, 19), (18, 11), (29, 19), (15, 7), (24, 2), (28, 0), (29, 4), (2, 8), (20, 0), (1, 22), (2, 13), (18, 19), (31, 16), (29, 11), (15, 22), (1, 8), (14, 8), (0, 4), (17, 8), (14, 16), (18, 1), (13, 2), (1, 21), (31, 21), (23, 10), (22, 17), (16, 12), (23, 5), (23, 9), (22, 7), (15, 19), (8, 20), (4, 2), (25, 8), (22, 21), (8, 29), (28, 3), (4, 11), (16, 29), (24, 25), (13, 26), (5, 26), (7, 15), (13, 23), (23, 11), (7, 7), (30, 10), (16, 19), (13, 21), (13, 24), (14, 20), (7, 22), (30, 21), (3, 25), (12, 10), (9, 27), (18, 2), (9, 14), (0, 30), (15, 11), (20, 6), (5, 29), (27, 30), (25, 25), (2, 24), (30, 0), (22, 5), (9, 7), (7, 4), (6, 24), (2, 11), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 24), (3, 26), (26, 16), (7, 32), (3, 11), (9, 28), (1, 11), (2, 18), (36, 5), (0, 28), (20, 21), (38, 25), (29, 16), (17, 15), (1, 13), (7, 8), (15, 32), (8, 22), (10, 6), (16, 13), (20, 10), (31, 1), (29, 26), (16, 4), (23, 15), (31, 32), (7, 12), (29, 20), (22, 32), (19, 21), (0, 19), (30, 18), (15, 33), (1, 20), (26, 0), (9, 13), (6, 34), (8, 1), (6, 0), (2, 26), (4, 4), (29, 11), (12, 24), (4, 33), (16, 11), (8, 10), (8, 6), (18, 24), (16, 25), (21, 21), (31, 0), (14, 18), (32, 28), (34, 17), (22, 9), (19, 33), (33, 2), (7, 11), (12, 20), (22, 12), (9, 17), (5, 35), (38, 29), (14, 4), (18, 11), (29, 10), (7, 22), (25, 2), (12, 3), (24, 5), (5, 1), (37, 6), (12, 2), (7, 19), (13, 12), (0, 4), (22, 29), (21, 3), (2, 7), (36, 34), (30, 22), (30, 30), (30, 28), (38, 12), (21, 4), (31, 14), (8, 32), (26, 29), (24, 35), (32, 19), (37, 7), (10, 14), (37, 32), (38, 26), (9, 11), (7, 21), (3, 30), (12, 8), (37, 30), (12, 29), (28, 21), (36, 10), (29, 21), (12, 7), (20, 23), (21, 6), (24, 22), (38, 22), (26, 6), (2, 11), (12, 35), (6, 20), (9, 7), (32, 26), (20, 17), (12, 19), (29, 14), (35, 7), (26, 3), (9, 2), (31, 17), (27, 16), (29, 1), (22, 2), (34, 32), (33, 24), (23, 13), (18, 13), (24, 7), (15, 23), (10, 28), (31, 12), (12, 31), (28, 33), (33, 33), (9, 16), (35, 0), (27, 1), (16, 31), (3, 24), (12, 4), (24, 9), (22, 15), (30, 8), (17, 3), (34, 15), (4, 23), (4, 6), (33, 26), (3, 32), (33, 5), (24, 6), (5, 9), (14, 19), (19, 4), (0, 25), (18, 31), (3, 5), (20, 30), (36, 9), (28, 7), (22, 0), (5, 4), (27, 28), (36, 8), (38, 4), (4, 28), (24, 25), (10, 15), (4, 34), (18, 34), (29, 31), (27, 35), (32, 3), (25, 14), (24, 20), (6, 26), (24, 30), (5, 6), (25, 28), (23, 30), (11, 22), (4, 13), (13, 7), (30, 12), (25, 33), (34, 16), (11, 7), (15, 34), (27, 14), (2, 6), (21, 11), (24, 16), (17, 26), (14, 8), (13, 14), (18, 32), (36, 6), (9, 3), (26, 24), (6, 35), (3, 19), (33, 25), (35, 8), (26, 26), (35, 33), (28, 20), (35, 25), (30, 32), (3, 12), (25, 9), (32, 12), (33, 30), (19, 8), (0, 24), (7, 28), (18, 16), (21, 16), (3, 34), (12, 28), (14, 5), (25, 23), (18, 18), (15, 3), (0, 35), (23, 27), (15, 15), (27, 4), (22, 19), (27, 15), (19, 16), (8, 7), (16, 18), (29, 8), (10, 35), (11, 34), (29, 29), (23, 12), (11, 35), (19, 29), (16, 32), (10, 17), (2, 9), (0, 15), (36, 32), (23, 1), (34, 26), (11, 32), (5, 0), (3, 35), (38, 32), (31, 7), (31, 19), (27, 8), (29, 2), (34, 14), (26, 28), (6, 10), (5, 19), (37, 22), (29, 28), (34, 6), (21, 0), (20, 35), (19, 18), (31, 25), (5, 12), (17, 12), (30, 34), (38, 34), (34, 5), (19, 19), (25, 13), (14, 11), (24, 13), (12, 0), (24, 26), (27, 19), (0, 8), (27, 0), (13, 18), (25, 24), (31, 9), (5, 23), (6, 32), (33, 28), (12, 11), (35, 26), (27, 26), (12, 33), (15, 13), (8, 19), (27, 33), (1, 28), (13, 8), (26, 34), (14, 27), (38, 27), (5, 20), (15, 11), (24, 10), (33, 12), (16, 27), (37, 33), (5, 21), (34, 0), (8, 26), (17, 19), (13, 9), (38, 20), (38, 1), (26, 14), (18, 20), (17, 9), (2, 24), (3, 13), (22, 24), (20, 32), (20, 22), (34, 12), (27, 25), (24, 15), (20, 26), (10, 20), (7, 3), (16, 14), (1, 30), (31, 29), (3, 8), (15, 28), (15, 12), (8, 30), (28, 5), (35, 14), (19, 12), (12, 21), (35, 34), (18, 21), (6, 19), (19, 23), (11, 20), (14, 25), (10, 29), (34, 8), (8, 9), (12, 17), (10, 13), (37, 25), (13, 5), (15, 19), (32, 7), (28, 35), (11, 25), (34, 19), (6, 6), (22, 28), (21, 28), (7, 1), (19, 27), (18, 19), (16, 9), (6, 15), (31, 35), (22, 21), (33, 31), (6, 16), (6, 7), (38, 33), (22, 33), (13, 20), (21, 26), (11, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427680", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (6, 15), (18, 24), (18, 8), (5, 17), (17, 2), (19, 20), (5, 27), (26, 23), (23, 25), (26, 11), (2, 1), (15, 21), (18, 28), (19, 6), (11, 17), (11, 23), (7, 11), (12, 13), (5, 11), (9, 15), (3, 15), (6, 29), (27, 22), (16, 27), (28, 7), (24, 14), (2, 20), (17, 14), (26, 15), (0, 5), (1, 29), (6, 24), (7, 23), (14, 0), (1, 25), (6, 6), (26, 26), (21, 5), (10, 28), (2, 24), (21, 0), (12, 1), (6, 19), (3, 29), (26, 20), (22, 27), (15, 2), (15, 11), (18, 6), (29, 12), (25, 2), (10, 22), (16, 13), (19, 0), (0, 20), (21, 15), (27, 25), (13, 11), (29, 17), (10, 1), (0, 17), (8, 10), (17, 24), (29, 3), (11, 4), (9, 27), (25, 10), (0, 28), (27, 15), (11, 28), (16, 14), (15, 1), (15, 5), (20, 22), (19, 8), (5, 28), (28, 22), (21, 12), (6, 10), (13, 0), (4, 2), (3, 22), (24, 25), (22, 11), (16, 28), (26, 13), (8, 13), (21, 24), (27, 2), (2, 8), (23, 10), (4, 27), (12, 5), (29, 27), (9, 20), (27, 4), (22, 8), (3, 26), (18, 10), (23, 3), (19, 27), (23, 20), (6, 9), (23, 4), (4, 26), (7, 13), (26, 19), (13, 14), (1, 17), (29, 19), (12, 24), (3, 16), (1, 12), (4, 16), (21, 21), (23, 14), (11, 12), (13, 4), (10, 29), (27, 18), (12, 23), (27, 11), (0, 6), (10, 10), (3, 1), (10, 3), (9, 23), (6, 25), (11, 26), (4, 28), (21, 25), (28, 3), (4, 18), (13, 16), (18, 23), (28, 9), (10, 11), (1, 15), (14, 15), (3, 20), (20, 10), (28, 11), (28, 8), (18, 5), (25, 27), (0, 25), (22, 16), (27, 8), (12, 25), (24, 27), (6, 7), (21, 19), (22, 5), (18, 15), (1, 1), (29, 8), (18, 13), (19, 12), (28, 16), (14, 9), (14, 8), (19, 3), (12, 20), (16, 10), (4, 20), (18, 17), (4, 17), (5, 4), (15, 8), (9, 19), (17, 0), (13, 18), (25, 9), (7, 7), (25, 19), (3, 3), (13, 10), (2, 15), (1, 18), (22, 24), (26, 1), (1, 4), (17, 10), (20, 3), (29, 14), (23, 24), (21, 16), (2, 4), (16, 17), (2, 2), (24, 26), (10, 2), (25, 21), (14, 28), (6, 17), (19, 16), (17, 25), (16, 23), (23, 18), (6, 14), (10, 20), (0, 16), (9, 1), (5, 6), (19, 26), (4, 8), (23, 0), (0, 19), (14, 17), (20, 24), (21, 28), (12, 7), (12, 15), (0, 1), (16, 6), (9, 17), (8, 28), (29, 21), (12, 27), (23, 19), (8, 6), (25, 16), (27, 1), (0, 12), (6, 8), (16, 18), (13, 24), (29, 13), (25, 13), (19, 23), (21, 14), (20, 12), (0, 13), (19, 14), (22, 0), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540720", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), 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), (6, 25), (4, 15), (16, 0), (17, 2), (7, 21), (31, 33), (16, 9), (16, 16), (23, 15), (16, 24), (19, 4), (11, 11), (3, 11), (0, 25), (2, 23), (23, 17), (22, 30), (11, 2), (17, 32), (25, 7), (27, 9), (9, 20), (24, 29), (12, 5), (5, 16), (24, 9), (21, 8), (1, 19), (21, 3), (5, 32), (12, 13), (21, 10), (13, 6), (24, 28), (26, 10), (18, 16), (5, 13), (4, 10), (17, 9), (19, 27), (6, 1), (0, 24), (7, 13), (11, 25), (32, 18), (8, 19), (23, 5), (15, 29), (28, 22), (24, 31), (23, 23), (31, 17), (18, 24), (18, 11), (27, 8), (16, 8), (12, 19), (15, 27), (12, 2), (25, 0), (1, 6), (20, 20), (29, 29), (10, 32), (11, 1), (20, 25), (14, 3), (22, 1), (7, 7), (28, 3), (27, 17), (8, 28), (10, 4), (22, 10), (6, 5), (4, 7), (3, 14), (1, 25), (18, 21), (14, 11), (24, 14), (18, 27), (12, 0), (3, 30), (19, 25), (23, 7), (30, 28), (21, 25), (17, 30), (29, 14), (29, 6), (0, 33), (16, 25), (10, 19), (17, 5), (22, 29), (8, 27), (8, 2), (1, 3), (13, 33), (26, 6), (13, 3), (18, 17), (9, 22), (17, 4), (11, 12), (30, 21), (25, 5), (3, 9), (32, 27), (21, 14), (2, 27), (24, 3), (15, 9), (13, 28), (14, 20), (2, 30), (25, 21), (4, 1), (28, 24), (16, 10), (13, 25), (10, 8), (24, 20), (7, 18), (12, 33), (13, 12), (18, 29), (28, 12), (11, 10), (26, 8), (29, 13), (8, 7), (10, 14), (4, 18), (0, 27), (10, 27), (32, 25), (29, 28), (17, 0), (17, 24), (5, 5), (3, 20), (25, 13), (19, 26), (19, 13), (26, 15), (25, 26), (6, 8), (9, 14), (20, 7), (14, 9), (29, 4), (14, 29), (31, 6), (27, 33), (24, 33), (3, 16), (4, 9), (15, 12), (14, 12), (30, 0), (16, 12), (18, 12), (9, 30), (24, 22), (29, 30), (3, 28), (30, 13), (30, 33), (17, 28), (31, 20), (30, 24), (12, 18), (30, 18), (26, 18), (29, 22), (1, 5), (2, 28), (11, 32), (9, 6), (31, 27), (5, 33), (19, 31), (10, 18), (29, 27), (26, 5), (8, 12), (1, 18), (13, 10), (4, 17), (16, 17), (2, 8), (10, 2), (10, 10), (18, 33), (10, 3), (10, 17), (23, 4), (20, 0), (24, 30), (26, 23), (14, 15), (0, 15), (30, 20), (28, 19), (7, 14), (8, 15), (18, 20), (5, 14), (8, 32), (13, 19), (12, 3), (24, 25), (28, 32), (29, 12), (25, 2), (6, 26), (0, 9), (14, 0), (1, 23), (4, 23), (31, 14), (15, 6), (19, 2), (14, 33), (10, 15), (12, 29), (11, 16), (13, 32), (19, 33), (18, 7), (21, 29), (10, 1), (14, 24), (1, 17), (9, 11), (8, 13), (25, 33), (0, 13), (15, 11), (7, 30), (1, 7), (30, 15), (9, 26), (14, 22), (6, 17), (20, 27), (24, 4), (26, 33), (1, 15), (22, 26), (15, 8), (1, 9), (11, 22), (28, 1), (20, 11), (26, 21), (22, 0), (28, 9), (29, 3), (21, 31), (20, 6), (19, 1), (11, 3), (19, 30), (14, 5), (6, 21), (16, 18), (23, 14), (4, 8), (7, 25), (12, 25), (19, 18), (18, 26), (9, 32), (31, 13), (4, 25), (25, 25), (13, 21), (3, 22), (24, 10), (30, 12), (28, 0), (20, 18), (15, 32), (27, 0), (27, 7), (22, 9), (1, 30), (14, 26), (21, 7), (2, 5), (9, 4), (15, 15), (30, 9), (18, 14), (2, 26), (6, 16), (31, 32), (7, 31), (30, 25), (18, 23), (18, 0), (23, 0), (32, 6), (9, 1), (0, 28), (26, 29), (12, 17), (14, 31), (11, 15), (31, 0), (3, 10), (13, 20), (32, 4), (18, 18), (1, 33), (10, 25), (22, 19), (6, 3), (10, 30), (28, 17), (26, 25), (21, 23), (32, 24), (21, 26), (29, 0), (29, 9), (32, 26), (23, 8), (12, 31), (12, 21), (23, 31), (5, 30), (11, 33), (30, 3), (12, 6), (0, 8), (22, 17), (15, 16), (6, 11), (6, 30), (25, 11), (25, 16), (6, 9), (12, 30), (11, 18), (11, 26), (8, 16), (9, 10), (32, 16), (28, 10), (27, 13), (21, 16), (1, 29), (2, 17), (29, 15), (0, 16), (12, 12), (1, 20), (31, 11), (11, 9), (9, 29), (2, 15), (20, 31), (14, 23), (3, 15), (8, 11), (26, 14), (4, 5), (32, 2), (8, 1), (15, 20), (19, 20), (30, 17), (18, 31), (11, 21), (1, 31), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "505440", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 35), (11, 1), (19, 10), (29, 3), (23, 31), (11, 8), (14, 20), (4, 17), (7, 29), (14, 9), (18, 8), (33, 0), (18, 30), (25, 32), (28, 3), (15, 21), (21, 18), (23, 21), (20, 14), (8, 0), (15, 6), (18, 25), (29, 6), (13, 16), (14, 2), (11, 31), (21, 22), (18, 22), (16, 34), (9, 13), (32, 1), (28, 13), (32, 23), (25, 28), (29, 33), (28, 0), (7, 15), (4, 29), (34, 7), (18, 23), (12, 34), (4, 10), (32, 32), (12, 35), (28, 9), (31, 20), (14, 14), (11, 14), (28, 14), (28, 17), (25, 11), (5, 28), (5, 11), (32, 2), (0, 23), (7, 20), (27, 20), (2, 16), (22, 36), (32, 21), (18, 9), (13, 12), (33, 30), (5, 7), (27, 24), (13, 23), (26, 15), (11, 18), (0, 16), (33, 32), (14, 4), (26, 33), (18, 24), (33, 31), (12, 31), (20, 20), (11, 13), (28, 23), (13, 6), (28, 33), (28, 28), (22, 24), (19, 20), (25, 8), (3, 16), (17, 34), (2, 0), (20, 35), (25, 22), (10, 4), (16, 7), (20, 17), (6, 2), (9, 12), (22, 18), (1, 24), (18, 3), (13, 28), (25, 0), (25, 10), (16, 10), (11, 6), (21, 8), (30, 15), (22, 8), (10, 26), (13, 4), (11, 35), (18, 13), (22, 5), (4, 19), (30, 31), (9, 32), (0, 6), (17, 20), (19, 15), (16, 0), (16, 4), (32, 0), (28, 36), (8, 14), (19, 25), (23, 26), (5, 1), (17, 29), (30, 19), (29, 19), (3, 31), (4, 24), (35, 0), (5, 2), (26, 30), (33, 4), (23, 23), (2, 3), (2, 28), (19, 28), (24, 24), (25, 3), (33, 35), (12, 4), (18, 35), (32, 36), (16, 23), (6, 26), (8, 33), (13, 33), (12, 13), (19, 0), (28, 5), (21, 0), (8, 3), (2, 14), (27, 11), (12, 23), (26, 21), (29, 10), (30, 6), (34, 32), (2, 8), (34, 22), (1, 5), (33, 28), (19, 13), (33, 23), (23, 10), (10, 29), (2, 35), (9, 9), (1, 4), (33, 25), (10, 19), (33, 13), (1, 9), (12, 32), (7, 35), (1, 35), (28, 8), (20, 8), (3, 8), (3, 36), (9, 33), (4, 0), (18, 29), (31, 10), (3, 34), (19, 29), (6, 11), (35, 10), (26, 28), (12, 21), (23, 33), (27, 27), (13, 2), (19, 2), (5, 8), (7, 4), (32, 30), (14, 10), (11, 20), (29, 31), (10, 14), (27, 17), (8, 26), (8, 1), (25, 18), (21, 27), (20, 32), (18, 28), (30, 25), (11, 30), (1, 28), (2, 20), (33, 2), (14, 17), (5, 26), (27, 30), (25, 12), (20, 21), (9, 0), (28, 18), (10, 15), (5, 6), (34, 18), (20, 19), (11, 27), (2, 22), (28, 2), (24, 36), (22, 1), (19, 22), (12, 26), (6, 29), (8, 34), (3, 29), (22, 12), (29, 9), (34, 25), (24, 10), (2, 9), (31, 15), (6, 20), (1, 10), (12, 10), (0, 19), (31, 27), (25, 14), (35, 9), (2, 29), (13, 34), (22, 13), (30, 30), (13, 31), (20, 6), (4, 2), (32, 14), (14, 29), (25, 17), (14, 31), (22, 19), (32, 6), (25, 13), (10, 7), (15, 11), (22, 34), (9, 17), (34, 4), (26, 25), (30, 11), (24, 6), (5, 25), (14, 24), (12, 11), (29, 18), (20, 30), (17, 7), (22, 4), (35, 20), (26, 2), (33, 20), (35, 21), (10, 5), (6, 33), (33, 14), (31, 12), (17, 0), (27, 19), (19, 1), (8, 8), (23, 22), (13, 18), (5, 14), (14, 27), (34, 1), (34, 36), (13, 27), (26, 0), (32, 29), (26, 10), (25, 31), (19, 32), (27, 32), (16, 11), (3, 14), (31, 33), (16, 36), (34, 27), (18, 17), (0, 13), (34, 24), (7, 23), (15, 36), (27, 12), (29, 25), (9, 3), (35, 19), (8, 11), (5, 5), (2, 36), (26, 20), (20, 29), (22, 23), (13, 19), (15, 31), (26, 22), (0, 12), (8, 2), (21, 13), (17, 3), (31, 17), (4, 7), (19, 3), (21, 29), (35, 2), (16, 22), (8, 24), (21, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "448560", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), 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), (28, 28), (0, 28), (8, 10), (33, 6), (30, 26), (6, 17), (19, 10), (16, 5), (36, 14), (23, 30), (34, 1), (0, 17), (16, 10), (25, 11), (31, 1), (7, 18), (9, 1), (31, 12), (12, 11), (0, 5), (10, 0), (25, 3), (5, 21), (14, 4), (15, 30), (37, 26), (16, 27), (19, 29), (4, 10), (33, 10), (14, 26), (2, 0), (34, 24), (22, 16), (30, 15), (17, 6), (10, 6), (35, 10), (27, 8), (34, 13), (1, 16), (18, 7), (38, 8), (8, 30), (9, 18), (13, 5), (36, 10), (34, 12), (9, 20), (21, 13), (9, 14), (21, 21), (27, 21), (15, 14), (23, 12), (26, 5), (25, 20), (13, 15), (24, 10), (15, 7), (30, 5), (36, 29), (30, 3), (17, 23), (18, 12), (14, 23), (4, 13), (16, 9), (30, 1), (7, 21), (37, 4), (7, 13), (13, 10), (0, 8), (14, 21), (12, 7), (9, 12), (5, 22), (14, 2), (26, 7), (24, 6), (22, 11), (37, 6), (30, 23), (0, 24), (18, 28), (0, 12), (9, 6), (5, 28), (9, 22), (3, 30), (32, 13), (15, 1), (3, 20), (15, 11), (38, 25), (28, 22), (21, 28), (25, 7), (4, 4), (10, 1), (30, 6), (11, 16), (0, 13), (37, 11), (2, 16), (22, 19), (23, 8), (22, 30), (7, 16), (10, 13), (4, 19), (31, 17), (8, 18), (12, 6), (2, 11), (9, 7), (31, 22), (23, 18), (35, 15), (34, 10), (12, 12), (0, 16), (30, 27), (26, 18), (26, 10), (14, 14), (29, 24), (31, 27), (31, 19), (33, 17), (27, 24), (16, 8), (30, 30), (21, 17), (29, 6), (22, 1), (32, 1), (14, 22), (32, 11), (35, 9), (31, 14), (20, 4), (35, 8), (11, 1), (3, 10), (27, 16), (38, 10), (3, 24), (18, 27), (2, 4), (16, 0), (12, 22), (28, 23), (11, 27), (30, 4), (4, 21), (11, 6), (12, 16), (6, 25), (30, 7), (11, 9), (34, 30), (34, 19), (29, 28), (31, 13), (35, 13), (17, 10), (1, 2), (33, 14), (36, 0), (37, 2), (15, 21), (7, 7), (22, 2), (17, 17), (21, 23), (8, 6), (19, 21), (32, 4), (9, 21), (29, 11), (1, 18), (3, 25), (5, 20), (36, 28), (28, 29), (19, 3), (33, 23), (38, 3), (1, 3), (10, 17), (2, 2), (3, 13), (10, 25), (20, 29), (4, 11), (3, 16), (11, 10), (7, 24), (23, 13), (17, 30), (31, 24), (17, 16), (5, 8), (25, 13), (14, 0), (32, 27), (11, 13), (15, 20), (19, 18), (5, 9), (14, 10), (36, 17), (33, 5), (3, 21), (34, 7), (5, 14), (2, 5), (3, 3), (14, 20), (23, 4), (6, 16), (3, 15), (6, 0), (22, 24), (33, 19), (33, 29), (29, 17), (25, 1), (9, 16), (0, 11), (13, 12), (12, 26), (6, 30), (14, 11), (32, 0), (18, 11), (17, 24), (17, 29), (28, 20), (21, 2), (25, 25), (30, 17), (13, 30), (6, 12), (17, 20), (36, 8), (36, 19), (30, 10), (30, 2), (6, 3), (30, 20), (32, 17), (5, 24), (0, 21), (2, 24), (29, 12), (27, 28), (35, 24), (6, 9), (30, 28), (5, 29), (6, 27), (27, 13), (20, 5), (32, 20), (25, 27), (1, 23), (16, 23), (7, 10), (25, 24), (21, 29), (34, 23), (22, 4), (16, 3), (36, 20), (26, 1), (38, 16), (7, 2), (21, 12), (12, 10), (31, 21), (1, 30), (31, 9), (0, 6), (25, 16), (17, 2), (7, 6), (23, 21), (29, 20), (6, 19), (9, 27), (31, 18), (35, 23), (22, 10), (4, 3), (32, 19), (31, 11), (22, 25), (9, 25), (34, 27), (27, 29), (14, 6), (19, 24), (1, 27), (1, 13), (38, 6), (29, 16), (0, 26), (22, 5), (5, 4), (29, 23), (31, 0), (10, 11), (26, 26), (14, 12), (30, 8), (29, 2), (32, 8), (1, 11), (18, 20), (20, 15), (32, 9), (33, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822096", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), 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), (5, 0), (29, 16), (21, 17), (5, 4), (23, 8), (3, 21), (9, 1), (8, 29), (18, 9), (24, 21), (4, 22), (8, 34), (17, 25), (26, 19), (2, 34), (6, 25), (9, 12), (18, 17), (25, 23), (24, 28), (18, 21), (2, 16), (15, 34), (24, 0), (14, 12), (24, 34), (3, 34), (17, 1), (23, 23), (20, 24), (7, 29), (11, 31), (29, 4), (12, 28), (30, 15), (8, 17), (24, 5), (24, 6), (11, 20), (16, 12), (17, 2), (26, 0), (11, 11), (6, 33), (11, 18), (18, 18), (8, 0), (25, 7), (13, 29), (13, 6), (13, 5), (18, 28), (30, 28), (24, 23), (22, 12), (7, 1), (21, 6), (25, 5), (20, 7), (27, 22), (21, 3), (4, 27), (25, 21), (21, 21), (13, 19), (4, 23), (0, 4), (13, 21), (4, 25), (5, 19), (16, 1), (24, 1), (25, 15), (28, 8), (11, 10), (7, 12), (27, 16), (11, 26), (28, 19), (19, 8), (8, 31), (12, 33), (7, 9), (17, 6), (15, 1), (7, 25), (4, 2), (8, 14), (27, 30), (30, 16), (12, 2), (26, 1), (13, 17), (6, 35), (6, 34), (21, 12), (14, 29), (27, 20), (20, 13), (8, 21), (1, 1), (20, 23), (27, 29), (3, 8), (21, 24), (2, 1), (22, 27), (17, 27), (4, 24), (13, 22), (19, 16), (12, 18), (3, 9), (28, 25), (16, 5), (7, 2), (25, 33), (8, 7), (2, 17), (4, 18), (15, 20), (24, 12), (5, 1), (11, 22), (2, 21), (26, 3), (25, 14), (5, 14), (12, 17), (13, 11), (23, 6), (12, 27), (11, 24), (29, 3), (16, 11), (9, 2), (1, 15), (16, 8), (0, 17), (15, 5), (23, 19), (9, 33), (18, 1), (15, 17), (30, 23), (20, 12), (9, 29), (13, 15), (19, 9), (28, 4), (28, 24), (28, 1), (9, 11), (19, 22), (2, 4), (23, 21), (14, 20), (30, 12), (8, 35), (27, 26), (20, 0), (11, 4), (14, 31), (6, 7), (16, 31), (15, 7), (9, 25), (11, 1), (20, 33), (23, 5), (14, 3), (7, 26), (4, 5), (26, 28), (3, 12), (22, 18), (22, 20), (27, 24), (14, 32), (23, 27), (24, 3), (26, 33), (10, 15), (0, 14), (11, 23), (17, 8), (20, 14), (25, 9), (23, 25), (1, 20), (23, 3), (17, 14), (6, 27), (21, 8), (4, 0), (28, 18), (18, 15), (5, 27), (29, 2), (21, 31), (9, 8), (11, 15), (20, 22), (13, 35), (20, 26), (22, 6), (28, 30), (30, 5), (4, 29), (10, 11), (0, 26), (16, 13), (5, 16), (18, 20), (23, 10), (19, 2), (26, 2), (0, 28), (24, 33), (26, 11), (9, 28), (3, 1), (10, 30), (5, 21), (17, 20), (30, 7), (1, 17), (20, 15), (8, 13), (10, 31), (3, 31), (4, 14), (13, 2), (13, 4), (26, 35), (14, 13), (18, 13), (1, 3), (10, 5), (9, 30), (10, 7), (9, 0), (25, 35), (18, 14), (4, 31), (20, 19), (26, 30), (15, 21), (20, 18), (12, 4), (17, 35), (18, 24), (6, 31), (22, 21), (17, 7), (6, 17), (30, 19), (14, 7), (8, 10), (24, 13), (4, 21), (5, 35), (19, 28), (15, 28), (30, 30), (28, 33), (26, 34), (25, 19), (16, 22), (10, 16), (3, 19), (17, 34), (9, 6), (5, 28), (29, 17), (30, 31), (19, 7), (24, 11), (13, 23), (9, 34), (4, 33), (11, 14), (27, 19), (10, 18), (5, 2), (29, 10), (5, 25), (21, 35), (19, 11), (3, 5), (8, 12), (30, 21), (7, 10), (29, 23), (0, 24), (21, 19), (8, 22), (1, 18), (28, 14), (23, 35), (21, 9), (10, 21), (11, 27), (12, 10), (16, 32), (18, 12), (8, 23), (21, 33), (23, 13), (7, 14), (10, 6), (13, 30), (18, 31), (23, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "714240", "dataset": "MATH"}
{"messages": [{"content": "In a 33x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 34), 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), (18, 12), (28, 25), (6, 29), (12, 19), (21, 22), (21, 10), (13, 17), (18, 8), (14, 9), (5, 33), (25, 28), (3, 21), (27, 5), (3, 15), (12, 15), (1, 13), (30, 6), (2, 9), (3, 31), (20, 11), (20, 30), (5, 1), (25, 16), (15, 12), (15, 27), (1, 14), (1, 26), (26, 28), (17, 15), (26, 8), (8, 34), (11, 30), (13, 23), (15, 16), (29, 23), (11, 25), (21, 3), (32, 33), (7, 20), (8, 15), (25, 30), (19, 5), (25, 2), (21, 31), (28, 17), (7, 0), (23, 29), (14, 17), (29, 14), (13, 20), (8, 10), (9, 34), (14, 11), (27, 34), (23, 30), (18, 22), (22, 7), (27, 2), (11, 13), (24, 1), (24, 31), (31, 9), (24, 14), (31, 21), (30, 17), (6, 8), (5, 25), (15, 17), (26, 25), (8, 3), (8, 25), (9, 30), (13, 4), (20, 9), (32, 27), (0, 26), (18, 16), (2, 34), (6, 2), (4, 22), (10, 12), (9, 4), (4, 29), (20, 13), (2, 16), (16, 5), (19, 14), (1, 15), (25, 21), (10, 18), (12, 29), (3, 19), (23, 10), (11, 1), (20, 18), (13, 33), (4, 21), (14, 34), (29, 3), (13, 1), (27, 7), (31, 7), (19, 25), (27, 15), (3, 13), (23, 24), (6, 27), (11, 10), (3, 9), (30, 23), (31, 3), (30, 1), (12, 28), (4, 16), (12, 2), (9, 28), (10, 17), (29, 32), (29, 31), (29, 28), (9, 15), (22, 23), (6, 34), (21, 7), (24, 20), (30, 34), (4, 19), (25, 18), (23, 11), (26, 7), (9, 12), (22, 25), (7, 2), (28, 8), (19, 20), (12, 0), (0, 7), (14, 30), (23, 9), (29, 11), (4, 23), (24, 25), (10, 11), (7, 12), (16, 28), (15, 30), (5, 7), (5, 15), (2, 5), (25, 4), (23, 8), (11, 19), (17, 28), (24, 11), (25, 0), (30, 15), (22, 5), (24, 24), (8, 23), (25, 3), (24, 28), (11, 15), (32, 16), (3, 0), (0, 30), (6, 12), (7, 10), (14, 18), (14, 19), (8, 9), (27, 29), (23, 2), (5, 19), (16, 23), (17, 8), (5, 11), (27, 16), (19, 16), (15, 19), (5, 28), (3, 34), (11, 26), (2, 10), (17, 14), (14, 33), (29, 34), (18, 33), (6, 19), (9, 18), (16, 32), (10, 21), (28, 12), (16, 30), (22, 32), (6, 4), (14, 0), (7, 23), (26, 33), (26, 22), (16, 19), (31, 26), (16, 24), (19, 13), (8, 8), (0, 31), (27, 26), (23, 28), (21, 14), (21, 0), (24, 0), (14, 32), (0, 19), (6, 30), (13, 26), (22, 20), (4, 20), (7, 7), (20, 33), (13, 6), (4, 31), (8, 12), (22, 17), (5, 13), (22, 21), (3, 24), (18, 15), (32, 5), (12, 17), (10, 31), (18, 2), (11, 6), (14, 12), (20, 17), (30, 28), (24, 7), (4, 3), (0, 16), (28, 32), (0, 5), (4, 7), (28, 27), (4, 0), (1, 22), (18, 21), (12, 26), (3, 1), (16, 13), (7, 29), (9, 11), (12, 7), (17, 21), (29, 9), (15, 29), (4, 15), (26, 26), (13, 13), (14, 21), (21, 17), (29, 2), (0, 1), (27, 12), (0, 20), (29, 8), (1, 19), (2, 24), (21, 12), (20, 29), (31, 30), (21, 18), (15, 26), (30, 8), (30, 29), (10, 33), (26, 12), (25, 23), (2, 2), (22, 0), (28, 24), (31, 10), (13, 22), (2, 1), (29, 24), (2, 3), (7, 4), (18, 14), (28, 23), (23, 4), (8, 27), (7, 26), (6, 20), (5, 3), (8, 32), (6, 5), (3, 28), (9, 31), (21, 9), (29, 13), (15, 15), (17, 29), (11, 11), (24, 16), (19, 2), (1, 27), (30, 2), (12, 20), (7, 15), (28, 4), (29, 16), (19, 15), (11, 18), (32, 18), (0, 12), (12, 30), (19, 31), (23, 12), (14, 22), (16, 6), (12, 13), (17, 5), (6, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29835", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), 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), (25, 0), (26, 1), (27, 24), (1, 31), (1, 20), (24, 3), (13, 20), (5, 11), (10, 25), (31, 19), (13, 6), (9, 22), (12, 30), (20, 25), (14, 19), (16, 12), (3, 4), (3, 18), (30, 3), (32, 26), (0, 20), (28, 12), (6, 29), (11, 1), (29, 27), (21, 18), (19, 28), (31, 3), (13, 19), (23, 20), (3, 14), (1, 28), (31, 16), (10, 4), (12, 22), (30, 12), (14, 17), (16, 14), (6, 28), (21, 1), (19, 4), (9, 4), (1, 23), (0, 28), (13, 31), (15, 13), (5, 22), (19, 0), (4, 10), (16, 11), (25, 15), (1, 6), (10, 9), (27, 31), (11, 0), (20, 29), (23, 24), (18, 29), (26, 28), (27, 12), (19, 26), (27, 4), (21, 10), (8, 23), (21, 13), (27, 22), (9, 14), (24, 0), (27, 30), (31, 25), (31, 11), (19, 30), (10, 30), (6, 2), (6, 11), (25, 18), (11, 27), (23, 21), (19, 21), (2, 13), (29, 1), (4, 3), (2, 8), (5, 27), (23, 25), (27, 3), (1, 21), (25, 16), (31, 1), (24, 20), (7, 10), (6, 7), (0, 27), (31, 5), (3, 25), (6, 19), (3, 3), (7, 20), (10, 18), (8, 28), (5, 5), (2, 24), (24, 24), (8, 26), (3, 0), (5, 28), (22, 27), (32, 23), (7, 1), (30, 15), (9, 30), (0, 14), (0, 30), (17, 28), (28, 13), (25, 13), (7, 28), (30, 16), (15, 5), (1, 26), (26, 10), (15, 25), (5, 13), (11, 5), (24, 27), (8, 19), (22, 15), (19, 23), (25, 21), (15, 18), (18, 24), (25, 14), (4, 18), (32, 5), (30, 23), (3, 19), (14, 31), (17, 16), (21, 12), (23, 28), (10, 5), (30, 6), (31, 26), (25, 1), (14, 28), (15, 6), (9, 5), (0, 29), (10, 14), (23, 10), (2, 20), (22, 26), (15, 27), (27, 17), (11, 7), (16, 27), (32, 25), (30, 2), (9, 1), (29, 28), (11, 24), (24, 31), (20, 3), (20, 28), (13, 17), (1, 7), (13, 30), (26, 24), (23, 16), (20, 24), (10, 29), (15, 26), (28, 15), (20, 8), (4, 29), (3, 26), (9, 13), (12, 16), (28, 14), (15, 23), (20, 17), (30, 18), (14, 14), (13, 21), (20, 2), (25, 29), (27, 25), (31, 31), (7, 17), (30, 14), (5, 17), (22, 1), (8, 9), (20, 1), (16, 31), (32, 4), (13, 2), (11, 28), (22, 6), (3, 31), (14, 8), (4, 14), (11, 13), (13, 15), (5, 12), (32, 22), (24, 7), (6, 30), (28, 27), (30, 28), (9, 28), (31, 13), (9, 21), (16, 26), (14, 16), (4, 13), (4, 9), (7, 30), (20, 7), (4, 30), (19, 13), (24, 25), (15, 15), (27, 7), (9, 6), (4, 20), (21, 17), (31, 7), (31, 15), (29, 24), (11, 2), (4, 2), (25, 8), (8, 24), (7, 16), (22, 22), (14, 4), (13, 9), (3, 9), (10, 2), (19, 20), (29, 6), (4, 31), (22, 12), (17, 1), (5, 7), (18, 12), (6, 14), (11, 30), (28, 21), (20, 15), (22, 20), (2, 26), (14, 6), (20, 11), (23, 9), (30, 25), (12, 15), (8, 5), (0, 10), (10, 20), (24, 22), (24, 14), (17, 20), (18, 9), (8, 16), (26, 21), (11, 20), (8, 13), (32, 11), (13, 1), (32, 6), (2, 25), (13, 8), (12, 19), (10, 17), (10, 22), (1, 30), (16, 20), (5, 21), (8, 0), (14, 23), (2, 4), (3, 17), (10, 31), (7, 29), (1, 14), (8, 22), (30, 0), (27, 8), (29, 10), (18, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902880", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), 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), (27, 33), (7, 30), (11, 22), (22, 11), (12, 22), (30, 10), (22, 28), (26, 33), (27, 3), (1, 3), (26, 26), (18, 6), (4, 17), (6, 30), (16, 27), (10, 1), (17, 5), (2, 2), (12, 6), (22, 23), (28, 19), (2, 13), (7, 5), (13, 21), (29, 10), (2, 15), (15, 26), (20, 8), (27, 27), (7, 33), (5, 6), (5, 32), (9, 3), (0, 24), (4, 4), (30, 14), (0, 21), (28, 27), (7, 27), (23, 33), (29, 15), (8, 23), (29, 29), (9, 34), (5, 30), (27, 20), (9, 12), (12, 20), (5, 3), (6, 26), (18, 26), (11, 1), (12, 10), (20, 24), (20, 1), (10, 30), (15, 2), (8, 20), (21, 24), (27, 32), (3, 31), (21, 16), (27, 5), (20, 3), (5, 20), (7, 25), (10, 0), (9, 19), (18, 22), (10, 10), (10, 12), (5, 10), (7, 24), (11, 15), (28, 21), (28, 13), (22, 0), (17, 13), (31, 27), (30, 28), (12, 0), (16, 29), (5, 26), (2, 4), (0, 33), (28, 29), (23, 22), (25, 6), (3, 4), (11, 20), (6, 25), (19, 31), (18, 12), (12, 29), (25, 8), (25, 30), (28, 25), (18, 29), (24, 1), (12, 12), (18, 7), (3, 30), (1, 11), (7, 13), (27, 6), (20, 16), (8, 10), (11, 34), (17, 4), (15, 1), (20, 27), (10, 25), (16, 12), (21, 17), (26, 9), (21, 5), (30, 24), (21, 31), (26, 21), (6, 28), (26, 14), (11, 30), (5, 4), (10, 21), (23, 13), (5, 5), (10, 2), (5, 21), (6, 12), (28, 14), (2, 16), (14, 24), (1, 31), (3, 9), (28, 2), (27, 14), (30, 4), (19, 25), (30, 0), (22, 20), (23, 9), (14, 12), (2, 11), (3, 20), (6, 1), (21, 9), (0, 17), (24, 9), (6, 14), (18, 19), (4, 14), (19, 22), (2, 32), (4, 22), (20, 10), (17, 15), (18, 32), (30, 33), (17, 1), (26, 28), (0, 23), (24, 5), (24, 27), (0, 34), (31, 26), (0, 9), (20, 15), (23, 31), (28, 28), (6, 31), (31, 31), (6, 10), (4, 13), (12, 15), (5, 24), (25, 2), (11, 14), (6, 24), (1, 30), (4, 21), (3, 29), (23, 1), (10, 17), (16, 32), (30, 6), (4, 28), (23, 19), (4, 16), (3, 6), (15, 3), (16, 16), (9, 29), (2, 28), (24, 6), (26, 22), (8, 12), (7, 17), (24, 28), (21, 30), (17, 31), (26, 10), (17, 30), (26, 6), (27, 30), (18, 11), (10, 9), (22, 19), (8, 33), (24, 26), (19, 12), (31, 22), (4, 32), (6, 23), (2, 17), (29, 33), (8, 32), (6, 32), (9, 30), (31, 10), (18, 17), (19, 19), (3, 21), (10, 11), (29, 32), (8, 34), (19, 6), (5, 17), (15, 28), (11, 6), (22, 32), (16, 23), (19, 10), (4, 8), (23, 10), (11, 11), (29, 1), (7, 19), (26, 4), (10, 28), (30, 11), (24, 20), (10, 8), (11, 33), (25, 1), (11, 12), (27, 31), (7, 29), (6, 29), (14, 22), (2, 14), (21, 33), (18, 1), (5, 16), (8, 14), (29, 11), (11, 3), (10, 4), (25, 22), (25, 32), (29, 13), (17, 25), (12, 17), (17, 0), (18, 9), (0, 11), (31, 32), (0, 12), (0, 25), (7, 28), (0, 10), (1, 14), (5, 8), (26, 1), (0, 27), (26, 19), (29, 30), (4, 34), (15, 30), (31, 28), (13, 9), (0, 6), (24, 10), (16, 13), (11, 32), (13, 14), (2, 6), (25, 16), (7, 23), (15, 6), (6, 15), (19, 11), (28, 31), (19, 21), (18, 20), (15, 10), (4, 20), (9, 7), (16, 25), (12, 21), (6, 21), (31, 21), (28, 12), (2, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862416", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), 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), (12, 11), (9, 28), (33, 21), (21, 22), (33, 34), (0, 34), (23, 8), (18, 6), (11, 24), (32, 13), (22, 7), (25, 37), (23, 1), (16, 0), (31, 4), (19, 27), (4, 27), (10, 17), (17, 2), (31, 6), (3, 20), (29, 12), (30, 37), (17, 18), (28, 30), (10, 26), (8, 25), (9, 37), (20, 30), (23, 26), (23, 21), (30, 0), (7, 11), (15, 37), (8, 21), (2, 31), (5, 2), (7, 35), (25, 31), (15, 6), (31, 22), (13, 27), (31, 0), (8, 14), (4, 29), (14, 17), (23, 18), (18, 12), (13, 2), (19, 7), (19, 23), (11, 27), (32, 23), (18, 18), (11, 14), (30, 20), (21, 19), (20, 28), (18, 7), (19, 36), (11, 5), (13, 13), (9, 11), (16, 22), (18, 16), (0, 3), (24, 0), (15, 12), (33, 29), (4, 2), (7, 4), (32, 31), (7, 10), (31, 21), (15, 31), (0, 12), (14, 19), (31, 23), (26, 37), (32, 29), (21, 27), (32, 18), (2, 5), (33, 32), (3, 11), (32, 34), (9, 9), (11, 12), (27, 8), (24, 18), (33, 4), (6, 13), (11, 19), (16, 7), (31, 14), (27, 23), (10, 14), (18, 11), (2, 0), (12, 21), (32, 5), (7, 30), (26, 31), (28, 29), (14, 6), (16, 13), (6, 23), (2, 25), (21, 15), (19, 32), (31, 8), (15, 25), (32, 6), (19, 25), (14, 20), (19, 13), (18, 25), (1, 6), (21, 14), (19, 21), (29, 36), (5, 5), (9, 3), (8, 33), (7, 17), (0, 29), (26, 23), (24, 3), (28, 4), (15, 7), (17, 15), (27, 30), (7, 21), (2, 17), (9, 34), (10, 13), (10, 35), (19, 11), (15, 9), (32, 9), (29, 22), (32, 15), (29, 0), (7, 8), (19, 14), (4, 26), (17, 24), (11, 36), (15, 13), (32, 33), (21, 35), (24, 24), (3, 28), (17, 19), (14, 30), (31, 7), (22, 27), (11, 11), (21, 4), (26, 25), (4, 35), (4, 9), (33, 3), (12, 16), (8, 8), (22, 29), (24, 37), (26, 34), (4, 10), (11, 29), (23, 12), (3, 4), (1, 13), (27, 19), (11, 0), (21, 12), (13, 37), (26, 15), (20, 25), (0, 4), (30, 10), (12, 6), (25, 28), (28, 28), (8, 12), (27, 21), (14, 31), (21, 34), (28, 33), (31, 27), (10, 32), (4, 36), (33, 36), (7, 27), (0, 18), (10, 2), (21, 13), (32, 21), (5, 28), (3, 18), (21, 30), (28, 9), (23, 29), (30, 19), (23, 3), (30, 23), (4, 23), (2, 33), (32, 20), (23, 32), (32, 19), (9, 15), (0, 22), (13, 32), (13, 11), (0, 9), (33, 0), (29, 1), (20, 0), (5, 7), (3, 26), (11, 16), (22, 19), (19, 0), (19, 16), (5, 22), (25, 16), (33, 31), (26, 17), (19, 29), (16, 6), (27, 24), (22, 10), (30, 26), (27, 3), (7, 0), (33, 9), (28, 10), (5, 16), (15, 24), (16, 36), (9, 10), (10, 34), (8, 34), (13, 35), (1, 33), (15, 18), (21, 37), (23, 9), (10, 23), (6, 30), (27, 14), (25, 5), (5, 0), (32, 8), (20, 14), (8, 4), (5, 32), (23, 22), (6, 24), (10, 31), (17, 36), (20, 8), (26, 36), (1, 24), (30, 22), (6, 0), (0, 13), (2, 20), (17, 1), (3, 2), (22, 36), (20, 24), (32, 16), (19, 33), (29, 2), (0, 26), (29, 3), (3, 5), (22, 4), (13, 25), (13, 16), (27, 32), (18, 2), (14, 0), (10, 8), (32, 22), (6, 15), (13, 20), (31, 5), (3, 3), (25, 8), (4, 31), (30, 18), (15, 10), (0, 35), (2, 14), (15, 36), (27, 15), (10, 4), (5, 11), (8, 31), (10, 3), (27, 16), (10, 24), (30, 33), (25, 26), (32, 2), (3, 31), (32, 24), (16, 34), (7, 26), (22, 6), (9, 2), (8, 1), (16, 2), (12, 35), (28, 12), (31, 32), (15, 28), (1, 18), (18, 31), (30, 15), (12, 36), (18, 28), (1, 17), (9, 4), (17, 26), (29, 9), (18, 8), (2, 37), (14, 25), (10, 5), (19, 17), (6, 25), (16, 20), (27, 29), (5, 13), (33, 10), (32, 7), (12, 15), (2, 6), (11, 28), (1, 25), (22, 28), (13, 23), (22, 16), (16, 17), (19, 8), (31, 17), (32, 35), (18, 20), (31, 34), (24, 1), (12, 19), (6, 17), (19, 22), (16, 11), (30, 3), (0, 8), (2, 15), (5, 31), (16, 16), (19, 34), (9, 26), (12, 34), (15, 5), (4, 24), (3, 8), (2, 22), (26, 8), (33, 15), (7, 18), (26, 18), (11, 22), (33, 7), (25, 35), (22, 18), (27, 0), (25, 21), (1, 15), (17, 32), (25, 20), (31, 3), (0, 6), (2, 23), (8, 3), (24, 35), (9, 20), (21, 10), (20, 35), (21, 24), (9, 32), (7, 29), (18, 5), (29, 20), (12, 9), (6, 26), (18, 33), (28, 27), (19, 30), (20, 1), (14, 29), (10, 30), (0, 32), (15, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291456", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 9), (8, 22), (20, 25), (28, 25), (6, 27), (16, 23), (19, 1), (6, 18), (34, 25), (35, 10), (6, 2), (25, 9), (32, 3), (32, 18), (6, 8), (35, 19), (10, 21), (13, 9), (31, 24), (27, 18), (7, 19), (4, 28), (28, 11), (23, 20), (20, 6), (25, 8), (0, 8), (14, 11), (18, 16), (0, 18), (32, 22), (27, 12), (30, 16), (23, 19), (28, 17), (2, 28), (5, 4), (2, 14), (7, 12), (23, 22), (3, 21), (26, 6), (18, 24), (16, 17), (14, 29), (22, 25), (1, 0), (19, 6), (14, 21), (26, 19), (30, 4), (7, 23), (27, 19), (11, 26), (20, 16), (32, 5), (25, 28), (28, 29), (14, 28), (34, 12), (20, 7), (23, 23), (14, 17), (35, 4), (5, 14), (29, 11), (8, 9), (34, 27), (27, 29), (6, 6), (29, 4), (1, 4), (11, 25), (2, 1), (9, 23), (29, 6), (22, 1), (7, 0), (1, 2), (31, 9), (5, 10), (22, 14), (33, 8), (29, 2), (27, 28), (31, 5), (25, 2), (24, 26), (19, 15), (10, 7), (22, 11), (23, 9), (34, 16), (32, 10), (10, 27), (17, 26), (15, 6), (31, 18), (29, 18), (25, 21), (31, 13), (11, 10), (7, 18), (30, 9), (34, 26), (30, 19), (2, 5), (7, 7), (33, 19), (23, 2), (23, 3), (17, 25), (19, 8), (22, 3), (14, 1), (24, 11), (7, 22), (9, 12), (21, 25), (30, 21), (22, 5), (27, 11), (12, 28), (2, 29), (23, 5), (18, 15), (8, 6), (3, 11), (7, 5), (3, 29), (6, 3), (10, 23), (30, 1), (2, 2), (11, 18), (2, 15), (1, 19), (20, 27), (22, 2), (27, 1), (21, 5), (28, 26), (9, 11), (1, 6), (31, 1), (3, 1), (23, 17), (15, 24), (32, 16), (33, 18), (13, 0), (25, 24), (0, 10), (9, 4), (33, 3), (24, 24), (2, 0), (3, 7), (28, 18), (20, 26), (34, 29), (11, 2), (33, 23), (5, 21), (12, 21), (11, 29), (21, 29), (16, 1), (15, 1), (2, 16), (22, 19), (3, 18), (17, 6), (14, 20), (28, 1), (29, 27), (32, 25), (10, 24), (11, 22), (2, 19), (8, 8), (13, 2), (20, 14), (34, 4), (31, 27), (24, 9), (27, 15), (18, 5), (21, 22), (1, 15), (9, 3), (31, 17), (18, 2), (3, 2), (5, 7), (27, 6), (29, 26), (3, 19), (18, 28), (23, 7), (20, 12), (12, 19), (11, 19), (24, 7), (26, 2), (29, 24), (18, 21), (9, 15), (6, 16), (28, 23), (7, 9), (24, 22), (20, 8), (10, 0), (5, 27), (17, 7), (31, 10), (19, 10), (30, 23), (20, 20), (20, 9), (8, 12), (15, 4), (30, 8), (25, 5), (13, 18), (23, 6), (19, 14), (27, 4), (29, 16), (7, 20), (35, 5), (14, 9), (25, 17), (0, 7), (19, 23), (16, 28), (25, 29), (24, 15), (9, 20), (29, 17), (0, 27), (23, 8), (23, 11), (20, 21), (7, 14), (15, 25), (6, 15), (13, 26), (9, 7), (33, 24), (17, 11), (25, 1), (22, 12), (18, 0), (18, 20), (15, 3), (7, 4), (17, 4), (28, 5), (1, 29), (20, 24), (26, 22), (1, 5), (6, 7), (5, 13), (2, 17), (26, 26), (0, 25), (4, 16), (31, 19), (31, 6), (10, 20), (9, 6), (35, 8), (29, 3), (9, 21), (19, 3), (27, 23), (34, 0), (2, 11), (13, 12), (31, 20), (26, 29), (6, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876645", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (22, 21), (17, 4), (29, 34), (2, 14), (6, 37), (11, 37), (21, 11), (18, 3), (19, 13), (18, 21), (9, 32), (22, 17), (5, 25), (15, 25), (9, 22), (30, 20), (5, 34), (12, 16), (15, 34), (28, 34), (15, 16), (16, 29), (0, 27), (16, 26), (18, 13), (14, 16), (13, 20), (11, 4), (19, 4), (26, 18), (14, 36), (26, 8), (6, 3), (19, 5), (11, 10), (0, 14), (8, 1), (15, 26), (11, 23), (14, 12), (2, 9), (19, 11), (2, 27), (12, 0), (2, 0), (15, 22), (26, 10), (6, 26), (22, 24), (5, 32), (17, 7), (15, 27), (26, 20), (5, 23), (11, 22), (30, 12), (30, 29), (12, 21), (4, 9), (24, 35), (22, 11), (1, 29), (23, 8), (6, 29), (19, 15), (22, 32), (14, 10), (6, 7), (25, 23), (14, 9), (19, 6), (21, 10), (1, 9), (0, 13), (4, 35), (17, 20), (2, 22), (9, 10), (0, 21), (25, 16), (20, 28), (26, 16), (27, 35), (19, 8), (11, 27), (1, 2), (29, 6), (0, 34), (11, 26), (29, 17), (12, 15), (26, 17), (29, 33), (28, 21), (20, 7), (21, 32), (27, 18), (17, 2), (9, 24), (30, 19), (14, 15), (15, 31), (8, 19), (3, 28), (22, 26), (1, 23), (5, 21), (2, 33), (8, 11), (30, 8), (23, 36), (28, 11), (28, 8), (30, 3), (26, 29), (28, 18), (13, 34), (25, 28), (27, 26), (26, 12), (1, 1), (22, 28), (22, 13), (8, 37), (7, 30), (18, 27), (11, 24), (29, 18), (7, 6), (0, 20), (15, 24), (13, 5), (12, 13), (5, 19), (7, 26), (14, 23), (1, 32), (16, 36), (30, 13), (24, 1), (6, 2), (22, 2), (8, 8), (7, 34), (18, 4), (14, 28), (27, 31), (17, 24), (22, 3), (8, 18), (21, 20), (19, 37), (25, 32), (9, 31), (8, 5), (18, 31), (2, 16), (18, 15), (13, 28), (5, 1), (5, 12), (21, 34), (11, 6), (14, 17), (22, 18), (1, 35), (4, 20), (29, 35), (27, 33), (2, 1), (2, 11), (6, 19), (16, 21), (9, 3), (21, 14), (12, 34), (16, 4), (12, 2), (16, 27), (24, 3), (2, 21), (1, 19), (12, 14), (24, 18), (10, 29), (26, 15), (5, 13), (2, 8), (11, 14), (23, 20), (20, 10), (14, 18), (27, 23), (17, 31), (8, 3), (28, 33), (10, 8), (12, 6), (4, 32), (10, 10), (1, 18), (10, 5), (8, 4), (11, 21), (15, 5), (16, 30), (9, 9), (19, 20), (28, 35), (3, 1), (29, 23), (6, 0), (25, 31), (30, 11), (28, 12), (7, 25), (22, 6), (4, 17), (13, 12), (28, 29), (2, 19), (23, 31), (15, 35), (17, 18), (23, 23), (5, 7), (23, 18), (16, 33), (28, 4), (16, 37), (9, 13), (20, 3), (24, 15), (6, 11), (9, 29), (30, 7), (24, 33), (8, 21), (19, 34), (11, 3), (27, 34), (4, 7), (14, 30), (4, 31), (5, 10), (27, 30), (3, 0), (23, 1), (15, 4), (18, 6), (26, 31), (22, 31), (16, 17), (9, 14), (28, 25), (15, 6), (29, 19), (1, 8), (5, 11), (21, 7), (12, 35), (24, 23), (0, 7), (9, 17), (1, 24), (25, 21), (12, 31), (8, 28), (19, 23), (4, 23), (12, 26), (6, 36), (14, 33), (4, 27), (27, 15), (5, 17), (11, 19), (27, 9), (14, 29), (18, 8), (2, 23), (29, 29), (14, 1), (3, 6), (7, 21), (22, 5), (23, 14), (24, 19), (14, 34), (19, 33), (26, 25), (28, 36), (17, 35), (4, 16), (29, 10), (19, 19), (24, 36), (5, 18), (26, 19), (7, 13), (29, 25), (11, 17), (19, 29), (10, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316008", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 15), (12, 36), (28, 21), (10, 32), (6, 12), (31, 15), (29, 1), (15, 38), (12, 3), (25, 0), (35, 6), (26, 29), (36, 15), (23, 29), (2, 11), (37, 36), (35, 16), (1, 31), (9, 21), (25, 36), (9, 20), (30, 18), (25, 8), (12, 29), (32, 1), (20, 26), (26, 12), (7, 6), (35, 5), (32, 12), (4, 22), (15, 25), (36, 38), (6, 38), (30, 8), (21, 29), (26, 38), (14, 15), (22, 14), (23, 33), (35, 35), (3, 24), (33, 5), (26, 33), (5, 21), (37, 30), (0, 38), (5, 11), (6, 32), (34, 25), (0, 8), (2, 34), (4, 11), (9, 7), (2, 35), (30, 15), (15, 31), (1, 7), (22, 35), (11, 16), (25, 11), (27, 24), (5, 4), (35, 4), (1, 20), (10, 20), (3, 7), (18, 11), (7, 35), (27, 15), (4, 32), (30, 17), (26, 11), (27, 11), (26, 9), (28, 18), (36, 16), (21, 10), (27, 29), (8, 34), (11, 17), (38, 37), (3, 26), (36, 36), (32, 25), (34, 17), (30, 30), (33, 38), (5, 6), (5, 37), (2, 32), (24, 37), (16, 24), (37, 29), (29, 27), (12, 32), (32, 7), (12, 24), (38, 17), (19, 26), (38, 20), (12, 31), (32, 10), (12, 30), (34, 22), (30, 37), (15, 2), (33, 7), (29, 10), (28, 15), (17, 8), (13, 12), (20, 32), (38, 4), (5, 16), (37, 3), (4, 3), (5, 35), (0, 32), (0, 2), (0, 10), (30, 24), (3, 34), (33, 25), (33, 2), (0, 16), (16, 20), (15, 28), (21, 30), (11, 21), (4, 31), (2, 2), (33, 33), (14, 27), (1, 35), (20, 38), (10, 11), (10, 15), (20, 14), (25, 6), (9, 25), (29, 36), (15, 30), (23, 4), (3, 9), (35, 24), (15, 27), (25, 29), (12, 5), (0, 33), (23, 11), (17, 4), (2, 3), (28, 17), (1, 13), (26, 18), (4, 0), (28, 30), (33, 30), (2, 29), (29, 34), (36, 4), (35, 14), (14, 18), (15, 6), (32, 28), (32, 36), (27, 13), (11, 29), (9, 2), (5, 5), (12, 11), (3, 32), (14, 31), (5, 10), (34, 7), (19, 2), (19, 10), (4, 23), (31, 33), (14, 1), (9, 24), (13, 31), (38, 14), (17, 25), (21, 12), (38, 29), (11, 36), (15, 37), (6, 20), (15, 10), (22, 25), (23, 14), (24, 33), (10, 8), (31, 27), (32, 3), (22, 31), (16, 12), (11, 3), (34, 35), (27, 9), (6, 15), (21, 36), (9, 18), (33, 15), (23, 35), (27, 14), (14, 14), (21, 3), (1, 6), (18, 15), (14, 34), (18, 28), (17, 0), (2, 16), (28, 26), (16, 32), (27, 36), (10, 0), (32, 8), (32, 32), (6, 30), (18, 22), (8, 36), (5, 29), (28, 4), (25, 9), (36, 28), (12, 14), (31, 26), (24, 7), (6, 17), (30, 33), (7, 19), (15, 15), (13, 11), (25, 19), (0, 5), (6, 35), (24, 19), (13, 13), (34, 33), (11, 13), (13, 2), (28, 29), (15, 34), (32, 35), (4, 8), (19, 4), (29, 26), (22, 33), (13, 36), (27, 1), (7, 13), (19, 16), (1, 34), (11, 15), (22, 11), (33, 19), (15, 19), (7, 21), (9, 14), (4, 10), (18, 29), (13, 34), (35, 8), (31, 13), (2, 23), (20, 11), (19, 33), (6, 4), (11, 14), (21, 32), (6, 34), (13, 38), (32, 22), (24, 5), (12, 7), (32, 33), (25, 18), (20, 37), (33, 17), (25, 4), (26, 27), (24, 6), (17, 23), (38, 2), (8, 37), (16, 29), (5, 1), (30, 16), (35, 30), (7, 2), (33, 27), (17, 38), (22, 1), (24, 28), (26, 37), (38, 33), (27, 17), (4, 21), (20, 28), (26, 2), (22, 17), (7, 7), (1, 14), (3, 1), (19, 31), (0, 12), (33, 36), (3, 20), (26, 31), (21, 1), (25, 38), (3, 0), (17, 10), (7, 38), (13, 10), (19, 21), (33, 23), (34, 27), (38, 25), (17, 28), (12, 28), (17, 37), (31, 22), (11, 18), (30, 32), (0, 37), (4, 35), (3, 4), (8, 13), (22, 27), (29, 0), (4, 12), (9, 10), (23, 7), (10, 28), (11, 27), (36, 25), (5, 0), (14, 28), (22, 20), (5, 27), (30, 31), (0, 19), (8, 12), (22, 15), (7, 5), (22, 18), (4, 17), (37, 35), (37, 33), (33, 6), (14, 24), (28, 0), (6, 14), (14, 19), (30, 23), (21, 34), (18, 12), (18, 3), (16, 7), (22, 4), (27, 19), (34, 32), (24, 3), (12, 20), (28, 24), (10, 37), (0, 7), (29, 14), (37, 5), (22, 3), (6, 31), (1, 32), (21, 9), (0, 13), (13, 15), (17, 33), (24, 17), (17, 17), (16, 0), (36, 1), (9, 8), (30, 38), (21, 22), (5, 14), (18, 23), (34, 4), (2, 7), (12, 10), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347256", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 12), (28, 26), (3, 30), (22, 32), (11, 12), (25, 1), (10, 3), (11, 3), (11, 1), (23, 26), (17, 17), (21, 8), (29, 19), (26, 2), (20, 12), (10, 4), (21, 14), (19, 29), (26, 18), (19, 24), (22, 7), (1, 19), (11, 24), (11, 17), (14, 19), (8, 1), (4, 28), (25, 10), (20, 24), (26, 12), (6, 24), (25, 15), (24, 19), (29, 24), (26, 17), (27, 5), (9, 12), (7, 27), (20, 22), (14, 24), (12, 20), (29, 28), (10, 15), (5, 5), (2, 25), (13, 9), (14, 22), (14, 30), (17, 23), (17, 11), (12, 14), (28, 23), (23, 5), (17, 26), (27, 16), (17, 30), (19, 32), (6, 18), (21, 10), (11, 9), (5, 1), (29, 32), (15, 27), (12, 2), (13, 4), (23, 25), (19, 27), (1, 1), (31, 17), (17, 19), (18, 32), (26, 30), (17, 2), (28, 12), (8, 12), (9, 19), (29, 22), (18, 24), (12, 12), (26, 3), (27, 23), (6, 31), (17, 22), (11, 19), (18, 10), (2, 22), (25, 4), (2, 10), (25, 22), (10, 24), (30, 4), (6, 8), (22, 29), (18, 15), (0, 19), (7, 24), (0, 20), (30, 2), (14, 15), (8, 22), (5, 23), (22, 3), (22, 8), (18, 13), (6, 4), (4, 0), (5, 28), (5, 9), (3, 31), (15, 17), (12, 28), (17, 28), (14, 23), (29, 14), (20, 16), (20, 10), (15, 26), (10, 12), (6, 21), (12, 32), (2, 8), (27, 24), (25, 8), (23, 19), (6, 1), (5, 12), (13, 7), (13, 15), (6, 13), (16, 0), (10, 8), (16, 2), (31, 4), (1, 6), (1, 18), (30, 32), (18, 4), (15, 24), (13, 1), (1, 2), (2, 26), (9, 28), (26, 29), (24, 2), (27, 19), (11, 21), (5, 27), (10, 26), (29, 5), (23, 6), (7, 1), (18, 17), (4, 20), (13, 18), (24, 31), (26, 31), (31, 15), (10, 0), (18, 22), (15, 29), (27, 12), (10, 1), (26, 24), (13, 21), (6, 6), (5, 29), (21, 31), (10, 10), (1, 23), (30, 20), (21, 23), (28, 31), (3, 25), (7, 26), (19, 30), (23, 22), (28, 27), (10, 17), (23, 18), (2, 9), (21, 9), (15, 22), (31, 14), (10, 21), (23, 20), (13, 17), (1, 17), (2, 15), (2, 16), (11, 4), (3, 26), (10, 7), (14, 17), (19, 1), (4, 5), (25, 25), (3, 18), (29, 11), (26, 10), (24, 11), (18, 25), (12, 15), (26, 32), (18, 9), (18, 30), (16, 31), (11, 32), (22, 4), (21, 12), (17, 3), (3, 10), (10, 30), (24, 1), (28, 4), (2, 7), (11, 0), (3, 17), (14, 7), (21, 15), (27, 22), (29, 21), (5, 26), (25, 24), (19, 8), (22, 14), (14, 29), (31, 13), (12, 3), (2, 3), (10, 18), (6, 19), (11, 15), (30, 1), (26, 11), (19, 19), (5, 8), (25, 2), (30, 6), (26, 9), (19, 10), (16, 22), (1, 11), (25, 16), (17, 31), (0, 5), (29, 0), (25, 5), (3, 2), (4, 15), (13, 11), (0, 24), (11, 20), (24, 22), (5, 13), (0, 10), (3, 28), (10, 5), (17, 18), (14, 5), (14, 6), (16, 14), (6, 7), (10, 6), (7, 10), (31, 30), (9, 16), (1, 20), (8, 20), (14, 11), (10, 9), (4, 19), (18, 23), (17, 9), (17, 20), (10, 29), (13, 27), (21, 6), (22, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168960", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), 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), (23, 13), (23, 6), (2, 3), (10, 2), (1, 29), (9, 19), (2, 18), (13, 26), (7, 4), (17, 8), (19, 19), (3, 9), (14, 20), (3, 16), (4, 17), (27, 32), (33, 1), (34, 8), (9, 28), (27, 33), (10, 20), (4, 33), (29, 32), (18, 0), (6, 33), (0, 3), (34, 2), (35, 12), (4, 31), (19, 32), (16, 28), (16, 21), (33, 27), (8, 4), (2, 0), (3, 6), (22, 14), (3, 8), (15, 24), (30, 3), (19, 4), (13, 10), (12, 8), (11, 30), (35, 18), (12, 26), (19, 13), (31, 27), (17, 1), (10, 21), (11, 7), (32, 1), (18, 3), (16, 4), (11, 6), (5, 27), (8, 29), (15, 21), (14, 4), (4, 0), (23, 3), (26, 29), (9, 16), (32, 4), (35, 10), (10, 14), (21, 26), (28, 25), (27, 23), (16, 15), (23, 1), (20, 33), (5, 1), (12, 13), (24, 25), (31, 5), (9, 25), (22, 4), (6, 9), (27, 21), (3, 1), (5, 23), (6, 10), (35, 23), (19, 17), (18, 25), (33, 33), (2, 32), (22, 5), (34, 20), (23, 24), (31, 1), (14, 21), (18, 4), (16, 26), (19, 16), (30, 6), (5, 25), (11, 25), (33, 21), (6, 31), (33, 31), (11, 11), (8, 21), (27, 14), (7, 1), (17, 12), (33, 12), (25, 0), (11, 27), (19, 20), (8, 27), (20, 0), (8, 12), (35, 15), (13, 16), (9, 27), (29, 27), (15, 29), (23, 32), (24, 24), (30, 33), (16, 7), (1, 4), (33, 2), (1, 26), (7, 23), (9, 18), (28, 22), (27, 16), (22, 10), (28, 19), (28, 6), (13, 30), (8, 20), (14, 23), (33, 29), (2, 29), (23, 19), (20, 19), (24, 5), (4, 26), (20, 23), (27, 3), (12, 24), (30, 18), (12, 3), (15, 27), (27, 18), (22, 3), (1, 16), (10, 33), (3, 23), (17, 29), (15, 20), (30, 20), (29, 13), (1, 2), (32, 19), (19, 29), (10, 32), (33, 16), (17, 15), (0, 13), (24, 22), (5, 8), (3, 33), (22, 15), (19, 12), (6, 13), (28, 31), (30, 25), (4, 29), (0, 11), (28, 15), (22, 32), (30, 23), (30, 13), (0, 18), (31, 2), (6, 25), (28, 26), (18, 26), (22, 0), (11, 20), (32, 22), (5, 19), (31, 10), (20, 26), (23, 25), (12, 19), (4, 15), (17, 25), (24, 32), (34, 33), (0, 6), (13, 18), (35, 21), (11, 5), (1, 21), (21, 14), (0, 31), (10, 29), (26, 6), (17, 17), (19, 11), (22, 16), (7, 8), (23, 2), (26, 26), (0, 21), (30, 32), (27, 15), (9, 6), (14, 19), (25, 33), (20, 11), (34, 3), (5, 32), (1, 3), (5, 24), (9, 0), (21, 11), (12, 11), (16, 14), (18, 22), (2, 15), (34, 29), (23, 12), (27, 4), (7, 9), (31, 6), (31, 25), (7, 20), (34, 30), (15, 3), (14, 0), (35, 1), (11, 31), (31, 19), (14, 6), (7, 12), (17, 5), (34, 5), (1, 19), (7, 7), (1, 32), (2, 10), (35, 14), (18, 28), (6, 12), (12, 27), (9, 1), (34, 24), (15, 10), (33, 3), (7, 3), (13, 32), (9, 15), (11, 21), (25, 31), (22, 27), (1, 14), (21, 15), (3, 26), (5, 28), (18, 11), (11, 17), (29, 33), (35, 8), (23, 33), (19, 30), (8, 33), (12, 12), (12, 0), (5, 0), (21, 29), (25, 7), (24, 31), (11, 24), (27, 24), (6, 20), (5, 18), (34, 18), (30, 24), (16, 20), (31, 14), (27, 9), (23, 4), (28, 4), (28, 21), (3, 15), (26, 27), (25, 14), (4, 23), (20, 7), (8, 14), (26, 20), (33, 11), (10, 10), (13, 2), (22, 28), (13, 1), (35, 29), (20, 21), (10, 12), (9, 13), (32, 5), (0, 12), (9, 5), (8, 16), (31, 32), (0, 10), (10, 27), (28, 27), (17, 20), (28, 11), (17, 16), (2, 26), (23, 21), (29, 12), (13, 7), (18, 5), (6, 15), (12, 1), (32, 13), (18, 6), (32, 11), (26, 13), (17, 28), (5, 3), (8, 11), (34, 19), (26, 14), (13, 29), (26, 31), (12, 4), (8, 3), (19, 31), (7, 18), (9, 11), (25, 27), (32, 15), (25, 2), (10, 13), (28, 17), (29, 21), (31, 8), (29, 18), (33, 23), (4, 9), (30, 27), (8, 6), (2, 13), (14, 15), (12, 7), (33, 0), (11, 23), (3, 29), (12, 22), (5, 6), (19, 6), (30, 28), (19, 33), (14, 7), (13, 11), (29, 8), (30, 30), (32, 25), (10, 17), (32, 26), (23, 26), (11, 4), (8, 9), (13, 31), (29, 28), (4, 30), (4, 16), (3, 21), (18, 10), (6, 29), (30, 14), (35, 20), (6, 4), (34, 11), (27, 1), (8, 8), (26, 12), (23, 23), (18, 16), (33, 4), (5, 30), (17, 4), (1, 15), (12, 20), (29, 7), (23, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632920", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 29), (20, 18), (2, 33), (6, 10), (14, 32), (9, 14), (4, 24), (16, 23), (9, 18), (21, 7), (28, 24), (6, 34), (0, 10), (28, 10), (2, 13), (8, 0), (16, 19), (14, 16), (19, 28), (10, 14), (21, 4), (9, 12), (4, 15), (5, 27), (3, 28), (14, 33), (6, 33), (24, 36), (28, 32), (6, 31), (9, 29), (0, 24), (1, 10), (6, 36), (2, 9), (9, 23), (16, 11), (18, 14), (5, 11), (23, 9), (1, 7), (15, 8), (26, 3), (2, 34), (19, 27), (3, 23), (0, 25), (26, 13), (21, 22), (1, 31), (23, 3), (2, 25), (8, 20), (18, 19), (3, 27), (4, 20), (22, 11), (29, 30), (5, 22), (6, 2), (24, 32), (6, 22), (10, 25), (10, 1), (4, 21), (3, 33), (0, 12), (18, 11), (10, 4), (22, 13), (26, 27), (2, 37), (3, 16), (15, 25), (9, 27), (19, 3), (20, 19), (14, 7), (10, 22), (28, 28), (3, 6), (16, 13), (25, 13), (13, 12), (2, 23), (13, 24), (21, 25), (16, 5), (8, 34), (26, 34), (2, 18), (20, 37), (19, 15), (16, 22), (21, 3), (25, 5), (3, 5), (25, 22), (15, 20), (6, 3), (1, 13), (25, 1), (10, 16), (11, 20), (29, 36), (11, 8), (24, 37), (9, 17), (23, 21), (28, 4), (1, 6), (13, 10), (17, 5), (12, 22), (13, 19), (15, 11), (3, 35), (18, 4), (18, 10), (10, 32), (26, 5), (19, 26), (21, 9), (2, 12), (8, 2), (3, 19), (13, 13), (13, 1), (13, 22), (15, 2), (12, 25), (16, 16), (17, 32), (2, 31), (2, 26), (12, 17), (21, 11), (0, 13), (5, 35), (21, 36), (18, 27), (29, 28), (1, 29), (19, 0), (17, 0), (14, 20), (24, 13), (15, 33), (0, 18), (25, 8), (5, 23), (14, 37), (9, 16), (4, 22), (0, 3), (21, 8), (15, 23), (22, 12), (23, 18), (20, 35), (29, 14), (5, 30), (27, 8), (27, 16), (25, 0), (20, 34), (19, 10), (19, 13), (19, 32), (21, 17), (18, 9), (10, 5), (22, 34), (19, 36), (21, 30), (25, 4), (18, 36), (0, 22), (8, 19), (26, 31), (22, 25), (9, 36), (0, 32), (16, 15), (0, 15), (10, 11), (28, 22), (10, 26), (10, 23), (25, 10), (25, 35), (16, 37), (17, 12), (22, 26), (12, 23), (0, 30), (15, 16), (22, 7), (14, 23), (25, 18), (0, 33), (18, 15), (0, 35), (20, 31), (12, 8), (15, 12), (1, 28), (29, 13), (8, 27), (26, 33), (11, 16), (17, 9), (13, 20), (11, 0), (23, 10), (18, 33), (13, 6), (18, 30), (10, 20), (18, 20), (16, 33), (4, 32), (12, 30), (28, 20), (27, 10), (8, 33), (16, 24), (6, 7), (2, 0), (26, 9), (11, 3), (11, 30), (11, 29), (18, 17), (22, 15), (17, 36), (6, 12), (21, 21), (19, 30), (21, 29), (13, 14), (28, 7), (28, 0), (24, 18), (29, 34), (1, 11), (19, 31), (6, 18), (24, 8), (9, 3), (23, 26), (0, 6), (20, 29), (22, 2), (4, 35), (27, 24), (27, 4), (28, 8), (22, 4), (5, 5), (26, 4), (11, 22), (22, 16), (1, 33), (28, 9), (7, 32), (8, 15), (11, 18), (21, 37), (17, 8), (20, 9), (4, 2), (16, 8), (14, 8), (26, 25), (17, 7), (28, 5), (28, 6), (3, 30), (0, 23), (3, 32), (14, 29), (0, 31), (7, 7), (9, 21), (28, 11), (26, 28), (7, 1), (3, 3), (13, 29), (28, 33), (23, 5), (12, 32), (15, 13), (15, 15), (27, 19), (6, 20), (18, 5), (29, 6), (8, 37), (16, 28), (16, 9), (8, 18), (10, 36), (17, 28), (3, 21), (1, 27), (9, 30), (24, 10), (25, 3), (17, 15), (2, 35), (25, 17), (22, 18), (14, 25), (23, 17), (24, 19), (20, 21), (28, 29), (12, 37), (9, 34), (14, 22), (14, 26), (26, 16), (8, 1), (3, 1), (7, 31), (18, 16), (5, 31), (5, 4), (23, 25), (19, 22), (12, 13), (14, 2), (4, 0), (19, 4), (19, 25), (11, 24), (29, 16), (3, 17), (27, 23), (4, 11), (20, 15), (24, 24), (23, 27), (25, 32), (22, 27), (23, 6), (1, 30), (25, 29), (23, 22), (28, 15), (5, 29), (1, 17), (7, 36), (13, 21), (6, 27), (18, 35), (21, 15), (26, 7), (5, 7), (26, 32), (5, 26), (18, 21), (1, 23), (9, 8), (6, 35), (4, 9), (12, 24), (27, 13), (12, 19), (26, 35), (11, 32), (10, 19), (17, 24), (29, 17), (0, 16), (16, 31), (0, 1), (9, 2), (29, 10), (15, 7), (8, 24), (12, 6), (20, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236480", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 21), (18, 11), (3, 11), (6, 16), (1, 16), (13, 34), (25, 12), (27, 28), (21, 12), (4, 32), (24, 2), (4, 10), (17, 10), (29, 22), (28, 24), (15, 26), (12, 3), (18, 30), (8, 27), (16, 18), (21, 1), (25, 5), (13, 12), (25, 4), (8, 6), (9, 9), (3, 34), (7, 16), (26, 21), (17, 33), (4, 4), (17, 24), (0, 23), (4, 19), (1, 29), (29, 24), (25, 34), (1, 15), (21, 2), (18, 13), (17, 2), (20, 0), (5, 17), (6, 25), (5, 11), (15, 27), (13, 32), (12, 23), (1, 30), (4, 6), (22, 10), (28, 5), (0, 34), (15, 21), (4, 31), (15, 23), (5, 0), (9, 10), (29, 2), (7, 22), (10, 24), (2, 20), (25, 30), (2, 1), (27, 9), (15, 20), (27, 32), (27, 23), (9, 15), (8, 24), (25, 15), (14, 26), (13, 25), (11, 3), (18, 20), (1, 6), (13, 5), (7, 17), (8, 22), (6, 24), (20, 11), (16, 4), (22, 34), (22, 22), (26, 3), (10, 9), (6, 20), (7, 4), (22, 9), (23, 5), (2, 21), (11, 10), (10, 15), (9, 29), (16, 30), (29, 27), (20, 12), (23, 33), (16, 1), (11, 22), (10, 18), (18, 2), (10, 29), (27, 6), (22, 31), (18, 23), (23, 16), (7, 29), (23, 28), (11, 17), (19, 16), (6, 18), (29, 26), (12, 18), (27, 22), (22, 16), (8, 25), (9, 11), (18, 27), (15, 13), (16, 21), (28, 28), (6, 29), (4, 25), (21, 22), (24, 9), (14, 4), (22, 4), (5, 15), (22, 24), (16, 17), (1, 11), (13, 7), (13, 14), (21, 19), (13, 26), (11, 30), (9, 13), (18, 16), (0, 30), (3, 33), (21, 28), (26, 7), (6, 26), (15, 6), (0, 22), (24, 10), (27, 25), (5, 20), (9, 26), (17, 20), (29, 23), (15, 5), (28, 16), (14, 28), (0, 32), (19, 11), (18, 12), (3, 6), (14, 32), (14, 27), (11, 1), (5, 10), (25, 24), (12, 28), (10, 11), (12, 15), (18, 1), (17, 22), (19, 0), (3, 7), (27, 4), (22, 2), (28, 29), (22, 17), (24, 32), (11, 6), (19, 13), (24, 21), (3, 17), (3, 8), (14, 24), (14, 16), (10, 28), (0, 9), (19, 23), (25, 26), (17, 5), (0, 33), (6, 4), (26, 4), (23, 11), (16, 28), (29, 33), (29, 30), (2, 16), (23, 29), (24, 18), (15, 34), (7, 31), (14, 34), (0, 24), (18, 22), (24, 19), (14, 3), (23, 3), (23, 20), (28, 4), (26, 12), (23, 30), (2, 3), (3, 24), (18, 5), (21, 10), (5, 19), (23, 2), (19, 10), (7, 19), (11, 21), (14, 15), (14, 25), (3, 3), (0, 29), (24, 28), (28, 9), (25, 19), (29, 5), (24, 25), (23, 6), (21, 25), (19, 7), (19, 9), (28, 7), (13, 18), (3, 22), (19, 29), (29, 14), (27, 0), (22, 11), (25, 29), (18, 6), (20, 4), (1, 24), (1, 3), (3, 19), (14, 31), (24, 17), (12, 24), (15, 17), (27, 30), (16, 22), (28, 6), (5, 22), (11, 0), (0, 20), (22, 25), (9, 0), (1, 10), (8, 0), (19, 18), (27, 14), (6, 9), (21, 3), (17, 21), (25, 20), (19, 12), (15, 8), (13, 17), (3, 26), (2, 13), (19, 15), (1, 19), (7, 7), (4, 5), (22, 3), (9, 22), (4, 9), (0, 14), (2, 30), (5, 21), (5, 30), (16, 32), (10, 17), (13, 16), (25, 13), (10, 34), (7, 32), (28, 21), (29, 25), (1, 32), (25, 1), (22, 0), (23, 24), (26, 8), (18, 26), (1, 20), (0, 26), (9, 6), (19, 6), (13, 24), (25, 9), (0, 11), (13, 22), (5, 26), (1, 21), (4, 2), (9, 28), (28, 1), (3, 12), (1, 9), (20, 31), (15, 14), (19, 1), (3, 1), (6, 10), (0, 21), (16, 20), (10, 23), (27, 17), (25, 11), (18, 14), (25, 3), (23, 19), (23, 14), (21, 27), (27, 2), (4, 29), (4, 3), (13, 8), (4, 17), (24, 6), (6, 22), (22, 12), (2, 27), (17, 12), (28, 15), (26, 24), (11, 19), (21, 6), (26, 0), (19, 22), (20, 1), (20, 10), (24, 11), (8, 4), (11, 23), (9, 31), (11, 8), (26, 34), (18, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491040", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 28), (35, 16), (34, 10), (17, 36), (12, 32), (1, 19), (23, 30), (36, 11), (27, 16), (32, 26), (4, 9), (28, 2), (29, 19), (25, 13), (11, 23), (3, 20), (36, 31), (2, 23), (23, 18), (27, 37), (23, 37), (36, 35), (17, 15), (34, 0), (21, 23), (27, 2), (2, 11), (30, 5), (21, 35), (4, 21), (35, 23), (16, 13), (37, 11), (31, 33), (36, 5), (14, 7), (30, 24), (6, 0), (26, 12), (37, 4), (27, 24), (21, 0), (14, 18), (38, 30), (4, 25), (23, 16), (36, 25), (16, 6), (38, 27), (33, 17), (21, 34), (16, 8), (26, 20), (18, 33), (23, 23), (38, 15), (32, 12), (25, 19), (6, 13), (32, 35), (9, 21), (14, 29), (3, 33), (30, 37), (29, 37), (28, 26), (2, 31), (27, 20), (5, 36), (20, 30), (10, 6), (26, 30), (13, 24), (35, 18), (7, 10), (18, 13), (17, 3), (29, 18), (36, 33), (34, 13), (5, 30), (18, 1), (27, 21), (21, 20), (29, 28), (35, 31), (27, 36), (13, 13), (3, 13), (10, 2), (8, 23), (22, 33), (6, 22), (5, 5), (18, 3), (31, 15), (38, 31), (33, 38), (24, 33), (23, 32), (6, 28), (28, 6), (34, 34), (20, 13), (32, 20), (10, 3), (9, 0), (6, 25), (17, 37), (4, 19), (35, 34), (20, 24), (4, 13), (35, 32), (13, 10), (31, 0), (13, 15), (5, 21), (1, 30), (23, 33), (32, 31), (15, 38), (11, 35), (3, 34), (20, 11), (9, 18), (10, 0), (19, 7), (12, 24), (20, 38), (32, 1), (3, 11), (18, 16), (20, 32), (0, 32), (20, 4), (8, 17), (37, 25), (29, 36), (6, 12), (7, 9), (8, 14), (37, 3), (2, 5), (12, 16), (6, 16), (1, 18), (9, 9), (5, 18), (32, 28), (8, 8), (17, 34), (12, 2), (33, 25), (8, 1), (0, 24), (25, 8), (31, 17), (17, 12), (3, 32), (21, 27), (2, 38), (36, 10), (7, 33), (19, 25), (26, 28), (4, 14), (5, 25), (27, 28), (10, 26), (8, 37), (34, 37), (15, 23), (28, 21), (10, 32), (1, 1), (22, 35), (34, 16), (13, 22), (38, 32), (0, 31), (24, 38), (6, 15), (0, 21), (21, 37), (9, 25), (11, 12), (7, 22), (14, 15), (5, 0), (24, 27), (0, 8), (2, 20), (6, 18), (25, 15), (29, 5), (7, 4), (26, 1), (29, 22), (22, 7), (21, 25), (23, 7), (10, 5), (36, 27), (30, 19), (9, 6), (5, 20), (15, 12), (7, 8), (15, 17), (32, 18), (20, 19), (38, 18), (1, 0), (24, 19), (8, 9), (16, 12), (21, 12), (33, 23), (5, 15), (24, 13), (8, 5), (7, 14), (10, 19), (16, 5), (10, 27), (32, 32), (4, 7), (24, 32), (33, 34), (31, 37), (16, 0), (18, 5), (16, 3), (2, 22), (29, 27), (10, 14), (16, 27), (25, 32), (22, 11), (24, 34), (5, 3), (34, 17), (6, 3), (7, 20), (21, 9), (29, 35), (28, 7), (14, 3), (23, 4), (21, 4), (18, 34), (17, 19), (38, 9), (11, 26), (27, 4), (36, 3), (11, 20), (12, 23), (30, 26), (0, 10), (31, 5), (5, 12), (28, 28), (5, 7), (27, 12), (1, 32), (30, 33), (29, 23), (9, 12), (10, 10), (0, 35), (35, 30), (21, 7), (16, 24), (4, 0), (29, 14), (20, 9), (29, 32), (21, 14), (9, 38), (33, 31), (30, 3), (10, 13), (36, 2), (34, 38), (0, 29), (19, 0), (37, 23), (25, 16), (34, 2), (8, 26), (9, 35), (34, 32), (30, 38), (4, 3), (28, 15), (19, 10), (30, 25), (23, 24), (1, 29), (36, 7), (12, 17), (29, 4), (6, 23), (35, 7), (23, 38), (7, 17), (15, 27), (17, 31), (36, 30), (15, 7), (31, 28), (11, 1), (32, 27), (13, 8), (8, 18), (23, 13), (20, 35), (28, 30), (12, 22), (20, 28), (14, 8), (13, 21), (28, 14), (31, 27), (2, 32), (5, 37), (0, 6), (25, 14), (36, 21), (11, 6), (4, 28), (10, 28), (26, 31), (18, 18), (9, 3), (18, 10), (0, 37), (4, 27), (13, 6), (32, 33), (12, 14), (22, 17), (19, 1), (19, 4), (17, 21), (26, 37), (34, 8), (26, 19), (12, 34), (19, 22), (17, 18), (29, 10), (37, 28), (4, 11), (19, 36), (34, 36), (22, 38), (1, 25), (15, 20), (14, 9), (27, 7), (18, 9), (9, 30), (7, 7), (28, 34), (27, 8), (12, 35), (3, 6), (13, 35), (34, 31), (20, 20), (0, 20), (26, 36), (26, 32), (26, 15), (33, 16), (3, 14), (15, 26), (9, 14), (34, 25), (13, 20), (29, 3), (14, 36), (32, 3), (17, 20), (4, 16), (19, 27), (17, 2), (15, 31), (5, 34), (35, 28), (10, 17), (8, 10), (21, 11), (1, 4), (18, 25), (14, 19), (16, 34), (23, 2), (19, 24), (5, 1), (26, 9), (21, 2), (18, 37), (18, 32), (14, 20), (5, 11), (2, 0), (24, 5), (35, 15), (16, 9), (2, 8), (11, 0), (26, 34), (15, 22), (23, 6), (9, 8), (10, 8), (29, 8), (13, 26), (22, 27), (11, 4), (24, 35), (27, 10), (19, 2), (24, 25), (36, 17), (34, 11), (10, 12), (22, 18), (0, 11), (13, 29), (4, 5), (38, 3), (14, 16), (28, 0), (8, 20), (4, 23), (22, 25), (38, 36), (33, 3), (1, 9), (14, 22), (10, 11), (0, 7), (10, 38), (26, 17), (9, 23), (24, 12), (28, 8), (6, 14), (23, 26), (4, 35), (10, 37), (2, 19), (17, 27), (35, 19), (18, 29), (8, 19), (15, 18), (3, 10), (29, 16), (27, 3), (22, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987840", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (21, 24), (28, 26), (6, 27), (23, 19), (31, 24), (18, 20), (12, 12), (16, 34), (4, 2), (7, 8), (19, 31), (1, 26), (29, 20), (12, 18), (17, 5), (4, 0), (28, 4), (1, 4), (16, 14), (21, 28), (22, 30), (17, 0), (17, 25), (23, 35), (2, 23), (31, 34), (18, 27), (5, 14), (14, 15), (12, 20), (15, 24), (29, 35), (2, 20), (30, 7), (17, 26), (24, 4), (22, 19), (33, 0), (26, 27), (10, 17), (4, 15), (31, 26), (4, 27), (27, 1), (6, 34), (30, 32), (33, 15), (14, 0), (12, 0), (16, 15), (0, 15), (22, 21), (27, 21), (29, 26), (22, 16), (2, 14), (3, 15), (2, 10), (29, 30), (7, 10), (29, 16), (22, 1), (24, 20), (23, 27), (28, 3), (0, 16), (15, 11), (3, 8), (14, 35), (32, 28), (0, 30), (27, 0), (10, 14), (1, 19), (33, 28), (26, 6), (13, 18), (27, 4), (31, 29), (22, 24), (15, 5), (6, 6), (3, 24), (5, 8), (6, 13), (26, 14), (21, 33), (10, 21), (31, 27), (20, 28), (19, 11), (14, 16), (26, 31), (5, 21), (30, 26), (22, 12), (2, 31), (8, 16), (25, 2), (21, 6), (24, 13), (31, 16), (29, 2), (6, 33), (24, 26), (21, 20), (15, 1), (1, 18), (4, 30), (22, 13), (31, 1), (29, 4), (19, 30), (25, 4), (4, 14), (25, 21), (32, 12), (8, 34), (31, 20), (0, 27), (26, 26), (20, 32), (30, 34), (5, 29), (21, 12), (9, 6), (2, 9), (32, 32), (17, 27), (0, 19), (26, 22), (25, 27), (30, 28), (12, 19), (31, 12), (8, 11), (1, 5), (21, 23), (19, 14), (27, 32), (32, 29), (14, 18), (33, 3), (2, 12), (0, 23), (10, 23), (33, 23), (13, 21), (10, 32), (9, 12), (24, 29), (6, 23), (3, 10), (20, 19), (0, 12), (2, 32), (8, 14), (10, 28), (19, 23), (30, 3), (29, 8), (5, 22), (32, 20), (16, 9), (30, 11), (25, 8), (6, 14), (10, 1), (10, 33), (25, 14), (31, 30), (28, 22), (16, 29), (16, 1), (11, 29), (24, 32), (20, 26), (32, 34), (11, 13), (31, 22), (28, 5), (27, 31), (19, 26), (20, 9), (18, 0), (0, 5), (0, 2), (15, 0), (4, 23), (2, 29), (10, 19), (16, 23), (14, 29), (29, 14), (25, 31), (2, 7), (0, 1), (30, 15), (11, 8), (15, 17), (11, 23), (15, 14), (4, 21), (31, 21), (5, 5), (32, 8), (21, 27), (15, 4), (18, 23), (33, 5), (21, 16), (9, 32), (8, 21), (25, 13), (25, 5), (15, 26), (33, 24), (18, 4), (9, 28), (7, 32), (25, 19), (3, 9), (31, 13), (24, 35), (23, 29), (8, 5), (18, 22), (19, 12), (11, 25), (17, 7), (10, 0), (7, 11), (17, 13), (16, 16), (19, 9), (18, 35), (19, 24), (25, 29), (3, 22), (8, 23), (25, 16), (0, 8), (27, 18), (21, 3), (5, 28), (5, 7), (6, 22), (5, 4), (0, 31), (6, 4), (10, 2), (14, 21), (3, 27), (7, 17), (9, 25), (33, 9), (21, 18), (32, 21), (24, 7), (2, 3), (0, 24), (3, 6), (10, 26), (26, 13), (18, 24), (5, 13), (1, 12), (29, 31), (20, 8), (10, 4), (11, 16), (32, 10), (18, 36), (27, 6), (11, 21), (10, 18), (23, 18), (26, 23), (24, 30), (25, 3), (17, 34), (12, 32), (13, 6), (23, 2), (16, 26), (20, 27), (28, 6), (2, 2), (4, 25), (13, 12), (27, 13), (6, 1), (23, 20), (18, 2), (32, 11), (31, 17), (16, 22), (11, 9), (14, 25), (9, 14), (28, 15), (33, 14), (31, 28), (30, 25), (8, 20), (29, 36), (10, 29), (18, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267300", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 36), (26, 5), (18, 32), (6, 18), (13, 23), (19, 30), (12, 27), (31, 16), (18, 10), (32, 18), (33, 29), (14, 5), (1, 8), (27, 20), (5, 11), (27, 8), (11, 30), (33, 15), (4, 22), (32, 32), (19, 22), (10, 14), (26, 25), (23, 4), (9, 19), (32, 33), (0, 13), (29, 24), (22, 34), (14, 17), (20, 27), (16, 11), (10, 30), (4, 28), (33, 7), (28, 21), (20, 12), (12, 6), (1, 26), (25, 11), (0, 22), (9, 24), (21, 24), (32, 21), (16, 6), (11, 1), (29, 18), (15, 26), (31, 28), (26, 21), (11, 2), (27, 23), (19, 5), (21, 36), (29, 28), (5, 33), (24, 15), (3, 26), (7, 29), (24, 28), (2, 1), (30, 5), (14, 11), (19, 17), (30, 17), (20, 36), (15, 20), (2, 16), (25, 30), (14, 20), (2, 15), (10, 35), (33, 14), (18, 26), (13, 30), (28, 24), (18, 23), (12, 28), (18, 5), (10, 12), (32, 0), (30, 12), (24, 26), (30, 29), (1, 9), (8, 20), (7, 28), (9, 25), (5, 23), (7, 11), (29, 32), (18, 18), (21, 27), (32, 30), (1, 30), (26, 18), (20, 22), (16, 24), (7, 24), (2, 14), (20, 15), (16, 36), (7, 23), (32, 9), (21, 1), (28, 5), (2, 19), (23, 7), (29, 16), (5, 36), (14, 22), (4, 8), (32, 5), (7, 4), (2, 7), (2, 27), (26, 27), (30, 33), (5, 26), (13, 10), (30, 32), (12, 11), (6, 11), (24, 13), (17, 30), (3, 3), (30, 19), (6, 26), (0, 30), (6, 20), (1, 7), (5, 12), (33, 20), (10, 21), (14, 29), (15, 1), (18, 30), (31, 4), (20, 24), (2, 3), (12, 14), (27, 1), (32, 24), (13, 26), (31, 12), (7, 30), (8, 28), (22, 5), (23, 6), (21, 9), (25, 0), (17, 25), (28, 1), (10, 36), (11, 16), (27, 4), (15, 28), (13, 9), (28, 34), (26, 26), (25, 21), (25, 24), (4, 30), (12, 12), (27, 17), (13, 24), (5, 3), (17, 16), (9, 2), (12, 23), (4, 2), (0, 15), (11, 15), (10, 20), (22, 27), (22, 16), (17, 34), (20, 0), (16, 18), (21, 25), (21, 5), (18, 22), (33, 13), (13, 34), (9, 22), (28, 2), (24, 9), (16, 15), (14, 34), (22, 28), (33, 21), (17, 0), (12, 13), (33, 19), (16, 23), (23, 22), (31, 21), (29, 4), (9, 20), (19, 33), (24, 1), (3, 6), (6, 5), (15, 32), (19, 6), (29, 20), (14, 19), (29, 5), (22, 9), (2, 25), (29, 10), (16, 20), (16, 34), (9, 16), (11, 13), (26, 4), (17, 2), (8, 3), (8, 9), (1, 21), (13, 14), (27, 27), (25, 28), (16, 14), (4, 18), (32, 27), (16, 28), (16, 32), (27, 32), (25, 8), (15, 4), (22, 35), (3, 5), (29, 34), (12, 22), (24, 14), (7, 18), (0, 27), (25, 15), (6, 0), (21, 22), (5, 6), (18, 13), (20, 8), (13, 29), (0, 20), (33, 11), (9, 27), (29, 36), (1, 24), (12, 29), (23, 0), (29, 13), (0, 31), (21, 14), (28, 27), (26, 23), (22, 14), (17, 10), (19, 9), (0, 9), (23, 5), (19, 34), (13, 32), (8, 17), (20, 17), (7, 20), (23, 16), (27, 28), (2, 24), (15, 36), (4, 33), (6, 17), (20, 9), (16, 27), (13, 27), (15, 9), (32, 35), (8, 2), (25, 12), (19, 3), (0, 25), (17, 13), (20, 16), (26, 33), (10, 34), (33, 28), (28, 31), (13, 4), (20, 34), (22, 20), (5, 28), (4, 6), (26, 10), (8, 22), (2, 18), (17, 12), (30, 14), (30, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884520", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), 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), (3, 13), (18, 5), (1, 19), (22, 6), (2, 15), (23, 31), (17, 32), (21, 16), (1, 13), (19, 27), (13, 6), (10, 17), (2, 6), (15, 5), (15, 11), (9, 17), (25, 6), (10, 22), (13, 11), (12, 15), (4, 35), (25, 2), (17, 0), (6, 17), (26, 24), (19, 34), (24, 17), (24, 2), (28, 22), (8, 0), (7, 11), (26, 9), (25, 27), (4, 27), (28, 2), (29, 23), (5, 30), (9, 31), (27, 11), (23, 30), (24, 6), (21, 30), (17, 3), (10, 11), (27, 1), (13, 23), (7, 3), (21, 24), (18, 29), (13, 29), (10, 20), (3, 34), (20, 13), (15, 2), (15, 19), (13, 22), (8, 26), (28, 26), (9, 18), (11, 7), (0, 14), (18, 13), (4, 30), (28, 28), (0, 2), (1, 12), (15, 20), (26, 1), (28, 12), (19, 6), (15, 33), (17, 25), (23, 1), (14, 28), (12, 8), (2, 18), (5, 27), (0, 32), (19, 3), (4, 17), (12, 3), (23, 22), (13, 17), (8, 14), (13, 2), (27, 8), (18, 8), (0, 15), (14, 8), (21, 25), (10, 0), (8, 25), (1, 25), (7, 4), (17, 4), (18, 33), (22, 19), (19, 28), (5, 10), (26, 3), (22, 34), (13, 15), (10, 18), (16, 0), (21, 13), (14, 10), (9, 35), (12, 24), (9, 0), (11, 29), (29, 30), (5, 7), (5, 13), (2, 4), (24, 16), (28, 33), (27, 33), (23, 5), (19, 9), (17, 12), (1, 28), (28, 24), (24, 18), (25, 11), (12, 1), (1, 15), (20, 25), (11, 33), (7, 21), (21, 2), (5, 1), (20, 26), (7, 14), (14, 33), (10, 33), (21, 19), (16, 9), (16, 16), (2, 30), (12, 17), (21, 3), (13, 21), (27, 21), (2, 27), (6, 33), (6, 3), (22, 21), (14, 5), (20, 21), (25, 22), (8, 18), (6, 27), (18, 0), (14, 34), (21, 28), (3, 9), (28, 5), (8, 5), (3, 24), (12, 7), (3, 5), (12, 2), (20, 28), (7, 29), (29, 19), (0, 13), (10, 14), (4, 12), (6, 30), (13, 10), (0, 24), (9, 15), (19, 15), (27, 18), (24, 20), (22, 9), (28, 9), (12, 34), (16, 22), (25, 20), (2, 21), (5, 24), (10, 7), (5, 23), (12, 16), (4, 22), (20, 29), (15, 22), (23, 23), (27, 10), (28, 7), (4, 29), (11, 34), (26, 12), (11, 35), (26, 20), (6, 28), (27, 26), (8, 21), (24, 5), (3, 32), (5, 22), (5, 28), (29, 20), (2, 16), (0, 35), (3, 6), (17, 33), (17, 35), (26, 16), (6, 16), (4, 26), (28, 27), (15, 10), (29, 16), (9, 1), (2, 10), (29, 9), (6, 20), (16, 28), (12, 4), (5, 29), (16, 7), (20, 32), (1, 24), (11, 18), (18, 12), (9, 32), (23, 19), (29, 32), (21, 27), (12, 18), (11, 16), (29, 24), (23, 21), (17, 11), (14, 22), (24, 33), (5, 18), (2, 9), (24, 26), (24, 15), (5, 8), (12, 11), (18, 25), (13, 20), (12, 20), (7, 23), (7, 1), (2, 20), (28, 11), (5, 20), (16, 6), (27, 32), (15, 16), (4, 7), (7, 35), (21, 15), (1, 21), (10, 29), (14, 15), (15, 1), (20, 2), (29, 22), (10, 31), (4, 31), (21, 0), (27, 7), (20, 12), (8, 30), (11, 13), (0, 22), (2, 23), (15, 8), (2, 33), (17, 1), (17, 14), (22, 33), (4, 2), (2, 32), (25, 31), (22, 16), (3, 23), (9, 25), (3, 26), (8, 12), (21, 6), (19, 2), (1, 8), (14, 12), (8, 31), (14, 23), (18, 26), (5, 11), (4, 6), (14, 17), (12, 30), (19, 32), (23, 33), (22, 15), (11, 9), (19, 11), (0, 23), (20, 24), (1, 18), (7, 27), (10, 19), (12, 25), (19, 21), (10, 21), (14, 13), (10, 30), (7, 30), (8, 35), (0, 7), (4, 32), (27, 27), (20, 23), (22, 31), (17, 6), (19, 31), (24, 27), (0, 17), (28, 15), (15, 21), (20, 20), (11, 3), (8, 33), (21, 17), (7, 17), (17, 22), (29, 21), (19, 10), (21, 4), (12, 28), (25, 29), (19, 5), (3, 14), (0, 19), (9, 27), (16, 5), (22, 27), (18, 31), (17, 16), (28, 8), (9, 4), (12, 19), (22, 7), (25, 10), (24, 7), (12, 33), (5, 2), (27, 12), (23, 12), (16, 2), (28, 16), (5, 34), (23, 27), (19, 20), (13, 8), (1, 30), (14, 16), (14, 32), (21, 18), (3, 4), (16, 31), (25, 0), (0, 16), (16, 18), (9, 21), (12, 26), (24, 31), (23, 15), (5, 25), (13, 35), (18, 6), (20, 17), (28, 35), (4, 20), (13, 0), (17, 23), (23, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "452352", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (36, 26), (18, 24), (3, 13), (4, 25), (15, 9), (6, 13), (28, 18), (6, 11), (27, 22), (28, 7), (18, 8), (28, 32), (24, 28), (17, 31), (14, 26), (11, 3), (31, 8), (24, 8), (19, 10), (25, 15), (15, 22), (27, 23), (25, 24), (24, 24), (2, 28), (22, 25), (15, 26), (4, 29), (32, 21), (36, 8), (10, 5), (5, 21), (10, 2), (27, 6), (30, 29), (19, 8), (12, 14), (25, 28), (37, 24), (12, 31), (12, 23), (33, 22), (15, 5), (7, 11), (16, 6), (16, 11), (7, 23), (5, 5), (10, 21), (6, 29), (17, 27), (35, 20), (20, 30), (8, 32), (1, 19), (2, 3), (7, 5), (9, 21), (14, 31), (20, 9), (3, 8), (13, 6), (12, 3), (14, 15), (31, 3), (33, 23), (35, 31), (16, 4), (22, 30), (6, 1), (19, 23), (31, 21), (24, 12), (21, 6), (22, 32), (2, 24), (12, 25), (26, 6), (23, 5), (19, 16), (15, 16), (8, 19), (28, 11), (10, 13), (24, 5), (1, 15), (28, 6), (27, 30), (10, 14), (8, 25), (4, 8), (17, 29), (14, 20), (8, 14), (4, 32), (3, 5), (26, 3), (33, 21), (15, 23), (2, 22), (28, 4), (4, 18), (4, 13), (8, 18), (4, 2), (22, 1), (16, 12), (20, 20), (30, 22), (6, 3), (3, 11), (19, 17), (16, 21), (9, 7), (4, 11), (4, 17), (9, 10), (0, 20), (18, 17), (33, 24), (23, 32), (11, 9), (32, 27), (27, 5), (2, 10), (37, 4), (11, 7), (18, 32), (22, 24), (33, 13), (13, 21), (21, 13), (23, 25), (5, 9), (36, 3), (8, 13), (22, 6), (11, 17), (37, 12), (21, 15), (30, 6), (32, 5), (22, 18), (34, 22), (21, 20), (0, 13), (37, 26), (16, 29), (7, 25), (30, 23), (19, 21), (21, 27), (32, 7), (28, 10), (33, 19), (11, 27), (32, 30), (5, 28), (17, 15), (5, 18), (16, 16), (30, 10), (26, 26), (15, 7), (18, 10), (26, 13), (18, 16), (9, 2), (10, 26), (36, 2), (14, 1), (19, 31), (14, 25), (35, 22), (6, 31), (2, 14), (3, 15), (3, 16), (36, 6), (17, 6), (34, 26), (13, 14), (8, 31), (2, 31), (18, 29), (5, 6), (24, 0), (13, 3), (11, 30), (23, 2), (33, 18), (31, 9), (27, 2), (34, 29), (31, 28), (11, 4), (7, 21), (5, 31), (10, 12), (17, 22), (1, 20), (36, 30), (8, 26), (35, 2), (33, 3), (29, 21), (20, 28), (0, 9), (33, 4), (27, 3), (8, 17), (8, 6), (36, 4), (9, 24), (37, 23), (26, 12), (11, 31), (5, 24), (30, 14), (10, 32), (10, 20), (5, 32), (30, 2), (18, 27), (12, 21), (8, 11), (27, 29), (23, 6), (17, 24), (22, 13), (33, 8), (10, 0), (0, 26), (29, 26), (7, 20), (20, 23), (34, 24), (22, 5), (26, 17), (32, 25), (25, 17), (20, 16), (19, 30), (18, 11), (37, 11), (19, 25), (16, 14), (5, 7), (12, 22), (34, 8), (12, 29), (15, 25), (2, 6), (28, 26), (29, 23), (34, 25), (11, 11), (37, 20), (14, 22), (15, 0), (31, 13), (36, 23), (22, 29), (18, 31), (23, 3), (7, 8), (24, 27), (24, 15), (16, 17), (32, 24), (24, 1), (32, 10), (21, 3), (28, 29), (16, 18), (19, 5), (7, 22), (24, 18), (4, 27), (25, 30), (23, 12), (34, 15), (32, 23), (10, 17), (31, 0), (16, 8), (30, 24), (11, 20), (16, 28), (9, 1), (12, 9), (20, 24), (34, 11), (1, 18), (32, 12), (30, 9), (7, 18), (27, 21), (35, 19), (20, 12), (19, 1), (30, 0), (22, 4), (22, 0), (8, 22), (11, 0), (33, 2), (9, 31), (2, 25), (2, 16), (2, 20), (37, 18), (35, 24), (8, 30), (34, 23), (4, 12), (37, 17), (5, 20), (22, 3), (23, 16), (23, 20), (35, 14), (6, 24), (30, 15), (25, 29), (21, 18), (4, 22), (22, 15), (25, 32), (37, 13), (16, 0), (4, 31), (5, 10), (13, 22), (3, 30), (24, 17), (0, 8), (26, 22), (25, 25), (30, 1), (37, 29), (9, 18), (30, 16), (30, 20), (15, 31), (9, 5), (5, 15), (1, 14), (32, 32), (34, 21), (34, 27), (16, 20), (30, 31), (24, 7), (11, 19), (10, 11), (2, 1), (8, 23), (35, 10), (7, 13), (5, 8), (7, 24), (26, 11), (26, 0), (19, 27), (24, 3), (6, 21), (7, 16), (34, 13), (18, 19), (1, 5), (17, 28), (29, 17), (26, 23), (6, 22), (36, 11), (1, 26), (20, 10), (14, 27), (3, 19), (26, 32), (5, 2), (31, 30), (27, 0), (10, 16), (36, 21), (18, 2), (20, 32), (27, 32), (29, 1), (32, 11), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "295560", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 29), (19, 25), (3, 31), (8, 34), (9, 36), (21, 34), (19, 14), (32, 19), (10, 3), (29, 18), (20, 8), (33, 30), (20, 4), (0, 16), (14, 4), (24, 28), (16, 12), (38, 19), (2, 30), (11, 37), (9, 2), (7, 32), (25, 29), (15, 18), (33, 21), (11, 34), (9, 3), (10, 11), (36, 5), (38, 5), (32, 22), (28, 20), (23, 14), (4, 7), (21, 8), (0, 18), (28, 5), (28, 7), (4, 37), (29, 37), (3, 10), (33, 36), (17, 12), (21, 32), (20, 31), (31, 18), (25, 1), (31, 15), (26, 36), (31, 7), (17, 24), (24, 14), (37, 7), (0, 23), (9, 12), (29, 29), (12, 25), (32, 7), (18, 34), (22, 23), (13, 21), (5, 29), (17, 14), (1, 19), (9, 18), (19, 30), (9, 31), (36, 21), (29, 8), (33, 8), (28, 29), (34, 6), (14, 18), (19, 27), (17, 36), (26, 31), (14, 33), (17, 6), (23, 4), (38, 27), (5, 3), (5, 30), (18, 31), (32, 4), (33, 18), (30, 13), (30, 4), (23, 2), (29, 34), (28, 9), (30, 21), (0, 8), (36, 4), (25, 14), (27, 22), (3, 6), (34, 12), (25, 35), (4, 16), (13, 6), (21, 2), (9, 20), (16, 26), (12, 29), (2, 31), (31, 31), (12, 0), (13, 14), (0, 21), (22, 19), (10, 22), (15, 2), (3, 28), (7, 28), (5, 24), (32, 5), (27, 14), (24, 17), (23, 10), (12, 12), (7, 30), (13, 32), (27, 6), (15, 14), (18, 19), (3, 2), (17, 34), (25, 27), (14, 1), (37, 6), (29, 11), (38, 16), (19, 10), (18, 27), (18, 15), (19, 12), (8, 36), (37, 36), (28, 1), (18, 29), (14, 26), (2, 5), (26, 14), (15, 8), (29, 9), (36, 3), (25, 36), (11, 13), (6, 28), (23, 35), (1, 17), (10, 19), (12, 19), (6, 16), (20, 37), (19, 15), (19, 28), (1, 18), (8, 6), (8, 20), (30, 27), (32, 10), (0, 30), (36, 11), (17, 21), (32, 24), (25, 19), (0, 29), (19, 6), (25, 6), (32, 6), (22, 29), (12, 31), (15, 17), (6, 19), (24, 9), (30, 5), (4, 2), (31, 33), (2, 13), (1, 24), (1, 1), (37, 0), (2, 7), (8, 7), (31, 9), (28, 30), (20, 27), (36, 10), (23, 22), (10, 12), (10, 14), (26, 16), (24, 18), (21, 29), (35, 20), (38, 6), (23, 36), (6, 0), (29, 26), (31, 8), (37, 30), (36, 31), (8, 16), (16, 37), (2, 8), (33, 34), (10, 0), (31, 22), (12, 32), (38, 21), (23, 24), (36, 6), (29, 10), (38, 18), (18, 1), (13, 12), (30, 32), (28, 4), (31, 35), (27, 37), (10, 5), (15, 16), (19, 22), (13, 37), (26, 4), (26, 23), (25, 13), (37, 18), (4, 0), (26, 13), (23, 0), (2, 19), (15, 29), (12, 5), (15, 22), (35, 30), (20, 21), (33, 31), (36, 36), (7, 11), (34, 0), (11, 8), (14, 15), (0, 11), (18, 6), (37, 31), (18, 12), (30, 2), (1, 3), (23, 26), (7, 19), (10, 1), (38, 17), (37, 15), (21, 36), (19, 2), (6, 35), (12, 7), (23, 19), (4, 18), (27, 11), (27, 10), (26, 32), (18, 32), (1, 22), (37, 5), (22, 24), (28, 11), (34, 11), (33, 23), (29, 17), (38, 28), (17, 37), (34, 7), (25, 10), (8, 17), (37, 13), (5, 26), (21, 26), (20, 6), (32, 3), (16, 16), (3, 15), (6, 32), (21, 9), (34, 29), (37, 3), (9, 30), (24, 33), (36, 14), (26, 6), (17, 23), (25, 12), (25, 25), (31, 29), (25, 7), (4, 20), (36, 28), (7, 31), (27, 18), (3, 27), (18, 13), (12, 10), (20, 33), (8, 26), (28, 35), (7, 24), (14, 10), (7, 5), (7, 22), (3, 24), (13, 2), (23, 29), (25, 9), (10, 17), (20, 25), (1, 5), (0, 25), (5, 27), (4, 17), (36, 19), (14, 9), (17, 35), (26, 18), (24, 31), (9, 33), (36, 27), (6, 6), (6, 13), (35, 27), (5, 13), (13, 3), (16, 17), (28, 32), (1, 33), (37, 25), (0, 36), (13, 26), (20, 17), (18, 26), (8, 18), (2, 28), (31, 32), (20, 0), (32, 12), (33, 5), (14, 27), (33, 33), (7, 23), (11, 0), (21, 7), (15, 4), (16, 33), (12, 2), (14, 12), (33, 16), (34, 25), (7, 7), (18, 25), (31, 6), (7, 34), (20, 2), (34, 22), (38, 1), (36, 2), (27, 27), (12, 35), (31, 37), (15, 21), (38, 22), (4, 27), (25, 8), (4, 13), (11, 10), (13, 28), (38, 36), (27, 36), (31, 25), (3, 9), (37, 33), (12, 4), (11, 12), (28, 26), (23, 1), (15, 3), (28, 10), (30, 17), (27, 4), (6, 22), (27, 5), (11, 15), (0, 28), (23, 33), (31, 24), (21, 11), (26, 33), (2, 35), (14, 35), (21, 28), (6, 24), (16, 2), (16, 0), (18, 17), (18, 16), (21, 30), (35, 0), (3, 1), (26, 11), (7, 6), (17, 18), (28, 36), (31, 4), (28, 24), (34, 36), (28, 17), (7, 33), (23, 15), (0, 24), (9, 34), (2, 12), (8, 11), (32, 37), (24, 6), (13, 13), (36, 9), (18, 23), (37, 8), (8, 13), (21, 13), (26, 15), (24, 35), (16, 24), (9, 28), (16, 31), (29, 28), (2, 2), (0, 19), (11, 24), (14, 2), (7, 0), (19, 23), (0, 32), (28, 3), (13, 1), (1, 6), (16, 3), (33, 14), (26, 27), (0, 12), (32, 8), (34, 34), (20, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188811", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (0, 17), (29, 14), (28, 4), (19, 10), (12, 28), (13, 25), (0, 25), (1, 5), (8, 18), (9, 11), (30, 21), (28, 24), (25, 7), (12, 12), (12, 22), (4, 11), (17, 5), (11, 28), (14, 17), (18, 13), (27, 26), (10, 13), (22, 17), (2, 7), (24, 0), (4, 28), (1, 6), (7, 12), (30, 10), (17, 17), (20, 23), (5, 27), (16, 14), (24, 13), (5, 26), (30, 1), (24, 11), (10, 16), (18, 3), (0, 26), (30, 17), (27, 24), (21, 27), (2, 5), (24, 15), (13, 12), (1, 14), (15, 0), (24, 7), (12, 9), (26, 22), (16, 23), (7, 19), (5, 4), (20, 28), (7, 29), (8, 15), (6, 13), (26, 13), (25, 17), (2, 0), (24, 14), (10, 15), (13, 10), (25, 12), (25, 3), (1, 9), (2, 1), (4, 15), (14, 11), (4, 20), (16, 7), (17, 8), (23, 15), (18, 24), (5, 1), (30, 22), (20, 11), (30, 19), (8, 22), (10, 27), (22, 7), (29, 19), (11, 22), (26, 28), (22, 5), (13, 6), (8, 23), (11, 4), (0, 14), (14, 8), (12, 13), (27, 13), (11, 23), (17, 10), (23, 23), (14, 19), (28, 17), (30, 6), (9, 20), (15, 21), (3, 13), (13, 18), (8, 19), (21, 16), (8, 28), (26, 29), (16, 16), (14, 4), (18, 18), (29, 2), (19, 27), (11, 11), (16, 9), (17, 25), (15, 22), (21, 18), (21, 22), (18, 11), (24, 26), (0, 9), (4, 12), (3, 7), (16, 1), (27, 18), (19, 4), (1, 28), (6, 6), (23, 11), (4, 27), (1, 7), (1, 25), (18, 8), (30, 7), (27, 3), (16, 18), (7, 21), (7, 1), (28, 5), (29, 8), (20, 0), (27, 6), (8, 3), (9, 4), (3, 18), (26, 5), (23, 3), (4, 14), (14, 9), (4, 13), (7, 17), (9, 6), (1, 16), (23, 13), (30, 13), (4, 5), (18, 20), (1, 18), (6, 18), (0, 28), (7, 20), (8, 9), (26, 7), (23, 0), (6, 26), (2, 11), (14, 26), (14, 3), (9, 7), (3, 29), (2, 16), (21, 17), (23, 8), (22, 8), (30, 23), (8, 2), (5, 25), (2, 28), (9, 26), (3, 27), (30, 5), (7, 2), (6, 27), (16, 3), (13, 1), (12, 11), (1, 11), (17, 3), (9, 8), (27, 14), (26, 8), (24, 19), (28, 15), (24, 18), (20, 25), (13, 20), (13, 15), (11, 6), (2, 3), (16, 6), (26, 20), (19, 11), (18, 0), (27, 8), (29, 18), (30, 8), (22, 16), (1, 2), (19, 23), (14, 15), (16, 19), (21, 10), (23, 26), (13, 2), (7, 28), (13, 13), (9, 24), (12, 21), (0, 22), (6, 8), (13, 4), (26, 21), (17, 6), (3, 28), (30, 20), (5, 22), (22, 6), (6, 19), (13, 29), (10, 20), (18, 5), (11, 27), (23, 18), (17, 11), (29, 16), (6, 10), (25, 15), (6, 7), (6, 28), (15, 5), (3, 2), (8, 25), (20, 7), (8, 27), (23, 24), (19, 29), (9, 29), (7, 25), (7, 7), (8, 16), (24, 21), (25, 21), (22, 23), (0, 13), (24, 17), (18, 9), (18, 10), (6, 25), (23, 1), (7, 9), (16, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507200", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), 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, 10), (24, 22), (5, 24), (12, 35), (6, 36), (19, 19), (1, 18), (28, 3), (15, 14), (5, 22), (27, 33), (14, 13), (7, 4), (15, 28), (17, 37), (17, 25), (0, 20), (17, 11), (19, 9), (32, 18), (27, 31), (28, 30), (18, 30), (14, 37), (10, 16), (27, 30), (12, 30), (26, 38), (24, 30), (29, 12), (31, 30), (28, 13), (22, 25), (20, 36), (1, 3), (1, 26), (12, 1), (9, 0), (29, 35), (5, 5), (14, 38), (1, 22), (18, 26), (24, 23), (19, 24), (7, 3), (7, 21), (13, 22), (9, 22), (5, 20), (20, 31), (17, 17), (2, 18), (23, 1), (17, 19), (18, 15), (21, 24), (7, 1), (9, 10), (29, 21), (18, 10), (2, 31), (25, 19), (9, 28), (19, 23), (0, 18), (1, 38), (13, 6), (1, 33), (28, 1), (10, 20), (22, 5), (26, 4), (4, 28), (20, 19), (19, 17), (11, 21), (17, 0), (4, 0), (16, 36), (16, 12), (5, 9), (2, 12), (6, 14), (24, 37), (22, 29), (15, 19), (28, 28), (30, 23), (21, 9), (25, 20), (1, 11), (5, 18), (10, 27), (8, 24), (20, 3), (28, 22), (8, 32), (22, 32), (33, 5), (26, 35), (0, 31), (4, 34), (21, 38), (10, 34), (22, 9), (26, 12), (12, 34), (28, 2), (11, 2), (10, 21), (1, 12), (19, 35), (22, 36), (33, 15), (5, 21), (19, 5), (6, 22), (27, 35), (3, 14), (7, 7), (7, 34), (2, 0), (1, 0), (4, 6), (20, 38), (2, 30), (30, 30), (23, 12), (8, 33), (19, 36), (17, 4), (28, 8), (22, 38), (25, 10), (27, 25), (21, 5), (8, 19), (28, 27), (27, 11), (30, 31), (22, 37), (29, 23), (1, 10), (4, 37), (18, 13), (30, 16), (31, 13), (32, 21), (17, 1), (16, 29), (16, 11), (23, 34), (21, 19), (14, 1), (12, 24), (9, 8), (8, 28), (21, 14), (4, 21), (22, 14), (8, 36), (24, 16), (16, 23), (29, 32), (12, 16), (14, 28), (30, 9), (3, 37), (10, 10), (15, 36), (13, 17), (8, 29), (17, 16), (16, 0), (24, 17), (26, 23), (5, 4), (18, 17), (14, 19), (15, 12), (3, 3), (4, 30), (5, 6), (31, 38), (33, 37), (0, 32), (13, 14), (21, 18), (29, 9), (10, 35), (33, 11), (23, 0), (9, 38), (13, 16), (30, 37), (4, 5), (23, 7), (20, 17), (13, 4), (13, 35), (10, 4), (16, 35), (11, 19), (26, 31), (28, 23), (32, 9), (29, 27), (12, 13), (28, 26), (24, 14), (0, 19), (31, 17), (20, 0), (20, 9), (26, 17), (11, 38), (26, 2), (30, 35), (24, 4), (2, 23), (29, 22), (32, 19), (14, 29), (3, 26), (2, 3), (12, 15), (23, 17), (20, 21), (11, 26), (3, 25), (12, 10), (14, 15), (20, 15), (7, 30), (31, 8), (5, 11), (31, 2), (2, 33), (16, 15), (31, 6), (6, 27), (24, 1), (28, 5), (14, 31), (20, 6), (18, 21), (30, 3), (33, 33), (7, 10), (32, 27), (5, 3), (19, 26), (15, 18), (14, 6), (6, 2), (30, 25), (23, 14), (20, 2), (8, 27), (12, 33), (3, 33), (23, 35), (0, 10), (13, 21), (27, 17), (27, 19), (31, 27), (32, 34), (8, 34), (18, 14), (29, 5), (3, 28), (0, 7), (20, 7), (0, 9), (14, 10), (27, 38), (18, 6), (15, 27), (2, 24), (8, 22), (31, 15), (27, 24), (31, 10), (25, 5), (14, 20), (29, 31), (16, 18), (27, 15), (3, 17), (33, 34), (18, 35), (4, 12), (27, 37), (9, 3), (31, 24), (33, 1), (4, 32), (1, 34), (9, 14), (14, 3), (5, 16), (27, 3), (26, 7), (23, 15), (10, 25), (29, 29), (25, 8), (1, 2), (12, 4), (17, 28), (25, 36), (2, 25), (15, 17), (11, 24), (21, 23), (22, 13), (28, 19), (7, 6), (15, 11), (4, 11), (2, 8), (18, 37), (25, 35), (29, 0), (15, 29), (2, 11), (28, 9), (0, 33), (29, 16), (10, 37), (9, 6), (18, 22), (6, 38), (5, 35), (12, 9), (9, 35), (26, 19), (22, 12), (10, 31), (16, 2), (10, 3), (14, 9), (7, 25), (7, 12), (20, 25), (28, 29), (1, 31), (11, 33), (0, 38), (14, 4), (30, 13), (8, 20), (7, 22), (15, 22), (5, 17), (8, 17), (2, 10), (27, 6), (30, 26), (15, 25), (26, 20), (14, 14), (9, 7), (18, 31), (4, 4), (28, 20), (10, 24), (11, 6), (3, 19), (26, 5), (2, 7), (11, 7), (29, 15), (4, 2), (9, 23), (21, 37), (29, 11), (8, 30), (31, 14), (4, 15), (28, 18), (33, 14), (15, 31), (30, 11), (30, 20), (9, 32), (33, 25), (4, 20), (4, 26), (33, 35), (23, 30), (11, 18), (21, 27), (0, 28), (30, 38), (7, 20), (5, 10), (4, 10), (17, 18), (9, 4), (11, 10), (15, 26), (31, 32), (3, 34), (29, 25), (7, 16), (25, 30), (31, 26), (33, 30), (5, 36), (1, 4), (7, 13), (9, 36), (33, 4), (30, 15), (2, 15), (14, 32), (24, 10), (15, 4), (3, 30), (20, 1), (29, 17), (4, 7), (9, 12), (16, 8), (13, 12), (25, 14), (29, 10), (3, 1), (3, 2), (15, 1), (13, 36), (2, 36), (18, 36), (21, 13), (23, 27), (5, 15), (32, 2), (9, 1), (18, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "686004", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), 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), (21, 16), (8, 0), (19, 23), (23, 19), (10, 6), (5, 19), (6, 16), (9, 21), (28, 30), (6, 26), (10, 27), (11, 38), (5, 15), (24, 12), (1, 3), (6, 9), (7, 7), (0, 37), (16, 12), (27, 37), (14, 31), (9, 23), (2, 19), (14, 14), (4, 27), (10, 24), (29, 13), (27, 33), (17, 30), (1, 4), (17, 24), (24, 31), (3, 1), (4, 2), (15, 25), (8, 1), (25, 25), (16, 4), (4, 18), (24, 1), (17, 26), (5, 31), (23, 36), (1, 20), (13, 35), (23, 8), (24, 28), (31, 25), (30, 19), (23, 15), (28, 31), (5, 10), (9, 17), (14, 35), (27, 5), (11, 18), (22, 34), (15, 28), (11, 32), (25, 7), (24, 18), (26, 14), (26, 18), (0, 10), (3, 3), (9, 28), (15, 23), (9, 35), (23, 35), (27, 12), (21, 7), (26, 34), (18, 23), (18, 20), (22, 38), (25, 29), (28, 1), (21, 11), (18, 35), (15, 30), (21, 2), (12, 13), (9, 22), (30, 15), (0, 31), (23, 22), (19, 22), (8, 29), (2, 35), (13, 37), (26, 0), (30, 22), (20, 2), (5, 7), (15, 13), (1, 32), (19, 20), (23, 31), (2, 14), (16, 20), (1, 29), (22, 10), (26, 26), (20, 19), (0, 5), (13, 10), (21, 20), (14, 20), (9, 19), (15, 5), (10, 11), (30, 6), (7, 1), (6, 17), (10, 34), (21, 37), (8, 5), (2, 5), (15, 36), (11, 12), (22, 18), (24, 37), (8, 15), (27, 32), (24, 17), (12, 26), (28, 33), (6, 23), (3, 34), (12, 2), (22, 23), (26, 28), (9, 7), (28, 6), (13, 19), (1, 15), (2, 34), (28, 15), (26, 17), (12, 10), (24, 10), (30, 18), (20, 1), (31, 8), (19, 10), (7, 29), (17, 5), (29, 28), (13, 5), (3, 19), (7, 17), (3, 38), (4, 33), (1, 35), (31, 35), (31, 27), (9, 32), (13, 32), (1, 34), (25, 10), (19, 34), (17, 32), (24, 8), (13, 21), (26, 21), (4, 32), (20, 25), (6, 28), (18, 9), (15, 2), (21, 30), (19, 27), (27, 11), (2, 21), (4, 4), (20, 20), (19, 25), (21, 1), (8, 37), (25, 5), (13, 3), (20, 26), (9, 26), (20, 3), (23, 28), (12, 3), (0, 13), (13, 25), (28, 35), (3, 27), (31, 1), (18, 5), (28, 20), (15, 24), (23, 20), (16, 25), (2, 31), (26, 9), (1, 28), (31, 28), (0, 21), (25, 24), (25, 17), (5, 1), (15, 21), (31, 29), (9, 37), (10, 31), (10, 13), (9, 5), (5, 25), (2, 38), (30, 2), (20, 24), (7, 20), (29, 20), (17, 38), (16, 28), (28, 25), (25, 6), (4, 13), (9, 1), (3, 32), (28, 27), (27, 6), (25, 21), (4, 15), (14, 13), (9, 24), (14, 29), (30, 36), (11, 24), (26, 36), (19, 9), (4, 37), (6, 10), (18, 18), (26, 11), (8, 26), (28, 2), (13, 0), (11, 31), (9, 2), (0, 23), (15, 1), (25, 18), (20, 6), (20, 0), (20, 33), (20, 30), (12, 36), (27, 31), (27, 36), (7, 25), (26, 33), (4, 11), (14, 11), (17, 10), (16, 21), (21, 27), (21, 14), (17, 18), (5, 34), (15, 0), (27, 3), (16, 15), (23, 14), (2, 24), (6, 7), (1, 1), (24, 32), (7, 11), (19, 11), (4, 20), (13, 13), (6, 6), (13, 14), (26, 13), (8, 28), (21, 34), (6, 35), (10, 17), (28, 5), (22, 17), (30, 31), (1, 21), (25, 15), (26, 27), (9, 31), (15, 15), (18, 34), (24, 6), (16, 24), (28, 0), (23, 0), (23, 17), (26, 24), (18, 21), (26, 3), (30, 16), (30, 23), (19, 24), (21, 9), (18, 24), (16, 31), (10, 18), (22, 8), (13, 9), (20, 16), (22, 15), (14, 7), (21, 32), (12, 27), (23, 9), (26, 7), (13, 29), (24, 13), (25, 32), (30, 21), (12, 0), (22, 19), (17, 20), (1, 14), (12, 29), (1, 18), (3, 29), (5, 36), (14, 18), (21, 6), (8, 13), (4, 25), (19, 19), (14, 33), (26, 35), (23, 12), (12, 17), (22, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), 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), (31, 28), (25, 7), (23, 26), (7, 16), (2, 25), (0, 30), (33, 12), (29, 18), (2, 21), (26, 19), (22, 21), (33, 4), (33, 22), (2, 3), (12, 3), (32, 29), (2, 12), (30, 29), (20, 32), (15, 29), (9, 24), (21, 12), (2, 0), (18, 11), (19, 12), (21, 14), (1, 28), (10, 20), (29, 30), (11, 27), (0, 28), (13, 19), (28, 18), (11, 11), (14, 13), (25, 3), (5, 22), (11, 19), (24, 8), (8, 15), (12, 11), (4, 16), (1, 13), (14, 5), (20, 29), (1, 10), (7, 27), (32, 7), (21, 32), (33, 25), (32, 2), (6, 32), (3, 9), (15, 5), (5, 31), (22, 10), (18, 23), (29, 25), (32, 9), (16, 1), (33, 18), (24, 4), (6, 3), (16, 26), (16, 22), (14, 0), (35, 9), (8, 29), (28, 0), (34, 0), (13, 31), (16, 7), (31, 26), (25, 8), (7, 0), (23, 13), (26, 29), (27, 22), (27, 9), (26, 13), (26, 22), (4, 23), (26, 21), (23, 27), (35, 19), (23, 16), (7, 24), (19, 25), (18, 21), (20, 15), (33, 3), (26, 15), (30, 3), (6, 27), (35, 11), (31, 19), (35, 4), (14, 1), (22, 6), (19, 1), (33, 29), (15, 10), (23, 11), (21, 23), (6, 23), (10, 25), (12, 31), (3, 27), (6, 2), (35, 15), (22, 5), (17, 13), (17, 5), (21, 28), (29, 17), (32, 3), (3, 29), (20, 13), (33, 14), (31, 4), (20, 25), (11, 13), (3, 6), (2, 17), (15, 9), (11, 21), (30, 26), (25, 28), (7, 32), (23, 10), (18, 25), (24, 7), (29, 7), (15, 19), (9, 7), (3, 4), (5, 28), (24, 21), (21, 18), (11, 29), (34, 29), (32, 21), (32, 15), (16, 17), (26, 5), (32, 27), (5, 14), (6, 8), (33, 27), (18, 32), (7, 7), (33, 9), (27, 26), (32, 25), (1, 8), (32, 17), (6, 1), (3, 26), (15, 23), (25, 26), (8, 10), (23, 31), (10, 10), (13, 12), (21, 4), (11, 16), (24, 16), (21, 6), (15, 22), (9, 6), (6, 29), (5, 30), (26, 12), (15, 31), (30, 2), (34, 2), (27, 32), (25, 27), (10, 21), (22, 8), (24, 25), (4, 10), (0, 5), (7, 29), (7, 22), (31, 3), (16, 19), (35, 8), (34, 23), (15, 3), (32, 5), (16, 31), (23, 6), (13, 8), (20, 1), (0, 16), (21, 9), (23, 8), (30, 18), (5, 21), (5, 16), (6, 11), (10, 8), (6, 7), (5, 29), (13, 7), (28, 21), (1, 16), (2, 2), (20, 27), (3, 5), (22, 17), (24, 23), (8, 28), (34, 9), (15, 8), (3, 20), (16, 18), (30, 24), (29, 6), (9, 25), (17, 27), (17, 2), (35, 12), (28, 3), (18, 22), (5, 8), (27, 3), (16, 20), (1, 30), (25, 19), (27, 27), (9, 11), (15, 12), (29, 5), (5, 20), (22, 14), (0, 13), (27, 30), (8, 12), (25, 14), (27, 29), (33, 8), (12, 27), (29, 3), (15, 14), (0, 2), (13, 15), (29, 15), (31, 25), (2, 31), (19, 15), (27, 16), (9, 15), (18, 29), (26, 16), (24, 1), (29, 0), (30, 0), (7, 23), (12, 25), (34, 11), (10, 24), (28, 1), (28, 20), (8, 5), (19, 10), (6, 12), (11, 17), (12, 26), (31, 6), (17, 15), (17, 9), (28, 29), (2, 6), (5, 18), (23, 12), (6, 31), (2, 8), (6, 6), (35, 3), (27, 6), (3, 32), (20, 2), (26, 25), (5, 1), (4, 1), (10, 16), (13, 29), (30, 1), (17, 14), (11, 15), (31, 17), (0, 19), (33, 6), (0, 7), (10, 23), (31, 32), (25, 5), (10, 14), (16, 29), (25, 2), (24, 0), (27, 24), (5, 4), (32, 31), (12, 29), (11, 20), (1, 20), (20, 8), (14, 24), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302400", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), 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), (9, 15), (22, 29), (14, 26), (26, 37), (10, 32), (25, 35), (17, 15), (10, 7), (7, 32), (16, 32), (1, 24), (25, 34), (19, 5), (1, 26), (20, 22), (8, 22), (16, 16), (6, 15), (27, 15), (26, 1), (16, 6), (28, 1), (7, 17), (28, 25), (6, 18), (13, 26), (14, 35), (1, 34), (26, 35), (27, 2), (23, 21), (4, 36), (18, 11), (20, 11), (21, 0), (4, 14), (2, 23), (2, 24), (28, 29), (29, 29), (22, 36), (29, 18), (18, 9), (15, 3), (18, 22), (26, 9), (5, 16), (10, 6), (27, 21), (13, 9), (27, 12), (4, 27), (14, 22), (4, 20), (27, 1), (18, 34), (8, 17), (25, 2), (6, 5), (4, 0), (29, 32), (4, 4), (15, 19), (6, 29), (13, 11), (20, 0), (13, 19), (1, 16), (29, 4), (21, 27), (13, 18), (22, 7), (25, 9), (9, 0), (26, 34), (28, 30), (7, 23), (16, 17), (11, 19), (17, 7), (19, 29), (11, 24), (10, 17), (20, 8), (12, 32), (6, 9), (23, 30), (18, 30), (16, 24), (21, 8), (26, 20), (0, 13), (28, 9), (22, 12), (8, 27), (24, 32), (15, 28), (6, 16), (22, 0), (24, 10), (14, 14), (21, 24), (3, 33), (19, 6), (11, 31), (20, 37), (14, 13), (13, 12), (21, 36), (2, 20), (15, 35), (21, 3), (1, 11), (29, 2), (0, 24), (27, 14), (4, 16), (16, 15), (2, 10), (1, 36), (26, 33), (14, 4), (14, 6), (12, 6), (14, 5), (24, 20), (7, 31), (9, 7), (2, 31), (20, 20), (28, 6), (27, 17), (2, 30), (23, 26), (15, 25), (14, 37), (17, 27), (2, 3), (23, 37), (10, 22), (18, 25), (19, 25), (20, 13), (0, 6), (14, 21), (28, 21), (8, 7), (11, 9), (11, 3), (18, 33), (14, 16), (6, 28), (18, 27), (21, 37), (0, 15), (26, 23), (23, 10), (12, 30), (15, 8), (7, 8), (14, 36), (25, 26), (24, 7), (19, 12), (22, 14), (15, 12), (14, 32), (21, 33), (23, 0), (10, 2), (14, 28), (23, 36), (19, 13), (11, 2), (25, 14), (9, 16), (6, 36), (24, 8), (2, 2), (7, 20), (0, 10), (12, 19), (3, 35), (19, 33), (11, 33), (11, 13), (22, 13), (9, 9), (17, 1), (19, 32), (2, 32), (14, 15), (0, 3), (27, 33), (14, 18), (1, 21), (11, 17), (23, 28), (25, 31), (9, 36), (14, 31), (14, 24), (1, 10), (8, 11), (8, 33), (4, 7), (28, 22), (12, 4), (7, 16), (28, 0), (16, 33), (29, 35), (27, 5), (19, 20), (3, 17), (5, 23), (14, 29), (22, 17), (15, 6), (25, 18), (26, 21), (5, 30), (24, 1), (23, 27), (13, 13), (21, 16), (8, 15), (22, 22), (6, 32), (4, 26), (22, 18), (3, 14), (12, 26), (12, 36), (3, 29), (13, 21), (29, 24), (27, 9), (8, 35), (13, 24), (12, 0), (1, 13), (21, 4), (11, 5), (27, 30), (12, 23), (13, 20), (16, 25), (14, 2), (17, 21), (12, 7), (1, 31), (12, 3), (16, 3), (15, 34), (11, 8), (3, 37), (1, 23), (20, 25), (25, 25), (25, 1), (18, 3), (26, 7), (6, 1), (27, 16), (5, 24), (15, 1), (26, 17), (7, 14), (14, 7), (16, 26), (0, 22), (20, 14), (16, 10), (7, 18), (11, 35), (13, 8), (28, 14), (1, 4), (12, 15), (1, 1), (3, 12), (2, 27), (12, 29), (16, 13), (19, 36), (17, 18), (1, 15), (10, 27), (13, 23), (18, 17), (17, 3), (11, 23), (29, 22), (20, 4), (20, 27), (2, 16), (1, 6), (2, 5), (26, 25), (10, 23), (10, 20), (21, 20), (18, 31), (0, 37), (20, 24), (7, 36), (9, 5), (8, 9), (15, 22), (20, 30), (5, 37), (20, 5), (3, 34), (25, 27), (25, 32), (22, 9), (25, 0), (16, 22), (5, 10), (12, 21), (7, 12), (7, 24), (24, 19), (14, 19), (3, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979776", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 18), (3, 31), (30, 26), (12, 13), (22, 15), (8, 8), (21, 30), (32, 29), (6, 8), (17, 18), (28, 22), (11, 4), (25, 23), (27, 3), (23, 26), (14, 15), (29, 25), (2, 2), (17, 7), (3, 1), (25, 25), (26, 18), (8, 3), (33, 6), (12, 29), (29, 17), (6, 6), (23, 13), (22, 1), (16, 12), (21, 29), (19, 28), (21, 27), (2, 5), (24, 3), (20, 4), (23, 28), (22, 27), (11, 23), (24, 29), (20, 27), (7, 6), (25, 0), (3, 27), (17, 10), (27, 19), (30, 4), (9, 30), (22, 16), (21, 15), (7, 3), (30, 5), (7, 28), (15, 28), (4, 6), (8, 29), (23, 11), (4, 29), (24, 21), (33, 5), (12, 5), (22, 28), (18, 31), (30, 13), (0, 1), (32, 26), (6, 0), (26, 10), (6, 15), (18, 11), (7, 8), (23, 21), (17, 5), (1, 9), (15, 8), (7, 2), (31, 17), (18, 14), (31, 2), (0, 11), (13, 9), (23, 3), (33, 2), (5, 14), (29, 6), (3, 23), (1, 26), (26, 2), (6, 28), (23, 22), (3, 7), (13, 12), (23, 24), (26, 12), (10, 19), (18, 16), (10, 16), (2, 9), (26, 8), (18, 15), (2, 29), (21, 5), (7, 4), (20, 16), (15, 25), (7, 7), (23, 5), (30, 7), (12, 2), (27, 28), (32, 20), (4, 17), (3, 29), (24, 14), (9, 8), (17, 21), (28, 31), (19, 1), (25, 21), (1, 23), (13, 30), (2, 4), (28, 5), (10, 22), (12, 6), (30, 31), (29, 21), (30, 9), (28, 15), (15, 2), (12, 15), (19, 22), (10, 8), (24, 4), (7, 18), (15, 14), (24, 8), (10, 28), (26, 21), (28, 11), (12, 25), (11, 26), (22, 13), (13, 2), (26, 26), (17, 1), (25, 12), (15, 31), (12, 8), (11, 8), (14, 30), (28, 2), (21, 24), (25, 7), (6, 7), (9, 18), (22, 0), (3, 11), (3, 9), (24, 10), (4, 18), (11, 2), (20, 23), (14, 31), (0, 25), (33, 12), (29, 14), (2, 23), (19, 18), (11, 16), (10, 26), (30, 24), (31, 11), (28, 23), (6, 16), (24, 9), (3, 26), (9, 17), (8, 21), (31, 19), (5, 15), (17, 11), (13, 10), (25, 27), (18, 30), (21, 6), (18, 5), (18, 4), (16, 28), (0, 14), (1, 31), (15, 24), (3, 5), (1, 22), (3, 25), (26, 6), (31, 4), (20, 9), (21, 7), (2, 10), (11, 11), (25, 8), (10, 30), (25, 16), (0, 9), (13, 20), (4, 15), (8, 18), (33, 1), (30, 1), (6, 10), (9, 21), (3, 13), (9, 20), (10, 5), (26, 1), (14, 26), (5, 5), (7, 1), (19, 3), (28, 24), (14, 12), (16, 19), (13, 28), (13, 11), (10, 3), (12, 22), (32, 10), (20, 22), (17, 26), (8, 9), (10, 20), (2, 1), (22, 31), (20, 14), (30, 23), (31, 18), (28, 28), (26, 13), (1, 28), (32, 3), (18, 1), (9, 13), (16, 2), (28, 4), (13, 29), (24, 20), (31, 1), (22, 22), (9, 14), (25, 22), (24, 0), (1, 27), (1, 14), (2, 28), (25, 17), (1, 6), (25, 26), (5, 28), (27, 29), (10, 9), (0, 31), (23, 30), (33, 0), (31, 30), (28, 20), (30, 16), (1, 12), (14, 9), (20, 20), (4, 16), (32, 23), (2, 30), (27, 2), (12, 31), (15, 22), (30, 17), (19, 9), (33, 7), (5, 1), (23, 20), (23, 17), (32, 0), (1, 10), (7, 13), (26, 28), (21, 22), (5, 31), (29, 15), (27, 20), (8, 13), (3, 4), (17, 25), (5, 10), (23, 27), (18, 8), (8, 25), (29, 4), (2, 6), (0, 2), (18, 22), (5, 6), (23, 2), (32, 9), (16, 1), (30, 15), (19, 19), (9, 3), (10, 15), (16, 17), (31, 12), (20, 28), (27, 30), (31, 26), (28, 29), (32, 19), (6, 2), (22, 26), (24, 24), (21, 1), (7, 14), (31, 15), (28, 26), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483840", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (10, 4), (1, 14), (20, 3), (24, 17), (27, 25), (9, 27), (23, 5), (29, 26), (8, 14), (19, 29), (0, 8), (1, 28), (1, 1), (27, 12), (27, 10), (18, 30), (6, 9), (19, 0), (19, 22), (30, 20), (28, 14), (30, 28), (21, 3), (0, 24), (13, 22), (16, 4), (2, 21), (0, 25), (4, 11), (10, 26), (3, 27), (5, 1), (29, 16), (17, 1), (27, 5), (5, 6), (0, 26), (21, 28), (8, 25), (25, 1), (4, 22), (21, 26), (26, 6), (13, 21), (10, 28), (28, 21), (0, 17), (28, 29), (27, 1), (12, 7), (30, 4), (16, 26), (7, 25), (1, 17), (28, 4), (17, 8), (7, 19), (29, 8), (5, 21), (26, 2), (16, 19), (18, 5), (4, 7), (14, 16), (14, 15), (22, 17), (5, 28), (21, 27), (0, 30), (16, 1), (5, 4), (26, 25), (20, 8), (21, 8), (24, 1), (17, 5), (4, 15), (3, 19), (8, 6), (27, 30), (19, 20), (4, 24), (15, 13), (14, 22), (16, 25), (14, 17), (6, 5), (25, 30), (4, 9), (14, 25), (3, 0), (8, 7), (26, 9), (19, 21), (14, 12), (13, 26), (21, 19), (0, 10), (17, 15), (18, 26), (20, 25), (13, 29), (17, 26), (22, 22), (9, 19), (28, 8), (21, 7), (12, 26), (20, 18), (6, 27), (30, 2), (28, 9), (19, 15), (17, 28), (4, 30), (9, 20), (18, 22), (6, 7), (9, 1), (10, 2), (7, 3), (11, 22), (14, 24), (10, 11), (8, 22), (30, 0), (27, 11), (30, 16), (22, 27), (0, 13), (0, 16), (2, 13), (10, 24), (7, 11), (21, 14), (3, 11), (15, 25), (7, 23), (10, 6), (11, 7), (1, 24), (4, 13), (21, 18), (11, 14), (5, 8), (0, 12), (23, 18), (22, 18), (28, 0), (16, 21), (15, 5), (21, 13), (17, 2), (10, 13), (2, 20), (23, 1), (0, 27), (15, 21), (23, 8), (30, 25), (22, 3), (8, 12), (23, 19), (4, 0), (15, 2), (24, 4), (12, 29), (7, 30), (3, 4), (27, 7), (25, 18), (28, 22), (5, 13), (10, 19), (15, 22), (27, 24), (26, 22), (23, 28), (15, 18), (21, 24), (18, 25), (1, 22), (20, 22), (25, 6), (1, 4), (15, 23), (26, 19), (9, 8), (3, 25), (27, 29), (17, 6), (25, 27), (13, 16), (26, 1), (2, 25), (15, 17), (18, 7), (0, 19), (3, 23), (11, 11), (2, 12), (16, 22), (5, 22), (29, 20), (4, 17), (3, 14), (27, 28), (15, 8), (1, 20), (21, 25), (25, 26), (22, 16), (29, 15), (6, 18), (11, 23), (7, 16), (17, 18), (17, 21), (12, 3), (8, 18), (11, 5), (27, 26), (27, 16), (26, 21), (7, 2), (2, 10), (2, 23), (12, 4), (17, 22), (14, 6), (21, 5), (18, 27), (2, 18), (17, 30), (8, 26), (5, 24), (23, 11), (11, 24), (22, 7), (1, 2), (21, 20), (20, 24), (5, 25), (9, 2), (10, 18), (5, 2), (0, 1), (30, 9), (20, 9), (22, 0), (13, 1), (9, 24), (3, 6), (25, 11), (20, 2), (25, 16), (5, 7), (14, 4), (18, 23), (19, 23), (10, 20), (27, 2), (0, 20), (11, 6), (28, 16), (12, 23), (10, 17), (16, 17), (19, 4), (19, 16), (28, 6), (29, 5), (7, 8), (24, 26), (8, 9), (15, 20), (23, 4), (29, 22), (23, 25), (13, 5), (18, 16), (26, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "494424", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), 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), (26, 1), (2, 8), (36, 29), (29, 4), (26, 6), (2, 12), (13, 30), (35, 18), (21, 16), (34, 26), (15, 25), (8, 15), (13, 16), (20, 22), (35, 1), (11, 15), (21, 1), (11, 19), (9, 27), (35, 10), (16, 25), (4, 0), (10, 30), (25, 22), (9, 15), (18, 26), (16, 16), (17, 2), (29, 9), (15, 17), (14, 20), (29, 2), (17, 22), (10, 19), (16, 12), (26, 8), (9, 29), (29, 8), (8, 28), (4, 30), (16, 27), (12, 13), (22, 22), (12, 21), (10, 7), (37, 21), (4, 24), (21, 7), (6, 12), (19, 29), (0, 14), (36, 24), (30, 10), (31, 9), (22, 26), (36, 19), (34, 28), (26, 3), (27, 14), (32, 13), (0, 28), (24, 2), (12, 3), (29, 5), (8, 3), (3, 28), (32, 1), (1, 0), (25, 19), (32, 7), (30, 22), (13, 9), (15, 10), (35, 12), (30, 9), (14, 6), (34, 13), (32, 27), (24, 25), (19, 28), (3, 8), (16, 11), (5, 23), (21, 17), (23, 15), (1, 16), (11, 3), (3, 25), (27, 18), (9, 13), (4, 10), (9, 16), (28, 24), (2, 23), (14, 25), (15, 2), (1, 24), (16, 14), (29, 21), (0, 6), (26, 18), (35, 21), (23, 25), (6, 26), (4, 13), (5, 7), (31, 16), (28, 30), (10, 13), (36, 1), (0, 18), (6, 22), (24, 16), (34, 23), (22, 14), (36, 2), (31, 19), (29, 17), (2, 25), (24, 21), (24, 4), (23, 22), (10, 24), (9, 3), (17, 3), (16, 6), (36, 3), (24, 1), (9, 5), (22, 17), (16, 24), (14, 4), (36, 7), (28, 27), (11, 4), (36, 10), (12, 10), (33, 30), (1, 27), (2, 4), (25, 10), (19, 8), (22, 29), (23, 8), (31, 26), (4, 3), (5, 5), (22, 16), (13, 25), (22, 7), (5, 29), (25, 18), (34, 24), (9, 25), (20, 14), (15, 26), (30, 21), (21, 28), (35, 29), (9, 4), (31, 23), (11, 26), (37, 16), (30, 25), (31, 29), (30, 0), (30, 3), (25, 30), (37, 5), (24, 28), (37, 22), (2, 14), (8, 21), (28, 25), (6, 4), (37, 11), (8, 17), (18, 18), (6, 8), (29, 20), (27, 8), (37, 9), (13, 29), (24, 24), (7, 22), (9, 12), (19, 20), (29, 12), (12, 17), (12, 9), (35, 7), (21, 5), (13, 8), (17, 21), (1, 28), (31, 22), (20, 26), (33, 17), (14, 27), (12, 29), (16, 1), (28, 12), (11, 28), (18, 20), (19, 9), (7, 29), (9, 11), (23, 3), (8, 19), (20, 27), (14, 30), (10, 22), (18, 0), (27, 1), (30, 5), (15, 12), (31, 25), (9, 19), (27, 29), (37, 0), (35, 0), (14, 3), (3, 20), (35, 13), (2, 10), (3, 14), (28, 16), (19, 21), (12, 23), (33, 22), (20, 0), (28, 19), (4, 18), (32, 25), (29, 13), (3, 6), (0, 11), (26, 27), (36, 30), (20, 5), (37, 3), (36, 26), (24, 5), (12, 1), (8, 16), (26, 15), (7, 16), (9, 30), (5, 3), (15, 29), (27, 6), (8, 30), (21, 23), (1, 4), (13, 24), (29, 14), (24, 11), (24, 30), (18, 21), (10, 25), (14, 19), (2, 27), (9, 20), (8, 22), (8, 4), (25, 4), (25, 25), (34, 1), (22, 11), (35, 28), (29, 18), (11, 5), (33, 6), (23, 10), (36, 14), (2, 18), (13, 23), (28, 28), (10, 29), (33, 1), (37, 19), (19, 24), (35, 4), (1, 25), (6, 5), (4, 21), (5, 6), (19, 14), (24, 6), (33, 24), (18, 10), (36, 12), (25, 17), (36, 5), (24, 22), (6, 30), (27, 2), (17, 28), (37, 7), (9, 9), (5, 18), (23, 29), (17, 27), (35, 6), (15, 18), (12, 11), (30, 2), (21, 21), (27, 11), (8, 11), (1, 19), (33, 8), (20, 20), (35, 11), (28, 15), (21, 9), (21, 0), (10, 18), (9, 21), (37, 12), (14, 16), (2, 28), (32, 0), (3, 22), (0, 29), (30, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6048", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (26, 24), (7, 13), (20, 6), (10, 6), (10, 22), (10, 10), (18, 8), (6, 11), (18, 24), (12, 19), (5, 21), (7, 0), (23, 4), (16, 29), (21, 8), (26, 15), (3, 18), (5, 19), (8, 11), (18, 16), (8, 19), (5, 26), (15, 10), (10, 26), (8, 3), (6, 18), (22, 19), (16, 13), (25, 0), (1, 24), (22, 26), (7, 17), (10, 2), (20, 29), (3, 7), (20, 7), (13, 27), (17, 16), (23, 26), (17, 15), (14, 15), (18, 14), (23, 1), (22, 21), (27, 23), (13, 19), (13, 4), (19, 12), (20, 8), (25, 15), (22, 29), (0, 19), (23, 25), (20, 28), (5, 12), (4, 17), (5, 23), (4, 23), (7, 1), (3, 6), (16, 10), (15, 12), (11, 17), (12, 27), (23, 14), (13, 9), (26, 1), (11, 2), (16, 22), (26, 7), (4, 5), (26, 10), (16, 28), (3, 17), (3, 20), (15, 21), (27, 28), (29, 4), (26, 22), (19, 6), (11, 4), (26, 14), (24, 2), (20, 12), (19, 2), (23, 28), (28, 8), (28, 17), (25, 21), (5, 24), (9, 20), (29, 19), (20, 5), (14, 24), (7, 23), (21, 18), (1, 29), (26, 6), (7, 29), (8, 17), (22, 7), (15, 28), (16, 0), (13, 21), (17, 24), (6, 5), (9, 18), (19, 20), (11, 21), (6, 20), (28, 27), (13, 20), (12, 14), (29, 15), (24, 19), (24, 27), (21, 0), (27, 20), (27, 10), (9, 28), (7, 9), (29, 6), (1, 22), (18, 23), (0, 7), (5, 10), (0, 4), (4, 3), (18, 12), (7, 26), (0, 5), (21, 3), (27, 16), (6, 29), (0, 16), (14, 9), (26, 4), (15, 6), (16, 6), (4, 28), (23, 7), (16, 27), (6, 12), (4, 21), (26, 19), (10, 25), (27, 8), (18, 27), (15, 8), (0, 26), (19, 5), (3, 5), (13, 22), (7, 3), (23, 19), (11, 15), (28, 9), (23, 0), (11, 11), (13, 3), (14, 27), (19, 8), (19, 11), (15, 18), (17, 8), (2, 8), (6, 10), (8, 21), (8, 16), (1, 3), (23, 29), (11, 13), (18, 28), (25, 14), (18, 6), (9, 14), (21, 13), (9, 8), (27, 24), (29, 26), (26, 17), (11, 18), (9, 17), (10, 13), (8, 29), (6, 6), (3, 0), (8, 9), (1, 19), (29, 1), (18, 11), (15, 2), (9, 1), (15, 15), (19, 1), (7, 4), (25, 20), (19, 3), (17, 22), (11, 23), (26, 21), (28, 14), (4, 29), (0, 13), (9, 7), (19, 21), (24, 20), (27, 1), (28, 13), (24, 3), (9, 15), (8, 27), (29, 0), (24, 17), (22, 18), (11, 29), (10, 12), (15, 26), (28, 10), (6, 8), (12, 21), (21, 15), (19, 10), (20, 23), (4, 24), (2, 20), (22, 23), (2, 28), (27, 18), (8, 12), (21, 9), (21, 7), (8, 28), (21, 26), (4, 16), (20, 15), (0, 17), (17, 10), (15, 9), (7, 28), (3, 19), (15, 22), (11, 14), (18, 22), (17, 26), (27, 14), (11, 19), (0, 25), (1, 14), (24, 23), (12, 22), (2, 12), (9, 0), (4, 11), (22, 25), (21, 22), (27, 19), (1, 16), (17, 9), (11, 3), (18, 5), (5, 7), (23, 2), (23, 27), (8, 15), (1, 9), (8, 22), (2, 26), (1, 6), (12, 24), (3, 24), (10, 20), (22, 0), (4, 2), (22, 6), (17, 20), (14, 13), (17, 27), (4, 4), (27, 4), (18, 7), (19, 15), (16, 15), (29, 23), (22, 17), (17, 2), (12, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "217728", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 9), (34, 8), (4, 25), (21, 7), (10, 30), (33, 27), (0, 11), (24, 3), (10, 27), (23, 2), (13, 18), (7, 15), (24, 24), (19, 28), (13, 21), (30, 29), (3, 23), (22, 24), (19, 2), (15, 32), (33, 23), (11, 6), (14, 19), (23, 34), (1, 5), (0, 28), (26, 23), (6, 26), (13, 22), (5, 14), (10, 8), (25, 0), (19, 22), (15, 3), (34, 23), (23, 31), (0, 16), (30, 3), (3, 3), (5, 23), (17, 35), (31, 24), (29, 10), (8, 21), (1, 29), (11, 0), (16, 26), (32, 8), (23, 30), (24, 27), (19, 26), (29, 6), (14, 3), (14, 8), (28, 18), (26, 2), (0, 33), (17, 6), (22, 1), (21, 21), (33, 1), (18, 28), (11, 16), (28, 8), (12, 34), (0, 9), (26, 31), (0, 5), (28, 27), (16, 6), (11, 18), (24, 9), (31, 19), (26, 34), (17, 15), (0, 35), (31, 14), (12, 5), (17, 16), (15, 17), (28, 19), (2, 2), (22, 0), (17, 5), (23, 23), (34, 25), (0, 4), (8, 1), (33, 29), (19, 12), (23, 8), (6, 13), (4, 22), (15, 12), (12, 13), (2, 18), (10, 5), (21, 15), (3, 21), (29, 36), (28, 17), (28, 25), (18, 22), (19, 3), (19, 8), (13, 24), (22, 25), (32, 6), (31, 6), (11, 13), (9, 19), (2, 25), (8, 32), (5, 36), (25, 28), (21, 5), (21, 32), (30, 4), (4, 6), (7, 21), (20, 20), (31, 7), (32, 10), (11, 14), (30, 7), (9, 33), (9, 5), (16, 22), (29, 18), (14, 2), (27, 5), (21, 11), (16, 4), (27, 23), (2, 11), (13, 26), (26, 1), (19, 6), (10, 20), (0, 20), (28, 32), (28, 22), (7, 25), (4, 3), (25, 2), (12, 28), (18, 19), (19, 20), (20, 31), (19, 33), (11, 32), (11, 3), (6, 36), (22, 34), (10, 11), (31, 27), (13, 5), (20, 9), (1, 10), (5, 5), (34, 20), (9, 35), (6, 16), (12, 22), (20, 16), (8, 29), (12, 26), (20, 7), (24, 7), (13, 2), (30, 23), (19, 0), (33, 3), (14, 31), (31, 11), (34, 34), (12, 19), (26, 19), (1, 24), (6, 9), (0, 10), (18, 25), (28, 6), (11, 30), (33, 8), (3, 29), (25, 29), (32, 14), (23, 10), (32, 16), (4, 0), (21, 26), (5, 33), (17, 20), (20, 23), (10, 6), (6, 34), (31, 25), (18, 33), (28, 28), (15, 28), (9, 15), (34, 0), (14, 15), (15, 2), (34, 32), (22, 36), (25, 36), (34, 33), (32, 29), (2, 3), (18, 12), (33, 11), (2, 35), (17, 27), (34, 27), (27, 9), (14, 18), (1, 26), (3, 20), (15, 1), (16, 14), (20, 26), (16, 35), (8, 25), (6, 5), (20, 2), (28, 24), (32, 23), (1, 16), (34, 13), (5, 27), (13, 32), (30, 25), (6, 29), (3, 34), (8, 26), (11, 19), (30, 34), (1, 21), (13, 23), (26, 3), (27, 6), (27, 20), (19, 27), (5, 12), (34, 29), (4, 28), (11, 7), (21, 33), (24, 22), (23, 16), (23, 4), (5, 6), (21, 6), (0, 29), (20, 8), (6, 14), (12, 6), (21, 13), (29, 8), (10, 23), (24, 12), (30, 32), (27, 29), (28, 36), (31, 23), (34, 12), (21, 14), (24, 33), (9, 18), (14, 1), (31, 34), (12, 20), (24, 6), (7, 9), (17, 32), (14, 27), (27, 30), (20, 33), (8, 19), (2, 36), (22, 13), (32, 18), (33, 30), (0, 22), (8, 0), (2, 16), (32, 7), (6, 32), (32, 3), (31, 10), (21, 23), (8, 11), (24, 32), (12, 36), (17, 34), (13, 15), (3, 8), (23, 25), (16, 34), (11, 24), (18, 2), (29, 28), (30, 35), (21, 16), (29, 29), (2, 14), (3, 9), (18, 5), (18, 26), (28, 11), (33, 14), (17, 24), (34, 17), (9, 29), (22, 15), (32, 25), (21, 34), (15, 15), (25, 13), (14, 26), (3, 4), (1, 33), (15, 19), (13, 12), (12, 25), (22, 19), (10, 22), (31, 22), (24, 21), (13, 6), (6, 17), (32, 13), (15, 14), (33, 13), (30, 26), (17, 18), (12, 23), (22, 28), (16, 32), (32, 30), (11, 26), (6, 8), (24, 31), (30, 10), (4, 23), (7, 13), (5, 13), (8, 10), (15, 26), (5, 34), (34, 19), (5, 0), (22, 14), (19, 25), (14, 12), (20, 4), (28, 7), (6, 2), (6, 4), (18, 6), (34, 18), (24, 11), (2, 27), (33, 9), (2, 9), (32, 34), (1, 18), (17, 13), (7, 31), (29, 17), (22, 23), (10, 33), (20, 24), (11, 22), (29, 12), (25, 23), (12, 1), (9, 24), (15, 36), (31, 35), (27, 12), (8, 27), (1, 8), (13, 16), (30, 22), (3, 19), (23, 22), (7, 1), (13, 0), (9, 31), (31, 20), (5, 24), (18, 34), (33, 18), (32, 24), (33, 36), (26, 0), (30, 15), (1, 23), (12, 12), (6, 31), (15, 7), (17, 29), (9, 32), (1, 0), (28, 23), (2, 6), (13, 27), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (20, 11), (22, 12), (24, 22), (29, 37), (6, 6), (7, 26), (21, 21), (16, 17), (24, 6), (10, 13), (2, 19), (25, 8), (10, 33), (18, 22), (14, 6), (14, 8), (7, 20), (7, 24), (1, 26), (9, 33), (26, 9), (0, 20), (0, 14), (26, 14), (1, 30), (10, 0), (0, 9), (13, 24), (28, 22), (17, 16), (18, 5), (22, 33), (3, 31), (1, 32), (21, 20), (2, 7), (27, 6), (13, 34), (20, 32), (17, 22), (10, 35), (28, 9), (26, 1), (21, 15), (30, 18), (0, 22), (22, 24), (25, 2), (14, 23), (23, 8), (18, 32), (9, 19), (24, 19), (18, 12), (13, 6), (25, 5), (1, 11), (1, 13), (24, 23), (8, 18), (3, 36), (11, 25), (28, 6), (21, 4), (17, 14), (27, 31), (6, 20), (10, 17), (26, 18), (16, 22), (12, 32), (27, 11), (19, 34), (24, 10), (25, 28), (21, 35), (9, 28), (29, 34), (0, 3), (23, 3), (13, 25), (24, 4), (2, 12), (2, 10), (17, 6), (28, 10), (20, 33), (29, 22), (19, 6), (25, 10), (26, 4), (14, 18), (28, 2), (20, 18), (15, 31), (20, 27), (20, 30), (0, 26), (16, 25), (11, 20), (19, 21), (25, 31), (18, 26), (4, 3), (9, 37), (23, 7), (3, 18), (22, 18), (19, 16), (6, 18), (15, 8), (5, 9), (18, 28), (17, 23), (2, 29), (23, 26), (2, 22), (23, 15), (22, 27), (27, 1), (2, 30), (3, 14), (24, 13), (8, 23), (18, 11), (18, 34), (28, 28), (0, 33), (9, 20), (16, 4), (27, 30), (15, 11), (5, 31), (19, 12), (17, 10), (12, 6), (17, 15), (17, 12), (29, 13), (8, 37), (9, 5), (12, 12), (0, 29), (29, 3), (28, 0), (30, 0), (13, 23), (28, 33), (20, 35), (12, 3), (2, 24), (11, 14), (15, 18), (8, 20), (1, 16), (30, 19), (11, 9), (7, 15), (2, 35), (28, 4), (25, 25), (9, 15), (4, 26), (15, 22), (28, 37), (9, 6), (2, 2), (13, 5), (9, 34), (14, 22), (11, 37), (3, 23), (17, 1), (15, 1), (6, 23), (2, 0), (15, 3), (16, 8), (29, 6), (21, 16), (29, 15), (7, 17), (23, 19), (27, 5), (27, 19), (14, 28), (29, 32), (21, 25), (15, 28), (18, 37), (26, 34), (27, 17), (29, 31), (0, 15), (13, 13), (2, 16), (20, 8), (2, 23), (6, 29), (4, 37), (4, 5), (19, 30), (30, 7), (11, 6), (1, 23), (4, 21), (0, 19), (11, 29), (26, 30), (29, 35), (21, 36), (18, 6), (11, 12), (0, 30), (23, 21), (16, 21), (8, 28), (22, 26), (16, 5), (21, 27), (4, 32), (29, 7), (30, 9), (18, 31), (11, 19), (29, 20), (3, 2), (6, 26), (29, 30), (25, 22), (23, 0), (22, 11), (6, 30), (23, 5), (19, 18), (14, 20), (25, 19), (2, 1), (27, 12), (28, 31), (7, 37), (27, 13), (20, 24), (21, 8), (9, 23), (10, 29), (17, 30), (14, 31), (19, 3), (3, 8), (12, 28), (6, 28), (3, 4), (12, 7), (27, 9), (24, 5), (27, 26), (24, 17), (27, 35), (27, 33), (28, 24), (23, 12), (8, 14), (28, 20), (29, 2), (20, 16), (12, 33), (26, 20), (30, 15), (13, 4), (1, 29), (0, 13), (9, 2), (20, 19), (20, 10), (9, 32), (4, 29), (4, 13), (3, 13), (3, 28), (14, 3), (4, 16), (27, 25), (25, 4), (29, 16), (6, 13), (1, 35), (10, 36), (27, 22), (17, 34), (1, 10), (11, 13), (27, 29), (30, 33), (4, 1), (26, 17), (22, 9), (10, 26), (19, 13), (27, 27), (29, 9), (17, 25), (5, 7), (19, 10), (25, 7), (5, 21), (13, 28), (28, 15), (22, 30), (3, 19), (18, 1), (3, 17), (24, 11), (30, 1), (18, 25), (0, 31), (24, 34), (0, 35), (16, 13), (1, 8), (0, 25), (0, 2), (15, 26), (11, 4), (1, 12), (22, 4), (3, 5), (20, 15), (22, 7), (17, 13), (27, 16), (12, 13), (26, 0), (27, 15), (18, 33), (9, 4), (12, 17), (0, 1), (28, 19), (5, 11), (18, 14), (15, 6), (26, 11), (7, 18), (24, 21), (12, 8), (9, 0), (15, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407680", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), 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, 26), (13, 29), (7, 6), (21, 15), (5, 16), (2, 1), (23, 33), (19, 34), (15, 14), (17, 13), (12, 30), (1, 32), (0, 32), (36, 35), (36, 5), (6, 26), (37, 15), (1, 9), (10, 34), (2, 16), (4, 34), (14, 22), (33, 31), (5, 14), (32, 16), (9, 18), (15, 23), (10, 17), (29, 2), (23, 34), (19, 0), (10, 22), (29, 16), (26, 20), (17, 6), (13, 25), (11, 14), (20, 25), (23, 11), (31, 31), (6, 25), (16, 3), (21, 8), (30, 23), (16, 17), (1, 24), (26, 14), (21, 22), (6, 13), (15, 33), (8, 2), (15, 31), (27, 28), (19, 31), (18, 27), (13, 31), (10, 6), (17, 19), (3, 33), (5, 6), (26, 19), (9, 12), (35, 11), (36, 4), (1, 33), (21, 3), (18, 0), (33, 6), (36, 9), (32, 26), (2, 9), (0, 8), (9, 34), (30, 31), (5, 29), (2, 32), (23, 25), (36, 24), (23, 9), (3, 34), (16, 19), (19, 10), (10, 35), (12, 15), (30, 10), (28, 7), (9, 0), (8, 8), (34, 29), (12, 17), (24, 19), (25, 22), (3, 25), (15, 11), (30, 3), (0, 5), (35, 0), (19, 29), (0, 23), (22, 12), (12, 28), (16, 11), (4, 4), (32, 10), (35, 5), (35, 10), (9, 27), (29, 11), (21, 21), (29, 26), (24, 15), (34, 21), (35, 22), (34, 2), (14, 4), (21, 1), (25, 29), (27, 32), (23, 19), (31, 22), (29, 20), (33, 13), (3, 7), (12, 7), (24, 31), (24, 0), (13, 2), (18, 16), (19, 19), (16, 33), (28, 12), (7, 29), (0, 28), (0, 19), (28, 27), (29, 29), (5, 21), (22, 1), (22, 19), (32, 28), (14, 17), (4, 11), (27, 22), (36, 33), (20, 28), (10, 33), (1, 10), (32, 2), (21, 30), (3, 35), (30, 5), (31, 25), (9, 11), (13, 9), (19, 13), (20, 8), (18, 30), (32, 8), (2, 19), (0, 20), (2, 18), (28, 23), (1, 20), (13, 0), (29, 13), (8, 28), (36, 12), (2, 30), (17, 35), (16, 26), (36, 16), (21, 11), (31, 28), (12, 12), (7, 24), (0, 7), (30, 9), (29, 33), (21, 23), (7, 2), (20, 10), (15, 25), (17, 2), (36, 20), (36, 34), (2, 21), (30, 32), (16, 5), (26, 6), (31, 34), (28, 34), (29, 6), (4, 3), (18, 8), (36, 2), (31, 13), (17, 15), (6, 29), (11, 21), (6, 15), (23, 6), (19, 9), (10, 31), (1, 35), (12, 3), (17, 28), (25, 23), (37, 31), (34, 6), (5, 7), (2, 29), (7, 15), (11, 26), (10, 13), (12, 20), (15, 10), (6, 19), (4, 24), (31, 14), (16, 32), (33, 34), (28, 8), (25, 34), (18, 26), (9, 26), (21, 10), (20, 34), (20, 4), (23, 5), (3, 19), (27, 24), (18, 29), (12, 9), (37, 25), (5, 1), (9, 3), (11, 2), (3, 23), (36, 30), (33, 28), (14, 34), (29, 35), (21, 20), (4, 5), (3, 11), (12, 27), (8, 11), (20, 7), (23, 13), (33, 7), (13, 13), (37, 5), (22, 13), (25, 25), (0, 9), (6, 21), (13, 10), (34, 17), (13, 18), (30, 13), (6, 22), (34, 18), (33, 22), (7, 13), (16, 22), (32, 0), (30, 0), (9, 35), (26, 23), (18, 24), (6, 17), (8, 18), (34, 19), (26, 25), (13, 22), (9, 2), (13, 12), (21, 0), (16, 24), (14, 28), (6, 18), (37, 7), (29, 15), (23, 2), (31, 2), (10, 4), (8, 22), (1, 7), (18, 35), (15, 3), (15, 26), (20, 21), (6, 32), (11, 29), (8, 33), (22, 34), (37, 8), (7, 10), (35, 4), (31, 23), (0, 11), (26, 32), (8, 19), (14, 14), (32, 19), (18, 22), (8, 25), (24, 7), (30, 14), (21, 17), (32, 4), (17, 12), (33, 15), (8, 10), (27, 35), (34, 35), (19, 1), (14, 7), (36, 26), (33, 23), (6, 9), (34, 10), (21, 32), (2, 31), (31, 1), (36, 11), (6, 34), (4, 29), (16, 8), (15, 21), (37, 0), (10, 26), (33, 32), (30, 11), (33, 4), (30, 24), (1, 23), (1, 27), (13, 20), (1, 5), (27, 27), (34, 8), (37, 20), (24, 9), (23, 1), (5, 8), (22, 21), (15, 20), (26, 1), (11, 8), (8, 1), (8, 9), (13, 30), (3, 16), (26, 12), (20, 29), (11, 9), (29, 10), (0, 26), (5, 13), (6, 6), (34, 23), (37, 27), (17, 4), (26, 0), (4, 23), (30, 27), (12, 33), (4, 6), (3, 31), (0, 2), (16, 12), (12, 6), (28, 4), (11, 15), (19, 23), (4, 20), (26, 26), (1, 16), (29, 4), (17, 34), (25, 4), (21, 12), (21, 27), (34, 13), (30, 33), (6, 33), (8, 23), (16, 29), (7, 34), (1, 8), (6, 2), (25, 30), (33, 1), (32, 24), (11, 1), (0, 3), (25, 32), (37, 22), (1, 0), (22, 3), (20, 18), (35, 16), (21, 9), (23, 12), (36, 8), (16, 10), (33, 18), (15, 4), (11, 32), (22, 15), (14, 21), (25, 15), (5, 10), (6, 12), (16, 35), (28, 21), (7, 16), (12, 24), (31, 12), (35, 18), (18, 28), (20, 20), (12, 13), (36, 3), (20, 33), (6, 35), (11, 0), (9, 14), (21, 2), (2, 23), (4, 12), (2, 27), (22, 31), (25, 11), (36, 29), (32, 7), (11, 24), (34, 16), (29, 22), (10, 20), (32, 25), (12, 31), (24, 3), (27, 10), (25, 18), (9, 10), (27, 5), (28, 11), (6, 11), (29, 18), (3, 0), (10, 0), (4, 21), (21, 5), (32, 13), (27, 11), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65520", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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), (0, 22), (2, 34), (14, 7), (16, 23), (25, 0), (25, 22), (8, 30), (23, 34), (14, 30), (3, 27), (7, 34), (29, 30), (18, 6), (11, 7), (7, 7), (12, 5), (6, 30), (25, 24), (7, 1), (9, 7), (24, 13), (14, 15), (0, 6), (6, 20), (7, 28), (28, 14), (15, 12), (24, 24), (30, 33), (27, 10), (1, 2), (17, 22), (13, 30), (17, 8), (1, 19), (15, 23), (23, 23), (27, 15), (13, 18), (15, 9), (28, 17), (2, 17), (26, 25), (12, 22), (16, 27), (24, 35), (5, 23), (7, 8), (26, 17), (17, 31), (19, 32), (10, 17), (30, 30), (20, 9), (28, 27), (12, 10), (15, 36), (9, 15), (2, 0), (9, 30), (17, 21), (13, 9), (22, 15), (11, 30), (16, 28), (6, 36), (21, 29), (30, 14), (12, 28), (28, 16), (8, 4), (30, 25), (11, 0), (24, 8), (21, 2), (28, 23), (27, 22), (20, 6), (9, 5), (13, 16), (22, 10), (5, 27), (5, 13), (13, 26), (8, 2), (27, 16), (7, 27), (9, 1), (25, 36), (10, 14), (18, 31), (22, 0), (8, 19), (29, 16), (8, 7), (6, 25), (28, 0), (12, 9), (3, 25), (6, 21), (1, 24), (26, 3), (21, 32), (8, 15), (27, 35), (21, 16), (13, 6), (13, 24), (29, 5), (19, 21), (17, 2), (23, 3), (22, 36), (7, 4), (20, 20), (29, 3), (7, 17), (6, 2), (2, 15), (4, 34), (30, 17), (18, 13), (3, 12), (26, 12), (10, 24), (7, 14), (0, 36), (28, 12), (8, 5), (22, 32), (2, 20), (12, 29), (25, 13), (22, 6), (18, 35), (23, 28), (23, 29), (11, 5), (8, 1), (14, 6), (1, 33), (22, 13), (13, 8), (10, 30), (18, 17), (19, 16), (7, 29), (25, 1), (0, 18), (14, 17), (16, 16), (17, 18), (11, 19), (3, 28), (7, 36), (30, 32), (7, 9), (4, 23), (22, 4), (4, 32), (24, 19), (5, 17), (16, 35), (4, 15), (19, 3), (19, 7), (29, 25), (5, 11), (16, 25), (20, 30), (7, 13), (23, 4), (17, 17), (7, 10), (0, 27), (27, 1), (14, 24), (4, 35), (7, 5), (27, 21), (3, 7), (17, 10), (17, 32), (0, 7), (17, 27), (5, 8), (11, 14), (10, 8), (4, 13), (0, 26), (7, 24), (20, 23), (30, 19), (13, 29), (7, 2), (29, 20), (7, 35), (21, 31), (12, 1), (23, 15), (25, 35), (12, 7), (12, 34), (14, 11), (30, 34), (24, 9), (24, 3), (16, 22), (19, 28), (1, 7), (2, 35), (11, 11), (29, 15), (14, 26), (20, 29), (23, 27), (25, 30), (18, 12), (2, 1), (15, 19), (5, 29), (1, 22), (2, 19), (4, 36), (20, 14), (20, 3), (16, 7), (8, 23), (29, 19), (18, 26), (15, 2), (3, 31), (19, 22), (3, 3), (7, 22), (10, 26), (25, 32), (8, 35), (29, 18), (9, 31), (18, 5), (6, 3), (0, 31), (25, 5), (9, 26), (16, 36), (2, 16), (12, 16), (1, 16), (7, 32), (6, 1), (2, 29), (4, 17), (5, 30), (17, 35), (18, 30), (2, 18), (22, 14), (10, 35), (21, 12), (28, 19), (30, 26), (6, 23), (2, 33), (7, 0), (7, 18), (18, 24), (0, 33), (2, 32), (11, 25), (29, 35), (22, 8), (16, 11), (24, 14), (16, 32), (11, 36), (1, 5), (14, 20), (0, 25), (9, 8), (15, 13), (30, 20), (19, 26), (28, 24), (7, 33), (15, 7), (3, 8), (17, 9), (20, 26), (17, 20), (14, 36), (19, 13), (30, 27), (27, 7), (9, 22), (5, 25), (8, 34), (30, 11), (14, 1), (20, 10), (21, 18), (19, 12), (15, 21), (28, 7), (10, 33), (9, 36), (30, 6), (26, 27), (18, 7), (13, 13), (20, 27), (5, 7), (4, 24), (1, 12), (30, 24), (26, 24), (15, 28), (9, 0), (0, 29), (26, 7), (29, 21), (4, 29), (6, 24), (21, 24), (6, 12), (18, 20), (27, 17), (6, 15), (15, 6), (21, 11), (8, 21), (6, 34), (3, 22), (27, 20), (29, 0), (14, 28), (13, 2), (7, 19), (11, 18), (12, 32), (10, 1), (2, 14), (28, 20), (21, 3), (2, 2), (26, 34), (12, 15), (26, 10), (15, 32), (15, 26), (19, 27), (6, 22), (9, 12), (28, 25), (22, 24), (28, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980856", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 22), (11, 18), (10, 2), (8, 13), (0, 2), (21, 23), (15, 2), (9, 10), (30, 17), (18, 21), (7, 31), (12, 33), (1, 12), (0, 32), (6, 7), (7, 15), (11, 10), (5, 29), (3, 20), (27, 24), (4, 9), (18, 2), (30, 33), (21, 16), (14, 3), (5, 18), (30, 26), (8, 19), (24, 36), (30, 25), (18, 10), (9, 14), (11, 3), (31, 29), (16, 13), (4, 7), (11, 25), (32, 15), (4, 21), (19, 2), (31, 34), (13, 22), (12, 15), (22, 30), (12, 34), (27, 5), (32, 25), (0, 3), (21, 1), (30, 2), (0, 25), (19, 6), (3, 28), (29, 25), (16, 26), (16, 0), (31, 25), (3, 5), (4, 33), (21, 35), (28, 1), (2, 25), (9, 16), (3, 15), (6, 29), (31, 4), (25, 2), (30, 19), (29, 16), (25, 33), (4, 23), (11, 26), (3, 8), (2, 21), (25, 6), (14, 21), (26, 32), (28, 22), (7, 10), (8, 18), (15, 11), (22, 14), (11, 16), (8, 33), (23, 1), (20, 28), (2, 7), (21, 12), (9, 0), (5, 33), (32, 4), (28, 32), (20, 11), (5, 13), (28, 5), (20, 32), (27, 13), (23, 14), (2, 17), (29, 11), (13, 2), (4, 0), (22, 18), (12, 0), (32, 17), (4, 26), (16, 35), (12, 4), (18, 14), (14, 27), (29, 29), (8, 16), (18, 22), (15, 1), (26, 3), (24, 17), (9, 25), (22, 35), (5, 10), (23, 10), (12, 6), (3, 4), (9, 23), (22, 8), (22, 10), (20, 7), (31, 9), (8, 10), (31, 8), (9, 19), (11, 17), (32, 3), (20, 34), (9, 12), (4, 29), (4, 31), (5, 1), (31, 2), (21, 26), (6, 32), (5, 23), (0, 33), (15, 22), (27, 0), (9, 32), (23, 28), (25, 30), (21, 34), (25, 27), (27, 32), (26, 35), (28, 19), (24, 4), (5, 35), (6, 10), (6, 6), (25, 8), (14, 26), (0, 24), (29, 27), (22, 3), (26, 33), (25, 35), (21, 24), (7, 0), (6, 31), (2, 36), (6, 34), (13, 18), (3, 16), (9, 5), (2, 29), (17, 6), (18, 4), (24, 20), (11, 6), (8, 30), (0, 1), (3, 19), (2, 0), (11, 29), (24, 19), (30, 14), (15, 9), (23, 12), (25, 11), (31, 5), (19, 27), (24, 32), (2, 22), (9, 20), (31, 21), (27, 27), (30, 28), (31, 17), (2, 14), (27, 3), (6, 20), (17, 4), (22, 1), (31, 36), (29, 36), (12, 32), (7, 16), (3, 23), (20, 35), (32, 33), (25, 4), (20, 25), (14, 13), (31, 33), (17, 7), (16, 33), (16, 10), (31, 11), (26, 18), (2, 16), (6, 8), (5, 7), (6, 2), (12, 11), (8, 7), (28, 16), (21, 7), (10, 13), (14, 6), (18, 7), (12, 28), (22, 11), (26, 28), (20, 36), (19, 36), (14, 19), (9, 27), (14, 28), (13, 7), (25, 32), (8, 12), (25, 9), (11, 24), (18, 25), (8, 26), (5, 30), (19, 25), (26, 23), (3, 25), (11, 8), (9, 9), (30, 29), (2, 20), (1, 9), (5, 34), (14, 8), (5, 4), (12, 8), (14, 24), (12, 14), (3, 0), (7, 13), (18, 8), (21, 28), (12, 25), (6, 5), (30, 10), (29, 35), (24, 35), (5, 2), (28, 10), (20, 15), (8, 4), (7, 2), (18, 32), (12, 24), (2, 35), (5, 27), (30, 0), (27, 21), (18, 1), (11, 0), (9, 24), (32, 24), (18, 15), (10, 10), (7, 11), (5, 36), (27, 33), (26, 29), (8, 6), (6, 0), (19, 29), (21, 33), (26, 8), (16, 17), (16, 6), (17, 11), (0, 18), (14, 17), (8, 2), (2, 8), (20, 21), (5, 5), (15, 17), (21, 21), (21, 32), (13, 19), (29, 17), (20, 16), (23, 11), (20, 18), (0, 30), (17, 33), (24, 21), (11, 11), (32, 30), (17, 20), (22, 6), (24, 15), (25, 15), (9, 33), (6, 36), (26, 34), (19, 20), (24, 31), (13, 31), (16, 12), (14, 1), (24, 29), (7, 34), (24, 8), (26, 2), (12, 20), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866560", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), 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), (28, 24), (7, 15), (33, 14), (20, 27), (8, 24), (26, 10), (26, 18), (14, 5), (30, 23), (28, 15), (6, 29), (29, 8), (22, 24), (34, 23), (30, 7), (23, 22), (8, 15), (16, 26), (29, 23), (30, 6), (9, 7), (35, 28), (27, 18), (12, 28), (9, 23), (16, 8), (3, 24), (7, 16), (19, 10), (36, 26), (21, 3), (8, 17), (27, 15), (9, 4), (36, 0), (7, 24), (0, 11), (18, 28), (33, 19), (35, 5), (21, 17), (28, 21), (36, 16), (2, 15), (22, 28), (25, 22), (14, 6), (23, 4), (33, 17), (19, 23), (30, 20), (2, 20), (18, 10), (27, 26), (13, 17), (2, 0), (31, 11), (3, 22), (30, 5), (36, 2), (31, 6), (36, 12), (29, 25), (3, 21), (33, 28), (17, 7), (8, 21), (31, 19), (20, 12), (26, 8), (29, 5), (9, 9), (6, 19), (34, 0), (7, 12), (33, 15), (3, 0), (32, 4), (30, 1), (3, 29), (23, 11), (32, 29), (24, 12), (6, 8), (20, 10), (25, 11), (27, 25), (7, 13), (21, 21), (13, 25), (27, 9), (14, 13), (0, 18), (18, 24), (13, 1), (21, 22), (4, 20), (30, 27), (9, 5), (24, 25), (12, 17), (7, 9), (36, 20), (8, 13), (18, 25), (25, 0), (0, 14), (8, 26), (19, 28), (28, 28), (7, 2), (6, 4), (10, 3), (8, 16), (10, 8), (32, 27), (35, 18), (29, 0), (2, 6), (30, 15), (23, 2), (36, 17), (34, 5), (15, 7), (35, 3), (9, 24), (2, 1), (12, 3), (21, 11), (21, 0), (17, 28), (3, 25), (36, 4), (35, 6), (15, 16), (1, 11), (32, 6), (18, 16), (32, 10), (16, 29), (24, 5), (34, 19), (10, 9), (10, 20), (11, 14), (27, 16), (17, 14), (31, 27), (13, 9), (24, 27), (13, 3), (32, 25), (4, 28), (21, 10), (18, 27), (24, 7), (31, 21), (33, 12), (12, 13), (2, 12), (36, 1), (35, 27), (19, 12), (13, 22), (32, 7), (17, 12), (31, 13), (11, 7), (17, 11), (2, 18), (17, 15), (5, 1), (28, 11), (34, 4), (11, 15), (22, 0), (36, 3), (22, 1), (24, 4), (18, 21), (5, 2), (7, 8), (26, 26), (15, 20), (9, 15), (3, 7), (36, 9), (3, 8), (12, 16), (19, 16), (28, 29), (7, 6), (12, 20), (33, 2), (21, 7), (11, 18), (15, 8), (2, 7), (2, 5), (13, 29), (4, 11), (28, 26), (19, 25), (22, 15), (28, 19), (6, 28), (1, 3), (3, 18), (18, 2), (20, 25), (4, 29), (13, 23), (3, 13), (28, 0), (30, 22), (22, 23), (5, 26), (18, 14), (32, 9), (12, 18), (35, 24), (22, 12), (31, 29), (30, 2), (9, 27), (23, 18), (11, 4), (30, 8), (33, 1), (27, 6), (33, 13), (11, 20), (15, 25), (2, 8), (7, 3), (25, 8), (10, 17), (27, 24), (6, 16), (29, 14), (25, 4), (13, 26), (24, 0), (9, 2), (32, 12), (36, 5), (20, 11), (30, 21), (14, 2), (22, 25), (35, 11), (8, 23), (14, 19), (22, 5), (23, 14), (21, 4), (6, 14), (34, 20), (1, 2), (30, 4), (1, 29), (24, 9), (2, 4), (14, 25), (19, 8), (1, 19), (22, 18), (32, 14), (16, 28), (22, 26), (6, 1), (15, 24), (12, 5), (1, 5), (2, 23), (7, 0), (7, 1), (30, 18), (25, 7), (33, 4), (15, 6), (12, 1), (32, 2), (27, 12), (27, 27), (25, 21), (33, 0), (5, 0), (36, 13), (35, 4), (23, 0), (9, 1), (14, 20), (17, 4), (36, 15), (19, 27), (3, 2), (29, 27), (34, 17), (6, 3), (18, 4), (27, 11), (14, 8), (4, 7), (7, 27), (0, 9), (1, 25), (21, 16), (20, 4), (22, 7), (15, 17), (33, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632400", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 31), (13, 14), (10, 16), (16, 2), (38, 19), (8, 11), (4, 24), (19, 21), (31, 28), (19, 26), (19, 27), (8, 19), (1, 2), (16, 9), (37, 13), (3, 25), (31, 17), (21, 11), (7, 26), (36, 14), (0, 28), (27, 29), (23, 27), (7, 8), (13, 27), (23, 0), (22, 17), (21, 5), (37, 31), (7, 21), (36, 20), (7, 7), (37, 21), (19, 10), (19, 9), (27, 31), (1, 11), (18, 7), (19, 7), (35, 19), (4, 30), (2, 16), (4, 4), (24, 10), (14, 22), (22, 12), (16, 10), (28, 4), (13, 30), (7, 1), (11, 4), (20, 25), (10, 7), (34, 29), (38, 5), (5, 30), (8, 14), (6, 12), (2, 3), (34, 27), (38, 17), (7, 15), (23, 1), (0, 9), (10, 23), (18, 5), (3, 0), (26, 19), (24, 12), (14, 28), (8, 1), (11, 19), (26, 0), (1, 29), (25, 12), (3, 17), (24, 28), (28, 12), (16, 8), (27, 13), (2, 10), (8, 3), (15, 17), (37, 3), (6, 14), (18, 4), (28, 18), (0, 12), (15, 6), (16, 5), (30, 3), (38, 2), (5, 25), (31, 5), (34, 19), (31, 30), (20, 0), (20, 27), (29, 27), (38, 12), (18, 0), (26, 29), (31, 0), (28, 14), (24, 21), (30, 27), (20, 2), (3, 29), (4, 8), (9, 21), (11, 13), (24, 5), (4, 1), (14, 20), (8, 21), (22, 1), (27, 6), (1, 31), (13, 6), (25, 22), (10, 10), (2, 28), (37, 27), (6, 25), (20, 7), (8, 4), (37, 8), (21, 19), (27, 28), (30, 11), (33, 29), (10, 0), (19, 14), (35, 27), (17, 11), (14, 10), (13, 24), (32, 2), (20, 15), (22, 10), (1, 9), (18, 27), (19, 1), (20, 17), (13, 9), (35, 17), (5, 1), (5, 7), (38, 10), (6, 5), (32, 5), (4, 17), (14, 8), (29, 12), (25, 20), (27, 30), (34, 1), (23, 8), (10, 15), (8, 24), (7, 13), (16, 14), (25, 11), (12, 6), (13, 19), (3, 24), (21, 17), (21, 12), (12, 2), (1, 30), (33, 3), (11, 27), (2, 31), (34, 3), (33, 22), (29, 29), (23, 20), (20, 26), (2, 9), (10, 3), (30, 29), (14, 25), (34, 24), (29, 14), (8, 22), (23, 3), (27, 12), (26, 25), (32, 23), (7, 3), (6, 3), (25, 0), (17, 10), (23, 15), (35, 9), (14, 15), (6, 11), (11, 2), (18, 28), (35, 29), (38, 13), (17, 4), (31, 18), (6, 30), (34, 10), (19, 13), (26, 2), (5, 2), (36, 7), (23, 29), (25, 14), (18, 9), (18, 30), (1, 5), (18, 20), (2, 19), (26, 4), (28, 1), (11, 28), (32, 15), (36, 6), (6, 8), (1, 28), (0, 22), (28, 6), (29, 21), (12, 28), (1, 18), (22, 14), (6, 4), (1, 10), (30, 21), (36, 26), (28, 21), (26, 21), (13, 22), (25, 24), (32, 18), (25, 25), (4, 2), (6, 15), (24, 2), (0, 20), (22, 25), (4, 26), (18, 8), (32, 16), (36, 10), (16, 6), (3, 20), (14, 7), (12, 17), (13, 20), (33, 31), (6, 29), (0, 4), (4, 3), (0, 11), (3, 2), (26, 5), (36, 30), (23, 14), (24, 25), (4, 6), (37, 15), (25, 7), (5, 28), (19, 0), (23, 4), (8, 29), (17, 8), (8, 20), (30, 7), (27, 24), (24, 30), (24, 17), (30, 6), (32, 22), (34, 17), (33, 24), (26, 9), (3, 26), (35, 8), (33, 14), (15, 20), (31, 19), (37, 10), (10, 20), (30, 13), (27, 8), (6, 31), (35, 7), (6, 10), (16, 17), (29, 9), (34, 4), (5, 26), (29, 16), (1, 12), (21, 28), (12, 18), (31, 14), (0, 21), (5, 6), (22, 8), (31, 25), (36, 23), (38, 7), (6, 17), (15, 5), (27, 18), (17, 23), (4, 27), (35, 13), (29, 31), (36, 25), (37, 20), (36, 27), (11, 23), (17, 31), (15, 3), (6, 26), (30, 26), (21, 22), (27, 1), (26, 18), (11, 11), (32, 12), (14, 9), (34, 25), (30, 30), (29, 20), (33, 16), (8, 26), (21, 2), (29, 3), (38, 23), (6, 2), (11, 3), (14, 29), (9, 24), (9, 18), (35, 3), (5, 24), (21, 0), (6, 20), (35, 28), (18, 22), (11, 31), (29, 1), (14, 23), (24, 19), (5, 21), (16, 26), (11, 17), (1, 21), (17, 24), (30, 15), (23, 26), (11, 10), (7, 22), (2, 8), (33, 8), (14, 26), (23, 12), (15, 23), (15, 7), (29, 5), (37, 22), (20, 9), (15, 2), (22, 6), (37, 26), (30, 28), (35, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914688", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (10, 12), (29, 8), (14, 35), (16, 3), (8, 11), (1, 32), (11, 10), (3, 24), (25, 6), (16, 8), (4, 3), (10, 28), (29, 20), (22, 3), (6, 31), (15, 32), (1, 20), (6, 19), (22, 32), (21, 29), (3, 22), (11, 9), (28, 21), (8, 28), (9, 34), (1, 11), (12, 3), (22, 2), (27, 23), (16, 31), (25, 12), (2, 14), (0, 13), (18, 25), (10, 7), (5, 18), (14, 1), (28, 1), (17, 17), (5, 19), (7, 19), (18, 7), (22, 8), (22, 22), (25, 35), (0, 22), (8, 16), (22, 20), (18, 12), (14, 18), (14, 8), (5, 17), (14, 15), (0, 6), (19, 31), (28, 8), (8, 3), (23, 11), (8, 2), (25, 20), (16, 1), (27, 28), (4, 7), (25, 2), (3, 5), (16, 36), (11, 18), (23, 14), (12, 6), (11, 8), (23, 27), (3, 3), (3, 14), (20, 34), (7, 9), (23, 1), (20, 11), (15, 17), (10, 35), (8, 5), (7, 33), (15, 29), (7, 16), (26, 16), (14, 6), (4, 12), (19, 17), (18, 8), (20, 13), (9, 23), (0, 11), (8, 26), (13, 32), (24, 15), (9, 18), (21, 28), (22, 23), (3, 1), (21, 14), (17, 4), (1, 4), (9, 14), (12, 21), (9, 30), (11, 23), (29, 15), (7, 3), (5, 29), (2, 20), (27, 8), (17, 6), (28, 14), (13, 20), (1, 7), (19, 36), (20, 1), (15, 13), (10, 6), (24, 21), (2, 32), (21, 16), (20, 29), (8, 1), (14, 0), (27, 10), (21, 32), (4, 14), (28, 31), (24, 6), (28, 0), (10, 24), (14, 10), (18, 35), (2, 34), (15, 36), (22, 6), (9, 24), (12, 28), (11, 13), (17, 32), (3, 7), (4, 28), (19, 18), (23, 9), (19, 8), (8, 24), (8, 25), (1, 30), (11, 32), (0, 33), (27, 31), (2, 23), (16, 17), (28, 18), (28, 35), (21, 2), (16, 24), (12, 10), (13, 28), (23, 33), (23, 7), (7, 32), (3, 30), (27, 3), (29, 14), (29, 16), (8, 19), (3, 28), (2, 7), (25, 8), (1, 1), (13, 33), (25, 4), (17, 30), (10, 13), (12, 14), (11, 15), (4, 25), (15, 9), (17, 29), (6, 11), (14, 3), (27, 35), (0, 18), (19, 22), (3, 36), (0, 14), (0, 12), (26, 10), (9, 28), (8, 14), (2, 26), (11, 3), (8, 27), (19, 9), (7, 22), (6, 36), (8, 32), (13, 35), (21, 36), (14, 29), (10, 14), (1, 15), (3, 34), (25, 31), (26, 22), (21, 21), (27, 30), (17, 5), (20, 18), (10, 25), (14, 7), (17, 36), (23, 21), (4, 27), (9, 19), (29, 12), (14, 33), (24, 14), (15, 19), (20, 17), (29, 31), (0, 23), (11, 17), (9, 7), (0, 34), (1, 35), (19, 28), (6, 33), (0, 27), (8, 33), (4, 18), (23, 2), (26, 21), (0, 35), (7, 1), (20, 23), (19, 23), (9, 17), (4, 8), (20, 27), (29, 5), (13, 9), (8, 13), (28, 4), (14, 25), (7, 7), (15, 20), (1, 13), (5, 34), (19, 5), (5, 23), (7, 34), (5, 21), (18, 34), (14, 21), (2, 4), (17, 9), (23, 10), (19, 34), (22, 29), (26, 30), (16, 16), (26, 11), (11, 4), (16, 28), (2, 17), (17, 11), (24, 24), (19, 3), (15, 8), (5, 4), (6, 25), (1, 18), (19, 35), (2, 13), (28, 2), (18, 4), (29, 30), (24, 9), (27, 20), (8, 18), (5, 35), (10, 0), (29, 9), (29, 7), (12, 30), (2, 36), (23, 12), (17, 26), (0, 21), (4, 19), (15, 0), (13, 24), (21, 20), (21, 35), (12, 33), (8, 35), (6, 9), (2, 22), (22, 12), (16, 4), (2, 33), (11, 20), (16, 12), (17, 35), (14, 24), (4, 34), (23, 26), (18, 21), (13, 18), (24, 18), (5, 6), (29, 27), (22, 30), (22, 18), (25, 30), (6, 7), (19, 16), (25, 9), (8, 0), (0, 5), (2, 1), (7, 25), (21, 19), (1, 9), (12, 35), (2, 15), (22, 36), (19, 10), (7, 8), (4, 22), (7, 20), (12, 5), (16, 32), (5, 30), (12, 20), (23, 5), (8, 4), (14, 11), (0, 20), (28, 11), (13, 27), (8, 34), (3, 10), (15, 21), (14, 17), (26, 18), (22, 25), (10, 2), (21, 25), (28, 28), (10, 27), (4, 17), (9, 25), (22, 10), (20, 3), (10, 32), (22, 1), (27, 34), (28, 19), (22, 13), (28, 24), (4, 1), (26, 25), (8, 10), (16, 2), (2, 28), (17, 23), (23, 16), (15, 12), (26, 8), (17, 7), (24, 12), (16, 19), (15, 5), (13, 21), (27, 21), (23, 32), (12, 19), (11, 1), (28, 30), (9, 26), (24, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "974610", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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), (32, 10), (17, 10), (15, 22), (14, 17), (2, 1), (32, 6), (17, 24), (26, 29), (14, 4), (20, 16), (13, 11), (20, 2), (30, 13), (9, 12), (26, 12), (16, 16), (1, 6), (33, 14), (23, 16), (10, 10), (1, 1), (26, 4), (30, 7), (0, 18), (27, 11), (27, 5), (10, 24), (1, 10), (5, 17), (28, 22), (3, 12), (24, 18), (6, 4), (18, 9), (18, 19), (2, 10), (25, 30), (24, 3), (29, 16), (21, 27), (32, 29), (9, 18), (10, 15), (33, 15), (22, 3), (8, 21), (18, 18), (11, 12), (30, 19), (14, 15), (14, 0), (13, 21), (24, 21), (6, 27), (12, 1), (8, 12), (20, 8), (27, 23), (9, 22), (14, 19), (24, 10), (2, 15), (9, 14), (18, 13), (24, 11), (14, 27), (19, 13), (17, 26), (21, 22), (6, 22), (26, 25), (17, 18), (0, 30), (8, 14), (7, 1), (26, 8), (13, 22), (16, 5), (23, 4), (21, 9), (31, 17), (33, 20), (22, 27), (10, 9), (32, 20), (31, 13), (5, 9), (7, 19), (27, 2), (23, 6), (32, 3), (30, 2), (4, 30), (17, 15), (15, 28), (27, 3), (30, 10), (27, 19), (26, 14), (15, 6), (27, 22), (13, 4), (4, 4), (10, 19), (23, 11), (10, 14), (1, 9), (15, 10), (32, 21), (2, 19), (13, 23), (10, 29), (10, 16), (26, 7), (7, 0), (16, 24), (33, 26), (22, 23), (3, 1), (27, 17), (26, 1), (15, 9), (7, 24), (27, 14), (3, 0), (1, 30), (6, 29), (23, 19), (16, 10), (7, 8), (8, 18), (18, 14), (20, 21), (16, 27), (25, 22), (12, 4), (22, 25), (19, 21), (11, 24), (0, 16), (15, 24), (0, 14), (4, 20), (17, 1), (32, 22), (23, 0), (4, 5), (31, 5), (16, 14), (31, 26), (8, 16), (8, 17), (26, 11), (20, 15), (25, 6), (25, 14), (16, 15), (19, 0), (17, 8), (16, 4), (1, 0), (0, 22), (11, 14), (27, 9), (19, 8), (9, 6), (5, 29), (20, 26), (33, 25), (4, 14), (9, 9), (26, 22), (3, 4), (13, 9), (26, 23), (24, 17), (15, 17), (19, 18), (31, 12), (13, 29), (10, 3), (23, 23), (25, 5), (30, 27), (3, 11), (2, 30), (8, 28), (29, 1), (14, 18), (9, 24), (28, 18), (17, 22), (3, 26), (31, 30), (25, 18), (33, 4), (10, 17), (15, 14), (11, 3), (16, 28), (23, 28), (25, 25), (1, 18), (3, 22), (16, 23), (7, 18), (9, 0), (17, 25), (26, 2), (12, 5), (28, 11), (7, 12), (23, 18), (10, 0), (1, 11), (26, 21), (4, 21), (12, 3), (25, 15), (25, 11), (3, 8), (8, 20), (1, 15), (0, 6), (7, 13), (28, 7), (12, 14), (25, 21), (31, 3), (8, 30), (29, 13), (11, 16), (31, 19), (8, 11), (5, 0), (2, 25), (14, 26), (0, 12), (12, 17), (5, 8), (24, 24), (13, 0), (12, 10), (31, 28), (1, 28), (10, 4), (22, 16), (31, 21), (15, 5), (20, 13), (9, 23), (30, 29), (14, 22), (20, 20), (3, 3), (19, 23), (11, 11), (18, 28), (13, 25), (32, 14), (29, 12), (29, 10), (6, 14), (0, 17), (11, 9), (16, 12), (24, 26), (24, 4), (0, 8), (8, 1), (2, 17), (6, 13), (7, 9), (11, 7), (18, 27), (29, 22), (13, 26), (24, 29), (9, 25), (4, 9), (14, 3), (24, 1), (32, 19), (19, 3), (14, 6), (11, 25), (22, 18), (25, 13), (33, 27), (16, 0), (31, 18), (5, 18), (15, 18), (30, 17), (3, 2), (8, 19), (29, 15), (15, 13), (27, 0), (29, 18), (28, 8), (28, 27), (29, 23), (31, 25), (33, 9), (25, 10), (21, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 36), (18, 30), (12, 24), (34, 28), (33, 26), (16, 9), (15, 9), (37, 7), (2, 4), (16, 28), (19, 17), (37, 28), (7, 18), (5, 25), (20, 4), (30, 9), (18, 15), (27, 27), (29, 31), (3, 24), (8, 8), (38, 18), (38, 28), (27, 30), (15, 27), (2, 10), (9, 9), (36, 1), (25, 14), (37, 16), (1, 24), (0, 36), (17, 30), (18, 5), (38, 7), (23, 33), (11, 2), (32, 19), (24, 9), (38, 2), (14, 5), (24, 10), (1, 12), (7, 11), (24, 1), (8, 11), (28, 34), (8, 16), (31, 21), (9, 25), (17, 16), (26, 11), (19, 22), (28, 6), (29, 7), (24, 27), (11, 32), (23, 8), (30, 15), (12, 13), (28, 24), (9, 21), (11, 7), (3, 31), (25, 22), (24, 31), (38, 8), (25, 34), (37, 36), (9, 14), (18, 23), (16, 18), (27, 31), (18, 31), (26, 9), (37, 26), (24, 19), (37, 32), (9, 33), (30, 31), (31, 30), (24, 29), (1, 10), (37, 21), (5, 6), (1, 29), (19, 34), (13, 36), (22, 25), (6, 14), (30, 16), (13, 8), (36, 34), (9, 16), (0, 35), (32, 24), (3, 15), (23, 19), (0, 6), (0, 19), (33, 10), (13, 23), (20, 10), (10, 6), (10, 34), (8, 1), (37, 18), (26, 22), (7, 32), (30, 7), (27, 26), (8, 31), (31, 35), (26, 35), (14, 26), (6, 10), (22, 33), (7, 2), (12, 14), (26, 14), (17, 6), (8, 9), (30, 11), (12, 27), (31, 8), (33, 15), (1, 21), (38, 3), (15, 17), (32, 4), (7, 14), (22, 22), (33, 16), (9, 3), (10, 7), (23, 7), (35, 33), (29, 27), (0, 2), (17, 12), (22, 13), (8, 23), (10, 22), (29, 18), (2, 5), (21, 35), (12, 19), (14, 22), (0, 8), (30, 3), (24, 11), (20, 2), (37, 15), (33, 30), (6, 30), (28, 10), (30, 22), (17, 22), (11, 25), (33, 19), (19, 5), (9, 31), (24, 12), (33, 32), (15, 7), (9, 0), (19, 25), (28, 21), (6, 15), (7, 34), (32, 14), (35, 23), (4, 36), (22, 24), (34, 16), (4, 5), (26, 29), (23, 5), (27, 12), (19, 33), (34, 25), (8, 13), (20, 29), (14, 15), (36, 13), (7, 8), (18, 18), (30, 29), (28, 23), (35, 13), (15, 30), (33, 31), (5, 12), (8, 28), (10, 8), (20, 34), (20, 31), (10, 29), (38, 21), (10, 3), (27, 32), (9, 22), (11, 11), (4, 35), (36, 9), (18, 24), (14, 35), (29, 14), (32, 21), (25, 5), (16, 36), (21, 31), (26, 13), (2, 31), (34, 24), (33, 35), (36, 32), (21, 0), (17, 28), (17, 23), (38, 17), (0, 22), (1, 23), (29, 8), (29, 6), (35, 12), (2, 2), (30, 14), (27, 22), (2, 26), (4, 12), (30, 32), (0, 34), (6, 28), (31, 0), (6, 7), (29, 3), (21, 17), (4, 24), (3, 18), (15, 35), (5, 26), (10, 27), (36, 17), (38, 34), (24, 26), (31, 24), (30, 34), (23, 22), (2, 22), (19, 24), (25, 13), (34, 32), (26, 25), (35, 22), (5, 3), (5, 9), (22, 30), (28, 22), (21, 29), (36, 20), (1, 7), (3, 19), (4, 33), (17, 8), (19, 4), (28, 14), (23, 28), (28, 4), (6, 8), (37, 27), (22, 12), (36, 7), (6, 23), (26, 31), (37, 31), (20, 19), (17, 24), (25, 27), (20, 22), (36, 36), (14, 33), (34, 29), (11, 19), (6, 11), (22, 16), (15, 28), (21, 13), (12, 34), (33, 22), (17, 29), (32, 26), (5, 14), (24, 22), (4, 30), (26, 18), (15, 33), (15, 25), (36, 24), (29, 25), (22, 27), (21, 20), (7, 17), (3, 7), (0, 7), (1, 30), (22, 5), (18, 26), (17, 0), (29, 19), (14, 16), (14, 8), (36, 6), (3, 28), (32, 1), (27, 4), (23, 27), (10, 35), (9, 23), (10, 16), (33, 25), (3, 20), (19, 1), (15, 15), (10, 28), (23, 0), (34, 27), (2, 13), (13, 2), (12, 9), (14, 13), (1, 35), (25, 15), (6, 34), (14, 32), (8, 35), (18, 34), (3, 22), (37, 30), (21, 26), (16, 31), (25, 33), (23, 21), (26, 16), (38, 12), (33, 33), (30, 36), (6, 5), (22, 28), (8, 2), (30, 20), (18, 6), (17, 15), (9, 28), (5, 19), (8, 25), (15, 32), (19, 7), (2, 32), (35, 15), (37, 14), (31, 2), (20, 30), (18, 9), (29, 23), (7, 13), (8, 15), (29, 9), (5, 34), (15, 13), (16, 6), (7, 36), (2, 28), (11, 1), (2, 25), (8, 7), (19, 14), (5, 24), (5, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481280", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 3), (2, 29), (27, 0), (26, 28), (30, 22), (26, 19), (27, 14), (12, 29), (10, 12), (16, 8), (21, 27), (0, 14), (30, 28), (5, 4), (24, 5), (13, 16), (10, 14), (25, 30), (21, 12), (27, 15), (3, 17), (21, 20), (20, 21), (1, 22), (10, 15), (14, 25), (3, 15), (11, 17), (12, 0), (30, 10), (9, 22), (13, 12), (16, 2), (19, 23), (11, 8), (19, 12), (14, 22), (16, 10), (17, 19), (19, 24), (21, 8), (26, 0), (5, 13), (30, 26), (12, 14), (17, 23), (21, 24), (27, 5), (27, 16), (25, 4), (10, 7), (20, 7), (28, 29), (21, 0), (22, 1), (3, 0), (25, 13), (17, 29), (18, 8), (22, 0), (3, 6), (30, 13), (13, 0), (26, 13), (22, 17), (3, 9), (26, 24), (27, 26), (24, 12), (29, 29), (16, 27), (8, 12), (5, 14), (23, 18), (11, 12), (28, 3), (22, 12), (25, 20), (30, 19), (25, 11), (0, 18), (2, 10), (13, 24), (10, 0), (10, 29), (18, 20), (15, 8), (11, 20), (6, 2), (13, 14), (20, 17), (25, 23), (16, 4), (15, 29), (29, 19), (26, 6), (8, 1), (1, 16), (5, 28), (14, 7), (13, 2), (20, 16), (31, 5), (29, 6), (5, 25), (5, 6), (14, 26), (26, 27), (6, 4), (0, 27), (11, 16), (15, 19), (26, 9), (0, 1), (24, 4), (14, 3), (9, 14), (16, 26), (26, 2), (25, 0), (1, 21), (27, 22), (14, 30), (25, 2), (3, 25), (21, 15), (22, 26), (18, 5), (0, 6), (29, 24), (18, 9), (12, 4), (20, 23), (23, 19), (31, 13), (18, 29), (20, 10), (7, 14), (6, 0), (13, 29), (15, 3), (30, 25), (10, 27), (0, 7), (16, 20), (16, 24), (17, 15), (25, 5), (12, 12), (23, 12), (6, 19), (19, 5), (8, 11), (1, 3), (30, 23), (25, 16), (8, 9), (2, 15), (13, 22), (27, 24), (17, 7), (13, 5), (28, 21), (30, 11), (25, 27), (2, 25), (1, 10), (6, 1), (18, 26), (9, 2), (4, 19), (21, 2), (13, 19), (4, 18), (1, 26), (5, 0), (27, 20), (22, 13), (17, 11), (22, 21), (20, 2), (0, 21), (12, 11), (10, 3), (21, 18), (7, 16), (30, 27), (10, 20), (17, 18), (6, 20), (20, 12), (18, 1), (24, 15), (13, 21), (23, 14), (25, 18), (14, 2), (23, 10), (21, 7), (21, 30), (24, 25), (30, 6), (18, 2), (5, 24), (2, 9), (18, 13), (8, 19), (12, 15), (29, 2), (9, 5), (28, 14), (9, 15), (29, 23), (0, 25), (12, 19), (14, 6), (17, 10), (15, 30), (22, 11), (9, 27), (31, 12), (5, 19), (24, 21), (27, 7), (16, 17), (29, 13), (2, 5), (19, 11), (17, 8), (30, 2), (26, 4), (17, 30), (28, 9), (9, 13), (31, 17), (31, 16), (7, 21), (1, 20), (11, 9), (2, 21), (7, 9), (23, 23), (20, 5), (1, 23), (5, 23), (10, 21), (14, 21), (28, 13), (27, 4), (25, 9), (23, 1), (30, 15), (25, 10), (23, 26), (5, 8), (20, 24), (11, 14), (21, 16), (0, 23), (26, 29), (25, 14), (20, 22), (12, 25), (8, 5), (18, 23), (24, 13), (1, 30), (15, 14), (20, 3), (14, 24), (13, 11), (14, 5), (15, 1), (17, 24), (11, 28), (13, 10), (1, 28), (1, 18), (22, 10), (4, 9), (1, 11), (10, 8), (3, 29), (0, 19), (28, 6), (18, 7), (27, 27), (7, 2), (7, 19), (10, 4), (12, 30), (27, 19), (19, 21), (13, 28), (7, 18), (6, 29), (31, 15), (28, 16), (13, 13), (11, 3), (11, 26), (10, 22), (27, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "583296", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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), (26, 18), (29, 3), (2, 18), (23, 1), (10, 32), (0, 27), (7, 10), (3, 3), (6, 26), (15, 21), (25, 29), (19, 12), (23, 15), (29, 21), (22, 7), (12, 1), (0, 33), (10, 6), (3, 31), (12, 26), (26, 10), (15, 27), (1, 8), (28, 0), (17, 21), (9, 15), (26, 32), (4, 32), (11, 24), (11, 33), (24, 7), (27, 28), (20, 1), (18, 10), (24, 12), (9, 21), (15, 3), (9, 24), (27, 29), (2, 24), (1, 32), (6, 24), (15, 22), (12, 16), (17, 31), (23, 26), (6, 7), (15, 26), (12, 17), (22, 31), (26, 16), (16, 12), (28, 7), (12, 29), (29, 15), (4, 11), (25, 22), (15, 11), (24, 31), (21, 13), (29, 18), (9, 1), (12, 5), (12, 10), (13, 10), (13, 29), (29, 11), (6, 1), (18, 2), (5, 31), (21, 8), (22, 32), (29, 14), (21, 21), (3, 9), (28, 16), (18, 13), (4, 28), (7, 32), (9, 30), (17, 1), (26, 4), (16, 24), (29, 7), (2, 11), (5, 1), (7, 13), (9, 13), (17, 32), (17, 23), (6, 9), (12, 11), (26, 25), (14, 21), (8, 15), (9, 12), (12, 15), (3, 23), (17, 17), (4, 5), (10, 23), (4, 30), (19, 27), (21, 25), (3, 24), (18, 16), (20, 31), (19, 7), (2, 1), (9, 8), (20, 4), (22, 26), (5, 18), (12, 12), (10, 27), (12, 0), (1, 11), (23, 33), (13, 33), (11, 19), (4, 23), (11, 30), (29, 10), (13, 19), (4, 19), (6, 23), (2, 19), (29, 31), (4, 31), (13, 18), (19, 23), (17, 25), (13, 32), (27, 11), (11, 7), (16, 21), (10, 25), (27, 4), (13, 20), (6, 17), (28, 24), (29, 30), (19, 16), (20, 11), (16, 26), (24, 4), (0, 8), (7, 26), (2, 16), (27, 19), (6, 12), (0, 11), (28, 15), (7, 34), (4, 17), (24, 22), (17, 4), (0, 31), (0, 29), (16, 18), (20, 25), (21, 16), (27, 23), (11, 13), (20, 13), (22, 11), (21, 27), (20, 29), (28, 6), (3, 28), (6, 31), (18, 20), (14, 25), (7, 3), (27, 32), (26, 7), (13, 16), (21, 3), (21, 7), (27, 7), (13, 15), (5, 13), (2, 5), (4, 24), (13, 23), (12, 14), (18, 7), (17, 8), (8, 13), (12, 6), (18, 3), (21, 20), (26, 5), (22, 18), (14, 22), (22, 28), (11, 8), (26, 24), (6, 2), (0, 2), (23, 5), (3, 12), (14, 16), (20, 30), (26, 29), (22, 15), (0, 9), (10, 5), (5, 19), (8, 0), (14, 5), (8, 32), (4, 13), (10, 2), (21, 14), (3, 6), (26, 21), (28, 1), (22, 12), (16, 29), (22, 9), (26, 13), (7, 25), (27, 8), (24, 30), (23, 25), (18, 34), (11, 10), (3, 34), (15, 15), (8, 34), (9, 4), (6, 25), (10, 4), (14, 3), (5, 17), (18, 0), (14, 10), (0, 10), (0, 17), (29, 28), (3, 2), (19, 15), (17, 15), (11, 16), (15, 1), (18, 9), (24, 1), (0, 15), (8, 30), (0, 3), (20, 7), (25, 6), (1, 26), (21, 22), (21, 33), (0, 23), (21, 31), (23, 28), (25, 25), (18, 17), (24, 0), (25, 33), (27, 12), (14, 6), (7, 33), (12, 8), (26, 34), (7, 7), (16, 15), (4, 8), (0, 26), (18, 26), (3, 11), (2, 32), (16, 13), (5, 3), (8, 16), (23, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), 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), (25, 27), (29, 25), (18, 17), (22, 25), (18, 28), (31, 24), (22, 23), (32, 24), (8, 25), (6, 31), (27, 30), (8, 5), (21, 33), (32, 23), (34, 34), (7, 0), (24, 17), (30, 30), (9, 23), (17, 6), (1, 15), (24, 31), (20, 34), (27, 6), (19, 5), (17, 33), (21, 3), (9, 31), (19, 1), (15, 30), (25, 4), (26, 24), (13, 27), (17, 32), (4, 33), (9, 12), (15, 27), (11, 26), (0, 14), (1, 3), (22, 21), (0, 31), (14, 18), (9, 20), (21, 7), (21, 29), (13, 4), (11, 7), (2, 0), (5, 17), (14, 30), (0, 19), (31, 31), (12, 15), (8, 17), (19, 18), (6, 14), (7, 32), (34, 5), (12, 11), (8, 30), (4, 5), (6, 3), (33, 34), (14, 19), (28, 34), (31, 5), (28, 35), (9, 13), (26, 34), (9, 6), (30, 19), (29, 0), (5, 3), (27, 23), (29, 6), (3, 5), (16, 9), (14, 22), (3, 1), (8, 21), (2, 1), (7, 6), (34, 18), (12, 35), (33, 9), (34, 20), (13, 17), (0, 18), (13, 8), (12, 31), (34, 26), (2, 5), (28, 27), (20, 9), (4, 26), (7, 33), (22, 13), (27, 12), (4, 10), (6, 11), (20, 5), (14, 16), (31, 14), (30, 11), (19, 31), (19, 19), (31, 34), (16, 8), (3, 32), (27, 10), (10, 20), (33, 26), (16, 23), (2, 21), (0, 22), (16, 15), (7, 21), (25, 6), (32, 0), (13, 6), (28, 18), (6, 33), (25, 31), (29, 8), (34, 19), (28, 7), (22, 22), (16, 0), (4, 25), (12, 6), (19, 34), (8, 28), (27, 25), (22, 5), (19, 21), (21, 25), (6, 23), (27, 16), (5, 18), (11, 14), (25, 7), (1, 13), (21, 20), (9, 14), (13, 10), (28, 12), (5, 15), (30, 16), (4, 20), (22, 0), (33, 21), (10, 5), (3, 18), (11, 25), (19, 24), (0, 30), (7, 8), (19, 32), (29, 31), (32, 3), (12, 14), (29, 33), (17, 31), (27, 24), (6, 32), (22, 9), (29, 14), (25, 29), (22, 29), (15, 9), (5, 25), (10, 12), (23, 25), (0, 26), (10, 24), (29, 11), (17, 4), (4, 3), (6, 24), (10, 3), (34, 9), (20, 14), (20, 15), (11, 34), (3, 3), (0, 23), (4, 35), (22, 32), (23, 5), (16, 16), (17, 35), (12, 0), (31, 0), (18, 25), (8, 0), (19, 30), (11, 30), (0, 7), (0, 12), (5, 1), (14, 23), (18, 23), (20, 8), (34, 6), (21, 35), (20, 18), (0, 4), (18, 3), (19, 28), (34, 11), (31, 22), (15, 19), (29, 17), (19, 23), (1, 29), (14, 15), (22, 12), (21, 26), (20, 29), (4, 18), (34, 12), (5, 32), (0, 28), (13, 23), (30, 22), (17, 27), (34, 31), (33, 2), (8, 26), (3, 31), (18, 32), (18, 18), (4, 16), (27, 35), (19, 13), (17, 7), (27, 20), (34, 27), (8, 1), (6, 0), (27, 9), (4, 30), (26, 19), (2, 26), (15, 11), (6, 2), (20, 24), (25, 19), (17, 8), (15, 25), (13, 24), (28, 2), (10, 11), (28, 23), (17, 34), (3, 29), (15, 0), (14, 28), (5, 10), (23, 33), (15, 18), (24, 19), (34, 7), (9, 32), (20, 16), (32, 34), (9, 29), (7, 3), (1, 21), (10, 23), (9, 11), (22, 20), (3, 10), (14, 14), (12, 9), (9, 9), (33, 19), (7, 27), (7, 28), (13, 2), (11, 33), (16, 21), (22, 27), (4, 23), (25, 16), (31, 27), (18, 12), (30, 17), (1, 0), (27, 11), (26, 8), (6, 21), (7, 26), (4, 28), (33, 12), (0, 11), (8, 23), (13, 9), (2, 22), (9, 19), (8, 27), (2, 18), (31, 20), (25, 23), (31, 28), (5, 20), (34, 17), (34, 0), (31, 8), (29, 34), (21, 21), (1, 10), (6, 27), (25, 30), (33, 18), (26, 9), (24, 24), (30, 27), (26, 0), (29, 4), (15, 12), (26, 25), (5, 22), (19, 11), (9, 0), (12, 16), (27, 26), (18, 6), (26, 20), (18, 7), (3, 22), (26, 29), (13, 3), (2, 27), (0, 15), (21, 12), (16, 7), (28, 15), (27, 29), (12, 19), (23, 4), (7, 9), (3, 11), (10, 29), (2, 28), (21, 9), (11, 9), (30, 18), (24, 11), (1, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "598992", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 30), (28, 26), (16, 17), (9, 28), (6, 22), (24, 9), (5, 3), (2, 23), (0, 7), (6, 1), (22, 0), (9, 19), (23, 6), (29, 16), (28, 14), (24, 29), (6, 37), (20, 26), (9, 8), (8, 20), (28, 21), (30, 1), (28, 11), (4, 18), (11, 13), (29, 7), (30, 9), (14, 19), (25, 12), (11, 7), (0, 25), (17, 12), (20, 18), (29, 19), (31, 17), (11, 23), (29, 6), (13, 19), (2, 30), (7, 1), (22, 20), (6, 36), (7, 13), (30, 35), (30, 5), (29, 1), (23, 12), (28, 25), (24, 2), (3, 26), (32, 26), (23, 0), (7, 23), (1, 3), (11, 0), (29, 37), (24, 22), (19, 2), (16, 3), (9, 6), (19, 4), (27, 36), (30, 31), (15, 8), (26, 37), (17, 11), (25, 34), (8, 16), (15, 36), (13, 7), (18, 2), (27, 9), (10, 37), (10, 12), (18, 16), (20, 24), (7, 3), (8, 22), (15, 4), (13, 20), (1, 5), (13, 15), (7, 33), (23, 16), (1, 11), (19, 31), (7, 9), (16, 7), (20, 6), (26, 3), (25, 14), (22, 16), (10, 10), (19, 9), (6, 8), (21, 6), (11, 34), (18, 35), (22, 28), (15, 7), (15, 12), (17, 7), (10, 7), (11, 5), (30, 3), (9, 11), (2, 14), (4, 22), (27, 10), (1, 18), (25, 0), (24, 13), (1, 2), (30, 17), (29, 18), (11, 6), (3, 30), (2, 27), (30, 18), (0, 4), (14, 35), (13, 5), (31, 18), (9, 27), (14, 33), (16, 16), (23, 11), (12, 7), (5, 24), (7, 8), (5, 36), (21, 37), (31, 24), (13, 2), (13, 25), (19, 29), (23, 26), (3, 9), (16, 14), (17, 20), (23, 1), (29, 29), (25, 4), (30, 6), (7, 29), (17, 22), (0, 5), (32, 25), (15, 1), (20, 16), (10, 30), (24, 20), (23, 31), (18, 29), (17, 15), (15, 23), (11, 37), (32, 27), (2, 21), (31, 9), (16, 22), (27, 26), (5, 12), (27, 18), (1, 15), (13, 6), (4, 7), (21, 16), (14, 20), (3, 22), (18, 9), (17, 10), (10, 8), (26, 23), (0, 18), (21, 36), (4, 28), (22, 22), (29, 17), (15, 24), (14, 26), (19, 6), (8, 32), (11, 35), (25, 28), (1, 1), (28, 27), (8, 0), (16, 32), (6, 6), (27, 8), (20, 34), (3, 18), (22, 19), (12, 22), (0, 9), (24, 36), (11, 4), (16, 31), (6, 33), (27, 7), (27, 3), (24, 17), (20, 14), (20, 0), (24, 0), (29, 2), (2, 8), (17, 3), (7, 25), (22, 24), (27, 4), (15, 32), (22, 12), (11, 31), (16, 29), (30, 13), (32, 7), (13, 22), (25, 26), (17, 14), (31, 26), (14, 21), (1, 8), (2, 28), (10, 20), (28, 16), (7, 22), (8, 28), (30, 22), (29, 9), (0, 12), (27, 27), (6, 16), (26, 21), (5, 17), (19, 17), (21, 33), (19, 7), (22, 3), (9, 25), (12, 25), (27, 25), (4, 2), (3, 0), (26, 20), (6, 27), (2, 29), (8, 13), (7, 16), (9, 15), (10, 0), (5, 28), (2, 16), (20, 23), (13, 11), (19, 22), (31, 4), (1, 27), (17, 37), (5, 31), (6, 29), (12, 11), (24, 7), (16, 26), (28, 37), (23, 36), (9, 26), (14, 11), (20, 10), (0, 37), (6, 9), (1, 33), (7, 20), (12, 29), (32, 16), (9, 30), (17, 33), (19, 26), (22, 18), (5, 7), (7, 31), (25, 19), (3, 31), (5, 14), (16, 18), (3, 2), (22, 2), (26, 17), (29, 3), (14, 15), (16, 12), (7, 5), (31, 3), (22, 23), (0, 31), (3, 24), (17, 2), (31, 8), (12, 34), (29, 10), (9, 5), (13, 34), (23, 2), (32, 29), (14, 0), (8, 4), (3, 11), (29, 27), (11, 11), (32, 5), (7, 30), (30, 24), (24, 16), (27, 13), (2, 9), (23, 15), (18, 5), (15, 30), (14, 28), (15, 16), (22, 4), (26, 32), (20, 28), (2, 35), (32, 28), (4, 36), (28, 2), (9, 13), (32, 20), (32, 31), (6, 31), (27, 23), (6, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "406080", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), 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), (18, 10), (35, 2), (15, 28), (21, 24), (1, 29), (18, 18), (33, 0), (4, 6), (8, 18), (14, 27), (30, 13), (14, 21), (8, 17), (31, 3), (1, 14), (12, 19), (33, 35), (10, 12), (27, 14), (25, 7), (33, 28), (10, 7), (32, 3), (7, 2), (23, 10), (17, 25), (0, 20), (12, 15), (1, 31), (30, 25), (12, 17), (11, 29), (18, 29), (16, 28), (0, 10), (35, 16), (0, 25), (7, 35), (23, 21), (12, 24), (16, 32), (28, 6), (21, 15), (16, 19), (3, 11), (4, 35), (13, 27), (17, 32), (35, 12), (19, 4), (24, 20), (30, 0), (26, 1), (30, 32), (22, 18), (11, 22), (31, 2), (6, 23), (6, 17), (12, 2), (25, 1), (4, 13), (25, 9), (17, 5), (35, 5), (32, 33), (28, 27), (27, 7), (4, 18), (2, 4), (25, 10), (16, 2), (26, 22), (10, 5), (5, 11), (1, 28), (10, 2), (28, 21), (3, 15), (0, 29), (11, 34), (12, 4), (26, 8), (7, 20), (29, 30), (25, 34), (17, 2), (12, 7), (18, 28), (9, 6), (2, 0), (34, 34), (12, 34), (18, 6), (33, 13), (8, 30), (29, 27), (31, 14), (0, 15), (34, 1), (3, 34), (18, 26), (9, 10), (35, 15), (11, 17), (32, 9), (12, 1), (9, 30), (21, 2), (9, 7), (16, 14), (6, 1), (11, 9), (3, 12), (21, 19), (24, 31), (33, 3), (4, 27), (29, 21), (33, 16), (1, 4), (28, 16), (22, 23), (31, 29), (28, 8), (15, 32), (14, 23), (27, 24), (35, 24), (23, 6), (19, 16), (2, 6), (18, 7), (9, 17), (0, 7), (18, 21), (2, 1), (15, 15), (28, 20), (5, 13), (35, 30), (6, 13), (31, 7), (8, 13), (34, 25), (28, 13), (29, 4), (19, 22), (33, 10), (27, 28), (2, 15), (25, 33), (21, 14), (29, 11), (13, 13), (27, 16), (28, 32), (2, 2), (2, 18), (19, 31), (17, 26), (33, 12), (15, 8), (4, 22), (6, 16), (4, 14), (27, 33), (26, 30), (32, 35), (24, 0), (6, 14), (16, 20), (17, 24), (7, 29), (33, 25), (8, 25), (26, 5), (30, 10), (5, 19), (15, 21), (16, 7), (20, 21), (8, 19), (33, 21), (24, 14), (9, 31), (35, 28), (24, 35), (25, 15), (5, 17), (18, 0), (34, 11), (4, 32), (19, 33), (31, 17), (24, 1), (17, 31), (13, 2), (32, 6), (5, 12), (7, 25), (8, 5), (18, 17), (18, 15), (19, 35), (13, 25), (19, 29), (32, 8), (32, 5), (21, 26), (31, 13), (7, 1), (28, 34), (32, 2), (7, 9), (1, 6), (5, 29), (16, 25), (13, 26), (14, 35), (32, 26), (20, 20), (24, 22), (12, 9), (15, 25), (28, 0), (20, 29), (23, 16), (35, 29), (28, 28), (22, 28), (14, 16), (31, 26), (3, 20), (28, 31), (20, 14), (1, 13), (28, 9), (15, 13), (6, 4), (10, 3), (31, 21), (23, 27), (6, 19), (20, 6), (27, 9), (29, 14), (4, 11), (3, 21), (22, 19), (23, 5), (17, 6), (10, 16), (15, 20), (29, 33), (34, 13), (13, 11), (22, 8), (35, 0), (2, 20), (23, 28), (22, 12), (4, 4), (19, 21), (16, 18), (1, 34), (25, 18), (23, 12), (3, 28), (22, 31), (27, 30), (1, 9), (21, 31), (8, 6), (4, 21), (3, 22), (16, 35), (3, 4), (21, 4), (20, 32), (29, 10), (13, 1), (16, 13), (34, 18), (29, 17), (2, 11), (5, 4), (34, 35), (8, 9), (26, 33), (10, 6), (4, 1), (3, 33), (12, 6), (5, 10), (18, 32), (27, 8), (24, 7), (9, 22), (2, 32), (6, 9), (11, 4), (32, 29), (10, 23), (12, 3), (19, 25), (0, 28), (31, 16), (28, 35), (2, 22), (19, 27), (20, 23), (3, 32), (31, 24), (14, 7), (4, 0), (14, 6), (8, 28), (1, 3), (14, 12), (20, 1), (34, 20), (11, 1), (22, 11), (1, 15), (4, 8), (11, 18), (21, 30), (31, 6), (21, 16), (6, 5), (17, 22), (21, 20), (30, 29), (0, 21), (11, 21), (28, 17), (29, 15), (26, 31), (23, 20), (13, 17), (35, 18), (16, 11), (31, 1), (22, 34), (13, 9), (10, 34), (27, 6), (18, 30), (4, 20), (10, 1), (15, 18), (7, 23), (8, 4), (8, 24), (16, 9), (24, 15), (26, 29), (31, 35), (28, 18), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "650592", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 2), (12, 6), (24, 4), (19, 15), (32, 19), (31, 19), (0, 10), (34, 12), (4, 29), (6, 25), (35, 19), (18, 31), (33, 1), (23, 17), (28, 16), (0, 21), (9, 15), (14, 0), (5, 4), (23, 29), (14, 22), (26, 12), (4, 24), (16, 13), (17, 4), (18, 19), (7, 14), (13, 6), (35, 21), (4, 12), (20, 31), (31, 2), (19, 21), (30, 24), (26, 1), (33, 22), (5, 24), (33, 26), (14, 26), (6, 6), (34, 28), (29, 3), (4, 25), (10, 0), (31, 15), (29, 11), (18, 14), (26, 21), (16, 15), (11, 11), (7, 10), (4, 0), (27, 15), (6, 9), (31, 23), (19, 31), (24, 7), (34, 24), (11, 17), (27, 5), (12, 1), (3, 18), (18, 12), (12, 16), (20, 26), (31, 8), (34, 23), (15, 22), (27, 31), (34, 21), (35, 27), (14, 24), (29, 6), (29, 27), (17, 6), (28, 25), (20, 6), (8, 21), (24, 21), (2, 29), (16, 17), (29, 0), (6, 29), (20, 14), (5, 14), (28, 29), (21, 11), (20, 21), (1, 19), (28, 20), (13, 26), (17, 21), (9, 23), (22, 15), (21, 0), (12, 21), (2, 13), (27, 25), (9, 3), (27, 23), (12, 11), (10, 1), (25, 5), (24, 16), (3, 0), (33, 14), (14, 9), (23, 21), (15, 2), (9, 27), (29, 9), (20, 10), (11, 6), (31, 30), (15, 1), (1, 21), (14, 20), (1, 0), (11, 18), (10, 16), (15, 16), (19, 3), (9, 24), (22, 0), (1, 27), (35, 12), (32, 14), (16, 28), (32, 2), (11, 2), (24, 18), (32, 10), (3, 30), (34, 25), (30, 19), (1, 13), (7, 4), (34, 20), (27, 21), (1, 12), (25, 25), (1, 10), (20, 20), (17, 28), (21, 30), (9, 12), (28, 15), (34, 9), (35, 18), (30, 31), (18, 10), (13, 11), (14, 21), (20, 16), (30, 5), (24, 14), (22, 10), (24, 9), (22, 12), (35, 2), (11, 12), (4, 7), (6, 2), (21, 25), (28, 19), (23, 16), (3, 1), (6, 17), (6, 8), (26, 14), (0, 27), (12, 7), (16, 30), (25, 4), (8, 15), (7, 5), (17, 24), (31, 13), (9, 6), (32, 16), (0, 6), (34, 2), (14, 19), (1, 3), (10, 8), (22, 23), (2, 7), (6, 28), (10, 15), (4, 13), (34, 17), (15, 24), (3, 25), (2, 16), (13, 28), (10, 11), (10, 9), (30, 16), (18, 9), (2, 2), (31, 11), (12, 0), (5, 12), (19, 14), (7, 23), (15, 5), (34, 4), (9, 26), (23, 6), (25, 26), (24, 28), (1, 29), (19, 29), (23, 13), (30, 22), (33, 18), (5, 8), (26, 19), (11, 23), (19, 12), (15, 28), (3, 16), (17, 14), (34, 6), (31, 20), (33, 0), (32, 6), (12, 19), (29, 18), (12, 14), (0, 17), (33, 23), (2, 5), (10, 25), (8, 25), (11, 8), (16, 31), (10, 31), (28, 5), (27, 20), (8, 12), (11, 30), (28, 23), (27, 22), (5, 1), (26, 6), (10, 26), (20, 5), (8, 4), (7, 29), (30, 21), (18, 26), (18, 0), (0, 8), (11, 20), (9, 17), (2, 9), (30, 29), (5, 30), (19, 7), (32, 22), (28, 7), (10, 10), (26, 7), (6, 15), (23, 26), (10, 22), (20, 25), (31, 25), (30, 15), (33, 11), (11, 14), (23, 9), (14, 27), (12, 8), (34, 10), (2, 11), (35, 15), (6, 24), (8, 3), (35, 11), (24, 5), (24, 31), (28, 1), (13, 21), (23, 8), (22, 3), (19, 28), (28, 24), (0, 7), (34, 19), (19, 13), (30, 12), (13, 12), (15, 31), (20, 15), (1, 28), (8, 1), (22, 21), (1, 4), (18, 7), (25, 28), (30, 28), (11, 27), (19, 2), (26, 31), (3, 7), (24, 23), (21, 20), (3, 2), (14, 12), (25, 15), (9, 18), (26, 17), (9, 11), (25, 6), (34, 5), (12, 31), (25, 30), (13, 1), (11, 10), (31, 14), (0, 31), (21, 16), (14, 30), (31, 6), (14, 2), (8, 2), (15, 21), (13, 17), (11, 28), (2, 31), (28, 18), (0, 24), (28, 30), (9, 21), (33, 7), (17, 12), (13, 14), (32, 12), (11, 15), (10, 20), (13, 2), (9, 4), (26, 11), (21, 9), (2, 6), (5, 9), (13, 25), (33, 31), (29, 24), (33, 3), (19, 11), (11, 0), (6, 30), (1, 11), (8, 22), (32, 24), (33, 15), (14, 3), (34, 16), (8, 0), (22, 29), (20, 0), (23, 12), (18, 13), (0, 23), (14, 10), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432540", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), 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), (18, 18), (22, 3), (0, 31), (26, 1), (19, 2), (9, 33), (10, 26), (27, 18), (26, 18), (6, 7), (14, 7), (18, 15), (24, 12), (31, 17), (20, 23), (30, 19), (29, 31), (2, 25), (5, 4), (2, 1), (0, 10), (3, 24), (24, 16), (17, 5), (1, 33), (10, 23), (18, 32), (30, 11), (28, 33), (0, 23), (8, 14), (5, 19), (1, 32), (11, 24), (31, 5), (21, 25), (8, 25), (25, 24), (25, 20), (2, 20), (28, 22), (8, 1), (14, 24), (10, 17), (21, 11), (25, 18), (5, 29), (19, 11), (23, 11), (26, 15), (30, 10), (25, 27), (24, 32), (12, 29), (31, 25), (8, 23), (12, 0), (13, 11), (10, 32), (3, 20), (5, 17), (8, 33), (17, 11), (19, 10), (22, 29), (1, 21), (20, 2), (29, 3), (16, 15), (15, 21), (6, 18), (24, 4), (0, 22), (12, 20), (24, 3), (24, 5), (22, 4), (21, 3), (9, 11), (12, 6), (23, 0), (17, 23), (0, 11), (18, 28), (12, 32), (27, 26), (6, 33), (29, 6), (25, 29), (18, 33), (10, 18), (0, 8), (4, 24), (21, 32), (16, 5), (20, 1), (25, 1), (28, 26), (14, 8), (11, 32), (13, 9), (20, 28), (13, 7), (15, 8), (31, 27), (23, 12), (18, 3), (31, 22), (18, 1), (24, 0), (29, 16), (27, 32), (28, 20), (13, 14), (2, 7), (23, 1), (25, 2), (8, 22), (19, 3), (3, 10), (16, 21), (3, 11), (3, 6), (16, 4), (9, 24), (5, 3), (23, 5), (16, 1), (1, 5), (25, 11), (11, 9), (8, 3), (9, 8), (20, 3), (9, 27), (26, 23), (6, 9), (5, 24), (2, 2), (21, 13), (19, 27), (18, 6), (15, 2), (20, 5), (3, 33), (24, 10), (27, 20), (7, 12), (23, 20), (29, 1), (17, 16), (28, 29), (31, 19), (2, 33), (22, 30), (26, 22), (14, 15), (29, 30), (27, 12), (13, 31), (9, 2), (23, 27), (19, 32), (26, 7), (5, 28), (11, 2), (28, 27), (4, 15), (15, 12), (25, 0), (2, 26), (26, 12), (15, 31), (28, 28), (3, 18), (12, 9), (13, 23), (27, 28), (31, 31), (23, 17), (4, 4), (4, 30), (8, 26), (31, 10), (5, 7), (31, 6), (1, 27), (23, 30), (5, 1), (18, 27), (13, 1), (13, 13), (18, 0), (4, 11), (12, 10), (31, 30), (14, 19), (5, 9), (25, 17), (28, 19), (22, 19), (29, 8), (15, 7), (1, 31), (14, 12), (11, 14), (13, 15), (6, 29), (10, 10), (8, 20), (2, 12), (5, 32), (2, 22), (17, 4), (20, 9), (24, 7), (25, 22), (13, 17), (4, 13), (16, 10), (31, 1), (15, 28), (27, 30), (14, 3), (29, 9), (24, 24), (21, 9), (3, 14), (5, 8), (8, 16), (14, 22), (10, 6), (8, 8), (12, 1), (12, 30), (0, 25), (4, 14), (5, 21), (22, 10), (5, 31), (13, 33), (30, 6), (12, 25), (19, 16), (5, 22), (26, 27), (6, 27), (5, 11), (17, 29), (31, 16), (8, 29), (9, 6), (29, 18), (5, 25), (27, 15), (26, 24), (27, 33), (10, 29), (23, 21), (15, 19), (12, 24), (26, 4), (27, 17), (20, 22), (27, 11), (7, 33), (9, 15), (11, 11), (27, 3), (6, 14), (31, 32), (12, 26), (7, 25), (7, 27), (8, 6), (26, 19), (25, 14), (29, 22), (31, 13), (19, 15), (24, 20), (23, 33), (1, 10), (24, 1), (14, 14), (26, 5), (5, 20), (25, 7), (4, 26), (1, 19), (15, 23), (28, 25), (11, 30), (14, 16), (24, 29), (20, 24), (15, 26), (10, 9), (9, 19), (6, 21), (30, 25), (10, 4), (2, 13), (0, 19), (25, 32), (27, 25), (11, 8), (7, 6), (18, 7), (17, 26), (30, 7), (27, 10), (29, 0), (17, 9), (10, 20), (1, 8), (13, 18), (9, 4), (0, 2), (21, 23), (6, 32), (15, 0), (6, 13), (11, 4), (7, 31), (2, 21), (14, 29), (15, 14), (25, 23), (13, 2), (2, 29), (4, 20), (24, 15), (15, 20), (8, 21), (22, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789912", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 28), (15, 5), (2, 35), (23, 5), (19, 21), (5, 11), (23, 12), (11, 24), (2, 32), (3, 35), (1, 21), (19, 23), (24, 26), (16, 10), (13, 28), (11, 12), (28, 4), (22, 22), (3, 21), (13, 26), (20, 20), (28, 17), (18, 16), (17, 36), (2, 15), (25, 10), (4, 12), (6, 11), (0, 17), (17, 2), (30, 24), (30, 18), (20, 8), (20, 16), (29, 7), (1, 32), (2, 28), (29, 36), (24, 3), (24, 27), (4, 26), (0, 25), (22, 26), (20, 24), (22, 30), (27, 23), (1, 22), (14, 14), (11, 37), (8, 38), (18, 36), (17, 23), (28, 14), (15, 25), (25, 35), (2, 10), (31, 15), (12, 5), (23, 23), (29, 6), (9, 16), (31, 34), (26, 31), (25, 13), (21, 33), (31, 14), (6, 32), (28, 10), (7, 22), (27, 30), (12, 9), (5, 27), (12, 34), (23, 28), (17, 4), (20, 10), (21, 15), (19, 24), (4, 11), (21, 16), (1, 36), (27, 2), (17, 3), (8, 32), (4, 27), (14, 1), (30, 16), (28, 1), (2, 2), (16, 31), (12, 37), (23, 32), (14, 17), (24, 9), (29, 0), (30, 9), (28, 8), (23, 25), (6, 6), (13, 12), (5, 21), (15, 7), (0, 24), (19, 20), (14, 7), (3, 16), (26, 10), (18, 7), (26, 23), (29, 29), (4, 16), (7, 31), (0, 30), (18, 24), (9, 1), (19, 31), (5, 16), (7, 13), (1, 27), (9, 25), (26, 6), (14, 10), (12, 35), (4, 28), (5, 25), (1, 1), (1, 20), (5, 4), (17, 24), (12, 12), (10, 24), (19, 8), (11, 20), (20, 32), (9, 9), (4, 36), (8, 35), (8, 6), (25, 14), (4, 7), (3, 12), (2, 1), (6, 35), (7, 8), (8, 0), (13, 27), (11, 19), (15, 33), (0, 31), (31, 7), (17, 10), (27, 26), (27, 8), (8, 7), (30, 14), (27, 16), (14, 34), (7, 16), (28, 28), (10, 25), (23, 13), (21, 34), (0, 14), (13, 6), (10, 34), (0, 12), (12, 26), (31, 30), (11, 22), (17, 35), (7, 33), (15, 18), (15, 23), (29, 35), (19, 13), (31, 5), (3, 24), (27, 37), (25, 1), (16, 17), (17, 30), (23, 29), (30, 13), (9, 13), (3, 36), (13, 32), (11, 7), (15, 19), (22, 1), (13, 8), (13, 20), (29, 24), (20, 11), (3, 15), (26, 26), (29, 31), (25, 31), (2, 27), (15, 38), (3, 32), (28, 21), (14, 4), (26, 3), (14, 30), (2, 33), (12, 16), (27, 20), (10, 3), (6, 22), (22, 13), (5, 7), (10, 8), (9, 28), (19, 12), (10, 2), (26, 7), (16, 7), (0, 28), (18, 6), (3, 8), (22, 32), (11, 32), (4, 37), (26, 25), (18, 8), (9, 27), (17, 9), (2, 22), (17, 19), (19, 32), (8, 19), (10, 36), (16, 27), (20, 21), (6, 1), (4, 3), (2, 36), (5, 23), (25, 28), (13, 36), (23, 0), (13, 30), (23, 35), (28, 24), (16, 11), (24, 38), (16, 22), (29, 21), (15, 4), (19, 11), (6, 14), (25, 33), (7, 37), (3, 28), (30, 35), (13, 22), (8, 3), (21, 8), (7, 5), (21, 4), (0, 32), (30, 28), (1, 7), (12, 20), (30, 7), (12, 27), (25, 21), (29, 22), (9, 24), (15, 35), (14, 33), (30, 12), (31, 23), (26, 32), (9, 0), (6, 30), (10, 11), (19, 27), (1, 37), (18, 17), (16, 18), (24, 33), (27, 19), (28, 19), (26, 18), (16, 32), (12, 29), (5, 24), (1, 35), (6, 10), (10, 20), (30, 5), (2, 24), (28, 22), (17, 26), (0, 16), (15, 2), (17, 12), (14, 35), (31, 10), (1, 38), (22, 9), (27, 28), (19, 36), (4, 25), (27, 10), (10, 33), (25, 8), (16, 28), (22, 19), (1, 29), (23, 27), (30, 29), (25, 11), (1, 28), (6, 3), (9, 18), (5, 29), (16, 23), (12, 7), (23, 31), (25, 20), (29, 9), (8, 24), (0, 6), (23, 20), (2, 31), (7, 25), (7, 35), (21, 25), (20, 28), (18, 32), (10, 19), (20, 33), (11, 34), (26, 15), (23, 37), (25, 12), (30, 37), (14, 26), (5, 14), (30, 6), (1, 11), (10, 35), (21, 35), (24, 21), (12, 2), (27, 11), (9, 37), (11, 10), (30, 10), (0, 36), (14, 22), (8, 25), (21, 29), (10, 15), (29, 34), (8, 29), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "778752", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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), (17, 29), (1, 35), (16, 10), (17, 9), (29, 37), (21, 17), (5, 24), (4, 5), (19, 1), (7, 12), (22, 20), (11, 16), (9, 21), (11, 13), (17, 4), (8, 1), (28, 4), (0, 28), (12, 34), (27, 8), (30, 13), (24, 14), (17, 12), (13, 36), (14, 21), (25, 22), (21, 28), (25, 21), (27, 1), (18, 14), (6, 14), (0, 9), (18, 8), (28, 36), (19, 33), (22, 26), (23, 32), (30, 16), (9, 14), (4, 18), (13, 23), (28, 13), (8, 14), (6, 8), (8, 23), (15, 24), (24, 6), (16, 2), (8, 12), (2, 26), (19, 28), (7, 20), (30, 23), (21, 19), (11, 7), (2, 15), (11, 32), (0, 24), (21, 8), (19, 27), (25, 14), (28, 14), (29, 31), (1, 16), (0, 3), (12, 30), (7, 27), (11, 23), (22, 1), (24, 0), (20, 35), (12, 0), (18, 26), (17, 36), (30, 6), (4, 31), (28, 18), (20, 33), (17, 16), (15, 17), (12, 22), (18, 17), (5, 15), (9, 29), (2, 13), (2, 24), (12, 35), (21, 36), (26, 19), (3, 32), (16, 9), (23, 8), (0, 8), (2, 25), (11, 25), (12, 20), (12, 24), (5, 35), (26, 7), (23, 18), (1, 36), (30, 4), (10, 3), (12, 16), (11, 19), (30, 26), (3, 24), (23, 37), (19, 11), (17, 17), (6, 9), (24, 24), (15, 19), (24, 22), (2, 21), (16, 4), (18, 20), (22, 12), (13, 18), (21, 34), (9, 4), (1, 3), (7, 30), (5, 20), (15, 8), (16, 27), (7, 16), (24, 11), (26, 27), (28, 11), (30, 8), (27, 14), (19, 6), (12, 9), (13, 5), (15, 12), (20, 10), (13, 3), (6, 5), (1, 27), (20, 5), (15, 21), (8, 3), (22, 27), (28, 0), (4, 32), (19, 14), (21, 6), (24, 25), (21, 37), (0, 17), (16, 12), (3, 10), (11, 10), (13, 24), (6, 10), (0, 30), (17, 1), (15, 11), (13, 31), (22, 21), (2, 9), (1, 25), (14, 29), (25, 18), (10, 27), (16, 35), (1, 18), (20, 34), (2, 8), (5, 29), (28, 25), (20, 19), (23, 15), (29, 3), (15, 25), (29, 8), (19, 3), (4, 4), (24, 20), (10, 24), (0, 23), (3, 7), (3, 12), (29, 4), (17, 10), (17, 20), (7, 36), (5, 26), (18, 13), (15, 35), (8, 30), (28, 28), (14, 19), (27, 29), (11, 14), (6, 28), (6, 29), (7, 17), (27, 15), (14, 18), (19, 5), (28, 1), (5, 3), (30, 5), (10, 4), (30, 30), (1, 5), (22, 32), (23, 21), (1, 11), (17, 11), (23, 16), (0, 11), (11, 11), (6, 37), (14, 32), (22, 19), (28, 26), (0, 4), (19, 25), (20, 12), (13, 27), (1, 31), (16, 17), (7, 32), (5, 14), (2, 35), (13, 8), (3, 6), (4, 27), (4, 29), (4, 15), (7, 9), (21, 22), (27, 36), (30, 3), (8, 37), (3, 1), (29, 13), (15, 2), (11, 33), (20, 37), (19, 37), (5, 33), (8, 27), (25, 5), (29, 35), (13, 7), (11, 24), (23, 0), (15, 15), (0, 10), (20, 22), (8, 26), (6, 0), (20, 1), (2, 10), (11, 26), (9, 3), (3, 36), (4, 2), (28, 7), (26, 34), (21, 27), (24, 31), (0, 7), (1, 15), (28, 15), (24, 17), (12, 6), (29, 23), (28, 21), (7, 25), (25, 24), (28, 29), (23, 26), (24, 4), (5, 13), (24, 2), (25, 17), (9, 34), (17, 31), (13, 28), (29, 30), (24, 23), (19, 2), (16, 37), (27, 13), (16, 18), (15, 14), (19, 4), (20, 28), (25, 10), (0, 14), (20, 24), (29, 6), (18, 33), (24, 21), (18, 3), (15, 31), (26, 37), (24, 3), (26, 16), (22, 2), (18, 24), (14, 10), (23, 13), (25, 30), (2, 14), (12, 5), (5, 12), (6, 24), (3, 20), (1, 20), (10, 5), (15, 16), (4, 1), (12, 37), (19, 30), (17, 14), (3, 34), (13, 35), (13, 30), (19, 12), (26, 15), (6, 32), (29, 17), (26, 31), (10, 19), (27, 6), (18, 7), (29, 34), (3, 19), (10, 8), (9, 36), (19, 0), (0, 21), (13, 10), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "974610", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (36, 21), (17, 13), (11, 10), (28, 36), (29, 16), (18, 22), (18, 29), (7, 12), (20, 27), (25, 20), (34, 27), (11, 3), (7, 36), (32, 19), (1, 22), (36, 2), (36, 7), (16, 9), (11, 31), (3, 15), (24, 24), (18, 9), (12, 5), (24, 29), (19, 26), (27, 31), (22, 38), (4, 37), (17, 8), (29, 0), (26, 16), (11, 14), (21, 21), (25, 30), (0, 31), (11, 25), (9, 1), (32, 34), (21, 33), (2, 12), (36, 6), (20, 4), (28, 16), (18, 37), (12, 29), (11, 30), (27, 19), (22, 1), (13, 25), (37, 30), (7, 33), (14, 27), (29, 26), (14, 10), (33, 18), (27, 24), (21, 18), (35, 38), (8, 19), (28, 2), (21, 24), (33, 13), (9, 29), (6, 33), (34, 32), (8, 0), (36, 5), (0, 38), (17, 12), (9, 2), (19, 10), (23, 0), (37, 3), (10, 22), (16, 36), (35, 29), (14, 15), (34, 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{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (26, 30), (3, 12), (9, 21), (1, 0), (9, 1), (5, 29), (10, 27), (5, 14), (24, 20), (24, 24), (6, 24), (26, 23), (22, 2), (11, 29), (3, 29), (0, 17), (20, 9), (2, 30), (25, 11), (9, 16), (25, 9), (17, 0), (13, 19), (2, 18), (2, 26), (26, 24), (24, 12), (19, 12), (0, 9), (1, 3), (18, 20), (7, 9), (7, 17), (7, 20), (1, 25), (6, 28), (15, 27), (13, 30), (7, 5), (15, 4), (4, 27), (3, 20), (30, 17), (6, 4), (11, 4), (19, 5), (17, 24), (22, 12), (9, 6), (8, 25), (28, 20), (9, 17), (27, 3), (13, 21), (14, 7), (4, 22), (5, 4), (22, 17), (12, 18), (4, 16), (30, 24), (4, 28), (12, 9), (10, 7), (5, 5), (10, 13), (10, 5), (29, 9), (16, 28), (17, 3), (3, 19), (12, 22), (29, 3), (11, 27), (18, 13), (19, 29), (20, 0), (14, 24), (15, 9), (25, 12), (21, 21), (28, 9), (0, 25), (12, 17), (1, 24), (19, 0), (4, 4), (3, 14), (4, 1), (17, 25), (1, 2), (11, 8), (29, 28), (6, 16), (20, 22), (2, 14), (29, 5), (3, 15), (23, 0), (6, 23), (0, 16), (26, 12), (14, 25), (29, 25), (5, 25), (3, 7), (24, 2), (30, 10), (1, 28), (21, 25), (13, 12), (17, 8), (9, 9), (16, 12), (29, 12), (1, 27), (18, 17), (27, 0), (30, 20), (24, 28), (23, 29), (2, 8), (17, 9), (4, 25), (29, 8), (17, 5), (7, 4), (27, 10), (21, 14), (12, 0), (23, 10), (21, 24), (3, 21), (13, 26), (9, 14), (16, 10), (2, 22), (1, 10), (17, 11), (21, 3), (0, 30), (12, 3), (20, 6), (1, 7), (22, 30), (14, 6), (29, 30), (2, 6), (29, 7), (26, 18), (0, 12), (4, 2), (14, 28), (1, 6), (14, 13), (3, 2), (13, 11), (5, 19), (29, 17), (23, 20), (14, 9), (30, 12), (9, 20), (28, 3), (24, 8), (3, 0), (28, 22), (26, 27), (4, 9), (17, 6), (23, 30), (20, 15), (13, 27), (25, 16), (26, 0), (24, 10), (20, 29), (18, 7), (26, 4), (24, 4), (29, 13), (0, 29), (24, 29), (11, 17), (26, 22), (19, 3), (10, 8), (16, 20), (28, 1), (24, 16), (28, 5), (26, 28), (23, 16), (9, 3), (4, 6), (16, 14), (27, 18), (10, 11), (13, 1), (26, 19), (29, 1), (13, 2), (17, 10), (20, 26), (20, 27), (22, 5), (18, 3), (29, 26), (24, 26), (3, 9), (29, 16), (22, 14), (17, 26), (4, 21), (3, 27), (8, 11), (26, 20), (10, 24), (2, 9), (21, 0), (6, 13), (3, 16), (16, 6), (29, 10), (25, 8), (30, 27), (26, 11), (4, 29), (20, 3), (19, 11), (14, 27), (17, 29), (26, 2), (16, 1), (0, 26), (26, 29), (4, 15), (28, 28), (17, 27), (16, 21), (15, 3), (4, 19), (10, 1), (30, 25), (9, 26), (3, 22), (16, 27), (8, 24), (2, 27), (9, 7), (22, 22), (24, 6), (7, 8), (23, 5), (16, 30), (19, 30), (2, 29), (16, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "817058", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 29), (3, 12), (21, 28), (0, 1), (12, 23), (1, 20), (2, 24), (4, 4), (16, 23), (9, 16), (1, 18), (20, 2), (10, 18), (27, 26), (5, 6), (18, 28), (8, 7), (27, 22), (11, 15), (28, 9), (12, 17), (26, 7), (23, 27), (28, 8), (30, 21), (1, 19), (3, 27), (18, 4), (18, 24), (4, 2), (7, 24), (21, 15), (7, 8), (3, 18), (28, 3), (12, 9), (10, 24), (3, 20), (23, 29), (4, 5), (22, 21), (5, 9), (18, 17), (26, 5), (25, 4), (29, 15), (12, 27), (11, 8), (23, 8), (30, 16), (6, 1), (13, 11), (19, 15), (23, 4), (2, 12), (25, 9), (18, 0), (3, 14), (10, 14), (0, 4), (25, 15), (15, 27), (19, 25), (5, 15), (20, 16), (6, 17), (29, 6), (8, 26), (2, 15), (17, 13), (20, 1), (17, 11), (8, 2), (1, 5), (5, 18), (3, 15), (9, 14), (28, 14), (3, 2), (25, 11), (22, 25), (28, 27), (0, 21), (16, 19), (17, 2), (23, 15), (23, 30), (25, 18), (13, 28), (22, 27), (14, 16), (13, 3), (8, 17), (5, 0), (20, 0), (20, 29), (21, 27), (6, 24), (18, 29), (29, 17), (18, 21), (17, 8), (11, 0), (10, 5), (26, 18), (26, 17), (16, 26), (16, 11), (30, 8), (7, 30), (10, 27), (16, 29), (28, 6), (16, 24), (25, 10), (15, 28), (20, 30), (14, 2), (20, 8), (21, 2), (16, 1), (14, 5), (8, 10), (29, 11), (15, 2), (26, 24), (22, 5), (3, 26), (19, 11), (23, 2), (21, 22), (14, 9), (21, 23), (12, 8), (6, 2), (6, 28), (1, 16), (5, 5), (27, 10), (13, 9), (21, 16), (19, 29), (15, 30), (22, 7), (1, 24), (2, 2), (22, 26), (8, 1), (9, 22), (12, 16), (9, 0), (2, 7), (0, 27), (9, 30), (22, 10), (10, 17), (2, 5), (15, 23), (28, 18), (25, 24), (20, 3), (16, 6), (3, 24), (14, 4), (13, 29), (5, 16), (27, 8), (12, 1), (23, 14), (7, 4), (22, 30), (5, 21), (6, 18), (7, 23), (26, 16), (12, 28), (30, 13), (29, 3), (19, 20), (8, 25), (18, 26), (7, 19), (0, 16), (10, 1), (27, 20), (15, 5), (13, 2), (17, 24), (6, 19), (13, 18), (12, 15), (29, 4), (16, 4), (30, 24), (7, 10), (2, 4), (17, 4), (1, 23), (10, 21), (16, 9), (14, 15), (9, 18), (23, 1), (6, 13), (25, 19), (4, 25), (12, 29), (17, 16), (12, 20), (24, 9), (11, 14), (30, 19), (30, 1), (1, 15), (6, 3), (14, 14), (27, 15), (23, 11), (8, 5), (30, 29), (2, 18), (27, 21), (21, 4), (18, 27), (14, 24), (13, 1), (22, 18), (25, 1), (30, 7), (4, 13), (2, 22), (3, 13), (20, 4), (27, 12), (26, 28), (6, 27), (17, 26), (11, 6), (17, 19), (24, 4), (3, 1), (12, 22), (22, 23), (0, 25), (29, 7), (27, 29), (7, 26), (19, 7), (6, 12), (9, 3), (26, 23), (25, 16), (14, 26), (19, 27), (28, 29), (16, 10), (22, 16), (27, 24), (11, 17), (7, 22), (3, 5), (19, 4), (21, 19), (30, 23), (29, 5), (11, 28), (0, 14), (1, 30), (6, 0), (13, 26), (17, 7), (27, 6), (20, 22), (9, 9), (22, 12), (14, 20), (18, 5), (4, 21), (0, 30), (21, 10), (29, 1), (7, 16), (14, 25), (11, 29), (20, 18), (9, 15), (11, 19), (25, 13), (1, 3), (22, 22), (27, 3), (14, 30), (13, 8), (5, 20), (13, 24), (24, 1), (2, 17), (22, 9), (15, 17), (7, 2), (9, 8), (7, 25), (26, 3), (11, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744452", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (27, 0), (12, 2), (15, 5), (7, 13), (3, 6), (2, 7), (9, 11), (10, 0), (27, 24), (12, 1), (13, 7), (0, 1), (17, 10), (13, 25), (20, 12), (20, 7), (15, 17), (29, 0), (29, 8), (27, 8), (27, 25), (17, 4), (22, 26), (24, 1), (17, 21), (11, 3), (2, 23), (24, 22), (6, 18), (3, 14), (6, 3), (16, 6), (10, 2), (27, 2), (6, 5), (4, 0), (25, 27), (14, 10), (30, 15), (18, 9), (19, 2), (28, 7), (0, 12), (3, 12), (25, 16), (20, 27), (1, 18), (16, 0), (15, 27), (13, 6), (31, 7), (19, 16), (30, 13), (2, 25), (4, 7), (11, 29), (1, 5), (16, 23), (24, 9), (7, 9), (19, 24), (17, 13), (26, 15), (2, 14), (0, 27), (13, 29), (15, 24), (7, 21), (31, 27), (29, 17), (5, 16), (8, 19), (21, 4), (15, 20), (25, 7), (17, 3), (25, 5), (11, 6), (21, 5), (11, 19), (17, 17), (6, 22), (1, 14), (30, 8), (1, 29), (20, 1), (6, 7), (26, 3), (21, 17), (3, 7), (1, 1), (16, 5), (6, 29), (31, 14), (22, 11), (0, 29), (6, 13), (20, 17), (12, 18), (11, 24), (16, 10), (29, 20), (13, 14), (4, 28), (30, 5), (28, 8), (29, 5), (7, 3), (26, 21), (27, 12), (13, 26), (8, 27), (21, 14), (10, 7), (21, 25), (0, 6), (5, 22), (9, 21), (23, 16), (21, 16), (24, 18), (1, 10), (4, 3), (10, 26), (11, 22), (15, 4), (7, 15), (3, 18), (14, 14), (26, 0), (21, 29), (8, 5), (18, 10), (17, 23), (11, 23), (2, 6), (16, 8), (29, 22), (2, 16), (1, 7), (16, 11), (11, 0), (10, 22), (12, 13), (2, 28), (1, 2), (25, 21), (25, 26), (31, 0), (23, 9), (7, 6), (10, 6), (15, 25), (28, 18), (26, 23), (16, 22), (5, 0), (8, 23), (18, 17), (22, 9), (20, 5), (8, 7), (8, 0), (11, 1), (16, 15), (26, 27), (24, 28), (14, 6), (28, 2), (17, 2), (25, 3), (9, 19), (6, 14), (28, 24), (15, 8), (17, 9), (3, 25), (22, 15), (14, 23), (21, 9), (3, 27), (31, 4), (13, 9), (5, 5), (23, 22), (9, 16), (0, 5), (18, 14), (3, 13), (6, 17), (9, 4), (29, 11), (3, 10), (27, 20), (24, 4), (8, 13), (15, 22), (28, 6), (9, 1), (27, 1), (30, 19), (14, 1), (24, 2), (2, 5), (13, 18), (29, 26), (18, 21), (30, 20), (4, 8), (0, 24), (17, 29), (29, 19), (12, 6), (10, 12), (28, 29), (12, 21), (21, 11), (29, 3), (10, 25), (29, 12), (22, 20), (19, 14), (6, 26), (19, 15), (30, 6), (11, 14), (7, 0), (21, 21), (0, 13), (16, 28), (2, 26), (25, 1), (1, 17), (7, 25), (29, 6), (18, 23), (9, 25), (11, 4), (5, 14), (29, 29), (5, 20), (11, 8), (13, 12), (7, 20), (14, 27), (22, 2), (15, 14), (25, 18), (21, 18), (3, 20), (8, 10), (9, 7), (11, 11), (25, 15), (15, 10), (8, 22), (4, 13), (24, 20), (18, 26), (14, 16), (11, 16), (10, 9), (23, 17), (6, 20), (25, 17), (4, 17), (8, 3), (27, 17), (14, 5), (11, 25), (15, 28), (17, 7), (0, 14), (30, 16), (24, 3), (7, 22), (31, 16), (12, 9), (1, 11), (16, 24), (23, 3), (7, 28), (19, 12), (20, 11), (19, 4), (19, 22), (24, 15), (9, 26), (13, 22), (20, 16), (10, 3), (7, 23), (25, 28), (25, 25), (8, 18), (23, 20), (3, 11), (14, 17), (19, 6), (25, 8), (23, 25), (24, 6), (30, 26), (4, 4), (20, 2), (1, 13), (20, 26), (4, 1), (3, 15), (27, 3), (17, 5), (22, 8), (31, 5), (0, 9), (25, 4), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658350", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 16), (11, 13), (27, 19), (6, 9), (15, 10), (13, 24), (20, 4), (30, 21), (21, 33), (22, 10), (24, 33), (22, 36), (25, 26), (0, 9), (26, 1), (29, 7), (14, 0), (28, 2), (15, 7), (11, 15), (26, 19), (11, 19), (32, 9), (7, 10), (31, 10), (24, 20), (12, 28), (10, 13), (11, 30), (12, 27), (22, 2), (26, 18), (32, 33), (3, 19), (8, 14), (8, 19), (18, 18), (20, 14), (10, 4), (15, 34), (24, 28), (15, 35), (33, 35), (17, 8), (26, 2), (11, 12), (32, 31), (18, 11), (29, 33), (11, 25), (8, 30), (8, 20), (15, 23), (11, 32), (20, 11), (1, 8), (24, 13), (25, 33), (21, 22), (26, 8), (25, 35), (20, 22), (13, 2), (4, 36), (30, 18), (9, 22), (29, 6), (12, 30), (30, 27), (17, 32), (6, 12), (32, 2), (14, 5), (17, 25), (0, 18), (33, 19), (1, 1), (32, 6), (23, 33), (22, 7), (15, 19), (26, 34), (3, 2), (25, 10), (5, 14), (24, 11), (14, 18), (11, 8), (12, 13), (23, 28), (32, 10), (15, 20), (6, 25), (7, 19), (25, 11), (23, 24), (25, 12), (26, 5), (1, 10), (23, 15), (23, 34), (19, 34), (24, 14), (17, 31), (10, 35), (18, 4), (29, 0), (14, 21), (18, 21), (5, 18), (19, 16), (3, 24), (26, 6), (31, 12), (4, 2), (21, 10), (1, 17), (28, 7), (15, 2), (7, 35), (26, 3), (14, 32), (24, 19), (23, 18), (7, 12), (22, 35), (31, 9), (10, 10), (17, 13), (11, 26), (31, 24), (33, 25), (14, 23), (18, 16), (6, 4), (0, 5), (19, 11), (18, 0), (28, 4), (8, 15), (10, 34), (4, 35), (20, 1), (18, 2), (26, 31), (5, 2), (25, 29), (21, 4), (14, 35), (24, 21), (21, 28), (13, 32), (1, 29), (6, 32), (29, 12), (0, 3), (33, 33), (27, 34), (20, 29), (16, 34), (5, 29), (13, 20), (0, 2), (30, 14), (22, 28), (24, 17), (25, 17), (25, 25), (6, 29), (20, 2), (21, 21), (30, 8), (2, 23), (14, 15), (9, 11), (21, 27), (11, 24), (13, 31), (5, 13), (29, 9), (15, 3), (31, 16), (12, 20), (18, 1), (26, 23), (22, 30), (10, 16), (14, 29), (27, 20), (1, 34), (2, 26), (17, 4), (0, 36), (33, 20), (23, 8), (4, 28), (3, 30), (22, 27), (15, 5), (12, 11), (30, 11), (19, 26), (30, 9), (23, 10), (1, 13), (8, 28), (22, 22), (2, 24), (7, 32), (18, 25), (2, 25), (33, 2), (6, 15), (13, 7), (11, 14), (1, 35), (30, 26), (7, 36), (4, 18), (26, 17), (6, 18), (24, 2), (3, 0), (13, 6), (20, 20), (23, 32), (23, 6), (7, 2), (9, 6), (17, 0), (30, 19), (28, 12), (29, 34), (9, 9), (4, 12), (16, 28), (7, 20), (16, 14), (29, 24), (31, 31), (9, 23), (24, 3), (5, 22), (18, 12), (15, 18), (2, 34), (32, 32), (10, 27), (18, 27), (23, 14), (11, 35), (29, 16), (18, 29), (28, 35), (23, 22), (25, 23), (9, 27), (30, 3), (15, 14), (18, 13), (7, 6), (23, 35), (20, 9), (8, 25), (12, 19), (14, 34), (0, 12), (32, 24), (9, 28), (17, 24), (2, 29), (32, 11), (9, 13), (33, 3), (22, 0), (19, 1), (8, 35), (22, 24), (19, 36), (22, 12), (16, 18), (27, 23), (23, 27), (28, 1), (7, 3), (31, 33), (8, 10), (27, 4), (27, 8), (18, 26), (1, 32), (26, 4), (25, 14), (26, 21), (27, 16), (24, 1), (3, 11), (25, 19), (5, 16), (2, 8), (7, 11), (13, 16), (17, 3), (4, 14), (11, 17), (30, 15), (16, 24), (16, 1), (8, 33), (26, 33), (15, 11), (0, 20), (25, 21), (16, 20), (31, 18), (14, 6), (24, 22), (21, 17), (4, 0), (22, 4), (18, 20), (17, 33), (26, 24), (3, 9), (22, 26), (26, 29), (5, 33), (21, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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), (25, 12), (28, 4), (10, 9), (8, 15), (7, 21), (4, 23), (5, 16), (3, 20), (13, 17), (24, 16), (17, 36), (23, 10), (2, 27), (21, 5), (18, 5), (8, 1), (18, 29), (15, 16), (0, 18), (4, 17), (11, 36), (3, 31), (5, 19), (7, 17), (26, 29), (29, 31), (28, 22), (24, 32), (0, 29), (29, 33), (30, 22), (14, 38), (4, 32), (9, 38), (20, 13), (21, 38), (5, 26), (26, 18), (23, 1), (13, 24), (30, 23), (20, 10), (14, 28), (10, 28), (0, 16), (20, 21), (24, 34), (9, 28), (27, 14), (7, 4), (2, 37), (0, 26), (24, 27), (1, 36), (18, 1), (24, 18), (3, 21), (15, 9), (21, 33), (5, 4), (15, 29), (17, 13), (16, 21), (2, 19), (8, 5), (17, 6), (28, 38), (15, 0), (19, 27), (3, 24), (11, 6), (4, 19), (28, 28), (30, 28), (21, 8), (5, 1), (12, 35), (26, 9), (16, 12), (2, 12), (23, 36), (23, 14), (17, 3), (14, 32), (29, 19), (29, 1), (24, 5), (7, 29), (22, 23), (8, 30), (8, 29), (22, 10), (5, 21), (10, 38), (13, 32), (28, 13), (26, 15), (30, 30), (20, 38), (20, 20), (21, 23), (14, 34), (21, 12), (10, 6), (6, 22), (4, 29), (9, 34), (9, 15), (6, 31), (17, 0), (8, 28), (12, 6), (9, 17), (8, 26), (30, 3), (0, 32), (19, 31), (9, 5), (6, 33), (1, 24), (21, 9), (10, 23), (16, 28), (21, 6), (27, 2), (30, 5), (12, 20), (28, 3), (15, 38), (17, 30), (3, 23), (28, 1), (27, 13), (20, 29), (25, 24), (10, 19), (23, 0), (25, 26), (9, 37), (13, 10), (21, 32), (1, 1), (0, 36), (21, 7), (29, 9), (1, 17), (8, 24), (24, 2), (26, 16), (27, 36), (19, 25), (21, 26), (30, 11), (3, 7), (30, 13), (27, 29), (29, 10), (13, 11), (18, 4), (20, 36), (20, 15), (2, 1), (19, 33), (21, 36), (12, 5), (1, 18), (12, 24), (22, 35), (12, 23), (27, 38), (26, 5), (0, 12), (5, 35), (9, 13), (10, 37), (19, 36), (10, 15), (3, 36), (5, 25), (18, 27), (2, 11), (4, 21), (20, 2), (25, 35), (22, 9), (30, 31), (23, 35), (24, 21), (18, 34), (25, 32), (22, 16), (6, 12), (4, 28), (10, 30), (15, 14), (30, 26), (16, 35), (20, 23), (4, 10), (10, 0), (26, 4), (21, 16), (13, 33), (1, 38), (8, 22), (17, 4), (28, 37), (27, 9), (0, 23), (25, 15), (8, 12), (12, 19), (14, 36), (30, 32), (29, 35), (7, 37), (10, 20), (16, 8), (17, 24), (24, 3), (1, 31), (14, 1), (13, 29), (26, 17), (7, 32), (19, 13), (23, 28), (10, 27), (13, 26), (13, 30), (17, 34), (22, 0), (20, 9), (23, 13), (22, 12), (24, 23), (10, 35), (25, 36), (6, 24), (26, 19), (14, 9), (17, 35), (0, 17), (3, 25), (5, 37), (30, 4), (22, 7), (17, 28), (28, 12), (3, 34), (8, 14), (15, 8), (14, 29), (23, 7), (15, 17), (8, 2), (18, 38), (28, 15), (29, 26), (29, 34), (7, 28), (15, 12), (27, 30), (2, 3), (12, 7), (20, 8), (24, 37), (19, 19), (19, 30), (2, 7), (1, 2), (17, 12), (15, 19), (6, 36), (18, 35), (13, 28), (7, 30), (24, 1), (20, 22), (0, 8), (5, 20), (6, 9), (26, 13), (2, 25), (8, 6), (5, 2), (16, 2), (11, 21), (6, 14), (26, 12), (14, 7), (13, 31), (0, 24), (23, 11), (0, 21), (30, 19), (8, 4), (2, 8), (5, 34), (18, 19), (28, 24), (21, 4), (0, 2), (6, 13), (27, 16), (24, 38), (22, 30), (25, 1), (21, 18), (6, 17), (6, 18), (16, 32), (25, 4), (0, 27), (23, 27), (22, 1), (14, 25), (21, 24), (26, 35), (12, 31), (16, 36), (18, 22), (30, 34), (2, 21), (27, 6), (4, 16), (13, 4), (2, 26), (1, 22), (18, 7), (2, 32), (20, 27), (6, 19), (1, 33), (18, 13), (5, 33), (24, 15), (3, 30), (14, 21), (13, 18), (23, 33), (13, 22), (16, 19), (2, 30), (13, 36), (4, 9), (29, 22), (14, 37), (10, 12), (28, 19), (28, 31), (2, 4), (30, 8), (0, 5), (5, 30), (13, 16), (8, 35), (16, 20), (12, 30), (26, 33), (16, 26), (29, 24), (29, 14), (1, 12), (12, 9), (10, 17), (25, 13), (4, 15), (29, 38), (25, 34), (18, 15), (7, 7), (11, 13), (30, 2), (12, 3), (21, 22), (20, 31), (25, 37), (7, 9), (14, 23), (13, 3), (23, 32), (20, 0), (23, 20), (4, 27), (16, 10), (19, 17), (19, 10), (0, 30), (8, 27), (18, 21), (25, 14), (22, 11), (21, 0), (24, 35), (25, 0), (27, 34), (11, 33), (21, 27), (17, 23), (26, 10), (20, 12), (11, 11), (3, 38), (4, 14), (24, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485160", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 14), (25, 3), (5, 30), (29, 1), (0, 6), (15, 34), (17, 29), (5, 23), (38, 28), (12, 20), (29, 31), (0, 36), (29, 9), (6, 15), (22, 20), (20, 1), (13, 8), (38, 0), (15, 32), (34, 27), (21, 22), (4, 20), (36, 6), (6, 34), (14, 25), (21, 0), (20, 13), (31, 35), (38, 20), (1, 36), (9, 8), (35, 14), (34, 34), (37, 17), (19, 23), (33, 18), (34, 31), (36, 31), (37, 24), (17, 11), (38, 15), (26, 12), (20, 12), (29, 5), (3, 29), (1, 14), (16, 8), (20, 11), (2, 38), (2, 26), (0, 29), (27, 5), (25, 5), (6, 35), (18, 9), (29, 34), (12, 25), (31, 8), (19, 13), (34, 8), (9, 14), (5, 19), (19, 29), (30, 27), (32, 34), (0, 18), (15, 31), (20, 24), (7, 10), (23, 38), (2, 0), (22, 13), (4, 21), (38, 25), (10, 27), (21, 18), (7, 13), (2, 7), (9, 38), (22, 38), (17, 18), (1, 20), (18, 15), (19, 9), (17, 19), (8, 8), (16, 31), (8, 11), (32, 1), (17, 3), (32, 30), (29, 8), (31, 28), (30, 15), (5, 13), (14, 14), (22, 11), (14, 15), (32, 31), (9, 28), (20, 19), (30, 25), (18, 2), (16, 6), (21, 11), (35, 17), (31, 2), (23, 15), (10, 33), (38, 18), (24, 19), (17, 32), (20, 22), (7, 11), (18, 17), (9, 17), (18, 8), (23, 35), (24, 0), (15, 22), (11, 1), (20, 34), (11, 31), (5, 34), (35, 37), (24, 28), (26, 28), (26, 14), (20, 27), (15, 14), (33, 1), (30, 31), (23, 4), (33, 35), (7, 20), (11, 26), (29, 24), (7, 24), (32, 12), (20, 10), (12, 12), (38, 12), (33, 15), (38, 11), (22, 37), (33, 20), (37, 19), (22, 22), (34, 19), (26, 26), (28, 31), (37, 26), (35, 27), (19, 6), (0, 8), (35, 38), (16, 28), (0, 13), (11, 14), (9, 29), (15, 25), (5, 12), (11, 21), (31, 15), (29, 6), (20, 2), (31, 24), (6, 4), (14, 33), (27, 33), (11, 9), (20, 26), (22, 31), (11, 2), (2, 31), (35, 6), (23, 3), (5, 16), (33, 29), (8, 13), (6, 16), (6, 3), (36, 37), (23, 11), (24, 9), (28, 8), (27, 31), (21, 2), (16, 27), (34, 2), (21, 25), (6, 25), (25, 13), (31, 38), (4, 3), (12, 24), (14, 18), (4, 15), (18, 28), (27, 10), (29, 25), (37, 13), (33, 26), (14, 9), (30, 8), (5, 32), (18, 38), (5, 10), (29, 12), (28, 38), (25, 1), (21, 10), (35, 4), (13, 20), (5, 15), (19, 19), (36, 22), (29, 33), (22, 2), (6, 17), (8, 3), (1, 6), (28, 12), (31, 22), (20, 28), (36, 29), (26, 25), (25, 4), (0, 30), (19, 20), (4, 35), (7, 35), (27, 23), (15, 0), (5, 7), (2, 16), (6, 8), (28, 22), (29, 13), (32, 8), (23, 6), (16, 35), (2, 2), (24, 35), (2, 12), (22, 16), (4, 23), (22, 19), (20, 7), (35, 8), (35, 11), (21, 36), (36, 9), (30, 38), (35, 7), (22, 33), (6, 9), (27, 0), (5, 35), (26, 37), (37, 23), (20, 32), (22, 9), (3, 3), (34, 11), (8, 25), (36, 15), (17, 14), (14, 23), (27, 26), (22, 36), (30, 14), (27, 16), (2, 11), (36, 34), (5, 25), (7, 27), (17, 1), (21, 9), (13, 22), (27, 20), (17, 33), (5, 17), (20, 14), (31, 37), (4, 27), (15, 33), (25, 23), (2, 25), (29, 23), (30, 33), (28, 32), (25, 19), (20, 29), (32, 25), (26, 4), (22, 15), (23, 2), (16, 11), (29, 20), (4, 7), (17, 8), (8, 10), (1, 3), (10, 28), (3, 19), (25, 17), (37, 21), (12, 37), (10, 9), (31, 10), (22, 25), (19, 10), (37, 20), (1, 4), (10, 17), (14, 29), (8, 22), (35, 15), (33, 17), (7, 8), (30, 22), (25, 27), (28, 17), (6, 36), (33, 0), (14, 36), (17, 9), (18, 34), (3, 31), (11, 30), (2, 22), (35, 28), (35, 35), (11, 36), (10, 6), (22, 29), (27, 3), (32, 33), (3, 34), (23, 21), (35, 23), (23, 25), (31, 11), (4, 34), (20, 25), (28, 23), (15, 27), (32, 3), (25, 35), (24, 4), (24, 31), (27, 14), (12, 5), (21, 33), (16, 5), (3, 9), (15, 7), (30, 26), (22, 6), (26, 16), (9, 18), (10, 22), (8, 35), (1, 1), (26, 5), (1, 26), (1, 15), (34, 16), (13, 4), (9, 35), (4, 28), (21, 34), (23, 9), (13, 15), (18, 19), (21, 4), (3, 16), (8, 24), (28, 6), (2, 30), (22, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "597492", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 14), (22, 10), (18, 12), (4, 16), (24, 29), (20, 24), (30, 3), (12, 5), (18, 18), (20, 2), (5, 22), (28, 13), (4, 28), (7, 17), (24, 11), (29, 3), (24, 18), (21, 28), (16, 25), (5, 24), (20, 5), (18, 10), (6, 26), (19, 22), (30, 11), (4, 13), (25, 21), (9, 26), (18, 21), (17, 27), (7, 5), (13, 23), (2, 24), (3, 24), (28, 6), (8, 9), (14, 8), (32, 20), (26, 16), (5, 25), (12, 15), (24, 1), (2, 11), (29, 12), (1, 9), (24, 14), (31, 25), (12, 28), (4, 2), (23, 25), (22, 25), (32, 14), (10, 0), (2, 28), (7, 22), (18, 17), (27, 9), (11, 10), (21, 2), (18, 7), (8, 14), (29, 30), (32, 15), (25, 29), (26, 23), (0, 6), (27, 25), (33, 27), (35, 26), (11, 4), (6, 22), (0, 17), (19, 3), (13, 18), (14, 9), (32, 5), (15, 13), (20, 22), (27, 6), (8, 5), (10, 16), (11, 6), (17, 28), (8, 28), (11, 12), (14, 4), (26, 8), (33, 19), (19, 21), (3, 16), (14, 15), (13, 1), (22, 1), (12, 14), (7, 29), (23, 19), (9, 15), (20, 28), (19, 19), (5, 0), (29, 18), (23, 13), (8, 20), (5, 23), (26, 5), (21, 9), (5, 4), (28, 12), (13, 26), (25, 30), (32, 24), (24, 26), (5, 7), (8, 6), (28, 11), (16, 9), (11, 18), (29, 26), (7, 9), (8, 19), (3, 21), (34, 22), (33, 16), (1, 27), (34, 2), (17, 0), (35, 21), (35, 15), (0, 26), (29, 1), (5, 18), (27, 4), (4, 15), (31, 23), (31, 16), (0, 19), (14, 3), (4, 27), (34, 14), (10, 1), (34, 13), (2, 4), (22, 24), (28, 26), (35, 10), (10, 18), (16, 26), (14, 19), (22, 4), (30, 22), (14, 12), (23, 17), (17, 20), (14, 27), (10, 9), (3, 19), (0, 16), (16, 18), (24, 23), (1, 6), (29, 28), (31, 21), (6, 27), (7, 13), (10, 3), (31, 6), (23, 8), (11, 5), (13, 6), (35, 7), (20, 8), (13, 14), (35, 28), (30, 24), (3, 3), (1, 30), (23, 22), (1, 26), (1, 5), (25, 25), (14, 30), (26, 17), (18, 15), (34, 26), (9, 21), (16, 24), (16, 14), (5, 27), (21, 5), (35, 4), (1, 14), (12, 29), (8, 26), (28, 2), (26, 0), (5, 21), (26, 29), (9, 27), (11, 11), (30, 14), (24, 17), (1, 28), (2, 26), (35, 27), (7, 14), (32, 22), (26, 25), (6, 2), (18, 23), (1, 22), (23, 15), (11, 26), (13, 20), (20, 21), (2, 16), (14, 28), (18, 11), (17, 10), (27, 21), (6, 13), (12, 30), (8, 24), (4, 6), (11, 15), (29, 21), (18, 24), (12, 18), (24, 3), (16, 22), (24, 10), (6, 11), (8, 16), (14, 14), (21, 7), (15, 6), (1, 20), (13, 12), (23, 10), (19, 10), (16, 17), (14, 2), (34, 17), (30, 25), (17, 11), (32, 25), (12, 7), (7, 6), (24, 9), (25, 4), (35, 24), (12, 4), (3, 28), (6, 19), (26, 19), (16, 2), (6, 15), (26, 20), (7, 28), (24, 8), (29, 17), (14, 22), (16, 23), (9, 12), (30, 29), (6, 0), (17, 22), (28, 24), (7, 20), (5, 15), (16, 4), (25, 11), (9, 13), (4, 8), (13, 10), (3, 0), (24, 5), (33, 7), (0, 14), (0, 29), (2, 21), (7, 16), (20, 26), (19, 12), (27, 15), (19, 14), (18, 0), (22, 9), (17, 19), (30, 17), (9, 9), (12, 8), (2, 3), (8, 27), (24, 28), (5, 6), (31, 28), (29, 13), (3, 18), (0, 15), (11, 19), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404595", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (10, 15), (11, 8), (0, 16), (25, 5), (16, 8), (16, 2), (0, 25), (29, 3), (21, 0), (7, 24), (24, 21), (8, 7), (0, 31), (2, 24), (28, 30), (9, 21), (4, 14), (8, 21), (19, 18), (19, 24), (20, 8), (6, 30), (21, 22), (16, 7), (26, 4), (0, 13), (0, 11), (16, 25), (10, 31), (22, 1), (9, 11), (20, 1), (27, 11), (8, 3), (27, 1), (28, 6), (4, 28), (5, 24), (3, 4), (18, 7), (23, 29), (17, 19), (1, 3), (16, 17), (24, 27), (28, 7), (27, 26), (25, 1), (18, 3), (11, 12), (12, 5), (8, 22), (16, 5), (11, 21), (6, 11), (19, 12), (27, 8), (1, 15), (9, 23), (28, 0), (21, 8), (6, 5), (9, 1), (8, 29), (24, 25), (7, 31), (14, 14), (29, 18), (8, 11), (13, 19), (2, 26), (1, 24), (8, 16), (13, 9), (15, 22), (18, 11), (25, 12), (7, 8), (4, 10), (6, 0), (9, 15), (22, 25), (25, 0), (21, 13), (11, 3), (19, 2), (5, 20), (3, 24), (15, 27), (17, 17), (4, 29), (9, 14), (18, 8), (10, 1), (13, 5), (16, 30), (18, 0), (30, 15), (6, 6), (22, 20), (23, 13), (24, 23), (22, 14), (4, 2), (20, 11), (19, 9), (12, 1), (18, 24), (3, 28), (1, 30), (16, 15), (4, 4), (8, 17), (5, 1), (7, 18), (7, 26), (5, 14), (25, 3), (19, 4), (28, 11), (29, 9), (13, 17), (2, 15), (23, 1), (0, 4), (0, 6), (9, 3), (29, 15), (16, 1), (27, 4), (25, 26), (25, 31), (28, 18), (30, 22), (13, 7), (25, 16), (6, 29), (25, 21), (17, 31), (7, 15), (14, 21), (15, 1), (14, 13), (25, 9), (3, 17), (3, 23), (24, 24), (26, 19), (14, 5), (9, 5), (19, 6), (14, 27), (7, 29), (13, 1), (21, 28), (8, 9), (27, 19), (12, 15), (6, 9), (22, 12), (1, 25), (12, 21), (9, 22), (1, 22), (9, 10), (21, 21), (23, 23), (15, 5), (8, 31), (16, 11), (4, 5), (26, 12), (22, 29), (8, 14), (4, 16), (12, 0), (22, 27), (29, 2), (5, 19), (2, 22), (30, 29), (10, 23), (9, 30), (3, 22), (4, 22), (22, 10), (8, 10), (17, 1), (16, 21), (15, 11), (19, 16), (21, 3), (12, 3), (20, 3), (9, 25), (15, 14), (18, 9), (30, 2), (28, 16), (2, 14), (3, 31), (8, 6), (17, 28), (29, 28), (14, 16), (17, 6), (19, 25), (20, 26), (13, 21), (8, 15), (5, 16), (27, 15), (29, 21), (13, 23), (7, 2), (9, 27), (9, 16), (14, 4), (27, 16), (20, 25), (18, 20), (28, 28), (5, 10), (25, 23), (10, 27), (12, 16), (13, 28), (24, 22), (28, 15), (30, 24), (17, 10), (13, 26), (11, 6), (15, 19), (4, 6), (10, 12), (29, 27), (14, 8), (0, 22), (7, 3), (19, 0), (1, 26), (25, 24), (2, 17), (2, 13), (30, 1), (15, 31), (5, 30), (6, 15), (24, 5), (21, 24), (25, 18), (6, 19), (15, 2), (20, 16), (3, 21), (25, 13), (21, 14), (3, 12), (7, 21), (29, 1), (26, 24), (28, 26), (20, 24), (15, 0), (6, 13), (23, 19), (18, 27), (30, 0), (5, 21), (7, 1), (22, 30), (13, 27), (26, 7), (14, 26), (11, 24), (20, 7), (29, 0), (3, 5), (10, 20), (27, 28), (14, 22), (15, 28), (11, 9), (2, 30), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "714420", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 1), (13, 16), (1, 17), (5, 3), (16, 10), (9, 9), (24, 6), (27, 31), (5, 4), (20, 19), (24, 30), (12, 25), (8, 3), (4, 19), (3, 14), (21, 4), (11, 4), (1, 26), (26, 27), (15, 20), (9, 19), (11, 19), (23, 26), (28, 14), (16, 27), (8, 29), (10, 0), (20, 1), (0, 16), (15, 29), (16, 6), (5, 22), (15, 30), (26, 1), (4, 9), (9, 2), (5, 0), (10, 15), (11, 30), (16, 23), (23, 0), (11, 15), (3, 18), (2, 8), (8, 19), (6, 5), (13, 1), (9, 28), (18, 27), (9, 13), (26, 16), (25, 14), (27, 16), (6, 2), (17, 27), (12, 15), (16, 9), (6, 14), (22, 28), (25, 7), (12, 21), (23, 7), (21, 31), (15, 3), (26, 23), (15, 17), (20, 21), (13, 10), (4, 15), (23, 1), (6, 0), (6, 19), (26, 25), (7, 26), (17, 7), (5, 11), (2, 22), (13, 30), (9, 22), (14, 1), (8, 25), (22, 17), (23, 15), (3, 25), (27, 23), (5, 28), (26, 22), (13, 28), (19, 11), (22, 26), (27, 3), (14, 12), (29, 23), (19, 25), (11, 26), (9, 8), (29, 16), (28, 31), (29, 19), (19, 19), (13, 13), (0, 22), (28, 28), (19, 15), (14, 16), (14, 2), (29, 3), (18, 26), (26, 18), (1, 0), (30, 13), (14, 4), (6, 23), (30, 0), (16, 8), (17, 29), (23, 21), (17, 31), (0, 6), (10, 12), (18, 25), (29, 30), (12, 1), (9, 24), (21, 9), (11, 18), (24, 19), (6, 24), (29, 5), (1, 2), (0, 4), (8, 7), (19, 14), (24, 14), (7, 4), (4, 4), (22, 2), (9, 20), (25, 30), (2, 20), (3, 24), (21, 10), (21, 20), (14, 10), (13, 0), (19, 20), (3, 26), (22, 4), (20, 30), (27, 25), (23, 11), (22, 14), (17, 0), (18, 1), (6, 13), (4, 2), (6, 17), (0, 31), (22, 18), (23, 2), (19, 13), (3, 8), (19, 23), (9, 4), (29, 4), (8, 4), (23, 4), (22, 6), (3, 2), (26, 30), (26, 28), (25, 3), (6, 8), (28, 13), (27, 5), (12, 8), (20, 12), (2, 30), (16, 13), (20, 8), (12, 18), (6, 10), (17, 25), (8, 12), (11, 1), (20, 10), (23, 20), (11, 31), (16, 16), (5, 1), (0, 30), (2, 18), (19, 7), (14, 23), (4, 16), (21, 7), (7, 16), (13, 31), (2, 5), (10, 31), (24, 5), (26, 9), (14, 26), (7, 24), (18, 19), (6, 12), (29, 13), (17, 16), (21, 1), (9, 0), (11, 2), (8, 30), (11, 29), (27, 20), (13, 22), (13, 8), (9, 1), (9, 29), (12, 5), (29, 28), (7, 6), (15, 16), (20, 9), (26, 4), (10, 23), (28, 11), (7, 31), (12, 10), (30, 9), (30, 20), (11, 8), (17, 9), (18, 20), (6, 31), (20, 31), (15, 5), (28, 12), (7, 11), (14, 27), (17, 26), (5, 18), (14, 15), (1, 20), (12, 28), (5, 31), (0, 3), (25, 17), (20, 5), (28, 20), (4, 20), (3, 13), (9, 23), (4, 24), (17, 3), (16, 20), (13, 15), (9, 26), (7, 0), (3, 22), (4, 0), (12, 27), (12, 17), (0, 7), (23, 12), (26, 31), (3, 23), (6, 11), (23, 10), (25, 1), (7, 30), (5, 13), (2, 25), (19, 9), (26, 29), (1, 6), (29, 12), (13, 19), (14, 9), (1, 28), (11, 23), (1, 22), (28, 4), (24, 21), (30, 17), (19, 5), (30, 5), (5, 12), (1, 12), (4, 25), (14, 22), (13, 12), (20, 0), (20, 26), (24, 4), (18, 4), (19, 3), (11, 6), (20, 16), (11, 3), (6, 1), (7, 17), (25, 29), (23, 6), (18, 0), (13, 26), (6, 27), (6, 3), (10, 28), (17, 11), (24, 10), (28, 25), (21, 12), (15, 14), (0, 20), (24, 9), (18, 9), (7, 23), (18, 24), (20, 17), (21, 2), (16, 3), (15, 24), (28, 3), (0, 15), (1, 25), (23, 5), (15, 26), (8, 17), (10, 8), (27, 15), (30, 21), (18, 29), (1, 29), (13, 6), (0, 19), (21, 5), (26, 20), (14, 3), (13, 5), (7, 15), (11, 28), (30, 18), (28, 9), (12, 6), (29, 24), (12, 12), (24, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (22, 9), (27, 5), (25, 19), (10, 4), (18, 8), (16, 7), (28, 2), (20, 29), (17, 0), (14, 18), (13, 23), (15, 4), (21, 5), (24, 22), (30, 20), (1, 27), (16, 10), (10, 29), (5, 20), (19, 4), (19, 19), (1, 20), (25, 9), (9, 31), (3, 25), (26, 13), (12, 0), (7, 9), (2, 8), (16, 12), (16, 23), (11, 12), (11, 26), (13, 16), (18, 1), (24, 8), (8, 26), (13, 20), (7, 23), (6, 6), (1, 10), (1, 26), (13, 5), (21, 18), (28, 21), (21, 17), (28, 11), (12, 7), (17, 15), (27, 30), (4, 20), (22, 3), (26, 11), (3, 5), (12, 5), (11, 9), (17, 25), (1, 25), (13, 22), (9, 6), (21, 25), (29, 18), (1, 30), (13, 25), (1, 11), (20, 26), (7, 8), (2, 4), (22, 25), (8, 2), (23, 2), (7, 29), (1, 18), (7, 26), (25, 30), (20, 3), (0, 14), (24, 11), (3, 10), (13, 26), (21, 10), (22, 28), (3, 30), (26, 17), (11, 18), (17, 1), (11, 22), (12, 4), (30, 5), (25, 11), (4, 10), (0, 18), (27, 29), (1, 6), (15, 23), (4, 1), (20, 9), (9, 8), (29, 2), (28, 31), (27, 11), (29, 10), (29, 13), (21, 9), (27, 4), (20, 22), (26, 15), (3, 27), (10, 8), (22, 5), (19, 28), (4, 29), (1, 17), (26, 12), (19, 23), (7, 16), (16, 27), (14, 17), (13, 24), (5, 23), (3, 1), (16, 25), (29, 20), (0, 21), (22, 7), (22, 18), (21, 11), (16, 17), (12, 17), (4, 18), (3, 11), (3, 19), (18, 18), (12, 10), (23, 28), (3, 20), (0, 20), (17, 11), (5, 4), (15, 2), (5, 22), (2, 1), (22, 20), (5, 3), (2, 29), (20, 8), (28, 28), (25, 27), (4, 19), (4, 17), (11, 29), (25, 4), (5, 11), (30, 26), (11, 11), (16, 6), (19, 7), (15, 6), (8, 12), (22, 6), (26, 4), (25, 25), (20, 2), (19, 13), (29, 30), (18, 7), (18, 10), (9, 10), (11, 20), (23, 4), (10, 12), (8, 25), (24, 20), (30, 22), (0, 17), (19, 5), (8, 17), (20, 24), (24, 10), (5, 12), (6, 29), (8, 11), (8, 30), (17, 18), (6, 3), (7, 19), (6, 15), (13, 13), (10, 21), (21, 28), (22, 27), (29, 28), (5, 9), (17, 8), (17, 13), (24, 15), (25, 10), (14, 22), (10, 25), (5, 27), (2, 12), (11, 0), (2, 31), (29, 4), (3, 8), (29, 23), (17, 16), (24, 6), (23, 14), (16, 5), (23, 9), (30, 11), (8, 31), (14, 23), (4, 12), (13, 30), (14, 28), (26, 8), (10, 20), (23, 8), (7, 0), (18, 27), (22, 8), (9, 12), (17, 10), (15, 30), (23, 27), (8, 7), (10, 23), (20, 30), (25, 20), (5, 17), (18, 17), (12, 24), (12, 16), (0, 29), (8, 4), (28, 16), (3, 15), (7, 2), (25, 6), (19, 20), (21, 1), (0, 3), (6, 30), (23, 17), (2, 5), (21, 8), (15, 29), (11, 28), (9, 27), (30, 13), (12, 2), (12, 18), (28, 3), (11, 7), (30, 15), (10, 22), (6, 27), (28, 10), (27, 9), (5, 13), (18, 13), (2, 3), (8, 28), (29, 11), (11, 21), (20, 16), (13, 0), (15, 11), (5, 21), (17, 29), (8, 10), (18, 20), (0, 9), (5, 26), (23, 30), (24, 17), (7, 21), (3, 18), (7, 4), (16, 15), (27, 17), (4, 11), (7, 22), (19, 2), (2, 2), (23, 22), (27, 26), (8, 29), (0, 22), (22, 14), (20, 7), (18, 5), (26, 14), (5, 30), (0, 12), (14, 21), (19, 6), (17, 6), (14, 14), (24, 9), (0, 1), (1, 5), (0, 25), (26, 1), (15, 26), (1, 28), (21, 4), (3, 16), (9, 5), (28, 19), (18, 12), (4, 3), (5, 29), (14, 12), (27, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "574080", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), 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), (24, 3), (2, 20), (1, 11), (10, 27), (4, 4), (31, 11), (24, 2), (19, 30), (0, 22), (28, 5), (20, 12), (17, 13), (8, 12), (25, 27), (11, 3), (0, 12), (0, 17), (1, 4), (27, 1), (29, 18), (24, 4), (13, 11), (13, 5), (25, 31), (24, 19), (17, 14), (12, 10), (30, 0), (4, 13), (8, 26), (9, 19), (10, 21), (4, 24), (23, 4), (28, 28), (27, 12), (13, 30), (3, 18), (25, 21), (9, 2), (7, 2), (24, 22), (31, 26), (13, 9), (29, 11), (19, 24), (12, 13), (2, 9), (0, 9), (15, 24), (30, 6), (24, 13), (19, 18), (24, 18), (21, 31), (19, 15), (18, 31), (6, 31), (22, 22), (25, 16), (15, 19), (7, 27), (29, 10), (1, 23), (14, 27), (5, 23), (2, 19), (20, 13), (27, 10), (23, 28), (22, 5), (17, 22), (16, 9), (23, 7), (26, 15), (28, 22), (11, 20), (20, 30), (2, 32), (21, 4), (14, 31), (23, 22), (3, 20), (24, 11), (8, 18), (12, 26), (21, 14), (18, 25), (10, 11), (28, 8), (12, 5), (32, 19), (32, 7), (24, 29), (6, 19), (1, 24), (0, 30), (2, 17), (5, 29), (22, 20), (17, 20), (4, 7), (11, 12), (12, 12), (5, 32), (2, 26), (25, 19), (7, 10), (25, 1), (29, 1), (1, 22), (25, 9), (15, 9), (10, 23), (4, 17), (0, 26), (13, 31), (25, 22), (15, 21), (13, 21), (9, 20), (10, 14), (27, 6), (23, 17), (18, 14), (28, 7), (15, 0), (28, 11), (18, 13), (17, 17), (24, 15), (17, 26), (7, 12), (32, 11), (15, 6), (16, 28), (9, 16), (12, 0), (17, 28), (6, 2), (13, 18), (7, 16), (10, 15), (27, 15), (3, 31), (1, 26), (0, 18), (2, 18), (2, 29), (12, 6), (10, 0), (22, 7), (29, 17), (13, 27), (3, 7), (18, 4), (8, 5), (26, 5), (5, 30), (30, 30), (16, 30), (25, 32), (24, 25), (7, 14), (11, 18), (16, 23), (26, 25), (5, 22), (30, 14), (19, 7), (11, 5), (1, 8), (22, 6), (6, 3), (14, 13), (18, 0), (23, 32), (31, 10), (10, 26), (22, 27), (12, 9), (6, 13), (27, 32), (11, 32), (22, 9), (29, 14), (16, 13), (11, 24), (8, 31), (28, 12), (9, 30), (11, 27), (3, 25), (1, 30), (23, 24), (18, 18), (27, 30), (3, 21), (11, 29), (29, 9), (9, 25), (12, 1), (30, 18), (18, 10), (17, 30), (7, 4), (23, 10), (17, 9), (20, 7), (14, 1), (15, 8), (31, 29), (0, 10), (0, 23), (17, 7), (13, 6), (26, 9), (29, 28), (8, 25), (23, 19), (11, 9), (19, 14), (31, 13), (2, 21), (2, 12), (27, 2), (1, 19), (8, 23), (29, 22), (4, 30), (8, 11), (32, 21), (15, 25), (1, 31), (16, 8), (12, 29), (10, 6), (21, 5), (14, 7), (11, 13), (14, 10), (24, 17), (4, 19), (26, 19), (30, 32), (15, 20), (23, 15), (9, 32), (21, 10), (10, 7), (32, 10), (2, 8), (30, 17), (22, 11), (6, 27), (8, 29), (8, 7), (24, 26), (24, 21), (7, 26), (13, 1), (6, 25), (19, 13), (18, 29), (1, 9), (7, 15), (4, 31), (21, 23), (21, 9), (6, 22), (7, 25), (4, 21), (21, 7), (30, 4), (10, 29), (13, 13), (2, 4), (19, 4), (22, 25), (11, 10), (17, 3), (6, 18), (25, 8), (2, 30), (29, 0), (16, 16), (5, 20), (28, 30), (18, 3), (23, 12), (11, 0), (8, 30), (7, 8), (28, 20), (22, 32), (5, 0), (9, 10), (23, 11), (1, 27), (6, 15), (0, 32), (26, 12), (21, 32), (9, 26), (3, 14), (2, 28), (24, 5), (16, 21), (17, 25), (18, 32), (19, 25), (6, 30), (32, 1), (9, 14), (26, 13), (16, 1), (8, 13), (8, 24), (25, 15), (31, 6), (14, 28), (18, 19), (7, 28), (0, 11), (14, 21), (26, 31), (27, 11), (12, 31), (1, 28), (27, 26), (17, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876900", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 20), (9, 18), (9, 23), (1, 24), (15, 38), (19, 14), (21, 32), (21, 13), (16, 30), (0, 31), (1, 16), (11, 8), (6, 37), (22, 23), (0, 23), (8, 9), (5, 17), (23, 36), (14, 17), (28, 7), (5, 6), (28, 17), (3, 24), (12, 33), (19, 28), (5, 3), (29, 6), (6, 27), (1, 25), (1, 5), (25, 21), (27, 3), (25, 37), (3, 7), (28, 25), (4, 19), (9, 13), (5, 27), (23, 14), (29, 3), (11, 17), (19, 8), (19, 18), (19, 3), (28, 29), (23, 38), (21, 36), (12, 0), (26, 24), (15, 6), (4, 16), (28, 14), (23, 26), (2, 27), (4, 5), (19, 19), (18, 13), (23, 15), (18, 20), (9, 20), (29, 20), (0, 15), (29, 38), (10, 24), (8, 5), (4, 37), (21, 14), (7, 18), (13, 27), (13, 19), (9, 28), (15, 23), (5, 13), (11, 9), (26, 5), (14, 3), (28, 6), (1, 15), (6, 32), (26, 26), (13, 32), (12, 19), (6, 21), (9, 17), (28, 19), (1, 35), (3, 21), (7, 7), (11, 26), (18, 0), (14, 11), (30, 3), (9, 29), (29, 23), (30, 33), (12, 27), (17, 18), (19, 30), (22, 11), (11, 15), (26, 15), (16, 9), (26, 18), (7, 10), (26, 12), (14, 10), (22, 32), (25, 14), (26, 29), (15, 22), (30, 6), (19, 22), (23, 21), (25, 13), (29, 15), (30, 0), (1, 9), (4, 35), (10, 22), (2, 24), (29, 36), (23, 3), (24, 20), (16, 35), (12, 16), (20, 8), (17, 6), (1, 32), (16, 33), (19, 27), (16, 2), (25, 25), (15, 4), (27, 5), (17, 8), (11, 35), (27, 10), (15, 19), (6, 25), (29, 2), (16, 24), (21, 34), (4, 26), (3, 36), (3, 10), (22, 0), (27, 6), (24, 36), (10, 10), (19, 7), (18, 16), (2, 3), (14, 1), (9, 0), (22, 36), (7, 21), (21, 3), (28, 8), (27, 14), (30, 14), (3, 17), (14, 33), (22, 13), (6, 36), (28, 11), (1, 26), (19, 17), (13, 28), (2, 2), (29, 12), (1, 28), (6, 31), (28, 30), (0, 22), (3, 2), (6, 4), (20, 30), (29, 24), (4, 24), (5, 24), (5, 15), (30, 21), (30, 10), (30, 28), (20, 33), (12, 30), (25, 0), (3, 14), (6, 11), (24, 26), (25, 11), (28, 28), (3, 4), (21, 31), (22, 7), (4, 21), (14, 28), (1, 14), (3, 26), (24, 4), (2, 30), (30, 4), (29, 7), (16, 38), (13, 20), (3, 37), (1, 20), (26, 33), (13, 10), (7, 17), (23, 11), (28, 26), (20, 2), (18, 2), (21, 8), (11, 21), (19, 34), (8, 0), (26, 3), (17, 13), (5, 10), (16, 1), (17, 15), (15, 10), (21, 17), (24, 1), (29, 8), (14, 18), (2, 6), (15, 29), (22, 22), (13, 5), (18, 24), (2, 7), (0, 27), (8, 19), (8, 17), (23, 22), (15, 25), (6, 38), (26, 17), (28, 37), (17, 7), (17, 36), (4, 20), (2, 9), (18, 27), (30, 29), (23, 5), (14, 6), (3, 33), (6, 19), (9, 21), (28, 31), (16, 25), (27, 37), (17, 2), (22, 29), (7, 15), (19, 38), (19, 35), (14, 23), (12, 3), (6, 34), (9, 37), (6, 26), (13, 17), (20, 18), (8, 2), (12, 8), (8, 24), (15, 8), (7, 11), (3, 6), (2, 20), (10, 8), (2, 29), (23, 8), (26, 7), (1, 31), (13, 7), (6, 12), (4, 10), (9, 15), (29, 33), (2, 18), (17, 29), (24, 21), (25, 33), (22, 4), (1, 2), (21, 2), (27, 2), (2, 26), (27, 11), (26, 31), (26, 35), (15, 5), (18, 5), (5, 19), (25, 3), (27, 38), (30, 15), (15, 36), (21, 38), (26, 21), (10, 26), (20, 21), (26, 32), (16, 27), (28, 34), (20, 17), (2, 17), (1, 34), (27, 32), (4, 31), (28, 20), (19, 1), (23, 16), (26, 23), (30, 30), (14, 9), (11, 33), (18, 21), (22, 25), (21, 22), (5, 5), (28, 16), (2, 13), (16, 31), (0, 20), (5, 31), (5, 34), (0, 7), (22, 37), (16, 16), (13, 8), (29, 28), (14, 38), (11, 14), (15, 35), (6, 33), (8, 14), (3, 23), (21, 0), (17, 4), (22, 20), (23, 7), (1, 36), (29, 16), (6, 2), (23, 32), (19, 4), (12, 17), (27, 29), (25, 29), (22, 27), (18, 23), (13, 12), (21, 23), (12, 22), (18, 12), (12, 37), (3, 34), (2, 19), (27, 19), (22, 35), (15, 20), (15, 13), (2, 28), (3, 29), (13, 22), (11, 18), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172992", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (14, 30), (15, 17), (14, 18), (18, 31), (8, 36), (17, 13), (28, 8), (27, 32), (13, 0), (30, 30), (20, 10), (20, 26), (27, 15), (29, 8), (18, 29), (9, 7), (31, 27), (30, 21), (24, 8), (20, 1), (7, 29), (26, 17), (0, 36), (1, 0), (15, 34), (0, 16), (13, 22), (15, 31), (13, 12), (30, 4), (28, 31), (22, 9), (27, 16), (21, 14), (30, 16), (0, 32), (4, 10), (25, 5), (16, 32), (25, 17), (4, 23), (19, 20), (23, 23), (28, 29), (27, 33), (20, 20), (23, 9), (3, 35), (24, 10), (17, 2), (12, 10), (24, 28), (26, 29), (2, 31), (27, 20), (9, 5), (1, 14), (4, 16), (26, 5), (25, 11), (2, 21), (24, 14), (6, 8), (2, 18), (5, 16), (24, 29), (19, 18), (10, 27), (8, 22), (8, 2), (25, 28), (11, 6), (19, 27), (2, 19), (6, 18), (20, 8), (23, 27), (28, 27), (14, 20), (23, 36), (4, 17), (24, 15), (3, 7), (27, 26), (15, 32), (10, 25), (12, 28), (26, 20), (9, 34), (19, 17), (15, 5), (26, 30), (28, 1), (14, 35), (3, 26), (3, 31), (2, 8), (5, 15), (25, 27), (3, 21), (6, 11), (15, 2), (29, 4), (19, 10), (10, 6), (19, 6), (31, 5), (3, 28), (23, 7), (25, 31), (2, 23), (30, 3), (18, 30), (11, 27), (19, 28), (24, 22), (12, 24), (12, 13), (0, 10), (28, 14), (12, 0), (0, 11), (3, 2), (9, 20), (16, 35), (18, 19), (9, 36), (23, 10), (25, 7), (23, 18), (30, 1), (18, 27), (19, 24), (11, 2), (1, 23), (20, 16), (21, 13), (27, 23), (11, 32), (11, 33), (4, 34), (3, 33), (10, 10), (5, 19), (6, 31), (27, 30), (6, 21), (10, 9), (13, 32), (7, 17), (4, 13), (30, 0), (3, 34), (0, 5), (24, 17), (12, 16), (21, 34), (9, 0), (20, 5), (8, 9), (27, 31), (1, 16), (18, 32), (24, 12), (11, 22), (9, 2), (17, 3), (13, 27), (20, 36), (29, 35), (5, 8), (5, 4), (1, 19), (4, 6), (20, 3), (14, 6), (28, 10), (13, 15), (12, 33), (14, 4), (7, 3), (25, 4), (25, 29), (16, 9), (0, 34), (25, 10), (2, 1), (29, 36), (15, 0), (0, 13), (7, 36), (29, 12), (24, 9), (18, 6), (22, 14), (2, 6), (15, 36), (29, 2), (29, 29), (7, 7), (22, 35), (4, 2), (28, 9), (21, 9), (17, 30), (13, 7), (30, 2), (18, 22), (0, 8), (13, 14), (5, 30), (17, 8), (23, 2), (4, 35), (14, 28), (12, 3), (15, 1), (12, 36), (15, 24), (5, 11), (24, 7), (26, 18), (23, 4), (15, 25), (22, 1), (22, 18), (2, 9), (27, 4), (5, 23), (23, 14), (26, 13), (10, 3), (1, 29), (7, 19), (17, 14), (29, 18), (1, 25), (2, 34), (4, 12), (19, 3), (19, 5), (9, 4), (13, 34), (29, 7), (6, 26), (22, 23), (25, 0), (0, 7), (12, 12), (6, 36), (22, 26), (22, 30), (27, 6), (10, 32), (6, 6), (23, 19), (17, 35), (8, 28), (21, 32), (31, 35), (29, 31), (23, 3), (31, 16), (18, 4), (20, 6), (8, 33), (14, 26), (11, 4), (7, 12), (1, 9), (15, 35), (20, 34), (25, 23), (21, 22), (6, 19), (15, 18), (12, 6), (7, 32), (21, 21), (27, 8), (30, 29), (14, 23), (30, 20), (5, 6), (31, 4), (25, 1), (9, 19), (29, 23), (21, 30), (30, 7), (19, 23), (17, 29), (13, 30), (9, 9), (22, 0), (23, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238680", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), 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), (19, 11), (14, 2), (13, 23), (5, 24), (6, 0), (1, 5), (25, 29), (3, 3), (18, 29), (22, 1), (23, 9), (15, 28), (10, 6), (12, 31), (10, 28), (11, 12), (13, 31), (15, 23), (29, 3), (30, 31), (25, 31), (24, 25), (22, 27), (30, 20), (19, 13), (28, 21), (16, 8), (22, 5), (3, 30), (6, 19), (20, 34), (10, 0), (2, 19), (5, 29), (23, 5), (6, 1), (1, 20), (11, 19), (3, 0), (25, 26), (12, 24), (27, 33), (21, 24), (28, 35), (5, 9), (19, 6), (8, 3), (10, 33), (0, 31), (23, 20), (9, 20), (20, 25), (12, 4), (24, 24), (15, 24), (29, 27), (22, 35), (10, 16), (26, 23), (16, 25), (21, 19), (17, 11), (15, 1), (3, 35), (20, 21), (16, 20), (14, 17), (13, 9), (5, 13), (17, 21), (12, 32), (11, 8), (21, 16), (22, 24), (25, 20), (14, 5), (27, 19), (24, 26), (9, 11), (22, 0), (7, 25), (24, 13), (17, 2), (13, 3), (30, 5), (16, 3), (25, 18), (2, 2), (27, 12), (6, 15), (27, 13), (27, 2), (11, 18), (8, 12), (8, 28), (26, 29), (5, 16), (4, 4), (15, 8), (7, 4), (7, 21), (16, 19), (7, 34), (20, 7), (14, 33), (9, 7), (10, 1), (24, 19), (3, 28), (13, 35), (28, 19), (29, 14), (3, 12), (22, 4), (0, 21), (19, 14), (24, 28), (22, 10), (17, 4), (26, 1), (19, 27), (8, 8), (0, 18), (13, 16), (18, 12), (3, 15), (24, 33), (10, 29), (3, 21), (19, 5), (4, 8), (9, 21), (1, 29), (12, 22), (7, 20), (14, 29), (21, 34), (13, 19), (25, 21), (0, 11), (26, 11), (27, 30), (16, 17), (12, 34), (15, 32), (12, 1), (19, 0), (8, 19), (7, 2), (3, 27), (7, 27), (27, 8), (8, 14), (30, 1), (21, 28), (19, 35), (4, 10), (0, 6), (9, 24), (9, 1), (30, 16), (5, 35), (2, 28), (16, 1), (16, 5), (2, 25), (27, 34), (22, 19), (3, 13), (5, 1), (9, 35), (3, 11), (14, 14), (25, 9), (25, 22), (7, 9), (25, 10), (0, 28), (25, 28), (10, 20), (11, 14), (9, 0), (15, 22), (12, 19), (9, 23), (5, 25), (5, 2), (13, 20), (16, 0), (12, 6), (1, 34), (26, 13), (12, 28), (10, 2), (5, 3), (19, 30), (18, 34), (29, 2), (10, 24), (10, 25), (19, 9), (23, 6), (13, 32), (2, 32), (5, 20), (22, 20), (5, 15), (21, 5), (11, 3), (5, 27), (17, 22), (18, 10), (2, 22), (17, 19), (30, 7), (18, 2), (8, 30), (20, 5), (9, 32), (1, 16), (15, 4), (9, 3), (26, 0), (18, 23), (6, 11), (11, 32), (27, 32), (11, 25), (26, 24), (4, 17), (13, 8), (16, 32), (13, 0), (5, 17), (11, 9), (23, 30), (3, 5), (17, 17), (2, 30), (10, 7), (5, 30), (14, 7), (3, 1), (29, 25), (20, 15), (4, 18), (8, 21), (24, 23), (7, 24), (6, 2), (14, 32), (13, 6), (13, 13), (25, 34), (11, 35), (26, 5), (3, 17), (18, 13), (18, 5), (6, 30), (5, 28), (7, 32), (27, 29), (29, 34), (20, 10), (17, 15), (15, 10), (12, 13), (11, 15), (27, 16), (18, 7), (7, 15), (4, 24), (6, 20), (29, 24), (25, 23), (0, 14), (15, 29), (21, 18), (6, 27), (12, 20), (30, 17), (4, 13), (2, 10), (28, 7), (1, 18), (3, 29), (11, 17), (14, 28), (25, 13), (15, 20), (29, 12), (16, 29), (7, 8), (2, 26), (11, 30), (20, 30), (10, 18), (29, 4), (11, 1), (22, 32), (27, 5), (16, 6), (8, 17), (4, 35), (7, 16), (8, 7), (8, 20), (14, 31), (10, 8), (30, 15), (25, 33), (21, 23), (22, 33), (26, 12), (7, 19), (7, 0), (23, 21), (20, 16), (8, 31), (10, 26), (13, 17), (5, 14), (1, 13), (25, 16), (3, 10), (13, 21), (14, 20), (8, 2), (23, 16), (9, 9), (8, 5), (9, 16), (30, 11), (16, 16), (2, 16), (14, 10), (14, 4), (26, 3), (28, 27), (11, 21), (8, 35), (5, 31), (19, 19), (19, 25), (20, 20), (6, 35), (0, 4), (14, 15), (6, 21), (21, 1), (28, 16), (3, 2), (12, 27), (20, 28), (7, 30), (26, 9), (17, 24), (5, 4), (17, 28), (29, 19), (12, 35), (13, 27), (26, 4), (5, 10), (15, 27), (26, 7), (29, 10), (22, 7), (22, 6), (16, 11), (30, 23), (11, 33), (11, 7), (2, 9), (12, 17), (9, 18), (8, 34), (8, 29), (9, 19), (24, 18), (30, 13), (25, 3), (17, 7), (27, 24), (1, 19), (7, 18), (7, 22), (28, 17), (25, 2), (21, 15), (2, 24), (5, 18), (22, 13), (25, 14), (13, 25), (17, 26), (19, 15), (18, 22), (18, 30), (21, 29), (11, 27), (21, 33), (14, 34), (17, 35), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128736", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), 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), (17, 31), (5, 29), (2, 28), (6, 27), (7, 16), (2, 22), (34, 33), (7, 32), (14, 13), (18, 17), (33, 23), (25, 33), (6, 23), (24, 15), (22, 31), (12, 10), (9, 23), (27, 3), (18, 5), (9, 32), (16, 5), (21, 30), (3, 35), (28, 18), (15, 21), (3, 5), (33, 13), (25, 4), (12, 27), (19, 3), (16, 11), (32, 8), (28, 9), (3, 32), (11, 23), (19, 15), (15, 30), (5, 4), (6, 21), (22, 4), (13, 31), (21, 29), (26, 35), (24, 8), (13, 17), (6, 18), (27, 8), (2, 11), (1, 0), (20, 25), (24, 13), (9, 7), (0, 28), (14, 15), (8, 4), (7, 34), (33, 3), (18, 2), (29, 19), (27, 21), (4, 20), (24, 27), (13, 22), (8, 24), (10, 33), (28, 28), (16, 12), (7, 33), (13, 10), (22, 19), (13, 2), (20, 33), (6, 6), (27, 16), (31, 26), (8, 6), (15, 12), (9, 6), (6, 25), (16, 33), (23, 22), (19, 27), (16, 31), (29, 13), (6, 12), (29, 14), (12, 7), (17, 3), (2, 26), (33, 7), (27, 5), (16, 21), (21, 25), (24, 3), (23, 24), (14, 1), (16, 30), (2, 13), (11, 9), (7, 13), (31, 4), (9, 19), (12, 30), (17, 20), (22, 26), (18, 15), (19, 25), (12, 16), (29, 20), (23, 19), (3, 31), (13, 23), (11, 4), (34, 34), (28, 25), (14, 22), (15, 25), (12, 29), (2, 19), (31, 24), (19, 34), (27, 7), (20, 31), (0, 6), (2, 35), (21, 22), (0, 18), (25, 12), (3, 17), (1, 3), (6, 20), (32, 31), (16, 35), (4, 2), (16, 29), (17, 13), (4, 31), (32, 29), (5, 18), (12, 35), (20, 7), (17, 29), (14, 6), (2, 0), (22, 9), (21, 13), (31, 27), (27, 33), (24, 6), (5, 26), (13, 26), (13, 1), (24, 14), (11, 1), (3, 34), (10, 18), (22, 17), (0, 25), (15, 20), (21, 8), (34, 25), (27, 6), (34, 10), (6, 0), (8, 25), (19, 26), (13, 21), (18, 21), (32, 19), (18, 23), (14, 8), (17, 23), (17, 19), (10, 8), (15, 19), (26, 21), (19, 22), (0, 30), (8, 15), (2, 27), (1, 7), (8, 19), (9, 1), (28, 7), (28, 11), (18, 32), (30, 33), (33, 29), (12, 28), (3, 21), (11, 8), (9, 4), (4, 18), (26, 15), (32, 0), (13, 28), (6, 19), (5, 25), (22, 18), (17, 6), (23, 10), (25, 6), (6, 1), (30, 35), (9, 5), (28, 21), (11, 16), (6, 9), (20, 15), (17, 30), (24, 11), (22, 28), (14, 12), (21, 11), (11, 28), (28, 20), (17, 22), (33, 25), (28, 33), (33, 15), (29, 9), (5, 22), (29, 23), (15, 14), (28, 14), (18, 1), (1, 27), (34, 5), (13, 32), (7, 29), (33, 5), (25, 25), (21, 34), (5, 2), (10, 35), (32, 16), (24, 4), (2, 32), (26, 18), (2, 20), (12, 31), (26, 4), (21, 18), (23, 26), (5, 1), (13, 4), (21, 1), (23, 25), (5, 9), (7, 5), (32, 27), (22, 20), (0, 27), (17, 0), (9, 14), (14, 14), (4, 28), (15, 9), (21, 16), (7, 35), (26, 29), (8, 27), (0, 14), (28, 16), (10, 17), (31, 15), (16, 6), (7, 22), (19, 11), (3, 33), (9, 16), (3, 22), (23, 8), (6, 34), (23, 3), (19, 1), (22, 33), (33, 24), (18, 33), (30, 29), (29, 32), (11, 24), (1, 23), (28, 12), (28, 31), (22, 27), (11, 2), (3, 27), (11, 27), (14, 5), (3, 9), (16, 19), (30, 32), (27, 10), (14, 19), (16, 1), (10, 1), (0, 35), (24, 30), (26, 28), (29, 5), (23, 20), (3, 13), (26, 31), (13, 8), (3, 12), (25, 11), (22, 0), (10, 6), (34, 0), (11, 5), (12, 24), (0, 3), (10, 22), (33, 16), (23, 32), (17, 9), (0, 17), (2, 21), (32, 3), (28, 19), (26, 17), (22, 8), (22, 32), (34, 28), (5, 30), (25, 23), (0, 15), (29, 17), (22, 29), (30, 14), (15, 11), (6, 22), (12, 13), (14, 34), (29, 29), (27, 27), (31, 7), (25, 34), (24, 32), (19, 35), (21, 15), (26, 27), (31, 31), (29, 26), (7, 31), (4, 5), (7, 24), (18, 31), (9, 0), (4, 15), (14, 4), (30, 28), (24, 33), (2, 12), (10, 5), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27216", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 24), (30, 17), (4, 4), (7, 10), (11, 0), (18, 8), (7, 18), (21, 7), (13, 32), (25, 17), (0, 31), (19, 20), (10, 18), (23, 33), (20, 17), (30, 27), (1, 8), (4, 9), (20, 6), (12, 27), (19, 33), (30, 13), (26, 32), (12, 2), (11, 28), (12, 11), (16, 12), (14, 5), (6, 1), (22, 7), (5, 12), (16, 31), (30, 10), (3, 0), (5, 5), (9, 21), (11, 20), (28, 20), (17, 26), (14, 25), (13, 17), (28, 25), (18, 30), (3, 24), (15, 17), (23, 25), (0, 6), (16, 32), (17, 0), (23, 5), (6, 3), (27, 33), (9, 7), (0, 7), (20, 15), (22, 24), (19, 19), (14, 30), (23, 15), (8, 14), (8, 0), (12, 23), (18, 12), (7, 15), (15, 29), (4, 10), (1, 31), (26, 3), (28, 13), (20, 7), (8, 26), (0, 29), (23, 20), (15, 23), (17, 23), (13, 20), (8, 6), (18, 10), (10, 28), (22, 2), (5, 16), (12, 7), (24, 4), (19, 16), (28, 33), (27, 24), (27, 7), (23, 29), (24, 0), (2, 30), (30, 28), (13, 10), (17, 13), (4, 29), (25, 11), (18, 5), (15, 25), (6, 9), (16, 26), (20, 26), (11, 22), (8, 19), (23, 32), (21, 6), (25, 19), (12, 8), (28, 15), (14, 28), (27, 5), (27, 2), (22, 15), (24, 25), (2, 10), (8, 12), (14, 20), (26, 31), (18, 28), (27, 4), (13, 6), (8, 7), (26, 4), (2, 25), (3, 9), (1, 17), (1, 26), (3, 12), (4, 26), (27, 20), (9, 30), (28, 3), (19, 15), (4, 32), (20, 11), (5, 14), (17, 32), (12, 32), (14, 9), (0, 5), (2, 32), (13, 28), (1, 23), (10, 19), (4, 16), (10, 25), (28, 12), (14, 29), (0, 27), (11, 33), (17, 5), (6, 11), (14, 32), (8, 1), (17, 29), (9, 11), (30, 6), (5, 8), (6, 0), (20, 4), (0, 30), (8, 23), (28, 31), (28, 0), (10, 13), (7, 12), (26, 6), (21, 10), (1, 4), (17, 4), (21, 9), (0, 12), (9, 27), (10, 2), (29, 3), (7, 17), (11, 27), (29, 0), (11, 14), (4, 25), (1, 24), (3, 20), (22, 3), (7, 7), (22, 29), (30, 21), (1, 2), (27, 19), (1, 33), (23, 11), (16, 5), (7, 28), (8, 25), (9, 10), (9, 1), (7, 30), (16, 3), (18, 19), (26, 17), (13, 0), (12, 3), (7, 32), (15, 28), (26, 11), (6, 30), (15, 15), (28, 27), (22, 14), (3, 33), (16, 0), (22, 21), (2, 22), (0, 33), (27, 21), (12, 12), (23, 19), (0, 10), (2, 3), (23, 12), (14, 15), (7, 14), (2, 31), (11, 13), (29, 28), (26, 23), (3, 13), (21, 3), (29, 6), (27, 0), (25, 10), (21, 30), (12, 13), (20, 8), (22, 10), (5, 9), (2, 2), (6, 27), (11, 30), (0, 8), (27, 11), (15, 7), (23, 3), (4, 18), (17, 27), (3, 31), (17, 3), (30, 30), (5, 10), (27, 13), (27, 16), (2, 9), (30, 1), (18, 20), (29, 17), (3, 28), (29, 21), (2, 4), (18, 11), (7, 4), (14, 0), (6, 21), (17, 31), (18, 24), (21, 12), (20, 18), (23, 22), (30, 26), (24, 24), (4, 0), (17, 28), (18, 31), (3, 8), (19, 18), (17, 22), (18, 6), (3, 3), (1, 16), (30, 9), (29, 18), (27, 6), (29, 33), (10, 11), (30, 15), (8, 30), (13, 21), (1, 29), (1, 11), (11, 17), (27, 12), (16, 11), (18, 22), (12, 21), (20, 0), (18, 29), (29, 20), (0, 4), (7, 6), (9, 19), (0, 26), (10, 5), (21, 32), (17, 15), (24, 6), (22, 18), (13, 2), (16, 2), (2, 15), (27, 30), (30, 12), (1, 18), (24, 28), (12, 6), (19, 31), (14, 24), (29, 8), (9, 32), (19, 14), (6, 13), (21, 33), (27, 14), (15, 0), (17, 25), (0, 14), (25, 0), (13, 9), (1, 3), (25, 6), (11, 15), (22, 31), (8, 8), (15, 21), (7, 5), (10, 16), (13, 19), (20, 12), (5, 28), (13, 30), (11, 7), (0, 20), (6, 20), (5, 26), (3, 25), (18, 7), (27, 18), (26, 9), (6, 4), (28, 10), (25, 5), (21, 8), (29, 9), (5, 21), (17, 1), (9, 20), (13, 26), (9, 31), (3, 2), (7, 16), (25, 20), (17, 10), (14, 26), (29, 12), (7, 27), (22, 0), (24, 26), (8, 24), (16, 25), (2, 13), (8, 33), (1, 9), (21, 26), (5, 20), (13, 12), (4, 28), (1, 27), (5, 0), (2, 5), (6, 18), (14, 13), (18, 4), (10, 10), (25, 31), (14, 10), (2, 26), (12, 14), (24, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181632", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), 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), (10, 33), (3, 25), (3, 17), (23, 22), (24, 19), (20, 24), (5, 6), (12, 0), (20, 23), (19, 28), (10, 34), (28, 22), (0, 38), (13, 23), (33, 31), (18, 26), (5, 25), (15, 11), (29, 36), (13, 25), (22, 18), (23, 1), (29, 5), (9, 38), (22, 12), (14, 32), (13, 4), (2, 27), (14, 29), (3, 7), (15, 13), (6, 8), (13, 24), (27, 26), (12, 25), (6, 36), (5, 20), (24, 16), (17, 28), (27, 16), (26, 2), (23, 17), (12, 12), (4, 12), (4, 29), (19, 14), (3, 9), (33, 2), (25, 13), (7, 27), (32, 8), (14, 16), (11, 22), (22, 20), (0, 17), (25, 32), (14, 0), (12, 10), (29, 27), (30, 24), (8, 1), (19, 18), (15, 5), (1, 15), (16, 11), (4, 1), (26, 8), (28, 9), (1, 8), (0, 11), (6, 29), (12, 30), (24, 25), (19, 25), (30, 36), (7, 25), (30, 13), (26, 35), (4, 26), (17, 10), (25, 20), (24, 17), (17, 17), (1, 2), (29, 10), (30, 16), (26, 4), (4, 20), (20, 10), (7, 28), (3, 36), (22, 22), (19, 36), (30, 31), (31, 0), (17, 13), (11, 6), (7, 4), (23, 37), (30, 26), (13, 14), (33, 36), (20, 0), (26, 5), (17, 30), (19, 33), (26, 38), (24, 12), (4, 16), (17, 34), (30, 35), (28, 25), (3, 12), (7, 5), (27, 25), (15, 30), (19, 0), (19, 11), (22, 27), (2, 30), (11, 36), (25, 7), (27, 34), (4, 10), (31, 38), (2, 23), (33, 24), (4, 18), (32, 14), (18, 21), (23, 13), (18, 6), (25, 4), (1, 16), (31, 19), (29, 0), (22, 15), (10, 3), (18, 34), (14, 27), (5, 19), (3, 37), (25, 18), (21, 21), (6, 13), (12, 28), (3, 29), (9, 23), (14, 34), (29, 21), (1, 18), (4, 34), (5, 22), (0, 2), (32, 5), (1, 37), (27, 31), (11, 30), (19, 35), (12, 23), (33, 30), (3, 26), (21, 0), (4, 0), (5, 1), (17, 18), (29, 22), (16, 6), (15, 10), (6, 18), (30, 22), (13, 27), (8, 38), (4, 9), (32, 19), (11, 32), (27, 10), (24, 2), (26, 25), (16, 27), (30, 29), (33, 35), (28, 37), (13, 18), (14, 38), (1, 10), (29, 3), (10, 28), (4, 2), (28, 31), (7, 6), (23, 5), (19, 2), (19, 10), (2, 5), (18, 32), (13, 31), (8, 25), (12, 27), (4, 15), (5, 37), (9, 13), (6, 10), (22, 33), (23, 27), (30, 33), (5, 14), (7, 24), (10, 5), (23, 35), (23, 16), (19, 32), (25, 15), (26, 14), (11, 31), (5, 15), (29, 33), (7, 30), (3, 38), (15, 0), (15, 38), (21, 28), (18, 1), (12, 34), (27, 6), (25, 5), (0, 28), (0, 26), (33, 27), (26, 29), (23, 26), (14, 23), (29, 37), (22, 19), (30, 30), (14, 35), (13, 17), (14, 33), (10, 8), (20, 14), (18, 30), (28, 23), (31, 30), (22, 5), (7, 36), (24, 5), (27, 24), (9, 18), (32, 29), (32, 32), (33, 5), (10, 1), (25, 21), (9, 8), (18, 15), (24, 30), (4, 31), (18, 2), (1, 32), (30, 0), (33, 13), (31, 23), (17, 38), (6, 4), (23, 18), (22, 0), (1, 25), (23, 8), (14, 37), (18, 7), (15, 28), (33, 18), (7, 9), (31, 4), (28, 17), (16, 15), (30, 15), (32, 30), (26, 30), (33, 33), (22, 32), (2, 6), (16, 26), (33, 7), (14, 31), (24, 9), (26, 17), (25, 25), (11, 25), (15, 24), (17, 0), (3, 16), (8, 20), (18, 3), (18, 31), (4, 27), (24, 4), (22, 34), (17, 24), (29, 15), (9, 2), (11, 4), (19, 7), (14, 1), (10, 11), (31, 6), (12, 17), (0, 19), (9, 9), (27, 1), (30, 2), (5, 2), (18, 28), (27, 32), (12, 2), (24, 14), (28, 4), (31, 22), (16, 21), (14, 3), (21, 31), (32, 4), (7, 10), (28, 26), (31, 21), (25, 10), (1, 22), (6, 14), (10, 9), (20, 31), (33, 32), (19, 4), (11, 2), (19, 26), (9, 35), (1, 7), (25, 33), (21, 6), (32, 11), (0, 20), (19, 5), (28, 13), (17, 33), (16, 22), (7, 35), (28, 32), (7, 8), (8, 15), (3, 4), (26, 34), (20, 1), (1, 33), (13, 13), (31, 28), (11, 18), (31, 8), (12, 5), (2, 4), (9, 24), (22, 31), (24, 28), (23, 36), (21, 19), (25, 37), (28, 2), (3, 15), (0, 4), (5, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963600", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), 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), (31, 6), (23, 6), (15, 14), (6, 19), (5, 16), (4, 4), (30, 2), (36, 22), (1, 5), (36, 26), (28, 19), (30, 7), (14, 28), (13, 27), (4, 21), (25, 10), (34, 30), (14, 23), (24, 16), (11, 4), (35, 12), (24, 31), (12, 21), (1, 3), (35, 26), (4, 29), (13, 23), (13, 16), (13, 15), (3, 23), (8, 26), (26, 7), (13, 3), (36, 20), (24, 4), (17, 20), (3, 20), (29, 16), (18, 5), (20, 0), (27, 25), (33, 3), (22, 17), (27, 3), (33, 4), (34, 20), (9, 7), (32, 24), (36, 6), (34, 12), (27, 7), (27, 15), (33, 15), (3, 10), (14, 10), (13, 11), (28, 21), (8, 17), (29, 10), (34, 18), (26, 15), (22, 30), (9, 22), (7, 7), (26, 0), (36, 15), (25, 27), (33, 29), (15, 30), (2, 24), (26, 26), (9, 3), (19, 19), (15, 9), (14, 5), (27, 22), (19, 17), (23, 24), (24, 27), (1, 26), (4, 24), (2, 7), (9, 10), (27, 11), (0, 12), (3, 24), (13, 6), (29, 4), (7, 6), (30, 26), (6, 17), (14, 19), (3, 9), (12, 14), (23, 20), (24, 26), (17, 26), (11, 10), (4, 17), (31, 24), (24, 14), (23, 26), (11, 3), (6, 13), (21, 5), (21, 17), (33, 18), (24, 6), (22, 29), (26, 1), (30, 28), (26, 28), (27, 16), (31, 29), (10, 19), (33, 5), (34, 7), (12, 22), (23, 16), (10, 14), (17, 0), (16, 15), (36, 14), (12, 17), (6, 12), (19, 5), (30, 23), (1, 21), (3, 6), (28, 10), (0, 2), (5, 25), (3, 27), (4, 9), (7, 27), (4, 16), (31, 0), (3, 11), (17, 7), (27, 24), (18, 21), (0, 11), (3, 26), (25, 18), (10, 30), (20, 5), (2, 17), (24, 13), (24, 3), (36, 2), (28, 30), (19, 29), (31, 22), (24, 1), (0, 6), (8, 22), (35, 10), (8, 9), (32, 16), (34, 14), (35, 13), (23, 15), (24, 2), (7, 30), (7, 3), (32, 29), (4, 15), (34, 19), (22, 6), (25, 0), (10, 24), (20, 28), (4, 23), (17, 14), (30, 9), (0, 21), (25, 5), (21, 2), (21, 18), (26, 22), (0, 30), (1, 0), (4, 31), (26, 19), (22, 10), (21, 21), (17, 5), (8, 21), (14, 1), (4, 22), (5, 9), (26, 25), (21, 12), (33, 27), (22, 7), (19, 31), (26, 21), (8, 31), (6, 29), (35, 0), (18, 29), (17, 4), (31, 13), (29, 0), (10, 2), (36, 12), (34, 16), (7, 12), (3, 28), (7, 24), (33, 11), (29, 26), (27, 31), (24, 0), (23, 12), (0, 3), (7, 22), (26, 11), (16, 31), (7, 2), (6, 2), (15, 12), (36, 8), (1, 13), (16, 12), (33, 25), (26, 10), (33, 23), (17, 30), (31, 7), (5, 20), (20, 10), (31, 28), (0, 28), (31, 10), (29, 22), (24, 18), (0, 19), (28, 2), (36, 9), (34, 13), (25, 15), (4, 18), (6, 28), (11, 13), (10, 4), (2, 11), (22, 31), (12, 3), (23, 7), (11, 24), (15, 19), (36, 30), (26, 18), (11, 12), (10, 20), (30, 21), (5, 3), (26, 27), (15, 0), (15, 22), (16, 23), (3, 22), (22, 21), (32, 19), (25, 8), (16, 13), (14, 27), (32, 6), (33, 31), (1, 12), (18, 18), (20, 27), (27, 30), (7, 28), (5, 17), (18, 25), (19, 9), (5, 27), (35, 28), (36, 27), (0, 24), (25, 16), (15, 18), (30, 22), (36, 29), (32, 26), (29, 28), (23, 21), (36, 17), (30, 16), (29, 3), (7, 14), (15, 11), (24, 10), (30, 15), (33, 19), (20, 26), (32, 27), (8, 10), (4, 26), (29, 29), (19, 1), (26, 30), (14, 21), (6, 5), (24, 11), (22, 24), (4, 8), (10, 23), (36, 13), (1, 4), (33, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570216", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (18, 28), (4, 3), (31, 2), (21, 1), (28, 4), (8, 14), (18, 27), (30, 17), (32, 8), (14, 27), (5, 28), (21, 26), (26, 17), (0, 10), (14, 7), (5, 23), (32, 22), (3, 24), (26, 2), (15, 25), (28, 6), (5, 29), (29, 5), (26, 30), (8, 12), (21, 2), (10, 22), (32, 18), (21, 4), (27, 15), (7, 9), (19, 23), (23, 6), (26, 8), (28, 29), (22, 12), (16, 28), (17, 12), (7, 12), (5, 20), (5, 12), (2, 10), (28, 8), (19, 12), (18, 1), (21, 15), (31, 17), (19, 20), (24, 22), (3, 22), (15, 11), (25, 3), (32, 2), (4, 13), (9, 1), (16, 14), (24, 25), (24, 3), (6, 18), (6, 3), (24, 1), (11, 21), (26, 24), (19, 5), (17, 10), (26, 11), (8, 6), (29, 1), (2, 16), (9, 10), (24, 26), (25, 25), (13, 19), (2, 14), (14, 25), (13, 6), (31, 1), (9, 19), (18, 12), (24, 24), (20, 25), (6, 6), (16, 26), (14, 5), (12, 22), (5, 24), (31, 22), (0, 6), (5, 3), (5, 16), (12, 27), (29, 21), (23, 13), (9, 15), (21, 8), (19, 13), (25, 1), (14, 6), (9, 23), (17, 21), (5, 7), (9, 30), (10, 0), (15, 13), (12, 16), (31, 7), (20, 30), (3, 0), (7, 20), (12, 12), (3, 6), (2, 22), (13, 24), (7, 21), (13, 9), (25, 5), (18, 8), (4, 10), (13, 25), (8, 2), (9, 3), (20, 14), (14, 11), (4, 12), (17, 22), (27, 28), (16, 16), (10, 20), (9, 28), (9, 12), (0, 21), (22, 18), (14, 20), (6, 9), (24, 20), (20, 3), (22, 9), (12, 5), (29, 16), (4, 28), (25, 8), (0, 14), (23, 20), (12, 0), (32, 10), (10, 29), (31, 26), (16, 8), (3, 13), (7, 8), (17, 26), (15, 15), (8, 19), (11, 13), (22, 21), (29, 6), (12, 20), (29, 13), (2, 25), (23, 30), (26, 27), (3, 7), (22, 1), (13, 3), (32, 6), (17, 16), (21, 27), (25, 24), (16, 13), (8, 16), (22, 3), (20, 16), (1, 29), (11, 6), (9, 29), (28, 7), (29, 11), (30, 16), (15, 20), (6, 23), (21, 23), (10, 11), (18, 15), (0, 26), (30, 2), (28, 10), (5, 14), (10, 2), (3, 2), (29, 22), (7, 28), (16, 9), (31, 23), (13, 8), (28, 11), (27, 6), (17, 20), (9, 18), (21, 3), (24, 6), (5, 26), (13, 20), (29, 7), (30, 12), (22, 14), (31, 15), (2, 19), (13, 7), (20, 6), (26, 12), (17, 19), (27, 18), (22, 29), (27, 10), (3, 28), (0, 27), (29, 17), (24, 14), (6, 28), (7, 15), (11, 24), (23, 19), (5, 19), (28, 9), (24, 16), (6, 1), (17, 15), (11, 29), (4, 24), (29, 10), (13, 21), (26, 0), (31, 12), (30, 6), (19, 21), (1, 16), (21, 6), (14, 21), (6, 12), (10, 18), (6, 10), (12, 21), (29, 23), (21, 0), (19, 9), (19, 27), (14, 14), (1, 23), (20, 18), (23, 24), (15, 26), (21, 5), (23, 7), (2, 30), (3, 12), (18, 21), (14, 26), (11, 25), (19, 18), (19, 29), (7, 10), (7, 0), (27, 17), (30, 11), (18, 0), (4, 2), (3, 30), (21, 7), (12, 8), (19, 7), (14, 29), (3, 11), (32, 25), (27, 16), (31, 30), (27, 27), (13, 23), (25, 4), (23, 3), (1, 21), (19, 14), (18, 17), (12, 19), (22, 8), (28, 1), (1, 24), (32, 9), (18, 5), (0, 20), (10, 19), (31, 6), (30, 30), (13, 12), (10, 6), (11, 15), (10, 27), (32, 14), (28, 15), (12, 1), (14, 24), (15, 0), (4, 21), (6, 30), (15, 5), (27, 23), (28, 22), (20, 26), (24, 29), (7, 1), (1, 14), (27, 22), (24, 19), (4, 26), (22, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73656", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (4, 7), (22, 29), (29, 28), (25, 17), (20, 28), (27, 15), (3, 18), (3, 10), (20, 13), (30, 4), (12, 9), (15, 24), (17, 11), (17, 0), (6, 22), (0, 3), (30, 3), (1, 28), (20, 2), (21, 27), (29, 12), (19, 15), (15, 9), (6, 9), (16, 0), (25, 25), (13, 25), (27, 28), (10, 12), (13, 11), (1, 5), (21, 19), (12, 16), (6, 0), (1, 9), (25, 28), (2, 25), (8, 15), (6, 19), (5, 2), (21, 9), (0, 22), (13, 16), (28, 1), (28, 2), (19, 22), (23, 12), (14, 27), (21, 1), (21, 4), (20, 5), (8, 26), (25, 21), (5, 5), (8, 3), (16, 23), (17, 17), (9, 15), (7, 7), (15, 18), (24, 15), (13, 6), (9, 5), (29, 24), (9, 28), (8, 19), (17, 18), (20, 27), (4, 12), (2, 7), (6, 3), (26, 11), (7, 18), (22, 17), (30, 16), (17, 15), (22, 21), (1, 24), (19, 2), (24, 6), (0, 13), (1, 26), (14, 16), (26, 4), (7, 5), (21, 0), (23, 28), (24, 20), (22, 28), (27, 23), (2, 5), (3, 5), (29, 10), (27, 20), (21, 13), (13, 10), (8, 5), (2, 19), (13, 1), (23, 15), (17, 16), (11, 23), (3, 4), (11, 17), (27, 0), (3, 16), (30, 14), (30, 28), (12, 7), (1, 6), (28, 18), (13, 23), (11, 16), (16, 15), (27, 6), (30, 20), (17, 9), (13, 21), (19, 20), (2, 8), (13, 9), (20, 14), (25, 12), (23, 26), (14, 6), (22, 14), (4, 4), (29, 5), (1, 21), (10, 2), (2, 18), (13, 18), (5, 0), (21, 21), (14, 9), (22, 18), (11, 13), (15, 28), (26, 15), (4, 25), (0, 14), (18, 0), (2, 1), (29, 21), (4, 11), (28, 16), (28, 3), (10, 27), (21, 11), (24, 14), (7, 9), (1, 17), (15, 26), (24, 9), (9, 2), (30, 18), (18, 21), (27, 1), (5, 14), (15, 29), (18, 16), (9, 23), (24, 19), (19, 19), (19, 24), (18, 6), (22, 8), (17, 12), (12, 20), (14, 26), (19, 21), (16, 20), (27, 9), (16, 19), (30, 8), (12, 12), (8, 17), (14, 23), (23, 21), (27, 22), (29, 0), (10, 6), (14, 17), (2, 17), (8, 2), (18, 26), (17, 19), (23, 25), (10, 0), (24, 25), (12, 19), (24, 26), (23, 13), (21, 6), (11, 24), (10, 20), (10, 7), (24, 17), (3, 21), (21, 8), (15, 8), (22, 0), (0, 20), (8, 0), (8, 25), (29, 16), (12, 21), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766896", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (25, 28), (8, 22), (13, 3), (14, 28), (28, 14), (20, 19), (22, 0), (7, 5), (11, 17), (5, 21), (26, 0), (15, 6), (5, 28), (20, 14), (11, 29), (26, 17), (13, 27), (5, 1), (20, 28), (10, 2), (6, 7), (27, 19), (9, 7), (22, 22), (1, 14), (10, 12), (0, 20), (8, 25), (26, 2), (23, 9), (18, 15), (19, 17), (14, 4), (13, 13), (25, 20), (8, 18), (11, 10), (6, 29), (9, 6), (19, 24), (24, 22), (29, 14), (12, 9), (4, 8), (23, 20), (1, 3), (13, 21), (1, 26), (2, 29), (28, 10), (20, 25), (14, 22), (0, 12), (25, 23), (17, 11), (6, 3), (26, 24), (10, 29), (17, 2), (15, 4), (27, 17), (20, 2), (16, 5), (2, 22), (0, 19), (1, 11), (23, 23), (7, 28), (4, 10), (11, 27), (27, 6), (15, 19), (22, 23), (10, 20), (21, 10), (28, 16), (12, 26), (4, 1), (13, 26), (4, 6), (27, 11), (9, 27), (11, 15), (8, 26), (25, 4), (11, 3), (29, 2), (9, 13), (16, 12), (25, 6), (5, 20), (22, 2), (9, 25), (25, 19), (12, 27), (25, 14), (24, 17), (29, 16), (11, 4), (16, 23), (14, 2), (16, 19), (12, 20), (26, 11), (22, 16), (30, 28), (24, 9), (17, 4), (24, 13), (11, 16), (18, 13), (20, 17), (10, 11), (15, 23), (20, 5), (3, 22), (19, 7), (29, 11), (24, 25), (26, 16), (29, 1), (27, 26), (3, 3), (11, 0), (10, 7), (26, 22), (17, 1), (20, 16), (12, 14), (19, 15), (23, 6), (28, 0), (14, 0), (12, 3), (18, 5), (12, 21), (15, 14), (21, 29), (7, 18), (20, 3), (5, 10), (28, 12), (17, 7), (5, 6), (8, 17), (1, 9), (6, 1), (24, 15), (13, 14), (9, 5), (30, 4), (12, 8), (9, 26), (0, 7), (14, 7), (1, 8), (17, 0), (28, 23), (15, 18), (23, 0), (3, 14), (21, 5), (0, 11), (7, 3), (7, 25), (7, 23), (4, 17), (24, 1), (21, 13), (0, 27), (27, 20), (25, 13), (29, 21), (6, 19), (15, 9), (20, 12), (3, 13), (0, 13), (8, 7), (16, 9), (9, 12), (1, 17), (14, 10), (3, 1), (5, 23), (29, 7), (5, 14), (15, 2), (25, 29), (4, 25), (28, 18), (5, 12), (9, 2), (10, 19), (29, 8), (25, 12), (1, 22), (3, 6), (20, 9), (23, 24), (18, 8), (28, 4), (14, 21), (17, 6), (6, 13), (4, 26), (6, 16), (3, 25), (10, 21), (12, 24), (0, 26), (23, 26), (15, 1), (10, 17), (1, 13), (21, 21), (24, 27), (0, 17), (4, 0), (11, 26), (26, 18), (24, 20), (26, 6), (20, 15), (30, 9), (25, 24), (26, 4), (1, 18), (7, 14), (13, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566475", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 21), (3, 0), (24, 18), (19, 14), (2, 10), (14, 22), (0, 4), (27, 6), (2, 0), (20, 31), (6, 6), (5, 24), (11, 14), (26, 10), (23, 28), (3, 18), (12, 1), (6, 14), (20, 27), (7, 24), (6, 10), (9, 9), (24, 16), (21, 0), (6, 8), (28, 14), (25, 0), (5, 6), (13, 5), (18, 16), (11, 8), (14, 32), (25, 14), (1, 4), (1, 32), (10, 3), (18, 17), (25, 17), (4, 13), (28, 25), (24, 20), (19, 21), (11, 10), (28, 18), (5, 18), (3, 24), (1, 21), (15, 11), (12, 27), (23, 24), (8, 14), (9, 25), (5, 23), (25, 26), (19, 8), (29, 19), (27, 32), (16, 2), (29, 16), (25, 3), (2, 16), (22, 15), (4, 17), (11, 16), (19, 30), (11, 25), (1, 31), (19, 29), (5, 9), (20, 17), (12, 7), (6, 3), (1, 1), (19, 19), (12, 25), (21, 29), (18, 23), (15, 31), (9, 17), (3, 11), (17, 17), (2, 17), (25, 2), (10, 13), (16, 3), (13, 32), (7, 27), (12, 22), (9, 19), (11, 7), (10, 25), (10, 18), (27, 1), (28, 26), (20, 9), (23, 17), (24, 10), (2, 9), (22, 23), (16, 14), (27, 31), (28, 21), (11, 29), (12, 16), (21, 4), (11, 22), (5, 32), (0, 8), (10, 2), (11, 0), (1, 23), (27, 14), (3, 21), (18, 28), (24, 19), (11, 19), (14, 30), (19, 15), (9, 10), (4, 0), (6, 26), (18, 19), (1, 28), (9, 12), (26, 15), (20, 14), (7, 23), (23, 22), (12, 17), (28, 27), (6, 18), (6, 4), (4, 9), (26, 23), (18, 5), (29, 17), (27, 10), (3, 3), (16, 16), (13, 16), (13, 21), (25, 10), (26, 28), (13, 9), (26, 12), (2, 1), (18, 10), (29, 24), (19, 1), (29, 15), (15, 24), (25, 13), (21, 15), (5, 26), (11, 17), (8, 3), (6, 25), (27, 24), (19, 11), (26, 29), (24, 30), (1, 7), (9, 30), (21, 23), (17, 0), (25, 4), (24, 28), (28, 2), (18, 11), (16, 28), (7, 22), (15, 9), (23, 1), (12, 15), (0, 10), (18, 14), (7, 9), (0, 3), (21, 13), (14, 2), (14, 20), (5, 2), (19, 13), (0, 26), (18, 25), (27, 15), (25, 6), (10, 1), (18, 24), (15, 20), (29, 28), (24, 25), (25, 24), (22, 32), (18, 7), (7, 16), (21, 10), (2, 13), (15, 10), (18, 2), (7, 0), (24, 24), (28, 23), (5, 17), (16, 19), (7, 6), (26, 22), (11, 3), (18, 26), (28, 8), (24, 15), (2, 7), (8, 19), (22, 17), (25, 18), (16, 8), (20, 5), (21, 30), (24, 11), (17, 30), (0, 7), (27, 3), (25, 11), (22, 13), (10, 23), (12, 5), (14, 26), (14, 23), (9, 15), (9, 18), (23, 14), (28, 9), (25, 22), (3, 16), (11, 9), (1, 8), (20, 25), (28, 19), (8, 25), (4, 10), (22, 8), (27, 20), (2, 21), (18, 27), (1, 26), (15, 26), (8, 18), (23, 9), (23, 31), (25, 9), (3, 25), (15, 25), (21, 24), (22, 9), (8, 11), (24, 5), (6, 11), (21, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664956", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 19), (20, 2), (22, 35), (0, 19), (9, 33), (37, 13), (29, 5), (23, 34), (14, 6), (6, 14), (4, 22), (30, 11), (13, 9), (4, 24), (21, 17), (36, 16), (13, 37), (4, 9), (19, 5), (6, 37), (21, 24), (1, 28), (22, 31), (25, 33), (7, 10), (13, 22), (20, 0), (24, 30), (30, 30), (16, 4), (15, 17), (0, 36), (5, 31), (5, 33), (7, 8), (26, 38), (9, 10), (27, 8), (4, 31), (18, 38), (32, 8), (36, 9), (15, 20), (31, 35), (37, 5), (26, 5), (17, 24), (22, 37), (5, 29), (17, 12), (9, 2), (12, 10), (30, 7), (25, 12), (27, 22), (11, 22), (21, 0), (29, 18), (8, 7), (19, 15), (30, 1), (30, 26), (24, 34), (33, 17), (10, 4), (10, 27), (33, 28), (12, 0), (8, 33), (0, 1), (28, 0), (28, 21), (34, 26), (32, 9), (37, 20), (32, 26), (26, 24), (15, 7), (14, 18), (11, 21), (5, 2), (9, 23), (20, 31), (31, 16), (6, 17), (12, 23), (31, 9), (20, 27), (10, 2), (35, 7), (25, 19), (2, 4), (0, 37), (21, 36), (7, 25), (8, 12), (18, 9), (32, 20), (5, 28), (37, 35), (13, 38), (11, 29), (7, 2), (12, 7), (24, 10), (9, 19), (32, 29), (25, 30), (2, 13), (0, 26), (30, 2), (29, 0), (22, 11), (29, 12), (28, 10), (37, 22), (2, 0), (35, 19), (26, 3), (36, 23), (10, 18), (16, 2), (33, 22), (33, 27), (3, 29), (26, 23), (16, 13), (15, 12), (31, 0), (20, 22), (26, 6), (21, 10), (17, 32), (6, 21), (33, 31), (11, 10), (27, 25), (21, 35), (11, 16), (20, 23), (25, 7), (4, 32), (16, 11), (5, 35), (15, 29), (2, 26), (5, 20), (36, 5), (31, 28), (11, 13), (21, 27), (23, 25), (29, 10), (18, 29), (34, 33), (34, 17), (27, 6), (10, 11), (30, 15), (34, 4), (23, 22), (31, 37), (34, 12), (17, 6), (22, 17), (28, 17), (19, 9), (9, 30), (16, 25), (21, 30), (12, 16), (4, 29), (10, 16), (10, 7), (10, 14), (8, 24), (19, 13), (7, 19), (6, 2), (33, 38), (22, 27), (32, 0), (8, 25), (13, 15), (7, 31), (16, 23), (23, 18), (22, 38), (32, 3), (19, 27), (5, 32), (31, 6), (16, 35), (20, 18), (27, 1), (20, 10), (24, 24), (19, 20), (1, 38), (19, 29), (33, 25), (22, 36), (21, 31), (8, 11), (4, 36), (25, 16), (3, 24), (25, 18), (37, 11), (23, 9), (28, 11), (17, 16), (28, 19), (28, 38), (7, 16), (33, 30), (17, 25), (6, 0), (29, 24), (0, 8), (37, 25), (3, 37), (3, 28), (18, 4), (13, 36), (17, 2), (34, 7), (24, 37), (31, 4), (13, 10), (7, 30), (30, 29), (14, 23), (18, 33), (23, 24), (15, 38), (22, 15), (7, 35), (5, 25), (10, 30), (1, 14), (25, 35), (32, 28), (4, 37), (27, 24), (23, 36), (23, 33), (16, 26), (25, 37), (22, 2), (3, 4), (4, 38), (31, 27), (5, 19), (37, 4), (23, 4), (6, 16), (34, 6), (21, 34), (7, 15), (23, 31), (18, 32), (18, 8), (19, 24), (31, 12), (33, 7), (1, 36), (2, 27), (19, 28), (32, 10), (22, 18), (20, 21), (14, 3), (19, 34), (34, 10), (24, 20), (33, 20), (25, 23), (36, 20), (7, 34), (3, 25), (7, 9), (37, 21), (9, 7), (24, 26), (33, 8), (22, 13), (22, 10), (25, 8), (3, 2), (13, 21), (23, 37), (9, 36), (12, 36), (24, 19), (28, 31), (0, 22), (0, 27), (13, 18), (26, 0), (4, 19), (13, 17), (25, 9), (22, 22), (2, 31), (17, 13), (18, 22), (11, 24), (7, 6), (6, 19), (31, 33), (21, 32), (4, 8), (12, 17), (3, 18), (9, 27), (5, 9), (0, 18), (16, 17), (10, 32), (27, 20), (11, 5), (29, 11), (37, 23), (33, 19), (17, 31), (5, 7), (15, 8), (14, 14), (30, 36), (36, 19), (19, 36), (8, 29), (24, 27), (18, 13), (0, 5), (1, 15), (16, 10), (4, 6), (31, 32), (35, 31), (20, 20), (30, 31), (29, 3), (4, 16), (35, 13), (35, 37), (1, 35), (8, 23), (21, 9), (3, 7), (3, 20), (31, 14), (13, 0), (28, 6), (12, 14), (12, 18), (30, 35), (33, 14), (37, 33), (14, 13), (29, 33), (2, 24), (15, 6), (6, 20), (22, 30), (6, 11), (5, 24), (9, 18), (19, 35), (22, 3), (19, 6), (15, 14), (24, 17), (8, 34), (16, 1), (15, 25), (28, 24), (10, 5), (5, 27), (14, 30), (36, 36), (29, 31), (5, 4), (15, 26), (12, 30), (34, 11), (26, 14), (31, 29), (19, 10), (0, 12), (14, 38), (31, 30), (32, 15), (14, 28), (29, 27), (2, 29), (15, 2), (9, 31), (10, 17), (24, 3), (5, 26), (27, 29), (25, 31), (23, 38), (20, 35), (36, 31), (29, 14), (36, 37), (16, 34), (26, 13), (29, 20), (4, 26), (33, 29), (33, 26), (0, 9), (3, 5), (1, 21), (32, 6), (32, 19), (0, 14), (14, 12), (15, 22), (22, 9), (8, 14), (37, 17), (2, 38), (15, 24), (10, 25), (20, 14), (28, 9), (1, 7), (5, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 6), (28, 20), (19, 25), (17, 22), (25, 23), (21, 12), (14, 26), (17, 2), (11, 26), (12, 30), (13, 30), (0, 25), (1, 19), (21, 32), (30, 19), (26, 4), (12, 28), (17, 5), (0, 2), (3, 0), (12, 31), (27, 1), (23, 23), (12, 25), (23, 11), (25, 13), (9, 21), (5, 23), (1, 15), (15, 0), (14, 28), (6, 26), (25, 17), (26, 20), (13, 1), (16, 13), (24, 1), (4, 22), (23, 0), (6, 30), (0, 18), (8, 29), (8, 24), (18, 33), (19, 24), (2, 7), (10, 4), (27, 7), (30, 25), (14, 30), (21, 29), (22, 17), (8, 12), (3, 12), (13, 28), (9, 29), (22, 19), (7, 19), (23, 7), (24, 9), (27, 14), (2, 18), (20, 0), (16, 2), (25, 3), (20, 10), (12, 34), (15, 17), (5, 14), (4, 32), (6, 6), (5, 3), (29, 27), (15, 26), (10, 30), (29, 6), (25, 27), (16, 24), (9, 6), (28, 17), (17, 16), (5, 32), (7, 9), (10, 16), (1, 31), (13, 21), (10, 34), (16, 5), (10, 21), (11, 2), (13, 4), (28, 19), (22, 29), (3, 17), (22, 15), (19, 20), (4, 27), (29, 4), (9, 1), (17, 6), (7, 21), (2, 15), (28, 4), (1, 16), (5, 30), (28, 8), (30, 31), (15, 20), (12, 3), (5, 29), (28, 31), (22, 23), (2, 23), (1, 34), (22, 10), (28, 5), (24, 15), (22, 12), (25, 6), (0, 6), (1, 4), (6, 21), (26, 3), (16, 12), (24, 34), (19, 12), (27, 16), (26, 12), (26, 15), (28, 28), (6, 23), (5, 25), (7, 32), (13, 16), (30, 4), (8, 6), (12, 32), (9, 13), (20, 33), (7, 6), (26, 8), (21, 5), (18, 21), (24, 2), (4, 24), (12, 16), (12, 26), (28, 13), (29, 16), (4, 10), (6, 7), (1, 7), (27, 11), (23, 18), (19, 31), (11, 13), (29, 18), (12, 29), (24, 28), (10, 28), (29, 28), (21, 6), (9, 18), (8, 4), (18, 13), (3, 33), (12, 33), (6, 34), (22, 13), (24, 17), (30, 7), (8, 2), (1, 30), (28, 3), (5, 18), (26, 29), (7, 4), (26, 27), (28, 10), (16, 7), (19, 3), (7, 17), (30, 16), (30, 20), (10, 0), (7, 18), (16, 28), (20, 21), (16, 27), (2, 19), (24, 8), (18, 0), (6, 27), (16, 20), (28, 2), (9, 24), (5, 22), (7, 34), (28, 24), (16, 16), (19, 9), (12, 18), (20, 19), (4, 34), (2, 11), (2, 25), (2, 2), (27, 9), (17, 30), (20, 13), (0, 14), (11, 4), (10, 27), (19, 7), (30, 30), (28, 7), (6, 16), (5, 20), (29, 29), (18, 2), (20, 26), (14, 9), (10, 22), (4, 25), (8, 15), (11, 27), (23, 32), (15, 23), (14, 33), (3, 11), (13, 19), (25, 20), (16, 4), (0, 32), (3, 2), (4, 28), (3, 6), (21, 24), (24, 20), (9, 15), (21, 10), (15, 10), (27, 8), (29, 11), (29, 17), (7, 1), (27, 21), (20, 2), (16, 34), (17, 18), (1, 32), (28, 16), (6, 4), (1, 8), (6, 15), (1, 27), (1, 10), (23, 14), (5, 8), (28, 33), (10, 18), (17, 20), (9, 14), (13, 10), (27, 4), (29, 7), (17, 10), (22, 16), (8, 10), (12, 17), (13, 29), (12, 23), (30, 22), (13, 6), (29, 21), (2, 17), (6, 14), (30, 14), (23, 10), (8, 33), (22, 32), (19, 34), (15, 15), (15, 30), (14, 11), (0, 26), (19, 4), (4, 12), (19, 32), (17, 27), (6, 3), (5, 21), (5, 5), (10, 9), (15, 31), (5, 17), (7, 7), (29, 12), (6, 13), (25, 9), (17, 33), (1, 26), (24, 27), (18, 31), (1, 25), (14, 3), (17, 13), (26, 32), (23, 12), (11, 9), (24, 6), (19, 30), (14, 29), (6, 18), (27, 29), (29, 31), (24, 14), (11, 20), (20, 1), (13, 8), (17, 31), (11, 24), (10, 31), (25, 16), (9, 9), (22, 34), (4, 19), (28, 26), (15, 24), (24, 19), (25, 32), (30, 13), (23, 24), (4, 29), (26, 25), (1, 9), (16, 19), (22, 6), (11, 6), (1, 22), (19, 26), (3, 8), (23, 21), (20, 24), (29, 19), (2, 10), (0, 15), (25, 15), (17, 15), (5, 9), (15, 32), (9, 8), (30, 11), (15, 33), (2, 6), (17, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943488", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 34), (14, 10), (30, 36), (19, 21), (25, 28), (15, 25), (31, 5), (29, 6), (15, 9), (30, 32), (3, 14), (24, 14), (32, 0), (2, 1), (11, 4), (19, 24), (14, 8), (17, 7), (1, 4), (7, 30), (0, 20), (16, 28), (24, 29), (23, 35), (9, 26), (26, 29), (12, 3), (25, 35), (28, 14), (0, 3), (8, 30), (10, 35), (3, 33), (32, 23), (4, 19), (5, 1), (5, 7), (31, 27), (26, 0), (7, 36), (14, 17), (15, 22), (7, 24), (29, 22), (19, 11), (16, 11), (30, 13), (20, 34), (6, 19), (10, 27), (6, 35), (6, 4), (32, 26), (29, 2), (7, 3), (8, 35), (27, 25), (31, 13), (31, 11), (27, 17), (0, 13), (29, 30), (18, 35), (23, 15), (9, 8), (11, 28), (20, 36), (31, 26), (22, 23), (15, 4), (9, 7), (3, 24), (10, 24), (19, 30), (22, 35), (15, 1), (19, 13), (27, 30), (1, 27), (3, 10), (2, 21), (20, 3), (25, 15), (27, 7), (8, 4), (12, 0), (19, 9), (26, 28), (2, 19), (26, 16), (23, 32), (24, 31), (16, 32), (31, 28), (9, 5), (18, 2), (28, 12), (29, 7), (30, 5), (22, 0), (26, 15), (26, 3), (19, 29), (17, 25), (9, 21), (27, 18), (5, 9), (22, 16), (18, 26), (29, 12), (26, 36), (4, 28), (3, 34), (12, 11), (3, 26), (21, 19), (10, 23), (14, 9), (1, 11), (23, 1), (8, 6), (25, 27), (18, 24), (27, 34), (26, 10), (4, 33), (0, 35), (20, 9), (8, 36), (16, 8), (8, 20), (5, 8), (30, 14), (25, 34), (14, 1), (23, 23), (16, 10), (1, 34), (27, 22), (11, 12), (25, 33), (18, 11), (21, 18), (28, 9), (20, 2), (28, 24), (14, 2), (9, 6), (10, 21), (21, 20), (23, 10), (18, 30), (24, 11), (7, 16), (29, 5), (31, 2), (26, 26), (16, 5), (16, 25), (5, 24), (22, 29), (22, 18), (12, 29), (13, 27), (2, 28), (4, 20), (19, 27), (25, 3), (20, 12), (20, 0), (26, 25), (16, 35), (11, 24), (22, 5), (14, 21), (23, 0), (1, 6), (4, 14), (29, 1), (21, 27), (28, 26), (2, 24), (26, 23), (19, 35), (5, 29), (3, 3), (12, 27), (29, 34), (28, 27), (23, 28), (21, 17), (0, 29), (13, 16), (0, 21), (0, 14), (11, 33), (10, 9), (13, 11), (1, 30), (1, 15), (3, 9), (31, 3), (32, 22), (13, 29), (3, 1), (11, 20), (27, 4), (24, 7), (12, 25), (9, 17), (4, 23), (21, 11), (2, 36), (4, 7), (5, 6), (4, 1), (31, 0), (29, 18), (10, 11), (32, 4), (3, 6), (22, 12), (0, 23), (27, 10), (5, 28), (5, 23), (6, 16), (7, 14), (30, 18), (16, 26), (27, 11), (4, 6), (0, 6), (25, 26), (25, 20), (5, 5), (32, 12), (0, 31), (4, 29), (10, 32), (19, 15), (4, 16), (17, 6), (24, 22), (26, 6), (29, 21), (12, 17), (23, 9), (21, 8), (10, 6), (2, 14), (1, 13), (29, 31), (1, 2), (25, 29), (19, 28), (29, 14), (12, 36), (32, 27), (30, 19), (5, 19), (20, 5), (25, 12), (15, 7), (28, 20), (15, 10), (2, 15), (12, 7), (27, 20), (23, 21), (21, 6), (19, 3), (18, 18), (13, 34), (6, 30), (24, 32), (7, 7), (18, 20), (18, 15), (25, 19), (19, 22), (13, 0), (12, 24), (5, 20), (32, 6), (14, 19), (20, 22), (0, 9), (6, 28), (28, 5), (31, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "395010", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 14), (12, 29), (7, 18), (15, 15), (11, 2), (23, 30), (17, 20), (8, 20), (25, 17), (27, 15), (31, 27), (5, 19), (7, 4), (19, 5), (15, 20), (20, 19), (31, 11), (3, 25), (28, 17), (32, 1), (8, 19), (10, 15), (19, 25), (25, 5), (24, 19), (29, 20), (2, 21), (23, 23), (3, 21), (20, 24), (31, 19), (14, 18), (15, 8), (33, 10), (3, 16), (26, 28), (3, 28), (7, 13), (11, 18), (12, 10), (4, 6), (26, 5), (0, 5), (29, 24), (17, 22), (28, 16), (19, 2), (26, 9), (17, 9), (12, 4), (25, 13), (19, 0), (29, 11), (32, 7), (5, 15), (29, 16), (11, 23), (4, 13), (22, 4), (31, 5), (10, 5), (24, 1), (33, 16), (24, 27), (12, 8), (26, 6), (25, 19), (14, 9), (27, 4), (16, 30), (11, 12), (10, 9), (15, 10), (17, 5), (17, 2), (17, 14), (16, 14), (25, 4), (11, 25), (33, 17), (16, 9), (17, 10), (26, 7), (12, 21), (2, 16), (5, 4), (5, 20), (1, 8), (6, 14), (16, 23), (29, 23), (30, 16), (18, 12), (12, 23), (29, 18), (14, 12), (24, 0), (0, 24), (22, 20), (6, 3), (6, 12), (17, 8), (23, 2), (6, 6), (15, 3), (4, 2), (7, 24), (8, 29), (21, 28), (18, 29), (3, 22), (33, 5), (2, 9), (26, 13), (6, 10), (19, 6), (23, 13), (30, 10), (9, 26), (32, 30), (13, 12), (2, 30), (27, 11), (29, 25), (11, 9), (17, 16), (33, 26), (8, 3), (9, 0), (13, 6), (21, 25), (13, 4), (21, 6), (11, 5), (5, 5), (12, 19), (10, 30), (18, 9), (26, 19), (26, 17), (26, 24), (30, 4), (20, 23), (24, 20), (29, 12), (22, 17), (29, 27), (33, 2), (26, 18), (27, 2), (6, 30), (4, 7), (14, 21), (7, 30), (7, 14), (11, 3), (33, 24), (23, 15), (18, 25), (7, 5), (20, 27), (15, 1), (21, 17), (6, 20), (26, 25), (33, 19), (15, 18), (23, 21), (24, 16), (16, 6), (24, 21), (27, 23), (27, 17), (25, 11), (4, 16), (32, 17), (15, 23), (2, 12), (29, 29), (29, 17), (6, 15), (4, 1), (31, 28), (1, 6), (2, 14), (17, 13), (5, 10), (11, 16), (24, 25), (22, 0), (31, 23), (12, 0), (11, 20), (22, 3), (0, 26), (19, 20), (4, 26), (19, 15), (17, 15), (3, 24), (19, 13), (27, 13), (15, 13), (28, 12), (18, 27), (22, 2), (12, 6), (20, 29), (25, 12), (3, 20), (4, 24), (11, 29), (15, 0), (14, 6), (7, 16), (20, 7), (0, 29), (30, 13), (3, 29), (22, 14), (17, 6), (1, 9), (7, 3), (10, 10), (26, 4), (1, 1), (13, 7), (2, 11), (15, 21), (18, 23), (17, 27), (16, 11), (5, 30), (32, 25), (4, 30), (32, 27), (6, 5), (12, 16), (21, 26), (27, 18), (14, 7), (23, 8), (18, 16), (22, 9), (30, 25), (33, 7), (24, 24), (4, 3), (10, 1), (12, 17), (0, 1), (33, 3), (11, 24), (22, 26), (23, 0), (31, 7), (0, 6), (10, 6), (1, 19), (5, 24), (26, 11), (9, 27), (2, 17), (13, 8), (32, 22), (8, 16), (18, 15), (22, 8), (7, 11), (16, 16), (2, 19), (16, 27), (26, 2), (0, 19), (8, 22), (28, 4), (25, 6), (26, 26), (8, 28), (9, 24), (10, 3), (12, 3), (25, 3), (17, 12), (11, 10), (6, 22), (33, 0), (3, 19), (28, 11), (18, 18), (6, 9), (32, 15), (18, 24), (18, 13), (18, 14), (7, 26), (33, 4), (29, 1), (19, 7), (14, 30), (13, 17), (0, 22), (4, 28), (7, 27), (2, 13), (12, 25), (7, 20), (27, 19), (19, 10), (9, 15), (9, 19), (17, 0), (3, 14), (11, 6), (18, 3), (8, 8), (8, 9), (20, 9), (4, 29), (19, 22), (32, 26), (29, 6), (5, 17), (1, 7), (31, 17), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 22), (4, 20), (20, 7), (30, 10), (20, 12), (26, 23), (9, 27), (10, 9), (28, 12), (17, 20), (9, 20), (13, 13), (26, 16), (25, 0), (31, 11), (9, 6), (30, 9), (32, 20), (10, 3), (29, 20), (7, 16), (28, 22), (1, 16), (16, 29), (22, 8), (14, 11), (32, 9), (17, 1), (7, 10), (27, 5), (16, 5), (9, 29), (10, 13), (26, 26), (10, 20), (30, 18), (24, 6), (21, 18), (21, 19), (19, 19), (21, 10), (20, 2), (14, 8), (12, 8), (6, 19), (10, 6), (22, 21), (4, 28), (4, 21), (19, 7), (20, 22), (11, 9), (24, 14), (9, 3), (27, 11), (25, 17), (2, 4), (25, 5), (30, 2), (7, 28), (25, 8), (20, 23), (22, 2), (4, 29), (27, 12), (0, 21), (8, 8), (24, 2), (31, 27), (5, 8), (8, 4), (26, 21), (1, 25), (25, 25), (20, 10), (1, 12), (30, 22), (5, 24), (12, 18), (8, 5), (26, 15), (8, 27), (19, 5), (16, 16), (3, 22), (21, 15), (4, 16), (31, 26), (3, 3), (15, 10), (18, 26), (27, 15), (5, 9), (4, 0), (23, 24), (1, 9), (30, 11), (17, 12), (11, 16), (20, 21), (3, 28), (28, 11), (27, 29), (32, 23), (11, 17), (12, 27), (21, 5), (9, 12), (4, 9), (6, 0), (27, 25), (29, 16), (10, 7), (8, 17), (23, 1), (15, 0), (27, 24), (32, 24), (26, 13), (1, 4), (0, 11), (27, 2), (24, 0), (7, 25), (18, 25), (7, 19), (14, 1), (9, 2), (2, 21), (17, 19), (12, 28), (12, 25), (24, 15), (12, 17), (18, 9), (13, 24), (22, 28), (5, 16), (20, 4), (4, 11), (6, 8), (22, 22), (31, 3), (18, 20), (31, 1), (8, 16), (0, 25), (21, 8), (18, 18), (2, 17), (19, 6), (2, 2), (23, 26), (12, 1), (8, 19), (13, 26), (25, 11), (7, 23), (32, 22), (28, 19), (7, 15), (7, 24), (25, 19), (26, 24), (27, 7), (3, 23), (22, 20), (14, 6), (15, 29), (1, 17), (25, 18), (19, 10), (26, 9), (19, 12), (22, 13), (22, 15), (8, 24), (9, 8), (2, 28), (15, 9), (14, 14), (6, 23), (9, 23), (26, 7), (13, 8), (2, 14), (15, 12), (10, 4), (4, 6), (18, 12), (12, 4), (22, 0), (20, 24), (14, 3), (26, 12), (32, 18), (4, 22), (28, 10), (1, 7), (5, 23), (12, 3), (28, 20), (14, 29), (30, 20), (27, 23), (17, 4), (2, 7), (10, 16), (10, 12), (11, 13), (30, 24), (2, 1), (18, 22), (22, 6), (8, 11), (23, 0), (31, 19), (27, 0), (26, 14), (19, 24), (32, 3), (23, 25), (9, 24), (8, 10), (2, 24), (15, 20), (13, 0), (31, 28), (12, 10), (24, 1), (25, 16), (8, 22), (2, 0), (1, 0), (29, 12), (2, 11), (27, 20), (18, 29), (1, 28), (1, 23), (26, 5), (4, 19), (32, 10), (2, 8), (30, 27), (21, 14), (17, 25), (22, 5), (30, 8), (19, 18), (27, 16), (4, 5), (24, 26), (27, 4), (14, 18), (15, 27), (10, 15), (12, 6), (27, 13), (31, 24), (2, 22), (14, 27), (29, 13), (2, 16), (20, 16), (30, 14), (10, 1), (27, 22), (16, 10), (30, 23), (9, 5), (26, 22), (16, 24), (1, 10), (17, 5), (24, 19), (3, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400320", "dataset": "MATH"}
{"messages": [{"content": "In a 33x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 29), 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), (30, 8), (5, 16), (2, 2), (14, 21), (20, 19), (12, 11), (26, 26), (30, 16), (3, 14), (19, 5), (9, 28), (27, 27), (24, 25), (16, 19), (25, 12), (24, 6), (23, 6), (7, 1), (27, 0), (2, 13), (31, 7), (21, 1), (7, 6), (11, 13), (26, 18), (5, 20), (16, 21), (23, 1), (25, 0), (25, 2), (2, 26), (13, 7), (2, 12), (1, 25), (31, 26), (0, 26), (11, 16), (10, 29), (31, 14), (32, 10), (15, 23), (6, 12), (0, 29), (4, 10), (5, 22), (27, 4), (21, 6), (5, 9), (25, 5), (18, 15), (4, 16), (2, 14), (24, 16), (28, 15), (3, 8), (6, 17), (5, 21), (9, 4), (16, 20), (31, 4), (32, 12), (32, 0), (29, 17), (7, 25), (2, 9), (11, 2), (0, 1), (30, 19), (17, 10), (26, 22), (10, 2), (3, 26), (1, 20), (15, 13), (8, 2), (3, 11), (0, 17), (32, 11), (17, 20), (25, 19), (5, 17), (22, 9), (0, 9), (11, 8), (32, 20), (16, 1), (7, 7), (17, 4), (25, 4), (19, 12), (12, 21), (7, 18), (19, 26), (23, 27), (1, 9), (28, 9), (13, 9), (8, 1), (32, 26), (3, 12), (26, 8), (27, 23), (7, 12), (28, 6), (26, 24), (29, 26), (11, 24), (18, 0), (5, 28), (9, 16), (6, 2), (21, 25), (30, 11), (9, 12), (10, 15), (19, 23), (22, 20), (30, 0), (29, 14), (2, 29), (28, 11), (26, 9), (13, 11), (20, 0), (29, 2), (13, 27), (27, 22), (22, 15), (15, 2), (16, 10), (20, 7), (15, 29), (12, 23), (13, 26), (20, 13), (28, 17), (6, 28), (22, 18), (8, 25), (7, 21), (14, 9), (28, 27), (24, 13), (13, 12), (10, 19), (1, 21), (24, 8), (14, 29), (28, 23), (4, 29), (12, 12), (27, 14), (20, 18), (23, 20), (31, 29), (16, 18), (8, 6), (24, 4), (4, 1), (25, 29), (1, 1), (3, 24), (31, 2), (29, 6), (24, 22), (26, 23), (9, 27), (17, 11), (20, 2), (26, 10), (17, 19), (22, 16), (12, 13), (12, 4), (30, 12), (24, 7), (15, 6), (32, 3), (28, 12), (8, 10), (4, 27), (15, 17), (28, 25), (4, 23), (18, 13), (2, 8), (11, 21), (27, 6), (20, 23), (23, 28), (4, 26), (31, 15), (10, 11), (13, 22), (12, 14), (7, 28), (30, 29), (23, 17), (10, 3), (28, 1), (6, 19), (19, 14), (18, 3), (14, 5), (4, 20), (9, 18), (16, 22), (27, 15), (5, 13), (16, 4), (32, 9), (28, 7), (5, 0), (5, 24), (28, 8), (1, 26), (1, 19), (8, 28), (20, 10), (18, 24), (31, 12), (10, 12), (20, 21), (32, 24), (2, 27), (13, 19), (7, 24), (17, 2), (30, 9), (16, 26), (12, 26), (22, 5), (0, 18), (18, 28), (11, 23), (3, 20), (32, 13), (9, 29), (8, 3), (8, 19), (10, 14), (21, 29), (8, 9), (17, 0), (14, 1), (31, 20), (22, 2), (22, 0), (1, 8), (21, 19), (10, 28), (28, 0), (29, 11), (24, 3), (2, 5), (7, 22), (23, 9), (11, 10), (21, 7), (12, 10), (11, 6), (26, 14), (17, 29), (8, 22), (0, 19), (1, 14), (28, 5), (29, 16), (0, 25), (1, 4), (26, 7), (23, 12), (18, 16), (11, 29), (9, 23), (1, 2), (10, 24), (4, 19), (21, 10), (18, 23), (20, 20), (12, 28), (29, 8), (31, 21), (17, 9), (22, 22), (3, 23), (10, 21), (24, 23), (25, 25), (10, 10), (26, 5), (20, 3), (2, 24), (22, 13), (22, 6), (19, 28), (21, 21), (0, 22), (30, 6), (0, 6), (18, 27), (22, 27), (22, 25), (8, 7), (27, 9), (27, 16), (9, 20), (16, 6), (27, 26), (27, 17), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908160", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), 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), (3, 11), (5, 17), (6, 26), (32, 2), (19, 16), (13, 26), (18, 1), (26, 16), (26, 10), (17, 14), (11, 12), (4, 21), (3, 9), (15, 7), (20, 0), (17, 3), (29, 27), (28, 21), (33, 22), (32, 26), (27, 14), (14, 27), (5, 29), (14, 16), (34, 19), (25, 7), (0, 16), (21, 13), (28, 17), (24, 14), (3, 6), (23, 4), (4, 6), (7, 13), (10, 2), (12, 3), (23, 3), (12, 15), (30, 20), (31, 21), (13, 19), (35, 1), (15, 15), (16, 17), (4, 11), (6, 6), (17, 11), (25, 16), (20, 5), (28, 9), (0, 19), (15, 27), (23, 25), (3, 21), (10, 17), (14, 12), (13, 7), (24, 6), (15, 12), (4, 23), (5, 12), (13, 8), (21, 10), (0, 9), (10, 25), (1, 9), (12, 4), (16, 12), (10, 6), (23, 18), (34, 9), (16, 0), (20, 10), (5, 25), (9, 2), (32, 9), (10, 10), (10, 20), (11, 13), (19, 13), (4, 9), (19, 18), (3, 18), (10, 16), (9, 3), (4, 20), (26, 8), (24, 13), (18, 2), (27, 19), (7, 25), (14, 7), (10, 9), (15, 18), (23, 2), (34, 17), (7, 27), (33, 18), (35, 13), (25, 6), (16, 3), (11, 26), (3, 26), (25, 0), (33, 27), (25, 5), (28, 5), (3, 25), (29, 14), (16, 9), (9, 28), (1, 19), (26, 14), (27, 4), (8, 21), (11, 25), (30, 24), (32, 23), (22, 4), (9, 4), (1, 14), (0, 25), (11, 18), (16, 13), (29, 18), (34, 6), (29, 8), (34, 10), (28, 10), (33, 21), (9, 18), (14, 19), (6, 9), (8, 15), (33, 3), (17, 29), (7, 7), (30, 19), (1, 6), (15, 19), (25, 20), (7, 21), (18, 17), (33, 13), (8, 29), (14, 18), (23, 10), (21, 19), (6, 3), (12, 0), (22, 27), (9, 26), (5, 15), (6, 10), (2, 24), (13, 6), (18, 5), (12, 24), (29, 20), (33, 17), (10, 0), (30, 16), (13, 0), (26, 9), (26, 5), (3, 8), (8, 12), (18, 27), (25, 23), (18, 16), (32, 10), (15, 29), (35, 21), (33, 19), (11, 29), (10, 21), (35, 27), (27, 22), (14, 14), (31, 28), (15, 17), (2, 9), (3, 4), (17, 7), (9, 15), (26, 27), (0, 27), (0, 10), (29, 17), (1, 22), (21, 17), (12, 17), (1, 13), (9, 5), (9, 27), (26, 13), (19, 26), (22, 24), (20, 28), (16, 18), (17, 0), (12, 26), (13, 21), (35, 4), (32, 20), (1, 12), (13, 16), (15, 24), (9, 11), (15, 22), (23, 17), (7, 18), (25, 3), (22, 14), (15, 3), (20, 1), (13, 15), (8, 4), (6, 17), (16, 20), (34, 2), (32, 15), (21, 23), (11, 27), (25, 29), (33, 6), (6, 20), (0, 6), (6, 16), (23, 15), (17, 22), (18, 18), (29, 3), (30, 9), (21, 16), (22, 0), (18, 14), (32, 21), (31, 7), (32, 5), (35, 24), (32, 19), (27, 25), (32, 25), (3, 14), (20, 22), (4, 2), (31, 6), (18, 8), (22, 3), (18, 28), (13, 12), (17, 15), (27, 21), (20, 3), (34, 7), (32, 1), (23, 1), (32, 4), (17, 2), (22, 12), (31, 24), (23, 11), (10, 24), (30, 11), (34, 23), (1, 23), (12, 2), (6, 2), (18, 20), (26, 11), (5, 1), (23, 23), (1, 11), (28, 28), (8, 1), (22, 7), (21, 8), (13, 10), (14, 10), (7, 6), (35, 22), (12, 21), (4, 16), (19, 23), (35, 11), (12, 11), (35, 18), (33, 8), (10, 8), (5, 19), (11, 19), (15, 2), (29, 26), (2, 14), (32, 16), (16, 5), (7, 8), (33, 16), (11, 24), (3, 7), (31, 23), (21, 27), (4, 19), (21, 20), (7, 12), (23, 27), (30, 17), (27, 7), (34, 26), (19, 9), (4, 17), (3, 5), (17, 10), (2, 19), (14, 22), (15, 9), (18, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "436800", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 35), (27, 29), (18, 1), (22, 34), (8, 23), (20, 31), (3, 27), (6, 34), (3, 10), (1, 25), (26, 0), (30, 22), (13, 29), (13, 6), (12, 20), (6, 4), (4, 4), (17, 6), (7, 13), (30, 24), (9, 28), (8, 18), (21, 0), (2, 0), (2, 7), (3, 26), (7, 30), (21, 15), (14, 12), (26, 23), (24, 8), (12, 0), (21, 12), (21, 8), (19, 11), (0, 26), (20, 13), (27, 9), (27, 4), (21, 21), (6, 22), (1, 11), (20, 4), (1, 19), (2, 10), (17, 31), (15, 6), (0, 9), (15, 10), (26, 1), (5, 21), (21, 25), (1, 14), (26, 4), (1, 20), (11, 10), (24, 3), (12, 6), (2, 33), (5, 34), (14, 16), (21, 18), (13, 37), (2, 9), (9, 2), (7, 26), (29, 10), (0, 18), (29, 15), (19, 4), (23, 34), (14, 23), (25, 8), (0, 20), (12, 30), (4, 21), (28, 27), (18, 4), (19, 19), (2, 13), (3, 2), (25, 34), (24, 2), (30, 11), (19, 16), (25, 3), (13, 18), (30, 8), (26, 31), (14, 30), (6, 31), (3, 21), (3, 24), (18, 36), (7, 11), (13, 2), (28, 37), (27, 2), (21, 9), (6, 11), (12, 2), (14, 27), (9, 31), (8, 14), (26, 17), (16, 3), (6, 18), (13, 34), (16, 15), (5, 2), (20, 28), (20, 5), (27, 6), (12, 18), (6, 17), (26, 7), (22, 2), (18, 10), (28, 31), (7, 27), (1, 33), (26, 15), (1, 28), (23, 11), (22, 23), (13, 8), (25, 21), (29, 26), (12, 3), (14, 31), (19, 27), (1, 27), (19, 22), (15, 30), (24, 33), (25, 6), (16, 18), (8, 1), (7, 15), (4, 22), (4, 10), (22, 36), (8, 34), (7, 33), (4, 7), (2, 19), (0, 31), (22, 28), (27, 26), (17, 7), (19, 14), (4, 18), (22, 0), (29, 33), (7, 29), (14, 9), (6, 19), (23, 29), (21, 7), (20, 2), (18, 18), (9, 13), (22, 15), (10, 27), (1, 30), (13, 15), (2, 3), (22, 6), (10, 1), (3, 37), (21, 17), (11, 24), (15, 18), (19, 23), (17, 25), (20, 24), (29, 5), (11, 9), (25, 26), (9, 5), (21, 37), (25, 37), (13, 3), (16, 5), (9, 29), (13, 27), (7, 20), (30, 0), (17, 16), (8, 10), (11, 31), (28, 14), (11, 8), (4, 24), (17, 18), (11, 30), (30, 19), (14, 34), (26, 28), (19, 24), (6, 6), (13, 17), (6, 12), (11, 14), (27, 23), (5, 30), (23, 28), (13, 32), (8, 16), (19, 3), (19, 15), (8, 6), (4, 35), (5, 12), (1, 18), (21, 27), (22, 30), (3, 31), (16, 11), (22, 14), (0, 5), (10, 19), (25, 24), (25, 17), (19, 6), (27, 36), (20, 7), (11, 6), (8, 21), (9, 4), (20, 16), (13, 22), (1, 10), (16, 10), (14, 3), (24, 36), (6, 15), (11, 32), (8, 25), (29, 29), (12, 16), (10, 17), (5, 35), (20, 20), (5, 4), (20, 11), (1, 31), (4, 28), (24, 30), (28, 29), (22, 13), (16, 7), (11, 7), (20, 34), (12, 26), (17, 14), (28, 30), (28, 9), (9, 15), (3, 9), (22, 26), (25, 29), (23, 19), (10, 11), (11, 4), (29, 12), (25, 16), (15, 13), (13, 20), (22, 19), (28, 0), (22, 25), (25, 30), (25, 0), (20, 37), (20, 14), (16, 36), (24, 29), (22, 33), (30, 21), (11, 15), (29, 16), (20, 35), (4, 2), (8, 30), (12, 34), (0, 22), (3, 23), (25, 36), (21, 28), (12, 22), (19, 28), (12, 24), (16, 6), (12, 29), (2, 6), (24, 9), (24, 1), (9, 35), (17, 35), (28, 28), (12, 32), (21, 14), (23, 31), (15, 36), (25, 35), (24, 17), (5, 25), (30, 13), (7, 3), (18, 25), (18, 20), (27, 3), (25, 5), (10, 30), (30, 23), (30, 10), (5, 16), (30, 5), (1, 3), (1, 2), (8, 17), (0, 36), (11, 36), (28, 19), (3, 7), (8, 4), (29, 8), (26, 34), (16, 9), (10, 7), (2, 25), (16, 20), (7, 2), (24, 35), (10, 18), (10, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "937464", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 27), (29, 11), (22, 6), (0, 18), (8, 24), (29, 28), (16, 17), (15, 27), (19, 23), (4, 3), (16, 4), (11, 0), (16, 0), (13, 19), (13, 28), (28, 12), (2, 14), (4, 20), (18, 14), (8, 27), (9, 26), (10, 7), (16, 16), (6, 27), (13, 9), (21, 18), (27, 29), (17, 16), (7, 11), (13, 12), (7, 3), (27, 14), (3, 4), (5, 21), (25, 27), (27, 18), (22, 17), (12, 21), (7, 29), (15, 23), (18, 17), (11, 29), (17, 11), (21, 9), (11, 28), (18, 16), (3, 18), (27, 11), (15, 4), (8, 25), (21, 19), (21, 23), (11, 8), (1, 21), (24, 30), (29, 15), (9, 24), (25, 1), (9, 25), (5, 5), (14, 7), (20, 24), (2, 13), (20, 0), (24, 24), (24, 17), (24, 12), (13, 2), (5, 8), (2, 16), (29, 10), (16, 20), (12, 17), (2, 15), (9, 16), (12, 13), (6, 26), (11, 19), (3, 9), (19, 1), (25, 0), (13, 8), (5, 23), (12, 14), (14, 9), (0, 19), (6, 11), (17, 8), (1, 9), (26, 25), (26, 2), (11, 1), (24, 18), (12, 12), (20, 21), (11, 17), (24, 23), (29, 23), (27, 4), (13, 6), (20, 9), (1, 30), (14, 2), (18, 6), (6, 25), (29, 16), (13, 15), (6, 30), (5, 15), (23, 3), (14, 13), (17, 5), (11, 27), (17, 4), (11, 15), (25, 8), (23, 8), (15, 30), (29, 25), (17, 0), (16, 22), (16, 3), (23, 26), (21, 6), (21, 14), (0, 15), (12, 7), (9, 8), (10, 21), (18, 13), (4, 26), (2, 22), (27, 0), (13, 21), (1, 25), (21, 25), (8, 4), (20, 13), (10, 24), (10, 17), (2, 10), (29, 26), (0, 17), (3, 21), (12, 19), (7, 9), (0, 23), (28, 16), (5, 25), (22, 25), (13, 27), (27, 1), (17, 13), (10, 29), (28, 20), (14, 24), (19, 9), (4, 5), (8, 28), (23, 27), (15, 12), (19, 18), (7, 19), (23, 10), (24, 15), (23, 9), (26, 23), (12, 29), (22, 11), (15, 29), (1, 4), (6, 8), (2, 12), (15, 18), (18, 5), (15, 13), (28, 5), (22, 29), (24, 22), (4, 13), (29, 7), (2, 6), (9, 0), (8, 8), (0, 22), (29, 24), (8, 30), (20, 4), (11, 24), (4, 2), (7, 13), (18, 23), (13, 26), (1, 27), (4, 18), (3, 6), (21, 29), (7, 0), (5, 17), (6, 22), (26, 24), (14, 17), (5, 30), (16, 19), (10, 20), (5, 18), (13, 20), (14, 4), (14, 12), (17, 30), (17, 22), (9, 10), (17, 18), (9, 17), (18, 9), (12, 26), (23, 13), (13, 23), (23, 28), (8, 29), (12, 1), (14, 15), (17, 6), (24, 7), (22, 7), (28, 3), (18, 29), (28, 9), (5, 3), (2, 26), (25, 6), (11, 25), (17, 26), (10, 2), (8, 0), (26, 15), (5, 0), (21, 5), (27, 2), (4, 0), (3, 3), (0, 30), (19, 10), (22, 30), (16, 23), (19, 25), (10, 12), (21, 13), (0, 9), (7, 17), (3, 0), (18, 27), (3, 22), (4, 17), (24, 1), (28, 27), (17, 29), (25, 5), (19, 0), (16, 7), (24, 29), (11, 16), (26, 13), (14, 20), (29, 22), (16, 15), (28, 10), (23, 5), (29, 2), (5, 6), (12, 16), (12, 22), (13, 13), (5, 22), (25, 24), (18, 8), (10, 5), (29, 19), (6, 21), (17, 3), (8, 3), (10, 23), (24, 2), (10, 3), (6, 2), (23, 30), (3, 26), (13, 29), (4, 29), (21, 24), (2, 25), (13, 0), (19, 22), (0, 4), (5, 28), (13, 16), (26, 27), (27, 3), (19, 17), (17, 12), (28, 2), (0, 16), (3, 5), (12, 9), (28, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648648", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (15, 3), (26, 29), (31, 31), (30, 10), (8, 8), (1, 2), (21, 7), (18, 21), (19, 26), (0, 16), (24, 35), (18, 34), (28, 17), (20, 24), (6, 25), (23, 7), (11, 32), (6, 23), (11, 36), (26, 23), (28, 24), (30, 29), (15, 12), (22, 26), (11, 0), (11, 1), (7, 17), (30, 34), (27, 28), (30, 33), (15, 27), (29, 31), (15, 32), (13, 33), (2, 22), (25, 36), (20, 11), (29, 32), (28, 35), (7, 12), (17, 25), (22, 25), (13, 2), (26, 34), (6, 27), (20, 20), (30, 31), (1, 12), (24, 7), (19, 2), (16, 33), (16, 36), (5, 29), (18, 35), (27, 16), (21, 26), (18, 14), (6, 33), (5, 20), (26, 0), (17, 11), (21, 3), (30, 27), (2, 25), (9, 6), (15, 29), (3, 18), (4, 27), (10, 14), (27, 32), (17, 3), (16, 4), (10, 33), (0, 13), (11, 24), (18, 18), (19, 16), (19, 15), (4, 31), (31, 3), (31, 34), (26, 36), (16, 30), (5, 4), (3, 8), (23, 8), (11, 18), (0, 21), (20, 30), (16, 2), (20, 8), (29, 27), (23, 18), (7, 25), (10, 12), (22, 22), (12, 36), (12, 6), (28, 23), (31, 11), (7, 1), (1, 20), (20, 32), (16, 29), (21, 18), (0, 9), (12, 21), (4, 18), (9, 24), (3, 31), (13, 32), (21, 17), (16, 25), (30, 1), (24, 17), (29, 0), (23, 10), (21, 8), (12, 14), (5, 22), (22, 33), (3, 4), (4, 33), (31, 12), (4, 8), (20, 13), (20, 29), (9, 36), (21, 6), (14, 13), (17, 0), (3, 12), (1, 29), (13, 23), (28, 8), (6, 28), (8, 31), (9, 17), (25, 28), (4, 4), (18, 17), (0, 5), (10, 17), (25, 29), (31, 10), (5, 35), (26, 11), (22, 16), (20, 18), (27, 26), (2, 16), (20, 1), (25, 22), (31, 13), (23, 23), (22, 36), (18, 20), (12, 8), (28, 19), (28, 0), (0, 28), (14, 5), (7, 35), (12, 10), (14, 0), (3, 24), (10, 26), (10, 32), (26, 30), (16, 35), (27, 14), (2, 33), (30, 9), (24, 11), (30, 25), (23, 27), (4, 29), (7, 9), (28, 7), (4, 7), (28, 18), (14, 27), (5, 5), (21, 35), (24, 6), (9, 16), (27, 2), (30, 12), (13, 27), (11, 34), (18, 26), (22, 34), (7, 13), (18, 27), (15, 20), (14, 11), (1, 34), (2, 26), (3, 10), (20, 25), (11, 19), (29, 36), (22, 14), (25, 7), (8, 9), (1, 1), (31, 2), (22, 24), (18, 22), (19, 36), (8, 6), (2, 17), (26, 15), (0, 22), (10, 28), (7, 22), (6, 24), (12, 22), (12, 11), (4, 25), (29, 2), (30, 30), (8, 22), (29, 12), (3, 32), (26, 9), (28, 29), (3, 1), (5, 36), (0, 34), (25, 16), (19, 32), (26, 35), (18, 3), (14, 20), (3, 28), (29, 1), (3, 14), (18, 29), (9, 15), (27, 7), (20, 34), (11, 7), (17, 6), (1, 18), (2, 15), (20, 17), (6, 13), (3, 20), (10, 18), (30, 28), (0, 3), (13, 4), (9, 23), (1, 19), (5, 28), (8, 34), (26, 13), (17, 13), (5, 33), (5, 24), (11, 26), (11, 31), (13, 10), (24, 2), (21, 31), (16, 9), (22, 30), (11, 27), (15, 8), (4, 9), (4, 13), (4, 2), (22, 11), (8, 36), (20, 36), (14, 34), (2, 7), (17, 30), (22, 7), (16, 15), (8, 33), (0, 32), (1, 33), (7, 29), (13, 7), (18, 28), (1, 21), (4, 6), (16, 0), (10, 16), (17, 34), (27, 13), (19, 30), (11, 28), (6, 31), (22, 15), (31, 0), (7, 5), (26, 14), (28, 34), (4, 20), (10, 4), (25, 4), (25, 34), (15, 9), (28, 22), (4, 10), (7, 26), (14, 26), (19, 14), (30, 4), (27, 15), (23, 20), (17, 20), (28, 6), (1, 8), (25, 23), (25, 5), (6, 14), (23, 13), (24, 34), (14, 8), (20, 23), (29, 17), (29, 8), (7, 0), (4, 0), (0, 23), (15, 30), (3, 15), (31, 32), (27, 23), (0, 6), (17, 1), (9, 29), (3, 6), (2, 31), (20, 9), (16, 5), (11, 29), (5, 31), (26, 1), (23, 26), (20, 3), (13, 34), (28, 25), (23, 34), (30, 36), (18, 8), (27, 30), (22, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785136", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (6, 16), (3, 9), (23, 28), (16, 29), (6, 17), (4, 2), (9, 11), (0, 22), (6, 21), (15, 0), (31, 9), (17, 6), (23, 8), (31, 2), (9, 19), (25, 9), (20, 28), (29, 22), (11, 23), (31, 22), (26, 10), (3, 11), (2, 6), (5, 9), (16, 24), (3, 18), (10, 12), (24, 8), (24, 24), (20, 9), (17, 23), (5, 15), (10, 21), (2, 29), (0, 17), (14, 19), (8, 4), (27, 1), (7, 8), (13, 18), (20, 3), (21, 25), (31, 0), (5, 12), (14, 3), (30, 26), (19, 24), (5, 16), (6, 19), (20, 13), (20, 12), (6, 4), (29, 28), (3, 27), (5, 8), (7, 14), (28, 7), (11, 0), (15, 15), (1, 29), (27, 7), (14, 13), (16, 0), (30, 19), (18, 24), (0, 26), (8, 2), (11, 10), (29, 13), (8, 5), (2, 21), (15, 27), (27, 9), (11, 22), (8, 25), (10, 11), (7, 2), (22, 18), (24, 15), (30, 0), (13, 22), (1, 6), (10, 16), (7, 16), (19, 14), (30, 1), (27, 25), (13, 2), (4, 18), (6, 7), (17, 22), (9, 24), (31, 11), (17, 5), (29, 4), (13, 9), (3, 28), (19, 2), (16, 25), (14, 28), (23, 21), (3, 19), (6, 26), (22, 29), (3, 26), (5, 21), (23, 27), (23, 20), (23, 19), (29, 2), (6, 18), (14, 26), (26, 12), (28, 16), (10, 8), (27, 2), (22, 11), (3, 22), (26, 5), (29, 8), (30, 21), (15, 1), (23, 6), (27, 6), (27, 17), (31, 1), (23, 10), (19, 28), (17, 13), (30, 17), (7, 15), (4, 28), (31, 25), (23, 3), (6, 1), (13, 17), (31, 24), (30, 16), (0, 4), (29, 6), (4, 24), (11, 8), (26, 23), (6, 12), (9, 13), (5, 6), (14, 21), (2, 20), (29, 1), (20, 0), (30, 8), (28, 25), (17, 9), (3, 23), (20, 10), (24, 1), (10, 27), (1, 3), (14, 6), (22, 19), (9, 10), (27, 22), (19, 15), (16, 12), (10, 5), (27, 4), (19, 29), (1, 17), (13, 23), (5, 3), (18, 17), (14, 20), (2, 16), (12, 11), (18, 27), (29, 5), (17, 20), (8, 8), (11, 19), (20, 17), (19, 11), (5, 29), (8, 28), (12, 29), (23, 18), (5, 11), (24, 20), (29, 21), (22, 17), (5, 28), (25, 14), (25, 24), (21, 1), (23, 11), (9, 7), (26, 24), (30, 2), (26, 25), (7, 13), (18, 26), (5, 0), (10, 29), (0, 7), (10, 28), (10, 7), (26, 28), (23, 2), (19, 9), (7, 11), (30, 6), (12, 6), (13, 4), (23, 4), (15, 4), (20, 25), (19, 4), (21, 15), (30, 3), (1, 11), (18, 19), (1, 4), (7, 0), (1, 2), (29, 11), (19, 18), (8, 21), (17, 10), (18, 0), (16, 11), (17, 27), (10, 23), (19, 6), (10, 10), (16, 13), (0, 20), (31, 21), (6, 0), (11, 14), (3, 13), (21, 3), (27, 20), (10, 24), (16, 19), (5, 1), (26, 6), (14, 1), (24, 6), (4, 15), (26, 22), (20, 29), (14, 23), (11, 20), (11, 21), (10, 0), (9, 20), (30, 25), (13, 14), (0, 5), (1, 25), (17, 26), (14, 4), (22, 24), (15, 9), (28, 0), (1, 0), (25, 21), (4, 7), (28, 4), (18, 21), (23, 5), (7, 9), (7, 27), (27, 24), (25, 0), (21, 6), (7, 12), (9, 3), (7, 4), (2, 28), (18, 5), (1, 9), (17, 25), (14, 5), (9, 25), (27, 3), (23, 14), (24, 0), (21, 18), (12, 13), (24, 22), (25, 1), (0, 12), (13, 8), (25, 5), (30, 15), (22, 9), (3, 14), (20, 7), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20520", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 38), (24, 14), (29, 8), (31, 31), (14, 24), (31, 2), (31, 3), (13, 2), (5, 17), (25, 30), (20, 26), (12, 2), (20, 3), (26, 18), (25, 7), (9, 17), (26, 12), (26, 37), (1, 18), (12, 18), (15, 33), (13, 36), (20, 36), (2, 4), (28, 27), (24, 24), (8, 28), (25, 19), (26, 4), (7, 34), (25, 17), (30, 8), (27, 17), (3, 10), (23, 35), (24, 10), (29, 16), (7, 31), (24, 34), (9, 11), (27, 37), (3, 23), (16, 3), (6, 12), (20, 24), (26, 34), (12, 4), (30, 38), (24, 26), (21, 34), (30, 23), (18, 28), (28, 33), (13, 29), (31, 36), (12, 1), (6, 26), (16, 37), (16, 5), (14, 26), (2, 15), (23, 10), (30, 21), (10, 2), (0, 10), (30, 9), (4, 7), (27, 1), (10, 11), (26, 9), (19, 32), (7, 38), (15, 7), (12, 3), (12, 16), (31, 18), (29, 20), (11, 9), (4, 36), (28, 11), (4, 6), (2, 17), (5, 24), (15, 37), (1, 24), (7, 11), (21, 17), (17, 20), (1, 9), (30, 28), (11, 0), (20, 2), (6, 6), (31, 25), (17, 9), (8, 36), (27, 13), (24, 12), (16, 22), (13, 17), (25, 29), (11, 22), (20, 16), (18, 0), (10, 27), (31, 29), (12, 23), (8, 6), (6, 10), (14, 23), (16, 7), (2, 2), (2, 23), (12, 17), (9, 8), (24, 35), (11, 19), (19, 27), (7, 32), (3, 29), (22, 15), (24, 37), (26, 20), (14, 11), (8, 20), (12, 14), (0, 25), (24, 4), (20, 34), (4, 11), (27, 27), (22, 37), (24, 2), (15, 35), (21, 18), (25, 11), (0, 36), (4, 21), (17, 25), (8, 1), (14, 28), (4, 23), (6, 4), (13, 4), (28, 14), (4, 14), (21, 23), (11, 23), (18, 25), (28, 28), (0, 11), (23, 24), (15, 1), (0, 33), (8, 25), (3, 16), (19, 26), (5, 6), (18, 2), (29, 12), (19, 5), (31, 34), (15, 18), (15, 36), (31, 16), (30, 16), (0, 19), (15, 24), (31, 8), (8, 9), (6, 33), (23, 6), (30, 1), (11, 14), (3, 14), (13, 11), (29, 23), (9, 20), (21, 26), (15, 16), (1, 17), (7, 22), (28, 20), (11, 27), (30, 19), (11, 25), (1, 27), (4, 12), (20, 38), (16, 16), (30, 22), (7, 27), (3, 36), (6, 13), (6, 16), (4, 8), (18, 13), (22, 33), (20, 27), (19, 28), (10, 28), (11, 10), (13, 19), (4, 26), (25, 13), (10, 10), (18, 37), (26, 11), (9, 5), (14, 20), (2, 37), (9, 4), (18, 4), (29, 31), (21, 28), (11, 20), (21, 0), (13, 24), (31, 23), (31, 14), (1, 4), (2, 11), (9, 28), (29, 35), (24, 32), (9, 16), (29, 28), (23, 4), (2, 12), (25, 34), (15, 19), (10, 32), (0, 4), (15, 20), (8, 18), (29, 21), (11, 12), (1, 20), (4, 25), (1, 33), (21, 37), (24, 6), (9, 27), (12, 37), (24, 30), (29, 29), (0, 3), (19, 20), (1, 8), (15, 30), (6, 20), (13, 28), (29, 27), (20, 15), (14, 18), (8, 32), (3, 28), (28, 35), (19, 17), (30, 2), (1, 15), (3, 26), (7, 13), (7, 21), (9, 19), (31, 22), (30, 26), (11, 8), (26, 5), (18, 30), (2, 19), (17, 29), (12, 32), (1, 36), (4, 0), (2, 16), (9, 18), (9, 30), (19, 2), (2, 3), (12, 8), (19, 24), (21, 24), (13, 6), (1, 21), (19, 15), (5, 12), (30, 18), (0, 32), (8, 12), (26, 15), (2, 6), (4, 30), (7, 33), (17, 24), (23, 5), (16, 12), (16, 6), (9, 25), (6, 2), (30, 32), (19, 19), (21, 20), (18, 7), (5, 5), (13, 34), (29, 13), (3, 22), (5, 21), (26, 23), (23, 19), (18, 33), (23, 13), (9, 32), (21, 31), (19, 34), (19, 12), (31, 1), (28, 32), (20, 37), (6, 31), (2, 35), (7, 10), (4, 29), (2, 7), (5, 11), (27, 36), (19, 35), (21, 12), (27, 30), (15, 6), (15, 23), (29, 11), (25, 8), (17, 35), (20, 5), (3, 9), (0, 5), (4, 17), (24, 27), (4, 2), (28, 2), (3, 24), (0, 31), (0, 12), (8, 30), (17, 32), (23, 17), (28, 36), (25, 14), (23, 25), (31, 17), (8, 0), (28, 23), (1, 12), (18, 31), (7, 8), (15, 29), (29, 25), (23, 34), (6, 18), (21, 7), (10, 22), (26, 19), (25, 37), (27, 3), (24, 28), (30, 13), (29, 1), (16, 28), (27, 18), (7, 35), (7, 14), (29, 18), (31, 35), (0, 28), (18, 3), (28, 26), (2, 31), (21, 3), (7, 3), (7, 30), (18, 22), (14, 30), (2, 33), (1, 14), (31, 11), (25, 4), (10, 4), (8, 34), (25, 24), (30, 3), (25, 26), (30, 12), (0, 13), (10, 13), (4, 18), (22, 14), (19, 7), (30, 15), (9, 35), (12, 35), (18, 36), (20, 30), (26, 22), (19, 9), (11, 33), (18, 17), (22, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "875136", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (3, 21), (4, 6), (34, 0), (28, 2), (19, 24), (26, 29), (24, 28), (31, 20), (15, 7), (14, 0), (7, 5), (19, 9), (23, 12), (5, 10), (0, 23), (19, 5), (14, 3), (27, 15), (6, 17), (8, 18), (29, 14), (16, 5), (18, 16), (35, 17), (13, 13), (21, 3), (19, 17), (28, 0), (34, 4), (20, 4), (27, 26), (36, 7), (4, 18), (2, 11), (24, 22), (29, 6), (12, 28), (0, 14), (23, 11), (9, 6), (6, 9), (21, 29), (35, 2), (24, 12), (30, 28), (1, 5), (2, 29), (29, 26), (23, 0), (24, 1), (20, 2), (25, 20), (35, 25), (21, 13), (3, 15), (18, 20), (4, 21), (32, 12), (6, 24), (1, 12), (3, 24), (4, 17), (33, 6), (14, 29), (3, 19), (1, 3), (2, 27), (13, 15), (3, 18), (4, 25), (9, 13), (36, 9), (29, 20), (8, 10), (20, 15), (26, 15), (26, 1), (18, 4), (7, 18), (3, 0), (20, 6), (4, 12), (23, 8), (29, 17), (30, 11), (8, 28), (34, 28), (33, 15), (34, 13), (8, 20), (28, 17), (2, 12), (25, 19), (22, 21), (34, 19), (4, 27), (16, 23), (25, 15), (3, 11), (31, 27), (4, 10), (26, 26), (18, 12), (11, 0), (31, 6), (13, 23), (23, 17), (14, 2), (24, 5), (9, 4), (8, 23), (18, 9), (32, 19), (12, 13), (12, 8), (9, 28), (35, 12), (8, 13), (32, 20), (15, 6), (25, 29), (29, 0), (36, 22), (20, 1), (35, 10), (10, 26), (8, 2), (22, 22), (10, 17), (36, 1), (19, 29), (28, 19), (24, 15), (8, 5), (14, 16), (12, 17), (17, 8), (22, 1), (4, 22), (2, 25), (16, 29), (2, 21), (20, 7), (28, 18), (30, 19), (8, 4), (27, 8), (26, 19), (9, 16), (11, 24), (23, 22), (25, 2), (14, 1), (24, 25), (7, 19), (36, 19), (1, 26), (6, 25), (6, 13), (1, 22), (16, 7), (36, 25), (31, 18), (31, 9), (10, 24), (14, 9), (14, 27), (21, 14), (33, 11), (21, 27), (25, 16), (17, 21), (36, 11), (2, 0), (32, 6), (17, 10), (7, 26), (34, 26), (6, 11), (9, 25), (5, 13), (3, 25), (33, 22), (2, 23), (17, 7), (23, 23), (27, 2), (2, 18), (9, 24), (26, 12), (35, 21), (15, 10), (32, 25), (11, 27), (26, 25), (27, 27), (7, 13), (22, 24), (5, 22), (25, 13), (6, 27), (26, 23), (27, 21), (31, 24), (25, 11), (32, 29), (34, 16), (1, 1), (4, 4), (34, 29), (12, 7), (20, 9), (24, 3), (21, 24), (33, 7), (16, 18), (9, 26), (17, 19), (6, 10), (16, 1), (35, 3), (36, 3), (26, 7), (34, 23), (7, 29), (24, 19), (30, 24), (7, 7), (22, 27), (8, 17), (7, 21), (22, 23), (7, 25), (22, 9), (24, 7), (1, 16), (20, 10), (28, 16), (23, 25), (35, 24), (23, 29), (4, 5), (32, 10), (30, 18), (34, 12), (20, 18), (7, 22), (2, 15), (33, 17), (36, 14), (2, 17), (12, 21), (16, 3), (22, 8), (21, 25), (17, 1), (0, 7), (33, 24), (13, 16), (0, 28), (9, 7), (5, 19), (22, 28), (8, 16), (14, 7), (25, 21), (3, 20), (6, 6), (26, 9), (22, 14), (24, 20), (18, 10), (5, 0), (16, 26), (31, 14), (4, 2), (32, 1), (23, 3), (21, 8), (4, 13), (31, 4), (3, 2), (11, 12), (19, 6), (14, 11), (11, 3), (10, 23), (0, 6), (5, 6), (23, 20), (35, 20), (17, 15), (14, 28), (7, 24), (4, 29), (31, 15), (7, 17), (6, 29), (31, 10), (9, 17), (7, 23), (17, 29), (14, 21), (11, 16), (13, 8), (15, 25), (22, 6), (26, 2), (11, 8), (17, 12), (10, 19), (5, 7), (6, 2), (1, 0), (4, 19), (27, 10), (6, 16), (20, 17), (2, 26), (21, 7), (26, 21), (2, 4), (19, 10), (25, 22), (13, 27), (32, 2), (7, 27), (36, 21), (14, 6), (23, 14), (24, 24), (4, 14), (30, 14), (19, 2), (14, 26), (14, 15), (21, 0), (11, 23), (22, 18), (27, 25), (9, 19), (7, 4), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "615360", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 18), (5, 13), (0, 10), (30, 21), (29, 10), (28, 8), (16, 19), (5, 21), (4, 8), (34, 24), (15, 23), (16, 23), (11, 4), (25, 9), (28, 29), (11, 22), (2, 23), (27, 23), (33, 29), (6, 13), (6, 3), (33, 25), (21, 31), (7, 11), (25, 18), (36, 8), (14, 9), (3, 7), (7, 19), (15, 21), (37, 21), (7, 21), (35, 7), (13, 5), (37, 1), (1, 8), (13, 14), (22, 0), (38, 15), (19, 31), (3, 22), (38, 17), (9, 13), (6, 17), (31, 17), (2, 15), (0, 4), (8, 17), (3, 17), (31, 15), (19, 1), (38, 14), (36, 12), (32, 14), (16, 30), (23, 21), (28, 12), (10, 5), (5, 10), (13, 20), (14, 7), (19, 2), (3, 26), (33, 21), (25, 27), (30, 22), (27, 21), (38, 13), (4, 12), (13, 15), (22, 25), (7, 26), (33, 22), (13, 31), (14, 23), (8, 5), (35, 32), (2, 2), (2, 14), (12, 12), (21, 1), (18, 12), (14, 18), (17, 17), (25, 31), (4, 14), (17, 13), (5, 3), (8, 25), (25, 24), (2, 18), (13, 19), (7, 30), (20, 13), (35, 18), (5, 30), (21, 12), (22, 4), (20, 18), (12, 22), (7, 32), (29, 11), (12, 19), (25, 17), (37, 15), (16, 32), (15, 6), (19, 3), (18, 22), (1, 0), (14, 26), (13, 9), (16, 22), (28, 6), (4, 28), (23, 10), (18, 4), (6, 16), (36, 28), (26, 21), (33, 20), (18, 10), (22, 16), (21, 13), (36, 27), (14, 10), (14, 8), (17, 23), (1, 22), (24, 24), (24, 9), (11, 8), (17, 24), (36, 18), (30, 12), (5, 6), (14, 12), (13, 30), (4, 16), (18, 25), (33, 2), (5, 22), (17, 11), (3, 14), (26, 29), (15, 27), (21, 14), (32, 17), (2, 26), (24, 29), (22, 8), (29, 1), (22, 26), (18, 24), (9, 26), (33, 19), (15, 28), (30, 28), (33, 28), (7, 3), (35, 4), (0, 28), (5, 9), (28, 31), (19, 20), (3, 5), (12, 6), (26, 14), (38, 7), (2, 7), (18, 2), (32, 27), (6, 1), (24, 30), (0, 13), (34, 3), (8, 19), (32, 31), (28, 3), (13, 7), (32, 1), (0, 31), (18, 18), (36, 6), (34, 12), (17, 0), (24, 6), (4, 17), (25, 3), (23, 27), (32, 4), (20, 11), (16, 21), (7, 0), (4, 29), (25, 8), (26, 19), (23, 9), (10, 28), (3, 25), (34, 1), (18, 32), (10, 9), (22, 7), (28, 17), (28, 21), (26, 28), (34, 16), (13, 13), (1, 13), (29, 17), (6, 0), (22, 32), (35, 19), (32, 20), (12, 2), (29, 9), (17, 20), (15, 26), (13, 32), (3, 23), (37, 10), (14, 19), (8, 32), (10, 2), (12, 9), (1, 23), (2, 4), (34, 31), (30, 18), (30, 16), (38, 22), (11, 30), (17, 19), (20, 25), (3, 3), (24, 22), (31, 24), (13, 12), (34, 2), (17, 15), (5, 27), (36, 10), (6, 10), (12, 29), (7, 17), (29, 2), (24, 26), (32, 25), (26, 8), (8, 6), (22, 14), (19, 15), (1, 9), (34, 9), (24, 4), (18, 19), (0, 29), (32, 7), (2, 27), (2, 16), (15, 13), (27, 26), (27, 7), (8, 29), (0, 27), (9, 9), (5, 1), (22, 13), (27, 29), (35, 21), (29, 13), (4, 30), (37, 19), (24, 8), (10, 18), (16, 5), (28, 11), (4, 18), (24, 11), (31, 6), (7, 29), (25, 14), (14, 13), (5, 4), (9, 17), (23, 4), (8, 0), (29, 26), (34, 11), (16, 6), (32, 28), (0, 12), (11, 17), (12, 13), (21, 27), (26, 22), (14, 24), (16, 18), (12, 31), (1, 12), (21, 18), (12, 8), (8, 31), (16, 14), (13, 8), (13, 26), (34, 20), (5, 24), (2, 11), (1, 10), (1, 11), (18, 30), (6, 21), (19, 29), (13, 1), (2, 3), (26, 27), (31, 32), (35, 8), (7, 23), (2, 30), (5, 32), (1, 4), (35, 22), (31, 12), (27, 0), (31, 4), (22, 17), (9, 22), (6, 15), (9, 19), (14, 32), (6, 14), (13, 17), (15, 4), (10, 15), (2, 13), (28, 10), (0, 3), (15, 24), (23, 0), (36, 0), (5, 23), (33, 5), (9, 28), (25, 11), (23, 28), (9, 2), (15, 16), (28, 5), (31, 1), (3, 16), (29, 0), (20, 17), (15, 14), (9, 12), (36, 1), (17, 29), (22, 24), (8, 21), (23, 12), (33, 18), (16, 24), (1, 29), (13, 2), (35, 26), (33, 13), (9, 24), (4, 7), (11, 2), (35, 31), (4, 21), (16, 13), (6, 11), (29, 21), (25, 15), (16, 15), (37, 12), (36, 17), (35, 17), (21, 26), (35, 20), (24, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285480", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (9, 7), (26, 24), (1, 10), (19, 35), (1, 17), (0, 10), (13, 12), (5, 9), (27, 11), (12, 1), (15, 33), (25, 21), (11, 19), (31, 4), (19, 24), (29, 33), (7, 35), (24, 8), (27, 13), (14, 0), (14, 35), (21, 33), (31, 23), (31, 25), (4, 4), (15, 31), (17, 21), (30, 16), (17, 30), (29, 20), (25, 24), (2, 29), (8, 25), (7, 0), (0, 29), (14, 28), (2, 36), (4, 3), (24, 30), (22, 13), (4, 18), (15, 34), (12, 11), (4, 35), (5, 17), (14, 31), (8, 19), (20, 24), (23, 29), (12, 31), (19, 13), (11, 7), (28, 21), (1, 19), (30, 5), (7, 30), (19, 18), (17, 13), (12, 13), (20, 36), (29, 10), (19, 30), (7, 12), (18, 14), (11, 21), (28, 22), (30, 21), (24, 15), (21, 20), (10, 13), (21, 13), (29, 11), (5, 24), (28, 18), (22, 28), (6, 7), (1, 14), (16, 21), (26, 12), (4, 23), (27, 22), (7, 26), (21, 19), (17, 17), (14, 36), (22, 3), (31, 7), (29, 8), (13, 27), (9, 36), (28, 0), (10, 14), (26, 32), (31, 2), (3, 10), (31, 21), (0, 30), (8, 8), (16, 14), (3, 28), (12, 30), (31, 15), (8, 18), (12, 3), (23, 11), (14, 32), (14, 34), (7, 25), (30, 2), (12, 27), (11, 6), (25, 7), (0, 13), (13, 7), (10, 29), (29, 4), (8, 4), (16, 18), (11, 33), (25, 28), (9, 29), (18, 7), (8, 21), (27, 36), (19, 33), (4, 15), (26, 10), (12, 7), (24, 21), (2, 8), (31, 18), (0, 4), (9, 22), (24, 5), (5, 19), (26, 13), (1, 1), (25, 14), (2, 30), (12, 33), (11, 26), (16, 17), (17, 7), (13, 16), (27, 29), (5, 15), (28, 7), (21, 17), (20, 15), (10, 1), (5, 12), (4, 28), (20, 4), (31, 31), (11, 28), (24, 36), (16, 19), (2, 11), (26, 26), (11, 0), (24, 0), (1, 30), (4, 21), (2, 3), (26, 1), (15, 13), (14, 10), (30, 18), (30, 27), (20, 3), (5, 16), (16, 26), (11, 10), (28, 1), (17, 3), (22, 22), (30, 6), (21, 6), (10, 6), (15, 12), (8, 22), (4, 2), (8, 35), (24, 7), (31, 20), (21, 2), (15, 24), (16, 10), (9, 16), (27, 19), (0, 14), (8, 16), (8, 13), (10, 24), (3, 14), (17, 18), (1, 15), (12, 14), (2, 25), (18, 30), (19, 34), (16, 34), (9, 13), (23, 8), (25, 12), (6, 31), (1, 8), (20, 16), (22, 24), (22, 32), (25, 34), (6, 11), (22, 8), (11, 18), (29, 26), (27, 2), (13, 18), (24, 3), (6, 27), (22, 4), (14, 2), (23, 6), (17, 5), (13, 31), (2, 31), (25, 23), (28, 19), (23, 9), (19, 3), (24, 23), (17, 34), (25, 1), (22, 2), (23, 34), (19, 10), (10, 15), (7, 7), (17, 14), (29, 2), (21, 36), (14, 9), (2, 5), (30, 29), (24, 26), (27, 31), (20, 11), (12, 2), (29, 25), (3, 29), (19, 26), (29, 21), (24, 10), (14, 22), (30, 23), (19, 20), (8, 12), (20, 2), (20, 17), (26, 19), (26, 35), (23, 28), (20, 6), (2, 28), (14, 27), (10, 20), (9, 32), (3, 35), (14, 30), (17, 31), (2, 14), (10, 0), (9, 30), (3, 17), (25, 6), (17, 29), (19, 32), (19, 31), (28, 33), (21, 4), (4, 36), (26, 11), (28, 2), (28, 5), (9, 20), (26, 33), (6, 15), (27, 15), (28, 24), (0, 21), (2, 13), (9, 14), (15, 9), (9, 6), (11, 13), (8, 32), (2, 24), (12, 23), (29, 13), (20, 12), (18, 0), (20, 21), (24, 32), (10, 23), (4, 17), (29, 6), (22, 31), (7, 33), (26, 14), (24, 12), (6, 36), (20, 32), (24, 19), (31, 27), (24, 34), (7, 4), (6, 26), (2, 23), (24, 11), (30, 0), (21, 32), (22, 19), (10, 17), (21, 35), (20, 28), (17, 0), (3, 11), (21, 28), (28, 23), (21, 29), (11, 27), (3, 9), (4, 16), (24, 18), (19, 16), (0, 11), (14, 24), (0, 25), (3, 6), (23, 27), (8, 20), (21, 24), (24, 17), (4, 26), (20, 22), (14, 18), (18, 24), (4, 30), (29, 7), (27, 26), (9, 17), (0, 23), (30, 1), (29, 27), (26, 6), (9, 10), (0, 27), (16, 35), (13, 25), (8, 17), (23, 36), (4, 34), (13, 24), (29, 0), (13, 32), (22, 35), (5, 28), (14, 5), (9, 5), (0, 17), (1, 34), (30, 17), (20, 7), (12, 16), (31, 35), (0, 19), (12, 32), (19, 6), (13, 9), (16, 29), (4, 1), (24, 25), (5, 23), (7, 18), (16, 31), (23, 31), (31, 17), (3, 27), (19, 36), (4, 6), (23, 4), (22, 27), (7, 29), (9, 33), (26, 4), (6, 16), (5, 33), (7, 9), (6, 34), (14, 1), (18, 12), (15, 0), (12, 28), (4, 20), (3, 20), (25, 4), (21, 30), (5, 20), (13, 5), (16, 3), (3, 3), (16, 24), (4, 5), (31, 34), (7, 1), (12, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "336960", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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), (18, 26), (19, 18), (20, 29), (21, 14), (13, 5), (21, 0), (10, 7), (17, 14), (28, 7), (8, 7), (5, 26), (14, 21), (6, 12), (22, 19), (31, 2), (16, 21), (17, 10), (15, 1), (13, 13), (2, 20), (33, 4), (29, 5), (20, 14), (27, 7), (5, 16), (23, 14), (2, 23), (15, 27), (7, 17), (30, 26), (29, 28), (1, 28), (21, 16), (33, 8), (32, 25), (9, 23), (32, 29), (22, 17), (31, 21), (0, 20), (11, 11), (26, 10), (7, 16), (33, 14), (6, 24), (7, 27), (11, 28), (17, 24), (8, 19), (18, 24), (3, 15), (28, 18), (31, 28), (5, 8), (15, 7), (16, 23), (26, 14), (11, 29), (22, 21), (16, 3), (2, 26), (15, 17), (28, 17), (32, 27), (29, 1), (1, 22), (12, 20), (26, 0), (16, 25), (12, 3), (22, 25), (17, 22), (17, 12), (0, 4), (14, 29), (9, 16), (3, 2), (27, 21), (11, 16), (29, 21), (8, 22), (8, 4), (32, 14), (22, 29), (5, 18), (4, 13), (31, 15), (25, 8), (15, 26), (1, 30), (0, 13), (20, 12), (12, 7), (19, 30), (8, 15), (11, 30), (13, 10), (22, 1), (32, 7), (4, 3), (28, 1), (15, 14), (6, 21), (0, 22), (32, 12), (25, 2), (11, 13), (9, 25), (0, 3), (28, 24), (27, 8), (20, 2), (22, 23), (16, 8), (10, 2), (7, 9), (7, 1), (24, 2), (17, 16), (7, 2), (24, 9), (5, 23), (33, 21), (15, 19), (28, 11), (23, 24), (4, 14), (25, 18), (26, 12), (23, 4), (14, 3), (20, 24), (17, 20), (23, 18), (31, 3), (14, 28), (21, 19), (14, 23), (23, 10), (8, 0), (32, 23), (1, 15), (9, 28), (1, 2), (21, 15), (0, 10), (10, 19), (32, 16), (9, 22), (12, 23), (9, 30), (10, 22), (14, 13), (19, 13), (1, 6), (2, 30), (10, 6), (23, 19), (27, 26), (30, 8), (24, 4), (25, 7), (29, 19), (24, 22), (17, 15), (33, 12), (8, 8), (20, 3), (20, 11), (28, 2), (13, 21), (32, 18), (12, 0), (15, 9), (31, 13), (18, 27), (0, 19), (15, 21), (18, 18), (10, 4), (6, 17), (14, 6), (14, 4), (28, 8), (4, 7), (30, 24), (6, 3), (1, 8), (17, 9), (5, 22), (9, 12), (8, 2), (33, 13), (3, 20), (16, 30), (5, 11), (3, 25), (9, 6), (30, 5), (19, 28), (29, 22), (33, 16), (11, 8), (13, 8), (33, 7), (27, 29), (25, 0), (15, 22), (0, 11), (3, 12), (7, 21), (25, 4), (21, 24), (28, 12), (14, 17), (16, 12), (33, 23), (31, 23), (30, 11), (33, 24), (2, 16), (30, 30), (31, 1), (6, 5), (22, 20), (13, 22), (0, 8), (11, 26), (9, 5), (29, 10), (32, 20), (11, 0), (7, 4), (20, 28), (7, 11), (29, 4), (12, 10), (1, 20), (7, 15), (1, 27), (19, 8), (21, 13), (11, 15), (25, 17), (13, 4), (5, 2), (14, 14), (5, 1), (31, 30), (29, 13), (13, 0), (24, 14), (8, 17), (1, 9), (20, 6), (12, 17), (7, 28), (4, 6), (28, 5), (3, 30), (24, 8), (24, 26), (17, 4), (1, 14), (25, 16), (19, 16), (22, 15), (2, 4), (11, 18), (2, 14), (7, 20), (3, 22), (31, 9), (4, 11), (26, 16), (9, 21), (18, 13), (13, 12), (8, 26), (14, 9), (28, 26), (25, 27), (24, 6), (4, 8), (20, 1), (12, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825660", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 6), (16, 10), (7, 11), (23, 32), (2, 16), (23, 20), (24, 23), (19, 24), (13, 23), (31, 31), (30, 31), (13, 4), (11, 19), (26, 32), (9, 29), (30, 17), (10, 18), (18, 18), (29, 34), (1, 31), (0, 8), (1, 18), (7, 26), (25, 33), (20, 15), (18, 10), (14, 7), (36, 5), (31, 14), (24, 32), (18, 35), (25, 4), (10, 23), (13, 14), (11, 26), (33, 11), (3, 36), (36, 18), (12, 25), (0, 12), (33, 26), (4, 10), (6, 24), (9, 6), (9, 28), (34, 30), (30, 30), (13, 3), (6, 13), (19, 4), (14, 23), (23, 25), (30, 12), (4, 6), (6, 10), (32, 8), (20, 18), (24, 1), (16, 30), (26, 22), (27, 30), (32, 36), (33, 5), (18, 23), (20, 7), (4, 19), (13, 8), (23, 35), (4, 24), (26, 34), (10, 14), (25, 31), (2, 3), (34, 1), (27, 26), (3, 13), (31, 18), (15, 14), (5, 0), (25, 19), (2, 6), (14, 15), (12, 19), (28, 33), (13, 32), (15, 13), (31, 27), (0, 26), (27, 22), (16, 5), (29, 30), (15, 1), (2, 2), (2, 5), (29, 20), (7, 33), (13, 1), (16, 11), (1, 35), (36, 28), (3, 33), (30, 28), (28, 14), (36, 11), (8, 1), (0, 3), (1, 25), (6, 15), (32, 4), (9, 3), (31, 11), (19, 18), (8, 6), (4, 7), (11, 3), (11, 28), (31, 37), (7, 14), (4, 11), (31, 32), (15, 28), (32, 27), (36, 17), (22, 31), (3, 21), (14, 8), (26, 21), (34, 11), (5, 23), (23, 8), (6, 12), (20, 22), (26, 20), (9, 25), (10, 25), (27, 5), (29, 25), (16, 0), (14, 6), (36, 13), (20, 1), (31, 16), (3, 37), (33, 9), (0, 25), (20, 11), (17, 15), (5, 32), (15, 34), (17, 2), (31, 34), (14, 25), (27, 27), (18, 17), (35, 30), (12, 37), (25, 20), (1, 33), (21, 22), (30, 21), (9, 12), (24, 25), (10, 12), (7, 9), (2, 18), (15, 7), (12, 18), (28, 22), (3, 27), (10, 30), (18, 25), (34, 20), (5, 5), (23, 3), (21, 4), (14, 12), (10, 15), (31, 10), (11, 20), (17, 4), (2, 9), (15, 16), (13, 35), (32, 35), (15, 26), (1, 30), (23, 9), (22, 11), (15, 30), (27, 37), (25, 13), (10, 24), (9, 18), (4, 32), (20, 33), (10, 33), (2, 29), (28, 30), (26, 36), (13, 17), (1, 28), (1, 6), (28, 5), (21, 36), (27, 8), (15, 6), (32, 22), (28, 23), (21, 5), (12, 0), (32, 25), (31, 30), (3, 7), (0, 5), (13, 25), (16, 14), (19, 23), (12, 4), (30, 22), (33, 18), (29, 2), (19, 9), (23, 21), (9, 21), (25, 7), (15, 19), (0, 7), (14, 33), (1, 17), (5, 35), (13, 18), (1, 37), (18, 21), (33, 22), (19, 15), (25, 18), (33, 2), (17, 7), (34, 12), (17, 11), (11, 4), (13, 28), (2, 36), (35, 5), (21, 27), (20, 32), (35, 11), (31, 2), (17, 17), (16, 23), (14, 20), (11, 16), (13, 36), (31, 36), (5, 12), (31, 17), (27, 13), (12, 20), (24, 19), (6, 29), (2, 15), (8, 26), (11, 21), (1, 12), (7, 2), (30, 20), (8, 21), (12, 28), (16, 19), (25, 17), (35, 0), (23, 13), (15, 20), (11, 13), (17, 16), (36, 12), (28, 32), (5, 25), (24, 7), (32, 11), (29, 9), (26, 9), (25, 5), (20, 28), (35, 9), (3, 18), (2, 12), (30, 25), (30, 32), (24, 31), (32, 32), (21, 20), (35, 20), (5, 24), (28, 27), (22, 27), (21, 28), (13, 27), (9, 19), (1, 1), (32, 21), (3, 29), (14, 35), (27, 33), (20, 4), (33, 24), (20, 10), (9, 20), (34, 22), (24, 18), (21, 8), (8, 12), (12, 24), (23, 22), (27, 24), (8, 2), (22, 1), (12, 27), (9, 24), (12, 31), (0, 37), (29, 33), (23, 1), (10, 29), (2, 32), (23, 7), (11, 15), (0, 29), (25, 15), (24, 17), (10, 6), (4, 16), (6, 22), (9, 27), (10, 11), (36, 1), (4, 20), (0, 24), (2, 10), (17, 0), (33, 35), (11, 0), (24, 14), (13, 26), (29, 12), (13, 0), (29, 26), (30, 11), (21, 15), (4, 13), (36, 30), (36, 32), (2, 14), (21, 31), (0, 27), (20, 17), (5, 18), (36, 16), (23, 28), (31, 19), (31, 20), (26, 7), (33, 21), (4, 37), (28, 35), (5, 13), (8, 20), (34, 33), (3, 15), (22, 22), (32, 31), (8, 9), (34, 31), (30, 14), (31, 7), (4, 23), (14, 5), (24, 30), (25, 26), (2, 26), (19, 8), (19, 12), (28, 10), (17, 5), (33, 23), (10, 37), (35, 27), (6, 5), (11, 18), (30, 36), (36, 27), (22, 24), (3, 19), (8, 31), (3, 0), (28, 20), (21, 17), (16, 16), (19, 19), (13, 31), (0, 2), (3, 11), (34, 14), (30, 16), (26, 11), (22, 0), (27, 18), (0, 20), (32, 12), (6, 23), (33, 28), (8, 25), (21, 3), (13, 37), (33, 36), (9, 30), (6, 18), (20, 0), (11, 9), (7, 16), (31, 21), (8, 8), (1, 7), (26, 15), (36, 23), (22, 28), (35, 6), (7, 10), (11, 30), (33, 12), (2, 13), (8, 34), (19, 25), (36, 29), (25, 16), (23, 16), (27, 12), (1, 14), (18, 12), (10, 5), (11, 24), (32, 5), (26, 31), (13, 29), (15, 17), (36, 20), (36, 15), (22, 3), (19, 32), (0, 19), (33, 8), (8, 28), (5, 31), (29, 19), (33, 14), (26, 1), (16, 13), (34, 5), (16, 33), (11, 17), (20, 27), (26, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "460800", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (23, 12), (28, 5), (9, 2), (16, 12), (22, 31), (23, 10), (16, 8), (6, 1), (23, 34), (5, 17), (2, 33), (7, 10), (17, 11), (21, 27), (5, 18), (16, 20), (14, 18), (4, 24), (20, 3), (16, 13), (19, 0), (25, 34), (17, 3), (5, 23), (1, 2), (22, 26), (24, 26), (20, 14), (9, 28), (29, 3), (6, 0), (21, 12), (25, 22), (13, 19), (7, 24), (29, 19), (29, 14), (4, 25), (1, 32), (5, 32), (14, 31), (23, 29), (14, 28), (15, 9), (17, 0), (8, 14), (20, 2), (26, 29), (23, 14), (2, 27), (17, 30), (13, 22), (12, 19), (19, 25), (20, 33), (15, 0), (3, 20), (12, 35), (28, 21), (19, 34), (19, 31), (8, 29), (16, 33), (19, 11), (4, 8), (19, 28), (7, 35), (16, 3), (25, 35), (14, 30), (19, 36), (14, 6), (24, 13), (12, 5), (9, 36), (9, 0), (0, 22), (8, 22), (29, 10), (11, 30), (16, 4), (6, 36), (23, 15), (22, 1), (15, 20), (23, 30), (9, 33), (10, 10), (16, 28), (13, 32), (0, 31), (4, 12), (13, 6), (14, 36), (16, 29), (11, 3), (2, 18), (0, 11), (13, 33), (0, 6), (26, 5), (1, 25), (19, 33), (27, 11), (20, 19), (17, 2), (14, 35), (27, 9), (7, 33), (24, 5), (3, 12), (6, 23), (17, 28), (1, 11), (11, 5), (1, 21), (3, 9), (6, 9), (24, 17), (17, 32), (26, 35), (27, 28), (8, 8), (2, 1), (19, 3), (7, 16), (18, 4), (23, 28), (20, 17), (28, 33), (16, 10), (28, 2), (9, 3), (8, 17), (28, 9), (10, 11), (7, 17), (1, 28), (13, 36), (3, 23), (10, 8), (8, 10), (3, 33), (18, 36), (17, 4), (21, 25), (2, 34), (9, 23), (20, 16), (6, 22), (18, 32), (10, 6), (20, 26), (26, 22), (9, 32), (24, 25), (29, 34), (18, 0), (12, 34), (20, 32), (18, 25), (4, 26), (25, 6), (26, 32), (12, 25), (27, 27), (17, 24), (14, 34), (2, 19), (7, 19), (13, 13), (22, 15), (8, 35), (12, 33), (19, 20), (1, 9), (14, 27), (15, 21), (27, 8), (25, 10), (29, 13), (28, 22), (2, 8), (7, 29), (5, 31), (26, 31), (27, 16), (27, 32), (1, 10), (7, 22), (21, 30), (3, 24), (21, 28), (2, 2), (4, 1), (12, 3), (5, 16), (6, 14), (11, 14), (3, 28), (14, 11), (25, 28), (11, 10), (25, 26), (4, 27), (12, 27), (19, 14), (7, 0), (2, 11), (11, 23), (26, 28), (10, 18), (3, 4), (10, 19), (3, 2), (9, 34), (19, 2), (6, 6), (17, 6), (17, 20), (16, 19), (21, 2), (17, 21), (20, 7), (13, 7), (2, 28), (4, 31), (26, 12), (0, 2), (19, 16), (16, 23), (6, 19), (14, 25), (11, 17), (24, 18), (20, 5), (16, 35), (26, 33), (19, 30), (9, 18), (21, 1), (1, 30), (13, 34), (23, 31), (1, 18), (6, 8), (15, 31), (7, 5), (8, 18), (14, 3), (13, 23), (19, 7), (4, 18), (9, 24), (27, 35), (10, 5), (27, 7), (6, 29), (14, 21), (28, 7), (25, 0), (19, 21), (26, 34), (4, 3), (21, 22), (28, 23), (9, 12), (22, 19), (12, 30), (19, 29), (12, 26), (12, 20), (11, 16), (11, 2), (22, 30), (7, 11), (0, 7), (1, 22), (8, 6), (18, 20), (15, 4), (8, 9), (15, 1), (23, 0), (0, 9), (9, 22), (5, 12), (8, 36), (24, 6), (9, 30), (8, 7), (6, 4), (0, 21), (6, 7), (25, 32), (15, 24), (27, 6), (27, 17), (16, 26), (21, 32), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "879836", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 26), (16, 19), (25, 2), (18, 12), (24, 24), (1, 27), (3, 15), (11, 15), (10, 6), (36, 0), (1, 28), (12, 7), (29, 0), (23, 19), (10, 0), (25, 16), (23, 29), (15, 19), (35, 23), (30, 12), (1, 16), (11, 24), (27, 25), (16, 21), (27, 27), (14, 30), (10, 22), (28, 9), (25, 13), (27, 13), (19, 31), (23, 27), (12, 21), (20, 19), (29, 5), (13, 19), (14, 1), (13, 11), (31, 29), (26, 19), (33, 8), (37, 17), (30, 18), (5, 11), (38, 27), (3, 20), (10, 9), (27, 2), (35, 18), (29, 20), (26, 20), (31, 28), (26, 7), (8, 27), (25, 14), (27, 0), (11, 5), (36, 29), (3, 10), (27, 24), (21, 29), (13, 23), (33, 26), (35, 22), (7, 28), (28, 13), (0, 15), (20, 24), (2, 22), (8, 11), (20, 13), (21, 19), (24, 27), (21, 16), (11, 1), (24, 16), (36, 25), (6, 2), (18, 27), (6, 16), (26, 21), (19, 13), (4, 10), (34, 13), (15, 3), (3, 7), (22, 8), (5, 27), (20, 30), (14, 12), (11, 18), (22, 14), (5, 9), (26, 30), (14, 20), (1, 9), (21, 6), (33, 23), (30, 6), (29, 13), (30, 27), (4, 21), (30, 15), (36, 16), (19, 25), (4, 14), (3, 0), (6, 21), (33, 15), (12, 17), (16, 30), (30, 17), (5, 16), (31, 21), (22, 18), (24, 4), (17, 12), (27, 31), (32, 17), (2, 25), (24, 14), (12, 5), (13, 3), (22, 5), (13, 30), (37, 27), (28, 0), (14, 16), (20, 4), (18, 23), (1, 18), (2, 31), (11, 25), (27, 16), (36, 17), (2, 19), (2, 3), (35, 31), (2, 15), (30, 29), (33, 4), (21, 27), (0, 8), (15, 7), (9, 25), (7, 29), (22, 13), (30, 3), (11, 26), (30, 19), (17, 16), (18, 31), (16, 4), (9, 15), (18, 10), (2, 18), (29, 30), (30, 9), (16, 27), (32, 29), (9, 29), (3, 25), (5, 24), (3, 24), (9, 7), (5, 28), (21, 18), (29, 26), (38, 25), (18, 14), (22, 4), (8, 26), (28, 6), (37, 25), (27, 11), (1, 1), (17, 27), (3, 5), (6, 27), (11, 28), (34, 6), (21, 3), (12, 13), (36, 4), (6, 31), (2, 4), (35, 28), (3, 28), (27, 29), (12, 6), (19, 15), (3, 16), (36, 28), (1, 14), (3, 14), (10, 7), (9, 3), (28, 7), (22, 28), (3, 8), (32, 22), (38, 26), (27, 6), (2, 11), (11, 30), (9, 4), (33, 25), (5, 5), (31, 8), (13, 29), (1, 29), (7, 14), (11, 9), (32, 24), (21, 8), (14, 4), (17, 19), (30, 10), (12, 22), (27, 17), (16, 31), (6, 1), (0, 7), (7, 31), (37, 22), (13, 18), (21, 14), (9, 28), (34, 15), (37, 6), (25, 1), (16, 10), (19, 7), (2, 28), (30, 31), (15, 25), (29, 12), (6, 12), (24, 1), (2, 8), (24, 30), (31, 16), (5, 10), (19, 28), (37, 10), (36, 6), (4, 12), (25, 15), (25, 5), (16, 8), (25, 7), (23, 18), (13, 12), (11, 29), (35, 2), (29, 29), (4, 30), (0, 4), (15, 26), (16, 29), (32, 19), (14, 2), (20, 29), (9, 14), (11, 13), (30, 23), (21, 7), (25, 9), (4, 24), (31, 17), (26, 23), (6, 0), (7, 1), (32, 20), (15, 1), (36, 23), (28, 27), (27, 10), (35, 24), (14, 19), (37, 24), (4, 22), (16, 18), (7, 15), (11, 7), (35, 26), (25, 3), (14, 29), (23, 3), (7, 6), (22, 0), (29, 10), (34, 26), (2, 7), (25, 8), (14, 9), (30, 2), (34, 23), (22, 22), (15, 13), (10, 14), (31, 26), (19, 18), (32, 21), (34, 21), (37, 4), (27, 19), (28, 24), (17, 9), (31, 15), (17, 4), (3, 4), (4, 29), (27, 28), (0, 23), (23, 6), (23, 21), (14, 28), (2, 12), (29, 9), (37, 0), (15, 31), (1, 15), (9, 5), (14, 25), (7, 3), (28, 22), (38, 2), (38, 13), (33, 7), (10, 26), (13, 6), (23, 16), (11, 14), (17, 17), (30, 28), (0, 30), (12, 9), (34, 11), (11, 8), (0, 13), (16, 22), (20, 0), (7, 18), (37, 14), (10, 29), (4, 6), (3, 29), (13, 14), (25, 20), (31, 11), (5, 20), (30, 25), (21, 30), (14, 3), (22, 2), (3, 27), (11, 22), (24, 10), (18, 21), (15, 30), (26, 2), (2, 6), (9, 22), (1, 25), (1, 4), (28, 1), (7, 11), (38, 3), (18, 17), (1, 12), (4, 11), (31, 7), (24, 28), (14, 27), (6, 8), (10, 1), (14, 21), (14, 17), (3, 17), (21, 1), (37, 31), (28, 17), (22, 23), (35, 14), (25, 0), (36, 27), (3, 9), (9, 30), (27, 1), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471744", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (22, 30), (27, 7), (7, 27), (15, 5), (5, 29), (8, 21), (27, 13), (5, 7), (28, 2), (1, 29), (21, 15), (23, 19), (11, 8), (21, 35), (12, 15), (0, 12), (4, 11), (19, 27), (10, 25), (14, 0), (20, 11), (25, 1), (24, 0), (24, 20), (11, 10), (29, 8), (9, 27), (13, 3), (4, 13), (18, 11), (25, 31), (10, 14), (16, 20), (18, 20), (25, 13), (15, 1), (16, 23), (25, 4), (21, 27), (1, 0), (24, 36), (16, 9), (18, 4), (19, 15), (11, 13), (8, 26), (28, 16), (0, 7), (3, 3), (7, 31), (2, 29), (10, 18), (11, 2), (29, 31), (3, 14), (15, 12), (4, 5), (0, 20), (15, 11), (11, 26), (14, 12), (26, 32), (3, 13), (11, 11), (14, 14), (15, 36), (24, 33), (1, 20), (2, 31), (6, 1), (7, 10), (10, 23), (10, 22), (13, 21), (22, 4), (12, 7), (16, 24), (17, 22), (9, 6), (8, 2), (24, 11), (27, 22), (10, 34), (25, 32), (14, 30), (19, 5), (15, 15), (0, 18), (19, 3), (17, 33), (24, 28), (14, 34), (6, 8), (20, 2), (21, 29), (20, 10), (25, 23), (1, 23), (6, 13), (27, 27), (4, 33), (22, 10), (13, 15), (1, 17), (2, 27), (6, 22), (24, 4), (6, 21), (28, 33), (14, 26), (4, 12), (10, 13), (10, 4), (7, 6), (0, 15), (26, 4), (3, 18), (26, 17), (9, 12), (8, 14), (21, 25), (9, 13), (29, 17), (22, 22), (23, 6), (28, 21), (10, 8), (4, 28), (20, 7), (7, 36), (4, 35), (13, 14), (12, 33), (12, 18), (26, 8), (8, 27), (20, 4), (16, 31), (0, 25), (28, 32), (3, 31), (15, 10), (5, 25), (5, 5), (16, 11), (17, 6), (14, 9), (28, 29), (19, 4), (28, 31), (15, 9), (5, 16), (27, 4), (14, 7), (1, 12), (3, 15), (4, 16), (11, 25), (16, 33), (5, 26), (1, 28), (19, 12), (12, 9), (1, 32), (15, 20), (2, 19), (2, 18), (8, 12), (6, 14), (9, 2), (18, 32), (24, 6), (17, 0), (7, 30), (13, 0), (25, 28), (16, 27), (18, 12), (10, 29), (9, 32), (11, 27), (28, 7), (22, 1), (9, 33), (29, 28), (18, 22), (19, 13), (22, 23), (16, 16), (9, 24), (6, 26), (10, 3), (9, 25), (17, 18), (21, 9), (8, 34), (2, 22), (22, 16), (14, 2), (2, 2), (26, 20), (29, 13), (16, 13), (5, 15), (24, 25), (29, 20), (3, 19), (29, 32), (26, 18), (24, 26), (23, 7), (5, 14), (21, 6), (20, 0), (2, 6), (26, 31), (9, 10), (5, 22), (27, 15), (5, 6), (19, 14), (27, 6), (21, 19), (15, 22), (7, 34), (25, 5), (2, 24), (6, 2), (29, 12), (12, 10), (23, 16), (8, 6), (18, 6), (7, 9), (19, 25), (25, 15), (29, 7), (2, 20), (25, 27), (11, 14), (2, 1), (13, 22), (2, 17), (28, 25), (29, 14), (9, 4), (9, 20), (23, 22), (1, 22), (22, 5), (10, 10), (28, 35), (6, 31), (3, 34), (6, 11), (21, 16), (17, 27), (17, 12), (28, 27), (27, 3), (18, 0), (7, 33), (28, 13), (27, 16), (19, 9), (15, 28), (19, 23), (26, 11), (18, 21), (12, 34), (2, 28), (23, 23), (28, 26), (21, 30), (13, 18), (12, 30), (1, 6), (1, 21), (17, 26), (8, 20), (25, 25), (14, 32), (11, 32), (3, 2), (27, 30), (20, 23), (13, 4), (24, 27), (13, 26), (0, 2), (12, 36), (6, 24), (13, 6), (21, 20), (12, 1), (18, 36), (6, 28), (9, 15), (4, 23), (5, 21), (14, 25), (22, 14), (10, 17), (2, 8), (1, 15), (21, 36), (17, 2), (17, 24), (14, 21), (13, 16), (12, 32), (11, 1), (1, 9), (18, 15), (25, 29), (5, 18), (8, 35), (3, 22), (0, 36), (24, 14), (24, 16), (20, 25), (27, 5), (25, 18), (21, 8), (20, 33), (7, 20), (2, 15), (11, 20), (29, 9), (5, 8), (17, 16), (29, 19), (0, 30), (6, 4), (6, 17), (17, 17), (24, 34), (22, 28), (27, 8), (12, 13), (13, 23), (1, 24), (10, 28), (16, 28), (29, 0), (26, 3), (28, 30), (20, 1), (8, 9), (16, 7), (16, 3), (19, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844290", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), 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), (22, 1), (24, 20), (26, 10), (16, 16), (4, 23), (22, 8), (20, 29), (17, 22), (18, 30), (25, 6), (15, 27), (14, 13), (7, 30), (27, 13), (15, 20), (3, 0), (19, 20), (15, 6), (12, 22), (13, 2), (15, 18), (19, 22), (18, 10), (1, 1), (15, 2), (20, 17), (23, 18), (10, 6), (23, 14), (19, 24), (12, 28), (7, 18), (1, 3), (19, 25), (23, 13), (29, 21), (0, 6), (15, 16), (9, 5), (24, 22), (16, 15), (6, 9), (23, 7), (17, 11), (5, 23), (16, 13), (15, 7), (15, 14), (21, 29), (14, 10), (10, 10), (4, 25), (28, 4), (19, 21), (18, 15), (2, 13), (18, 13), (12, 30), (6, 12), (24, 28), (24, 24), (28, 15), (5, 7), (0, 20), (11, 3), (12, 27), (0, 24), (11, 17), (13, 13), (7, 19), (28, 1), (8, 29), (27, 0), (22, 5), (8, 3), (23, 8), (22, 4), (17, 26), (12, 29), (7, 10), (6, 8), (20, 5), (22, 27), (20, 25), (21, 21), (14, 2), (23, 15), (29, 14), (8, 22), (12, 9), (18, 3), (7, 20), (1, 15), (11, 16), (21, 4), (5, 28), (12, 0), (16, 7), (27, 25), (18, 0), (1, 25), (6, 23), (8, 2), (1, 22), (13, 22), (13, 19), (12, 4), (0, 25), (2, 0), (2, 10), (22, 25), (12, 26), (6, 16), (1, 10), (3, 9), (2, 11), (14, 16), (16, 4), (28, 24), (24, 15), (29, 9), (1, 27), (7, 1), (19, 11), (12, 5), (1, 24), (4, 28), (17, 27), (3, 18), (25, 19), (9, 19), (15, 4), (13, 9), (27, 26), (19, 26), (4, 12), (5, 24), (1, 14), (10, 22), (24, 30), (9, 14), (9, 12), (17, 12), (5, 5), (4, 15), (3, 12), (13, 21), (19, 13), (2, 23), (13, 8), (2, 29), (21, 19), (21, 3), (23, 26), (25, 26), (23, 27), (21, 14), (9, 30), (25, 15), (5, 10), (14, 19), (5, 19), (19, 16), (6, 4), (0, 4), (22, 11), (2, 6), (24, 13), (26, 24), (0, 28), (25, 14), (11, 10), (10, 19), (15, 5), (28, 14), (14, 5), (17, 16), (28, 28), (20, 11), (21, 11), (24, 2), (18, 5), (24, 6), (21, 9), (29, 16), (18, 4), (29, 2), (13, 14), (7, 15), (8, 13), (17, 1), (4, 1), (3, 1), (26, 22), (15, 15), (23, 10), (1, 17), (11, 22), (20, 21), (17, 23), (22, 30), (9, 24), (15, 29), (29, 27), (6, 15), (6, 27), (0, 22), (20, 27), (9, 3), (14, 1), (16, 19), (21, 18), (10, 30), (27, 30), (19, 4), (27, 12), (18, 27), (20, 23), (23, 2), (0, 7), (9, 15), (18, 26), (5, 17), (26, 3), (1, 28), (20, 18), (2, 24), (27, 19), (4, 0), (18, 25), (0, 12), (28, 6), (5, 27), (18, 22), (13, 30), (13, 24), (16, 25), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393392", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 28), (14, 31), (23, 18), (0, 7), (3, 7), (21, 30), (7, 33), (26, 6), (4, 36), (22, 26), (31, 35), (10, 36), (25, 25), (33, 20), (26, 19), (26, 15), (27, 25), (29, 10), (6, 35), (27, 0), (5, 18), (26, 8), (16, 27), (20, 21), (19, 6), (9, 29), (32, 6), (15, 6), (9, 12), (28, 5), (18, 13), (5, 3), (2, 20), (0, 31), (29, 0), (5, 30), (31, 18), (20, 26), (15, 23), (32, 8), (17, 15), (33, 33), (26, 35), (18, 6), (23, 29), (9, 1), (15, 3), (17, 29), (8, 19), (13, 4), (17, 10), (21, 31), (31, 29), (6, 5), (18, 12), (24, 4), (13, 15), (16, 25), (17, 32), (24, 0), (8, 13), (32, 7), (21, 37), (14, 5), (25, 9), (19, 30), (10, 14), (9, 30), (4, 26), (8, 21), (1, 35), (28, 23), (3, 5), (13, 25), (24, 25), (32, 4), (15, 28), (29, 28), (30, 10), (23, 5), (11, 18), (11, 24), (23, 37), (4, 15), (4, 7), (32, 20), (6, 34), (26, 24), (20, 17), (0, 34), (30, 0), (25, 1), (31, 31), (7, 7), (25, 32), (29, 31), (17, 2), (26, 25), (30, 7), (18, 14), (14, 0), (11, 30), (28, 3), (3, 22), (9, 25), (23, 32), (3, 24), (11, 27), (28, 36), (30, 24), (2, 14), (16, 19), (33, 25), (26, 9), (26, 14), (13, 31), (8, 3), (5, 7), (20, 9), (3, 18), (31, 7), (12, 2), (2, 11), (20, 8), (5, 20), (10, 28), (12, 31), (23, 11), (17, 11), (6, 24), (29, 17), (22, 25), (4, 22), (5, 11), (33, 26), (24, 1), (33, 22), (29, 25), (17, 27), (5, 35), (4, 13), (10, 32), (23, 1), (7, 36), (9, 28), (8, 15), (33, 17), (3, 15), (12, 22), (27, 16), (2, 7), (14, 2), (16, 26), (11, 28), (19, 4), (2, 27), (33, 9), (15, 16), (26, 30), (26, 17), (10, 37), (10, 18), (26, 7), (12, 1), (4, 19), (20, 37), (8, 37), (9, 35), (15, 21), (13, 21), (9, 0), (8, 33), (26, 1), (1, 1), (12, 18), (7, 10), (4, 4), (1, 37), (33, 24), (7, 6), (28, 28), (21, 8), (11, 15), (8, 25), (29, 7), (22, 34), (31, 30), (13, 27), (5, 16), (30, 33), (18, 37), (25, 11), (25, 5), (12, 20), (12, 6), (6, 6), (15, 5), (6, 31), (13, 37), (25, 2), (22, 10), (20, 13), (22, 6), (25, 16), (19, 8), (19, 11), (19, 5), (2, 10), (31, 9), (28, 12), (21, 15), (27, 37), (30, 21), (2, 5), (26, 12), (29, 24), (7, 5), (29, 9), (6, 25), (32, 10), (1, 3), (10, 26), (7, 20), (6, 32), (24, 23), (15, 34), (4, 16), (2, 6), (0, 17), (13, 11), (17, 20), (29, 34), (5, 25), (18, 20), (15, 1), (21, 24), (33, 1), (1, 5), (25, 36), (25, 20), (12, 26), (23, 2), (8, 18), (21, 0), (33, 13), (24, 36), (26, 0), (21, 23), (28, 2), (27, 3), (22, 19), (30, 31), (12, 34), (6, 8), (27, 2), (33, 10), (18, 31), (33, 0), (33, 32), (8, 34), (13, 34), (17, 8), (8, 32), (32, 26), (0, 20), (27, 1), (15, 33), (22, 0), (28, 33), (19, 0), (0, 14), (25, 21), (7, 12), (17, 1), (27, 15), (5, 14), (3, 34), (1, 29), (11, 19), (21, 28), (5, 26), (28, 21), (1, 21), (13, 10), (23, 13), (14, 22), (0, 6), (10, 1), (4, 30), (3, 33), (21, 4), (4, 33), (14, 23), (28, 11), (15, 7), (0, 29), (18, 4), (13, 5), (3, 11), (33, 7), (8, 6), (23, 4), (28, 14), (1, 34), (21, 25), (33, 6), (33, 14), (0, 36), (18, 22), (30, 26), (13, 19), (30, 35), (15, 27), (28, 27), (32, 22), (21, 32), (30, 18), (19, 17), (15, 25), (1, 8), (16, 12), (19, 16), (16, 4), (30, 22), (13, 8), (6, 12), (11, 26), (9, 18), (6, 2), (12, 19), (1, 17), (24, 37), (16, 13), (27, 14), (1, 20), (5, 10), (4, 34), (4, 25), (7, 22), (22, 24), (25, 23), (17, 26), (27, 34), (1, 25), (11, 7), (7, 28), (24, 24), (0, 4), (13, 24), (27, 7), (8, 36), (6, 13), (14, 26), (32, 5), (22, 12), (29, 35), (12, 27), (18, 7), (16, 32), (20, 35), (3, 10), (12, 10), (30, 23), (5, 6), (24, 26), (32, 32), (20, 34), (15, 26), (31, 6), (7, 21), (24, 14), (8, 16), (27, 21), (18, 29), (4, 17), (12, 12), (6, 16), (28, 31), (17, 24), (28, 17), (22, 28), (10, 10), (33, 31), (30, 20), (33, 12), (14, 37), (22, 4), (24, 28), (28, 24), (9, 6), (27, 12), (21, 2), (19, 22), (19, 34), (16, 33), (22, 35), (12, 16), (14, 25), (8, 8), (25, 33), (31, 22), (20, 32), (18, 24), (22, 21), (21, 18), (29, 19), (33, 2), (8, 14), (27, 31), (24, 12), (23, 33), (6, 21), (4, 12), (13, 36), (3, 19), (32, 17), (24, 7), (27, 29), (29, 12), (10, 20), (5, 23), (0, 22), (26, 16), (15, 20), (32, 37), (18, 1), (11, 0), (12, 3), (32, 35), (3, 17), (0, 21), (7, 8), (23, 30), (9, 13), (15, 8), (14, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845040", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (3, 27), (8, 13), (30, 1), (13, 22), (0, 11), (29, 14), (19, 18), (19, 19), (18, 30), (13, 9), (2, 22), (16, 10), (26, 3), (18, 10), (6, 9), (26, 26), (7, 6), (1, 3), (13, 11), (22, 4), (2, 17), (27, 10), (4, 1), (16, 18), (19, 16), (19, 7), (11, 19), (3, 15), (27, 6), (11, 22), (9, 18), (12, 29), (19, 3), (4, 30), (24, 9), (25, 27), (6, 21), (21, 15), (12, 18), (15, 2), (21, 6), (14, 9), (30, 24), (8, 23), (16, 3), (25, 17), (23, 20), (15, 7), (8, 17), (17, 1), (16, 19), (25, 9), (30, 15), (19, 1), (29, 15), (3, 24), (23, 6), (10, 8), (29, 26), (18, 8), (22, 19), (5, 11), (8, 28), (7, 17), (23, 18), (0, 4), (24, 4), (22, 3), (5, 21), (21, 21), (15, 18), (13, 0), (25, 22), (9, 17), (30, 3), (24, 17), (0, 30), (24, 1), (29, 8), (11, 10), (18, 27), (6, 14), (4, 27), (15, 15), (26, 25), (6, 27), (9, 6), (11, 25), (25, 13), (17, 24), (30, 6), (9, 11), (28, 20), (0, 24), (25, 6), (18, 11), (23, 10), (13, 4), (24, 28), (26, 27), (4, 20), (5, 30), (10, 9), (20, 11), (9, 9), (17, 27), (21, 23), (16, 9), (16, 12), (4, 12), (28, 25), (21, 13), (13, 29), (7, 23), (9, 0), (25, 5), (22, 18), (7, 5), (11, 12), (29, 18), (29, 16), (7, 3), (2, 24), (23, 15), (23, 0), (17, 7), (8, 27), (23, 19), (17, 5), (20, 7), (5, 25), (15, 10), (3, 23), (12, 7), (17, 10), (11, 14), (25, 25), (28, 10), (8, 14), (20, 16), (4, 9), (27, 28), (17, 11), (24, 19), (1, 20), (19, 27), (23, 5), (26, 23), (5, 14), (14, 21), (3, 9), (22, 15), (3, 26), (27, 7), (26, 29), (28, 18), (19, 29), (29, 13), (12, 19), (2, 13), (26, 7), (4, 13), (8, 18), (3, 4), (0, 26), (15, 11), (0, 19), (1, 16), (24, 13), (17, 12), (11, 26), (28, 26), (19, 6), (13, 10), (0, 18), (2, 2), (2, 1), (2, 27), (4, 17), (26, 9), (11, 15), (23, 4), (28, 4), (2, 28), (16, 4), (10, 24), (18, 12), (3, 6), (6, 16), (25, 30), (30, 18), (30, 8), (5, 1), (28, 1), (12, 3), (22, 14), (13, 14), (1, 29), (26, 16), (13, 25), (5, 27), (19, 12), (13, 17), (17, 14), (20, 9), (18, 15), (12, 11), (25, 8), (21, 27), (20, 2), (23, 3), (24, 16), (26, 5), (26, 30), (2, 15), (18, 18), (5, 12), (5, 19), (10, 25), (3, 17), (23, 30), (2, 23), (12, 22), (8, 24), (13, 24), (23, 13), (23, 11), (20, 4), (30, 13), (26, 12), (28, 15), (18, 21), (16, 2), (21, 11), (17, 26), (10, 29), (11, 29), (15, 29), (14, 12), (6, 30), (4, 23), (4, 6), (22, 21), (5, 4), (5, 15), (20, 19), (6, 3), (15, 26), (1, 26), (20, 14), (15, 22), (7, 21), (27, 25), (22, 9), (26, 18), (27, 27), (3, 30), (14, 7), (10, 4), (24, 12), (12, 25), (12, 26), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986605", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (4, 4), (5, 20), (7, 4), (18, 10), (15, 16), (11, 7), (25, 8), (4, 5), (8, 8), (9, 15), (11, 23), (18, 26), (17, 23), (18, 0), (28, 25), (11, 19), (25, 15), (27, 11), (27, 10), (17, 11), (0, 8), (21, 29), (5, 19), (10, 9), (25, 10), (25, 12), (7, 18), (19, 10), (16, 28), (23, 25), (19, 16), (13, 15), (13, 3), (2, 21), (3, 10), (27, 4), (12, 2), (7, 25), (12, 10), (5, 24), (0, 3), (14, 5), (21, 28), (15, 21), (4, 28), (5, 17), (16, 25), (24, 29), (21, 10), (16, 27), (29, 11), (20, 29), (22, 1), (25, 22), (16, 3), (10, 26), (29, 28), (11, 24), (23, 14), (4, 0), (3, 9), (9, 28), (16, 23), (11, 28), (26, 17), (17, 17), (3, 19), (14, 8), (29, 27), (2, 1), (24, 27), (13, 12), (14, 20), (17, 0), (11, 18), (24, 0), (5, 22), (18, 4), (25, 25), (6, 0), (8, 27), (12, 9), (3, 18), (29, 14), (6, 23), (9, 25), (22, 23), (15, 1), (21, 3), (8, 2), (20, 28), (21, 17), (14, 7), (21, 25), (7, 22), (16, 9), (5, 2), (2, 26), (14, 18), (18, 18), (1, 9), (27, 21), (22, 27), (2, 8), (29, 6), (8, 6), (28, 15), (3, 25), (20, 4), (22, 16), (7, 26), (23, 8), (5, 5), (27, 22), (15, 19), (10, 17), (2, 19), (1, 7), (20, 26), (15, 9), (26, 7), (10, 3), (6, 7), (19, 0), (7, 13), (10, 23), (16, 20), (9, 19), (29, 12), (23, 28), (15, 24), (15, 3), (1, 23), (17, 27), (8, 7), (25, 23), (1, 15), (9, 16), (17, 26), (21, 16), (16, 8), (4, 13), (26, 23), (0, 21), (8, 17), (7, 23), (15, 23), (9, 4), (12, 25), (9, 22), (14, 4), (14, 26), (23, 6), (1, 24), (20, 20), (14, 11), (2, 17), (0, 7), (13, 18), (24, 16), (8, 24), (1, 4), (3, 7), (29, 5), (1, 5), (4, 16), (16, 18), (15, 26), (24, 15), (10, 29), (22, 11), (29, 26), (22, 5), (28, 22), (26, 18), (10, 2), (0, 13), (24, 12), (11, 12), (12, 14), (17, 1), (20, 15), (21, 5), (20, 13), (15, 0), (23, 23), (3, 28), (4, 10), (18, 6), (2, 13), (1, 21), (4, 3), (21, 20), (8, 19), (27, 17), (26, 29), (23, 18), (20, 3), (9, 7), (16, 2), (3, 6), (5, 18), (19, 28), (26, 28), (8, 21), (13, 9), (8, 4), (28, 23), (20, 22), (22, 17), (4, 23), (10, 4), (20, 16), (26, 12), (23, 24), (6, 14), (23, 3), (19, 9), (4, 7), (25, 24), (29, 19), (14, 3), (22, 13), (6, 9), (20, 2), (26, 24), (13, 11), (23, 4), (0, 16), (8, 1), (9, 20), (0, 2), (27, 7), (14, 1), (28, 12), (16, 6), (28, 16), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68160", "dataset": "MATH"}
{"messages": [{"content": "In a 31x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 16), (15, 9), (20, 29), (1, 4), (21, 22), (7, 16), (29, 20), (22, 6), (28, 20), (27, 5), (4, 9), (4, 23), (25, 23), (29, 6), (17, 13), (4, 7), (14, 15), (8, 1), (14, 22), (11, 9), (7, 23), (24, 4), (22, 2), (2, 11), (5, 6), (15, 31), (4, 29), (25, 26), (28, 30), (12, 28), (23, 30), (22, 18), (3, 4), (8, 32), (11, 15), (24, 1), (22, 19), (2, 18), (4, 6), (9, 13), (12, 15), (8, 25), (25, 29), (7, 5), (21, 23), (10, 7), (4, 5), (6, 10), (4, 32), (18, 32), (29, 26), (3, 17), (24, 19), (6, 4), (23, 27), (12, 19), (16, 20), (12, 5), (23, 14), (2, 7), (25, 4), (28, 29), (28, 17), (13, 9), (6, 1), (27, 1), (8, 13), (15, 15), (24, 25), (29, 10), (1, 27), (5, 12), (17, 19), (24, 21), (2, 9), (13, 26), (0, 26), (11, 29), (2, 32), (25, 22), (14, 11), (11, 22), (20, 23), (28, 18), (8, 24), (10, 30), (17, 10), (2, 8), (10, 17), (14, 19), (9, 6), (5, 31), (18, 17), (8, 18), (18, 22), (18, 27), (1, 19), (9, 20), (4, 1), (4, 12), (5, 22), (17, 7), (11, 32), (9, 19), (11, 24), (27, 0), (15, 8), (0, 10), (25, 0), (22, 3), (16, 32), (2, 21), (1, 29), (13, 16), (5, 11), (20, 14), (29, 13), (3, 25), (29, 16), (2, 15), (15, 4), (3, 16), (24, 8), (26, 19), (29, 1), (18, 14), (26, 32), (1, 16), (17, 8), (24, 30), (26, 6), (10, 27), (8, 20), (29, 28), (18, 26), (5, 4), (2, 23), (30, 18), (19, 5), (8, 28), (6, 17), (15, 10), (15, 28), (13, 5), (3, 13), (21, 31), (6, 29), (21, 29), (6, 24), (28, 0), (26, 28), (24, 5), (17, 27), (30, 8), (9, 16), (15, 6), (19, 2), (6, 32), (27, 11), (24, 18), (19, 31), (15, 0), (22, 9), (24, 32), (1, 23), (8, 7), (6, 28), (27, 2), (23, 25), (30, 19), (4, 27), (25, 7), (2, 19), (19, 11), (8, 19), (18, 6), (1, 14), (20, 31), (7, 14), (29, 21), (26, 29), (1, 3), (13, 4), (26, 25), (14, 31), (9, 14), (14, 20), (0, 6), (17, 21), (4, 14), (24, 31), (8, 29), (6, 15), (18, 12), (23, 11), (6, 9), (15, 27), (22, 29), (19, 27), (20, 19), (20, 17), (10, 13), (3, 28), (28, 4), (29, 18), (19, 25), (22, 24), (23, 24), (6, 11), (14, 12), (16, 25), (23, 26), (12, 32), (19, 8), (29, 32), (14, 9), (3, 6), (27, 30), (16, 29), (14, 26), (1, 30), (23, 21), (12, 16), (17, 20), (20, 0), (28, 6), (17, 3), (10, 24), (2, 3), (11, 11), (11, 18), (7, 7), (20, 24), (16, 17), (25, 9), (8, 12), (19, 20), (16, 7), (25, 8), (21, 6), (30, 20), (21, 8), (28, 1), (7, 2), (5, 21), (13, 22), (6, 25), (9, 24), (17, 18), (22, 26), (30, 9), (11, 17), (2, 12), (23, 23), (25, 12), (23, 2), (24, 6), (14, 14), (10, 1), (1, 5), (7, 11), (16, 16), (9, 2), (13, 20), (30, 1), (19, 17), (4, 2), (22, 11), (25, 11), (19, 19), (3, 1), (10, 4), (5, 28), (30, 17), (30, 23), (0, 20), (1, 1), (8, 5), (17, 23), (25, 17), (28, 26), (29, 14), (7, 15), (4, 16), (11, 2), (28, 10), (5, 20), (16, 6), (7, 28), (16, 12), (3, 27), (5, 27), (14, 16), (13, 8), (1, 9), (2, 5), (10, 0), (6, 14), (23, 32), (1, 32), (5, 23), (30, 24), (19, 15), (26, 15), (8, 22), (10, 19), (21, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "670136", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 22), (27, 11), (19, 20), (7, 4), (4, 26), (12, 21), (5, 1), (15, 30), (21, 12), (15, 4), (15, 11), (25, 17), (23, 28), (30, 11), (6, 17), (1, 30), (3, 15), (14, 0), (20, 21), (9, 17), (9, 6), (8, 14), (19, 23), (4, 5), (2, 12), (3, 26), (26, 29), (30, 12), (24, 23), (22, 25), (25, 6), (10, 19), (31, 15), (31, 26), (11, 26), (8, 30), (6, 30), (22, 19), (33, 29), (29, 26), (19, 28), (15, 13), (3, 7), (6, 8), (3, 12), (1, 8), (35, 11), (18, 7), (28, 7), (7, 12), (32, 8), (19, 5), (15, 29), (10, 20), (33, 10), (1, 26), (7, 14), (11, 5), (10, 15), (29, 2), (12, 3), (7, 24), (7, 7), (6, 3), (28, 18), (19, 29), (14, 2), (25, 11), (5, 13), (18, 4), (23, 27), (21, 29), (27, 0), (26, 13), (2, 23), (31, 24), (23, 11), (16, 25), (6, 24), (2, 16), (16, 30), (6, 26), (9, 27), (18, 5), (32, 26), (1, 25), (8, 20), (32, 2), (30, 15), (0, 28), (9, 12), (22, 13), (4, 15), (2, 7), (35, 22), (11, 4), (18, 21), (26, 10), (11, 27), (28, 21), (15, 2), (11, 3), (26, 3), (25, 29), (35, 6), (32, 19), (18, 17), (33, 24), (34, 25), (4, 27), (17, 23), (20, 6), (7, 22), (27, 23), (1, 15), (35, 18), (23, 10), (3, 14), (31, 3), (16, 15), (35, 7), (15, 26), (25, 20), (30, 24), (13, 7), (1, 24), (26, 24), (26, 9), (19, 3), (16, 23), (13, 13), (19, 13), (18, 20), (27, 28), (20, 18), (31, 16), (24, 13), (32, 0), (0, 15), (9, 0), (21, 23), (8, 24), (27, 20), (4, 1), (16, 17), (13, 19), (13, 24), (25, 24), (24, 1), (9, 19), (14, 12), (23, 15), (26, 8), (9, 11), (21, 13), (29, 9), (2, 28), (22, 8), (18, 30), (12, 26), (26, 0), (5, 30), (5, 9), (32, 10), (9, 15), (30, 20), (7, 31), (29, 22), (23, 26), (15, 22), (4, 23), (32, 9), (23, 30), (31, 20), (19, 19), (12, 2), (17, 9), (18, 3), (33, 5), (20, 8), (8, 28), (22, 3), (35, 0), (3, 9), (24, 27), (13, 29), (25, 15), (18, 9), (28, 0), (12, 23), (27, 16), (25, 30), (19, 31), (22, 24), (25, 22), (14, 3), (33, 12), (10, 2), (29, 28), (29, 1), (21, 18), (32, 6), (33, 18), (31, 18), (11, 8), (26, 26), (10, 12), (4, 20), (21, 1), (29, 25), (18, 19), (10, 6), (33, 2), (1, 28), (18, 12), (19, 22), (17, 2), (17, 19), (30, 25), (23, 6), (34, 2), (8, 25), (12, 0), (22, 1), (27, 19), (31, 8), (19, 7), (13, 22), (7, 11), (4, 29), (3, 24), (15, 18), (18, 1), (3, 28), (28, 13), (23, 23), (33, 17), (19, 8), (1, 10), (10, 17), (12, 15), (34, 18), (2, 4), (18, 15), (19, 21), (17, 12), (33, 8), (22, 17), (7, 27), (13, 17), (29, 21), (24, 30), (0, 13), (16, 14), (5, 31), (1, 11), (0, 6), (10, 25), (30, 4), (33, 11), (31, 10), (27, 3), (14, 14), (5, 23), (2, 5), (5, 20), (17, 3), (17, 11), (22, 23), (35, 17), (1, 14), (32, 11), (32, 22), (11, 24), (35, 27), (27, 13), (15, 23), (30, 28), (14, 30), (18, 22), (35, 21), (18, 24), (33, 16), (14, 18), (17, 20), (24, 6), (9, 13), (20, 0), (15, 21), (5, 5), (21, 25), (2, 11), (0, 3), (31, 5), (2, 22), (12, 6), (17, 7), (19, 18), (1, 27), (11, 9), (27, 30), (0, 2), (35, 24), (16, 5), (27, 27), (14, 24), (19, 11), (25, 3), (11, 18), (18, 0), (12, 14), (27, 9), (32, 30), (9, 28), (13, 6), (21, 2), (12, 27), (25, 10), (10, 11), (18, 16), (35, 3), (0, 7), (2, 31), (29, 16), (29, 8), (6, 9), (10, 8), (6, 20), (20, 22), (1, 4), (6, 6), (5, 22), (35, 10), (15, 6), (29, 20), (34, 8), (6, 22), (5, 12), (30, 16), (5, 24), (0, 27), (22, 7), (15, 16), (29, 0), (27, 6), (7, 21), (27, 31), (14, 28), (16, 24), (10, 30), (14, 7), (22, 0), (6, 0), (34, 21), (16, 26), (7, 8), (5, 29), (5, 19), (19, 1), (16, 13), (23, 1), (2, 29), (22, 4), (1, 23), (21, 14), (8, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89856", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 16), (2, 20), (10, 9), (5, 25), (2, 30), (30, 21), (30, 5), (19, 23), (20, 20), (14, 25), (33, 22), (21, 5), (20, 13), (3, 1), (1, 25), (22, 2), (15, 26), (8, 6), (5, 9), (3, 18), (1, 7), (4, 4), (12, 17), (18, 24), (30, 8), (9, 5), (23, 1), (31, 17), (18, 19), (9, 7), (21, 15), (8, 26), (2, 21), (34, 10), (6, 14), (21, 19), (32, 27), (30, 18), (22, 30), (0, 21), (9, 3), (1, 20), (8, 19), (25, 9), (11, 1), (15, 25), (16, 5), (17, 8), (12, 7), (33, 23), (27, 5), (17, 19), (1, 9), (3, 9), (32, 0), (31, 12), (16, 24), (5, 19), (3, 12), (3, 19), (5, 27), (29, 8), (16, 7), (24, 15), (30, 12), (29, 24), (4, 25), (16, 4), (35, 24), (2, 27), (24, 4), (28, 1), (28, 23), (0, 19), (24, 20), (34, 6), (0, 3), (6, 2), (12, 18), (1, 17), (16, 11), (0, 22), (35, 4), (22, 12), (1, 3), (26, 13), (21, 25), (25, 1), (21, 28), (14, 14), (4, 13), (23, 10), (33, 3), (19, 7), (19, 15), (3, 27), (3, 26), (21, 23), (14, 19), (33, 30), (3, 25), (2, 28), (6, 12), (11, 3), (13, 22), (13, 8), (17, 24), (19, 29), (26, 24), (13, 24), (27, 30), (0, 5), (22, 3), (14, 2), (33, 24), (6, 17), (12, 0), (25, 8), (25, 21), (2, 16), (2, 14), (6, 22), (10, 29), (21, 30), (6, 11), (10, 22), (34, 0), (31, 0), (21, 9), (28, 10), (3, 16), (2, 12), (5, 29), (20, 29), (27, 14), (12, 26), (35, 5), (5, 22), (17, 28), (28, 20), (4, 19), (10, 15), (32, 4), (30, 19), (25, 19), (7, 28), (23, 28), (17, 5), (8, 1), (24, 22), (24, 14), (14, 21), (23, 29), (6, 25), (14, 17), (1, 13), (0, 29), (3, 28), (16, 2), (11, 26), (20, 19), (6, 13), (13, 30), (16, 27), (21, 6), (4, 15), (10, 25), (9, 10), (32, 13), (10, 0), (2, 18), (12, 2), (7, 18), (18, 30), (16, 28), (17, 1), (1, 12), (25, 10), (32, 9), (11, 22), (29, 6), (14, 13), (10, 5), (30, 24), (2, 0), (28, 2), (11, 23), (11, 28), (29, 17), (0, 12), (22, 7), (16, 21), (22, 1), (7, 27), (26, 20), (4, 14), (0, 27), (30, 28), (30, 22), (11, 10), (13, 3), (33, 1), (17, 27), (32, 1), (15, 9), (29, 4), (16, 6), (20, 6), (23, 15), (29, 0), (27, 10), (33, 7), (9, 8), (25, 24), (17, 16), (19, 25), (22, 11), (8, 13), (29, 2), (26, 15), (22, 17), (1, 15), (34, 16), (5, 28), (7, 5), (4, 8), (22, 26), (14, 11), (2, 6), (10, 17), (21, 14), (9, 6), (30, 29), (35, 1), (12, 10), (21, 24), (20, 14), (34, 15), (4, 22), (14, 18), (22, 24), (35, 7), (34, 22), (2, 19), (17, 26), (13, 28), (24, 0), (4, 1), (5, 24), (29, 16), (26, 26), (31, 7), (27, 2), (10, 18), (26, 8), (25, 17), (0, 26), (30, 7), (11, 13), (3, 13), (18, 1), (10, 10), (22, 21), (35, 14), (27, 1), (16, 12), (31, 26), (33, 14), (14, 28), (29, 11), (18, 17), (11, 19), (9, 21), (33, 25), (32, 19), (8, 23), (0, 15), (15, 5), (26, 2), (1, 27), (23, 26), (19, 17), (20, 25), (9, 17), (16, 30), (4, 0), (20, 0), (8, 15), (13, 0), (19, 9), (31, 21), (12, 24), (30, 11), (16, 9), (8, 7), (27, 25), (13, 21), (29, 19), (3, 6), (18, 28), (0, 4), (2, 11), (29, 18), (15, 21), (7, 15), (23, 24), (25, 27), (15, 4), (12, 29), (19, 24), (32, 28), (23, 16), (2, 8), (33, 8), (3, 24), (16, 13), (17, 29), (4, 30), (27, 17), (27, 15), (9, 19), (17, 9), (26, 19), (24, 7), (11, 20), (9, 26), (20, 17), (4, 29), (10, 19), (15, 6), (14, 4), (21, 18), (18, 7), (2, 24), (5, 20), (34, 26), (16, 17), (24, 19), (33, 19), (26, 1), (6, 20), (35, 20), (2, 4), (31, 8), (25, 14), (30, 25), (7, 7), (11, 8), (6, 7), (12, 19), (10, 24), (9, 15), (6, 26), (18, 18), (18, 3), (32, 6), (7, 3), (13, 1), (28, 30), (18, 9), (31, 23), (11, 16), (18, 8), (7, 12), (1, 4), (27, 19), (32, 8), (34, 20), (8, 16), (3, 3), (1, 14), (29, 7), (21, 8), (15, 8), (12, 30), (20, 5), (27, 13), (4, 7), (25, 30), (4, 12), (7, 14), (2, 13), (27, 21), (28, 21), (23, 25), (11, 30), (30, 4), (5, 0), (26, 3), (19, 30), (3, 20), (21, 0), (1, 1), (34, 3), (34, 7), (11, 29), (15, 29), (24, 11), (26, 10), (24, 9), (32, 15), (26, 21), (34, 1), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872640", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 27), (25, 32), (11, 10), (17, 20), (6, 12), (16, 28), (4, 21), (30, 12), (25, 17), (12, 0), (27, 24), (22, 8), (17, 0), (9, 32), (29, 30), (19, 31), (23, 13), (28, 3), (29, 26), (18, 28), (25, 33), (7, 0), (12, 9), (4, 29), (0, 29), (7, 22), (16, 4), (30, 32), (5, 20), (24, 5), (24, 3), (19, 18), (13, 22), (15, 28), (5, 34), (19, 15), (9, 26), (21, 4), (20, 14), (23, 34), (24, 4), (14, 16), (29, 13), (29, 24), (19, 16), (16, 14), (14, 6), (29, 4), (30, 33), (15, 16), (29, 25), (24, 12), (20, 26), (14, 9), (31, 4), (10, 29), (8, 1), (7, 13), (3, 19), (16, 21), (4, 16), (9, 9), (25, 24), (12, 29), (22, 11), (22, 24), (5, 33), (23, 33), (7, 4), (12, 24), (31, 28), (29, 0), (9, 21), (17, 27), (23, 16), (13, 0), (4, 28), (15, 31), (25, 26), (22, 25), (19, 9), (11, 33), (15, 13), (3, 16), (28, 16), (11, 23), (29, 20), (14, 2), (30, 9), (29, 16), (25, 12), (26, 11), (7, 28), (27, 6), (18, 17), (18, 22), (0, 21), (13, 28), (11, 17), (14, 15), (20, 32), (13, 13), (4, 8), (8, 30), (18, 4), (18, 18), (26, 23), (22, 33), (21, 6), (14, 20), (4, 1), (28, 28), (2, 22), (11, 32), (15, 0), (29, 23), (5, 11), (13, 26), (0, 22), (1, 31), (11, 3), (4, 33), (17, 7), (28, 1), (25, 7), (26, 34), (8, 28), (6, 31), (6, 4), (31, 13), (3, 14), (8, 34), (15, 24), (17, 16), (24, 30), (19, 29), (2, 30), (6, 21), (13, 6), (15, 25), (23, 4), (26, 28), (15, 27), (5, 28), (29, 11), (21, 27), (9, 14), (19, 6), (5, 1), (9, 0), (27, 15), (8, 12), (10, 19), (17, 25), (10, 0), (20, 31), (3, 1), (21, 10), (10, 20), (20, 15), (26, 26), (5, 13), (27, 26), (30, 20), (16, 16), (24, 34), (27, 10), (16, 3), (11, 18), (11, 9), (25, 20), (26, 2), (3, 2), (4, 26), (4, 9), (30, 7), (13, 33), (6, 26), (2, 11), (31, 23), (10, 25), (25, 16), (2, 19), (31, 17), (24, 1), (1, 16), (20, 23), (10, 6), (4, 3), (25, 34), (21, 7), (24, 9), (14, 29), (16, 20), (25, 11), (0, 2), (24, 0), (9, 1), (17, 33), (23, 5), (23, 10), (27, 31), (3, 30), (31, 24), (29, 6), (12, 32), (5, 2), (16, 29), (10, 11), (0, 33), (7, 34), (1, 11), (14, 1), (31, 9), (14, 25), (19, 14), (16, 17), (24, 11), (23, 30), (30, 13), (24, 32), (8, 31), (13, 4), (20, 24), (6, 15), (21, 33), (10, 15), (9, 3), (24, 26), (7, 26), (22, 6), (23, 24), (7, 29), (9, 22), (4, 31), (28, 34), (22, 19), (17, 4), (28, 27), (0, 11), (19, 7), (30, 19), (27, 18), (14, 17), (13, 27), (19, 30), (1, 9), (6, 22), (26, 0), (12, 13), (25, 15), (21, 19), (14, 3), (19, 17), (14, 5), (20, 12), (21, 14), (20, 34), (1, 2), (20, 28), (24, 19), (30, 29), (7, 32), (1, 3), (10, 9), (15, 23), (12, 27), (12, 3), (26, 9), (19, 3), (16, 25), (15, 9), (6, 6), (26, 5), (25, 3), (19, 28), (25, 6), (2, 4), (3, 34), (1, 7), (2, 25), (1, 26), (10, 30), (3, 31), (4, 13), (10, 12), (13, 5), (0, 26), (7, 18), (12, 1), (27, 33), (16, 15), (1, 21), (17, 14), (28, 26), (3, 10), (26, 29), (14, 10), (8, 33), (16, 26), (30, 2), (9, 8), (2, 16), (8, 11), (8, 23), (9, 18), (1, 20), (31, 3), (13, 15), (31, 20), (28, 9), (1, 18), (26, 12), (3, 17), (29, 22), (27, 7), (0, 5), (7, 2), (30, 25), (23, 0), (13, 23), (30, 14), (29, 32), (24, 31), (7, 5), (31, 11), (12, 17), (24, 13), (18, 2), (18, 1), (24, 27), (8, 25), (28, 4), (16, 1), (24, 10), (7, 7), (4, 0), (23, 2), (19, 20), (30, 23), (22, 5), (5, 4), (19, 27), (12, 31), (25, 1), (29, 28), (4, 20), (5, 14), (19, 2), (17, 26), (7, 14), (18, 11), (10, 14), (25, 21), (8, 15), (7, 8), (1, 27), (17, 12), (10, 8), (22, 12), (11, 1), (16, 24), (10, 28), (5, 31), (28, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688500", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), 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), (6, 5), (12, 1), (8, 3), (25, 12), (22, 30), (23, 11), (6, 7), (4, 22), (5, 30), (5, 3), (11, 8), (10, 21), (11, 31), (2, 25), (13, 15), (0, 6), (29, 21), (5, 15), (12, 14), (21, 29), (32, 9), (26, 1), (8, 4), (23, 26), (28, 11), (1, 17), (9, 8), (22, 5), (21, 23), (24, 0), (5, 31), (6, 2), (19, 17), (5, 16), (6, 20), (2, 22), (1, 32), (15, 26), (22, 23), (9, 21), (19, 3), (12, 3), (31, 28), (0, 18), (3, 4), (15, 7), (27, 15), (19, 8), (13, 14), (13, 16), (8, 2), (24, 25), (26, 14), (5, 23), (32, 14), (6, 21), (22, 1), (13, 18), (9, 25), (16, 21), (12, 27), (24, 17), (28, 20), (26, 16), (31, 10), (26, 20), (17, 18), (2, 11), (28, 6), (19, 22), (15, 5), (12, 21), (32, 29), (5, 25), (28, 14), (21, 21), (1, 14), (13, 9), (4, 15), (4, 26), (20, 8), (11, 2), (5, 24), (9, 27), (14, 8), (5, 8), (19, 13), (29, 7), (10, 30), (25, 17), (2, 32), (2, 30), (0, 1), (7, 15), (21, 4), (14, 4), (10, 33), (18, 32), (29, 0), (23, 19), (28, 24), (11, 28), (30, 23), (2, 1), (28, 15), (30, 26), (14, 30), (0, 12), (10, 10), (3, 29), (31, 13), (19, 14), (10, 27), (22, 32), (18, 31), (11, 0), (1, 23), (11, 14), (25, 26), (15, 9), (24, 23), (3, 30), (0, 31), (8, 7), (16, 25), (20, 0), (19, 1), (13, 13), (30, 12), (13, 3), (3, 26), (25, 3), (8, 18), (18, 16), (29, 18), (18, 7), (29, 32), (9, 31), (1, 11), (15, 17), (14, 16), (13, 28), (17, 7), (10, 4), (32, 8), (21, 20), (32, 0), (31, 17), (11, 17), (10, 12), (23, 21), (10, 19), (1, 3), (27, 21), (29, 23), (6, 19), (5, 1), (31, 3), (5, 7), (25, 11), (19, 6), (26, 29), (13, 0), (29, 25), (18, 1), (2, 2), (19, 5), (15, 22), (27, 10), (25, 1), (0, 29), (31, 24), (3, 9), (12, 28), (16, 27), (3, 24), (10, 28), (4, 33), (26, 23), (32, 5), (5, 32), (6, 30), (16, 30), (9, 14), (2, 28), (18, 2), (31, 14), (20, 1), (29, 24), (19, 29), (6, 27), (6, 25), (28, 5), (25, 16), (1, 33), (2, 29), (31, 9), (20, 23), (14, 15), (15, 28), (6, 33), (7, 22), (29, 5), (27, 1), (29, 9), (32, 27), (13, 25), (21, 6), (10, 8), (24, 1), (25, 24), (31, 6), (21, 9), (29, 20), (3, 2), (22, 21), (0, 14), (8, 29), (5, 26), (31, 23), (23, 28), (29, 29), (24, 28), (0, 27), (25, 23), (18, 23), (26, 31), (29, 28), (29, 6), (23, 5), (20, 30), (7, 12), (8, 6), (27, 23), (17, 20), (28, 17), (18, 12), (17, 25), (26, 32), (10, 24), (11, 13), (27, 27), (31, 30), (6, 10), (0, 16), (18, 17), (29, 11), (20, 11), (31, 25), (27, 30), (0, 17), (12, 24), (4, 2), (25, 25), (29, 26), (14, 28), (23, 16), (19, 10), (2, 16), (20, 9), (30, 28), (9, 15), (23, 0), (2, 27), (6, 22), (30, 21), (18, 25), (15, 11), (21, 28), (22, 17), (18, 0), (6, 12), (24, 29), (12, 16), (9, 10), (5, 5), (3, 17), (32, 15), (31, 0), (11, 12), (20, 3), (26, 27), (24, 6), (11, 24), (16, 4), (26, 24), (21, 15), (4, 20), (1, 19), (17, 27), (12, 25), (18, 13), (9, 7), (25, 21), (12, 20), (15, 23), (18, 27), (16, 16), (19, 31), (22, 22), (5, 14), (2, 6), (1, 4), (9, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799680", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 23), (25, 29), (14, 22), (20, 26), (1, 14), (17, 29), (11, 11), (8, 9), (13, 5), (2, 1), (21, 14), (23, 3), (21, 27), (8, 14), (1, 1), (2, 2), (1, 15), (11, 30), (11, 6), (21, 9), (12, 30), (13, 26), (2, 26), (9, 25), (5, 24), (0, 29), (4, 25), (11, 16), (24, 5), (21, 22), (1, 8), (10, 15), (28, 20), (19, 5), (27, 7), (3, 22), (20, 12), (6, 1), (24, 0), (18, 17), (3, 13), (17, 10), (26, 15), (14, 1), (25, 6), (4, 18), (8, 21), (26, 11), (4, 1), (25, 3), (12, 8), (26, 2), (20, 7), (2, 24), (20, 17), (30, 6), (14, 28), (11, 17), (26, 3), (8, 18), (5, 30), (1, 27), (10, 19), (20, 9), (29, 18), (25, 16), (23, 30), (6, 13), (0, 23), (26, 24), (29, 20), (18, 22), (11, 23), (1, 19), (26, 21), (9, 16), (3, 23), (24, 14), (19, 0), (22, 24), (2, 23), (14, 14), (9, 7), (26, 20), (15, 26), (10, 0), (11, 29), (20, 23), (7, 11), (19, 18), (20, 14), (5, 27), (16, 7), (11, 19), (16, 26), (28, 27), (2, 15), (24, 25), (22, 14), (16, 8), (10, 4), (19, 14), (2, 21), (11, 14), (2, 4), (4, 27), (24, 27), (16, 20), (22, 4), (11, 20), (27, 28), (4, 23), (20, 27), (19, 17), (29, 28), (1, 6), (28, 29), (22, 5), (2, 18), (11, 26), (1, 0), (16, 30), (9, 6), (28, 9), (5, 26), (19, 7), (14, 17), (14, 19), (23, 28), (6, 24), (27, 13), (29, 16), (18, 27), (22, 16), (27, 25), (24, 9), (24, 1), (18, 19), (13, 0), (21, 19), (7, 30), (21, 11), (11, 15), (7, 16), (11, 7), (27, 12), (3, 15), (5, 4), (12, 18), (19, 16), (29, 11), (24, 8), (23, 22), (19, 15), (14, 27), (15, 9), (8, 7), (26, 7), (18, 0), (7, 9), (13, 21), (27, 23), (23, 12), (1, 3), (29, 24), (7, 17), (29, 22), (15, 13), (16, 13), (7, 14), (4, 19), (27, 2), (9, 4), (25, 17), (10, 11), (4, 7), (17, 4), (8, 27), (20, 8), (9, 17), (9, 29), (8, 8), (3, 30), (3, 25), (0, 9), (12, 3), (18, 6), (2, 30), (6, 6), (12, 2), (4, 10), (3, 8), (0, 25), (19, 28), (1, 2), (12, 5), (3, 24), (14, 18), (4, 8), (25, 1), (10, 26), (17, 25), (13, 3), (24, 28), (5, 17), (22, 10), (7, 21), (4, 28), (8, 20), (22, 30), (0, 12), (7, 3), (11, 21), (30, 10), (16, 19), (3, 14), (25, 10), (26, 22), (25, 15), (29, 12), (5, 9), (14, 7), (25, 23), (8, 16), (4, 16), (12, 27), (0, 24), (26, 19), (8, 17), (17, 9), (4, 14), (10, 12), (3, 17), (9, 13), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602004", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (2, 8), (4, 33), (30, 9), (12, 5), (26, 32), (18, 4), (16, 36), (7, 29), (8, 13), (12, 25), (18, 10), (12, 19), (24, 26), (8, 33), (6, 36), (14, 4), (35, 0), (24, 23), (7, 2), (28, 36), (14, 3), (19, 26), (1, 27), (28, 18), (11, 27), (36, 9), (31, 36), (2, 24), (15, 22), (36, 24), (13, 17), (4, 27), (12, 12), (8, 23), (12, 3), (3, 24), (34, 29), (31, 0), (7, 26), (26, 29), (31, 20), (5, 19), (35, 34), (0, 15), (5, 32), (35, 33), (23, 23), (33, 30), (34, 6), (24, 13), (28, 21), (13, 7), (24, 5), (21, 10), (5, 1), (11, 11), (35, 36), (8, 2), (11, 31), (18, 26), (21, 18), (13, 15), (6, 11), (26, 7), (13, 10), (25, 2), (36, 30), (28, 34), (26, 2), (23, 22), (25, 1), (10, 17), (12, 32), (32, 16), (37, 15), (22, 32), (32, 3), (18, 23), (10, 36), (0, 35), (16, 11), (27, 29), (5, 13), (34, 4), (6, 20), (31, 16), (21, 19), (17, 26), (5, 23), (4, 22), (27, 6), (14, 28), (23, 7), (18, 27), (13, 25), (36, 18), (8, 32), (32, 32), (5, 20), (22, 17), (20, 17), (35, 12), (17, 27), (18, 0), (4, 28), (2, 0), (14, 1), (7, 14), (15, 27), (29, 25), (0, 23), (18, 9), (8, 6), (6, 4), (3, 15), (27, 13), (28, 10), (13, 16), (8, 3), (12, 27), (19, 15), (1, 3), (15, 2), (29, 33), (33, 10), (31, 13), (30, 30), (2, 30), (13, 11), (25, 17), (22, 26), (34, 33), (34, 30), (22, 23), (32, 0), (16, 18), (9, 0), (1, 31), (22, 21), (22, 35), (19, 7), (21, 35), (18, 12), (25, 14), (24, 25), (7, 17), (15, 15), (5, 26), (24, 28), (20, 13), (25, 23), (21, 21), (32, 7), (10, 12), (10, 23), (7, 31), (19, 9), (3, 7), (5, 9), (16, 32), (9, 18), (23, 3), (22, 8), (11, 1), (5, 7), (27, 20), (15, 20), (36, 4), (35, 18), (14, 30), (23, 34), (26, 27), (20, 33), (33, 23), (32, 4), (33, 19), (16, 21), (22, 9), (30, 19), (23, 32), (7, 3), (8, 35), (8, 28), (32, 29), (37, 9), (11, 21), (5, 28), (28, 8), (13, 23), (16, 35), (8, 25), (36, 0), (31, 4), (27, 34), (9, 8), (25, 29), (24, 32), (6, 29), (36, 36), (5, 6), (28, 22), (5, 8), (12, 2), (15, 3), (24, 8), (4, 36), (10, 2), (29, 12), (33, 32), (22, 30), (17, 35), (8, 4), (9, 27), (1, 21), (33, 17), (15, 11), (24, 19), (0, 22), (0, 18), (9, 28), (27, 23), (7, 4), (23, 11), (32, 22), (10, 4), (23, 26), (24, 24), (0, 28), (32, 15), (35, 3), (34, 14), (20, 23), (27, 0), (32, 11), (19, 16), (37, 21), (19, 30), (17, 25), (17, 24), (8, 27), (29, 34), (0, 24), (37, 2), (22, 22), (28, 7), (25, 32), (23, 14), (27, 27), (29, 28), (36, 23), (3, 28), (17, 4), (25, 24), (9, 13), (9, 21), (32, 30), (14, 14), (9, 17), (25, 35), (7, 8), (9, 14), (31, 14), (32, 1), (20, 32), (24, 9), (7, 13), (37, 29), (17, 32), (23, 31), (36, 35), (10, 29), (33, 13), (31, 7), (5, 35), (29, 9), (6, 9), (16, 26), (22, 14), (29, 21), (37, 6), (14, 7), (25, 7), (35, 9), (31, 30), (11, 15), (21, 11), (30, 5), (0, 36), (14, 10), (30, 11), (19, 5), (31, 28), (20, 31), (35, 25), (12, 4), (30, 14), (10, 31), (6, 22), (37, 18), (17, 16), (2, 4), (35, 15), (12, 0), (13, 4), (23, 0), (13, 31), (29, 32), (30, 17), (4, 35), (16, 34), (28, 3), (1, 5), (3, 26), (28, 9), (16, 14), (37, 28), (23, 28), (1, 12), (27, 28), (5, 14), (5, 36), (10, 35), (9, 19), (25, 0), (10, 5), (11, 25), (13, 28), (25, 12), (23, 12), (28, 5), (20, 28), (33, 20), (31, 2), (31, 21), (29, 13), (16, 13), (1, 10), (19, 33), (30, 22), (5, 31), (21, 13), (19, 25), (30, 36), (29, 0), (35, 5), (17, 36), (18, 13), (20, 16), (24, 22), (23, 9), (4, 7), (15, 18), (35, 14), (0, 31), (34, 8), (29, 8), (0, 7), (5, 4), (19, 6), (7, 1), (19, 24), (27, 26), (0, 27), (34, 1), (14, 15), (15, 5), (6, 10), (14, 26), (29, 2), (4, 2), (3, 11), (21, 28), (14, 34), (24, 0), (22, 10), (2, 16), (26, 19), (33, 0), (36, 34), (13, 18), (37, 8), (26, 26), (22, 15), (29, 7), (15, 4), (18, 8), (26, 13), (28, 17), (18, 29), (31, 24), (32, 23), (29, 27), (11, 20), (29, 24), (13, 27), (0, 3), (32, 36), (21, 25), (36, 3), (35, 8), (15, 17), (3, 32), (18, 30), (34, 20), (35, 26), (26, 20), (20, 35), (28, 32), (9, 1), (16, 31), (9, 12), (6, 35), (29, 10), (22, 13), (34, 9), (35, 27), (24, 18), (3, 4), (33, 27), (8, 34), (11, 34), (4, 0), (10, 26), (8, 8), (30, 20), (32, 35), (22, 36), (29, 26), (28, 0), (25, 3), (33, 21), (16, 24), (28, 24), (21, 17), (8, 18), (23, 16), (36, 5), (6, 18), (17, 15), (18, 35), (4, 20), (32, 18), (13, 30), (26, 21), (26, 17), (3, 8), (25, 13), (16, 1), (24, 35), (29, 29), (14, 24), (31, 10), (9, 33), (8, 15), (25, 5), (27, 17), (8, 7), (31, 33), (5, 21), (16, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535248", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 3), (10, 17), (25, 20), (15, 29), (7, 17), (21, 36), (30, 25), (25, 28), (3, 28), (5, 11), (16, 16), (13, 17), (0, 9), (1, 4), (27, 0), (26, 27), (26, 9), (14, 37), (23, 33), (16, 7), (21, 4), (26, 30), (24, 34), (22, 16), (18, 2), (11, 34), (6, 23), (18, 19), (15, 27), (7, 7), (26, 7), (29, 2), (18, 21), (30, 31), (21, 25), (5, 30), (22, 30), (29, 23), (26, 19), (16, 9), (12, 36), (16, 38), (8, 0), (3, 13), (10, 23), (10, 33), (26, 21), (6, 27), (26, 36), (9, 0), (12, 28), (9, 8), (12, 16), (17, 22), (13, 11), (27, 15), (15, 10), (1, 8), (14, 10), (23, 2), (30, 7), (7, 15), (24, 31), (27, 8), (6, 7), (15, 37), (26, 17), (21, 12), (8, 5), (9, 31), (22, 0), (2, 32), (3, 24), (14, 27), (13, 9), (12, 37), (22, 6), (19, 16), (20, 5), (29, 17), (19, 30), (13, 33), (28, 27), (18, 35), (10, 12), (14, 9), (16, 26), (16, 5), (17, 20), (27, 33), (1, 17), (25, 33), (29, 22), (31, 9), (24, 24), (19, 2), (28, 3), (5, 9), (0, 13), (6, 5), (29, 0), (31, 37), (19, 35), (24, 12), (6, 0), (19, 21), (24, 26), (4, 36), (1, 21), (12, 2), (20, 25), (27, 5), (11, 24), (2, 19), (5, 13), (2, 10), (6, 10), (24, 29), (7, 22), (6, 22), (21, 30), (4, 7), (27, 3), (19, 37), (9, 12), (5, 18), (18, 5), (4, 24), (13, 23), (26, 38), (21, 29), (5, 8), (8, 7), (20, 0), (4, 34), (15, 7), (15, 25), (8, 16), (3, 12), (7, 24), (28, 20), (17, 27), (6, 26), (14, 26), (3, 27), (3, 22), (25, 1), (15, 26), (23, 32), (21, 5), (15, 18), (17, 0), (8, 11), (14, 17), (2, 1), (24, 33), (28, 4), (15, 38), (17, 6), (0, 20), (31, 15), (26, 20), (20, 18), (17, 33), (27, 18), (2, 34), (25, 5), (28, 30), (19, 26), (17, 23), (20, 21), (2, 21), (6, 14), (24, 22), (6, 4), (1, 23), (10, 0), (31, 2), (28, 10), (12, 10), (1, 38), (28, 37), (1, 7), (30, 18), (17, 34), (0, 14), (8, 38), (29, 1), (31, 6), (1, 33), (13, 10), (24, 23), (6, 32), (12, 9), (29, 15), (0, 4), (27, 38), (23, 3), (10, 1), (14, 24), (14, 13), (5, 19), (15, 12), (17, 18), (4, 21), (10, 16), (28, 21), (31, 32), (22, 19), (21, 37), (29, 19), (31, 24), (3, 4), (11, 19), (3, 35), (11, 35), (18, 6), (9, 22), (19, 13), (21, 15), (29, 35), (24, 5), (3, 14), (9, 38), (11, 31), (26, 10), (2, 13), (23, 35), (8, 4), (30, 3), (31, 36), (8, 32), (12, 0), (4, 31), (27, 31), (23, 31), (25, 36), (27, 1), (22, 17), (12, 21), (23, 0), (19, 22), (11, 30), (4, 4), (2, 18), (15, 35), (0, 28), (13, 20), (17, 8), (6, 8), (19, 15), (11, 8), (21, 33), (9, 32), (21, 8), (13, 15), (6, 12), (16, 3), (19, 1), (0, 8), (10, 19), (17, 10), (5, 33), (10, 4), (29, 11), (20, 13), (16, 22), (14, 35), (4, 28), (30, 33), (31, 5), (5, 36), (19, 14), (15, 13), (25, 17), (1, 34), (25, 11), (27, 13), (3, 8), (20, 36), (26, 26), (1, 25), (21, 2), (16, 24), (21, 11), (5, 10), (9, 24), (25, 14), (23, 19), (13, 35), (22, 27), (31, 18), (21, 10), (27, 22), (9, 2), (29, 3), (31, 27), (17, 17), (20, 33), (30, 0), (25, 27), (1, 0), (25, 12), (15, 14), (30, 30), (18, 15), (26, 22), (18, 28), (14, 22), (31, 23), (28, 13), (21, 28), (14, 0), (2, 27), (18, 26), (9, 9), (17, 35), (27, 19), (31, 0), (13, 21), (0, 24), (19, 17), (19, 23), (11, 28), (31, 12), (0, 10), (2, 16), (8, 25), (16, 8), (12, 12), (27, 37), (26, 37), (17, 3), (22, 35), (24, 17), (25, 19), (23, 36), (12, 14), (30, 37)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386100", "dataset": "MATH"}
{"messages": [{"content": "In a 35x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 3), (7, 19), (15, 5), (19, 33), (27, 6), (19, 23), (5, 17), (18, 10), (26, 31), (12, 19), (7, 13), (31, 26), (8, 27), (7, 32), (9, 25), (19, 31), (1, 14), (30, 12), (13, 5), (10, 12), (31, 23), (2, 20), (18, 27), (21, 24), (26, 37), (7, 21), (12, 2), (21, 21), (18, 13), (17, 36), (15, 9), (32, 0), (2, 3), (25, 7), (27, 30), (21, 5), (8, 12), (31, 25), (34, 16), (19, 16), (26, 27), (14, 31), (16, 7), (16, 25), (25, 23), (20, 33), (7, 34), (26, 20), (19, 4), (24, 37), (24, 30), (31, 21), (6, 16), (23, 12), (31, 14), (23, 13), (31, 28), (23, 17), (29, 32), (5, 11), (30, 8), (28, 17), (16, 9), (19, 30), (16, 1), (8, 29), (4, 21), (14, 24), (34, 6), (13, 35), (23, 0), (6, 17), (21, 12), (2, 28), (28, 4), (18, 12), (11, 31), (8, 37), (19, 7), (30, 33), (33, 30), (13, 8), (33, 32), (5, 20), (19, 36), (16, 30), (27, 7), (21, 15), (29, 10), (2, 19), (5, 31), (7, 0), (6, 11), (12, 33), (34, 15), (10, 17), (19, 18), (8, 24), (16, 33), (1, 25), (31, 38), (29, 35), (3, 32), (32, 24), (4, 14), (10, 11), (31, 1), (13, 13), (4, 32), (29, 21), (7, 18), (18, 24), (32, 35), (17, 31), (13, 30), (23, 22), (8, 11), (22, 20), (8, 25), (19, 24), (28, 5), (26, 12), (31, 31), (19, 1), (5, 3), (3, 14), (14, 25), (5, 4), (22, 18), (17, 29), (34, 31), (9, 6), (26, 23), (22, 19), (34, 8), (15, 0), (17, 21), (9, 11), (14, 19), (9, 2), (8, 16), (7, 2), (2, 1), (8, 35), (15, 18), (16, 15), (3, 19), (9, 21), (5, 32), (22, 36), (17, 16), (33, 5), (20, 22), (10, 16), (20, 38), (13, 20), (20, 14), (11, 11), (26, 32), (26, 34), (10, 9), (22, 30), (9, 5), (11, 23), (3, 33), (23, 29), (13, 21), (33, 12), (34, 24), (18, 23), (3, 23), (30, 5), (19, 14), (23, 28), (4, 9), (14, 11), (1, 1), (16, 8), (12, 13), (3, 26), (4, 30), (2, 33), (23, 10), (22, 10), (22, 3), (13, 7), (21, 13), (11, 32), (4, 23), (3, 5), (19, 28), (23, 6), (21, 10), (33, 33), (8, 15), (14, 9), (13, 0), (5, 23), (30, 16), (22, 25), (34, 2), (34, 36), (27, 4), (0, 6), (11, 20), (0, 23), (5, 19), (13, 4), (17, 15), (18, 0), (33, 20), (31, 30), (10, 5), (0, 11), (32, 34), (30, 28), (23, 34), (19, 2), (32, 5), (6, 30), (0, 37), (27, 25), (21, 30), (5, 36), (24, 28), (8, 2), (26, 30), (33, 4), (27, 2), (32, 10), (18, 19), (25, 6), (27, 17), (8, 30), (33, 38), (29, 6), (23, 18), (28, 1), (34, 1), (10, 32), (34, 21), (28, 25), (8, 0), (25, 33), (24, 34), (34, 14), (19, 3), (6, 35), (18, 18), (16, 17), (32, 8), (2, 13), (12, 24), (5, 10), (3, 2), (8, 21), (16, 37), (7, 17), (11, 38), (27, 19), (14, 33), (16, 28), (17, 10), (31, 35), (10, 34), (0, 32), (16, 12), (0, 15), (31, 18), (31, 32), (15, 34), (2, 36), (5, 37), (22, 23), (8, 32), (19, 13), (13, 34), (14, 4), (18, 1), (15, 8), (28, 22), (20, 16), (8, 34), (3, 17), (10, 3), (13, 2), (23, 30), (28, 7), (21, 8), (27, 29), (20, 29), (27, 5), (25, 12), (18, 5), (6, 10), (25, 35), (23, 19), (26, 8), (28, 23), (8, 5), (24, 33), (20, 12), (19, 35), (17, 5), (13, 12), (20, 35), (4, 37), (13, 3), (4, 38), (22, 34), (2, 27), (4, 25), (21, 0), (30, 35), (33, 21), (4, 20), (22, 21), (34, 12), (14, 22), (17, 37), (2, 9), (25, 5), (26, 11), (0, 26), (0, 31), (16, 24), (20, 23), (26, 25), (14, 23), (33, 24), (6, 9), (10, 27), (12, 9), (11, 22), (13, 24), (11, 6), (11, 15), (17, 32), (7, 33), (14, 16), (12, 17), (1, 12), (22, 9), (25, 20), (22, 4), (25, 26), (25, 22), (10, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465720", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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), (7, 28), (7, 25), (0, 12), (15, 2), (0, 5), (27, 23), (9, 7), (7, 30), (22, 17), (14, 8), (3, 22), (10, 15), (0, 27), (26, 8), (24, 25), (5, 13), (8, 4), (24, 6), (19, 5), (20, 13), (17, 9), (5, 26), (20, 32), (9, 14), (21, 19), (11, 25), (29, 6), (8, 17), (4, 5), (7, 16), (20, 27), (19, 31), (9, 21), (4, 11), (15, 4), (19, 27), (24, 8), (25, 28), (12, 28), (13, 2), (16, 30), (16, 23), (16, 22), (7, 24), (22, 25), (7, 27), (7, 4), (21, 11), (19, 26), (14, 5), (19, 18), (12, 0), (13, 28), (18, 25), (13, 32), (23, 21), (1, 31), (16, 27), (15, 20), (18, 9), (24, 18), (0, 2), (21, 23), (18, 13), (1, 27), (13, 8), (15, 7), (10, 5), (11, 13), (15, 23), (15, 12), (0, 10), (7, 2), (29, 30), (17, 18), (25, 27), (17, 16), (0, 16), (17, 27), (24, 26), (0, 31), (24, 32), (3, 31), (2, 7), (18, 1), (13, 17), (29, 28), (20, 0), (27, 27), (3, 0), (15, 27), (8, 32), (19, 17), (28, 27), (6, 7), (25, 3), (1, 23), (22, 18), (5, 8), (7, 11), (5, 15), (27, 20), (2, 3), (12, 11), (22, 24), (11, 8), (4, 28), (23, 27), (19, 2), (7, 21), (6, 0), (22, 30), (12, 31), (21, 18), (3, 32), (15, 8), (8, 28), (12, 16), (17, 23), (16, 20), (15, 19), (12, 4), (10, 30), (28, 22), (22, 5), (15, 25), (0, 32), (1, 20), (7, 19), (19, 24), (25, 14), (22, 11), (4, 14), (21, 20), (26, 0), (10, 24), (28, 25), (27, 26), (25, 17), (26, 12), (1, 2), (23, 28), (11, 16), (16, 13), (12, 6), (23, 15), (29, 0), (27, 14), (15, 31), (4, 15), (29, 17), (16, 7), (8, 1), (8, 31), (12, 3), (14, 20), (1, 0), (3, 27), (26, 2), (21, 14), (4, 2), (12, 14), (28, 19), (29, 7), (3, 21), (5, 12), (15, 11), (14, 21), (28, 18), (13, 26), (3, 20), (1, 17), (26, 21), (29, 2), (9, 16), (2, 9), (5, 22), (0, 23), (21, 4), (19, 22), (28, 8), (5, 30), (15, 29), (26, 13), (7, 14), (18, 27), (2, 25), (23, 17), (10, 7), (24, 19), (9, 26), (20, 1), (7, 1), (8, 9), (8, 6), (12, 24), (8, 22), (9, 9), (15, 10), (22, 14), (25, 11), (7, 3), (20, 9), (25, 5), (13, 31), (14, 18), (26, 15), (3, 8), (19, 30), (6, 8), (3, 7), (25, 9), (13, 9), (14, 28), (10, 26), (6, 1), (6, 29), (28, 12), (13, 10), (28, 21), (14, 4), (6, 26), (16, 2), (0, 17), (21, 15), (15, 5), (14, 23), (20, 3), (13, 16), (6, 13), (23, 3), (3, 10), (2, 27), (27, 17), (10, 31), (8, 11), (26, 14), (22, 15), (15, 28), (22, 6), (13, 25), (5, 9), (17, 8), (17, 32), (5, 5), (13, 7), (7, 18), (5, 24), (18, 23), (29, 25), (2, 14), (20, 29), (28, 31), (10, 12), (26, 25), (4, 22), (8, 10), (29, 23), (2, 18), (14, 30), (29, 8), (29, 10), (2, 24), (22, 8), (29, 9), (23, 12), (16, 5), (1, 26), (15, 16), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315792", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 0), (24, 24), (29, 20), (0, 17), (19, 24), (6, 2), (25, 7), (4, 7), (0, 14), (7, 26), (31, 26), (24, 20), (9, 16), (26, 19), (6, 13), (21, 16), (3, 3), (31, 16), (8, 8), (1, 1), (22, 14), (1, 6), (26, 20), (9, 2), (6, 24), (28, 28), (9, 33), (6, 23), (16, 11), (30, 18), (12, 36), (9, 15), (3, 18), (15, 2), (23, 12), (12, 7), (0, 7), (22, 2), (14, 29), (0, 6), (18, 13), (3, 5), (23, 35), (10, 1), (16, 3), (5, 8), (1, 8), (9, 24), (13, 28), (31, 25), (17, 7), (13, 0), (20, 32), (26, 15), (15, 6), (27, 31), (25, 14), (3, 6), (2, 16), (14, 27), (26, 28), (26, 2), (3, 29), (26, 33), (24, 1), (21, 6), (4, 0), (3, 9), (26, 11), (30, 9), (29, 22), (29, 13), (19, 5), (6, 31), (7, 30), (1, 25), (26, 32), (21, 27), (16, 36), (15, 16), (1, 17), (12, 32), (6, 6), (30, 35), (2, 0), (20, 21), (20, 23), (0, 34), (11, 13), (3, 7), (0, 19), (11, 7), (17, 18), (24, 0), (7, 35), (28, 19), (23, 11), (11, 22), (0, 18), (23, 14), (21, 18), (16, 35), (7, 24), (12, 21), (28, 25), (25, 21), (31, 9), (26, 31), (28, 9), (9, 18), (13, 5), (9, 32), (13, 7), (27, 34), (10, 10), (25, 30), (22, 17), (20, 13), (4, 35), (25, 36), (5, 18), (18, 3), (19, 21), (22, 15), (20, 15), (31, 1), (4, 14), (13, 13), (8, 22), (30, 16), (3, 26), (7, 4), (19, 6), (8, 35), (4, 31), (12, 4), (24, 18), (22, 35), (29, 14), (4, 22), (15, 9), (3, 24), (13, 4), (21, 29), (5, 17), (8, 26), (16, 9), (18, 34), (4, 36), (13, 18), (6, 27), (7, 8), (13, 24), (1, 15), (31, 28), (19, 15), (10, 23), (31, 8), (5, 31), (25, 0), (24, 5), (20, 4), (17, 23), (20, 35), (24, 22), (21, 9), (19, 11), (8, 21), (30, 1), (15, 0), (22, 27), (28, 20), (14, 18), (25, 3), (22, 30), (6, 5), (2, 28), (13, 12), (0, 35), (30, 2), (7, 33), (8, 32), (27, 23), (19, 19), (27, 11), (15, 31), (4, 17), (31, 27), (11, 6), (19, 9), (29, 6), (6, 11), (0, 13), (25, 13), (17, 21), (17, 10), (19, 7), (22, 19), (12, 35), (29, 31), (29, 17), (23, 33), (14, 12), (2, 32), (24, 25), (24, 30), (30, 11), (4, 25), (6, 0), (20, 1), (6, 8), (3, 21), (1, 11), (23, 29), (0, 23), (14, 28), (8, 13), (8, 27), (16, 27), (18, 9), (25, 8), (30, 19), (20, 25), (17, 1), (10, 3), (12, 34), (15, 11), (20, 29), (24, 6), (20, 24), (15, 29), (18, 12), (13, 20), (26, 25), (21, 20), (27, 10), (24, 3), (4, 20), (18, 2), (27, 17), (22, 28), (25, 23), (1, 35), (7, 18), (4, 10), (11, 34), (8, 1), (10, 9), (24, 8), (12, 11), (14, 34), (16, 19), (25, 26), (15, 33), (5, 2), (5, 36), (27, 29), (0, 20), (16, 17), (4, 18), (11, 27), (2, 23), (12, 9), (16, 34), (5, 16), (20, 5), (4, 15), (14, 3), (29, 1), (1, 13), (27, 25), (15, 17), (12, 15), (24, 35), (31, 23), (10, 29), (18, 32), (19, 0), (31, 3), (29, 21), (6, 22), (28, 36), (9, 12), (7, 0), (27, 12), (27, 28), (13, 2), (30, 24), (27, 14), (30, 12), (26, 17), (29, 30), (27, 30), (1, 33), (14, 22), (2, 18), (20, 14), (6, 3), (18, 11), (28, 16), (15, 5), (17, 5), (3, 28), (24, 28), (10, 2), (27, 27), (17, 34), (29, 19), (24, 16), (6, 19), (15, 22), (20, 18), (13, 14), (14, 9), (7, 2), (16, 33), (21, 24), (10, 33), (2, 6), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84480", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 13), (18, 7), (5, 15), (12, 31), (15, 18), (19, 18), (15, 10), (29, 7), (3, 7), (24, 15), (21, 27), (29, 3), (23, 6), (29, 9), (15, 12), (19, 12), (12, 24), (17, 21), (15, 25), (24, 29), (1, 20), (21, 21), (3, 1), (24, 17), (21, 4), (25, 29), (1, 1), (0, 11), (12, 17), (27, 4), (9, 11), (17, 32), (27, 28), (6, 28), (21, 13), (21, 32), (3, 21), (24, 19), (13, 23), (5, 6), (8, 2), (24, 30), (6, 4), (22, 3), (0, 7), (17, 15), (6, 29), (21, 2), (23, 30), (7, 16), (1, 14), (28, 27), (13, 1), (16, 5), (5, 14), (4, 4), (15, 0), (10, 8), (27, 6), (8, 17), (15, 29), (8, 13), (26, 32), (15, 4), (9, 2), (19, 9), (26, 9), (3, 23), (6, 22), (25, 32), (23, 16), (5, 18), (2, 26), (29, 23), (12, 32), (28, 24), (5, 22), (21, 18), (5, 25), (6, 21), (2, 11), (7, 32), (12, 26), (13, 11), (6, 6), (16, 30), (21, 14), (6, 25), (26, 16), (19, 13), (17, 10), (29, 21), (14, 31), (16, 31), (4, 3), (7, 24), (10, 20), (22, 30), (12, 25), (24, 28), (1, 22), (2, 19), (7, 19), (27, 16), (26, 28), (17, 16), (21, 19), (10, 5), (20, 6), (2, 27), (18, 24), (9, 26), (7, 8), (15, 30), (9, 29), (2, 4), (19, 21), (5, 2), (23, 25), (14, 27), (3, 3), (6, 14), (26, 22), (20, 22), (27, 17), (2, 10), (14, 11), (3, 32), (25, 25), (19, 8), (24, 8), (0, 1), (11, 27), (8, 22), (29, 8), (4, 29), (18, 4), (0, 3), (3, 13), (22, 19), (17, 27), (16, 15), (21, 23), (20, 18), (19, 27), (3, 15), (20, 31), (14, 32), (5, 32), (3, 29), (15, 13), (18, 10), (4, 9), (5, 9), (3, 10), (10, 25), (11, 30), (22, 16), (25, 11), (8, 10), (1, 12), (18, 19), (25, 26), (12, 16), (4, 13), (29, 19), (15, 28), (26, 25), (19, 15), (19, 4), (0, 20), (7, 29), (23, 18), (20, 20), (25, 12), (22, 8), (7, 31), (28, 19), (10, 13), (29, 20), (20, 29), (6, 3), (15, 7), (12, 20), (19, 6), (11, 10), (6, 24), (21, 5), (23, 10), (2, 20), (10, 17), (14, 14), (23, 13), (12, 23), (7, 10), (29, 17), (19, 10), (7, 18), (25, 0), (9, 16), (18, 25), (5, 1), (6, 5), (21, 20), (24, 25), (20, 1), (2, 29), (11, 12), (21, 31), (3, 17), (12, 0), (16, 25), (8, 30), (1, 11), (26, 6), (10, 15), (25, 17), (1, 30), (15, 20), (7, 15), (5, 17), (27, 10), (29, 1), (14, 9), (8, 26), (4, 7), (13, 0), (12, 4), (6, 23), (14, 5), (16, 21), (22, 11), (3, 28), (10, 14), (5, 26), (16, 13), (15, 3), (15, 31), (3, 4), (19, 28), (12, 19), (11, 4), (17, 11), (24, 22), (4, 1), (16, 2), (1, 26), (23, 3), (27, 3), (22, 7), (13, 24), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "598500", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), 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), (12, 20), (25, 30), (28, 27), (17, 17), (29, 30), (5, 2), (2, 23), (12, 19), (10, 34), (15, 30), (15, 34), (1, 35), (21, 2), (4, 7), (5, 32), (10, 17), (2, 17), (7, 22), (17, 7), (7, 26), (24, 25), (11, 10), (25, 5), (11, 36), (13, 16), (29, 11), (28, 24), (27, 20), (24, 10), (17, 9), (17, 23), (6, 19), (21, 30), (11, 23), (21, 6), (5, 5), (7, 33), (22, 5), (22, 6), (7, 4), (19, 27), (21, 8), (16, 20), (17, 22), (28, 31), (25, 21), (17, 8), (2, 18), (4, 28), (3, 28), (1, 14), (15, 35), (23, 15), (17, 33), (17, 37), (14, 18), (24, 28), (24, 20), (21, 25), (15, 7), (12, 13), (8, 9), (10, 26), (6, 14), (5, 22), (7, 16), (9, 15), (26, 15), (16, 28), (25, 31), (6, 13), (24, 26), (20, 27), (22, 1), (24, 17), (16, 5), (6, 9), (3, 18), (29, 3), (21, 33), (10, 6), (4, 5), (9, 4), (4, 10), (0, 12), (5, 28), (27, 21), (23, 4), (4, 6), (8, 10), (2, 11), (0, 37), (14, 37), (12, 21), (28, 23), (15, 19), (8, 36), (19, 13), (6, 26), (26, 30), (16, 0), (25, 33), (24, 14), (14, 7), (0, 10), (5, 11), (5, 9), (15, 29), (3, 27), (21, 16), (0, 22), (9, 36), (3, 33), (7, 27), (14, 1), (9, 8), (29, 17), (25, 20), (19, 2), (2, 35), (19, 19), (11, 35), (9, 12), (22, 19), (20, 21), (8, 31), (13, 22), (29, 15), (28, 20), (16, 23), (26, 7), (2, 1), (6, 1), (11, 8), (24, 0), (14, 10), (3, 16), (3, 7), (28, 15), (1, 30), (12, 3), (5, 8), (1, 20), (8, 20), (25, 32), (8, 3), (3, 4), (12, 6), (26, 24), (20, 34), (19, 36), (10, 30), (4, 37), (21, 24), (18, 21), (4, 30), (29, 16), (26, 35), (25, 8), (9, 3), (11, 24), (10, 25), (12, 15), (8, 27), (8, 28), (0, 5), (22, 28), (14, 34), (10, 21), (22, 7), (5, 37), (17, 27), (12, 11), (23, 23), (4, 12), (3, 15), (1, 27), (26, 11), (14, 22), (10, 18), (26, 6), (20, 16), (26, 36), (18, 6), (27, 2), (5, 34), (19, 17), (17, 5), (8, 2), (18, 13), (20, 37), (24, 27), (13, 14), (27, 22), (21, 7), (19, 34), (11, 12), (20, 8), (24, 30), (8, 21), (18, 3), (7, 3), (9, 0), (23, 8), (6, 20), (8, 0), (1, 4), (10, 14), (12, 34), (19, 30), (2, 13), (9, 11), (6, 8), (22, 13), (8, 32), (27, 13), (18, 18), (20, 24), (1, 19), (18, 33), (15, 24), (3, 2), (28, 13), (16, 30), (5, 3), (14, 27), (6, 23), (0, 24), (11, 13), (20, 29), (11, 26), (19, 20), (25, 22), (14, 13), (18, 5), (17, 28), (29, 26), (24, 5), (23, 11), (27, 10), (18, 1), (12, 0), (11, 20), (22, 35), (15, 28), (2, 33), (15, 17), (29, 12), (10, 28), (1, 10), (18, 8), (24, 21), (4, 31), (25, 19), (13, 27), (1, 25), (15, 6), (14, 29), (10, 35), (22, 37), (15, 1), (20, 36), (13, 1), (3, 22), (0, 17), (23, 35), (4, 0), (26, 5), (15, 32), (12, 17), (10, 4), (18, 26), (25, 11), (0, 32), (27, 0), (6, 32), (1, 24), (13, 18), (13, 32), (29, 21), (5, 33), (15, 15), (25, 36), (8, 11), (7, 34), (15, 0), (17, 34), (28, 2), (17, 14), (26, 28), (11, 21), (21, 36), (26, 19), (13, 3), (29, 18), (9, 19), (16, 15), (9, 33), (18, 7), (17, 26), (19, 26), (25, 24), (24, 18), (11, 16), (1, 15), (13, 28), (13, 19), (11, 6), (29, 32), (7, 20), (26, 21), (22, 34), (12, 5), (27, 37), (20, 19), (0, 30), (12, 7), (4, 16), (1, 28), (0, 4), (5, 26), (26, 18), (28, 1), (10, 20), (28, 28), (23, 16), (1, 7), (1, 9), (0, 35), (13, 21), (25, 4), (4, 1), (4, 19), (27, 1), (14, 2), (9, 21), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449160", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 29), (4, 19), (21, 36), (35, 11), (37, 16), (22, 12), (26, 4), (8, 15), (17, 23), (19, 24), (34, 11), (14, 15), (15, 35), (1, 7), (34, 23), (14, 1), (25, 35), (23, 12), (29, 0), (7, 14), (14, 17), (34, 22), (35, 37), (34, 28), (24, 34), (10, 25), (22, 6), (2, 4), (0, 32), (18, 26), (22, 14), (33, 22), (7, 3), (19, 3), (33, 19), (24, 16), (15, 32), (14, 23), (37, 0), (14, 9), (12, 4), (28, 35), (20, 28), (12, 34), (26, 30), (1, 17), (31, 31), (37, 12), (21, 3), (32, 1), (21, 15), (8, 29), (2, 6), (33, 16), (37, 28), (18, 28), (5, 13), (7, 17), (23, 22), (25, 4), (18, 2), (14, 25), (3, 29), (15, 2), (30, 14), (24, 22), (23, 37), (36, 25), (7, 35), (20, 23), (16, 23), (1, 27), (36, 37), (24, 35), (26, 5), (31, 36), (30, 7), (36, 15), (36, 36), (12, 10), (19, 6), (37, 3), (6, 18), (22, 10), (13, 25), (11, 37), (12, 26), (33, 3), (8, 18), (17, 35), (2, 26), (34, 33), (19, 7), (22, 17), (27, 33), (21, 29), (22, 1), (8, 37), (31, 29), (1, 33), (2, 15), (19, 11), (25, 9), (9, 14), (37, 10), (9, 31), (32, 26), (8, 2), (3, 16), (33, 17), (33, 32), (26, 18), (13, 20), (18, 6), (12, 23), (19, 15), (25, 13), (17, 8), (22, 4), (4, 10), (29, 23), (0, 21), (33, 10), (10, 18), (3, 27), (14, 32), (25, 19), (8, 9), (23, 29), (6, 32), (34, 6), (37, 7), (25, 27), (21, 20), (6, 29), (30, 24), (6, 35), (18, 27), (4, 33), (17, 30), (21, 12), (12, 0), (4, 21), (20, 25), (11, 12), (8, 21), (25, 26), (17, 36), (35, 20), (16, 13), (26, 25), (1, 13), (17, 18), (11, 30), (12, 24), (30, 31), (4, 27), (37, 2), (3, 23), (29, 17), (15, 29), (0, 17), (16, 10), (27, 18), (28, 22), (21, 31), (23, 35), (32, 18), (14, 30), (9, 30), (1, 4), (3, 31), (0, 36), (26, 34), (6, 30), (18, 0), (1, 20), (37, 17), (8, 26), (23, 30), (36, 11), (3, 5), (31, 24), (15, 24), (13, 6), (15, 14), (21, 10), (4, 8), (22, 11), (0, 16), (20, 11), (37, 22), (24, 23), (36, 26), (30, 18), (28, 2), (4, 34), (25, 21), (21, 25), (34, 26), (10, 32), (4, 31), (33, 24), (14, 28), (9, 4), (25, 24), (32, 32), (37, 24), (7, 28), (5, 3), (12, 6), (7, 15), (18, 33), (14, 29), (2, 5), (5, 29), (16, 19), (37, 33), (31, 23), (26, 14), (11, 10), (33, 35), (13, 22), (26, 23), (34, 20), (20, 12), (3, 32), (12, 7), (14, 33), (16, 22), (29, 19), (8, 0), (0, 2), (24, 14), (8, 12), (4, 13), (25, 3), (32, 10), (2, 12), (2, 16), (5, 1), (0, 14), (16, 35), (29, 36), (20, 13), (34, 31), (3, 20), (4, 3), (32, 36), (16, 27), (6, 6), (17, 3), (7, 23), (0, 15), (7, 10), (5, 16), (11, 17), (0, 30), (32, 15), (37, 34), (6, 10), (31, 12), (11, 22), (15, 3), (19, 29), (19, 0), (14, 3), (27, 29), (12, 37), (9, 7), (33, 31), (24, 4), (21, 2), (8, 7), (5, 2), (30, 8), (5, 12), (3, 25), (18, 25), (7, 18), (0, 29), (21, 28), (6, 23), (9, 36), (5, 5), (14, 12), (29, 13), (31, 20), (36, 31), (2, 11), (1, 11), (7, 26), (10, 33), (28, 1), (27, 19), (29, 25), (6, 12), (14, 26), (23, 21), (12, 9), (4, 17), (1, 14), (23, 25), (11, 24), (20, 10), (30, 0), (22, 9), (0, 28), (26, 2), (35, 15), (34, 18), (14, 21), (5, 7), (23, 31), (35, 23), (35, 3), (21, 27), (3, 21), (28, 32), (20, 6), (23, 19), (27, 9), (17, 24), (8, 28), (9, 19), (32, 19), (19, 23), (29, 34), (32, 17), (14, 6), (7, 22), (35, 35), (20, 34), (13, 2), (34, 29), (2, 29), (17, 16), (2, 1), (9, 6), (1, 10), (29, 27), (12, 28), (2, 9), (4, 1), (25, 5), (10, 6), (27, 1), (30, 32), (24, 25), (27, 10), (25, 29), (13, 16), (31, 13), (34, 7), (10, 3), (26, 31), (26, 37), (5, 9), (16, 7), (1, 37), (31, 32), (0, 7), (29, 8), (9, 34), (27, 26), (19, 26), (4, 30), (4, 5), (4, 37), (37, 20), (2, 14), (3, 22), (11, 7), (16, 32), (12, 3), (0, 8), (1, 1), (11, 27), (17, 22), (29, 10), (7, 36), (7, 1), (36, 5), (20, 24), (15, 37), (19, 25), (25, 15), (26, 10), (10, 10), (11, 18), (6, 33), (6, 11), (9, 2), (16, 6), (24, 8), (15, 13), (2, 10), (24, 31), (9, 3), (35, 28), (10, 20), (20, 19), (36, 20), (21, 33), (29, 20), (17, 7), (6, 17), (0, 19), (12, 12), (20, 26), (2, 23), (21, 22), (8, 34), (16, 37), (9, 35), (10, 1), (33, 7), (25, 32), (21, 4), (6, 36), (2, 24), (14, 11), (8, 16), (13, 13), (4, 23), (7, 33), (28, 21), (9, 17), (23, 8), (12, 22), (8, 23), (29, 29), (22, 35), (28, 10), (28, 36), (14, 27), (23, 6), (3, 7), (20, 30), (35, 4), (23, 5), (6, 25), (35, 12), (28, 34), (35, 10), (33, 4), (4, 18), (17, 29), (16, 16), (2, 28), (24, 9), (24, 12), (28, 17), (7, 13), (33, 36), (1, 31), (27, 35), (3, 2), (20, 32), (18, 1), (3, 1), (35, 22), (11, 9), (28, 11), (5, 10), (28, 19), (6, 34), (9, 11), (23, 18), (29, 32), (9, 5), (4, 29), (30, 27), (5, 31), (33, 25), (22, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870912", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 21), (25, 7), (4, 2), (30, 29), (18, 2), (12, 21), (12, 1), (16, 13), (14, 20), (20, 10), (14, 18), (26, 28), (4, 16), (11, 18), (32, 13), (18, 22), (18, 5), (32, 1), (11, 27), (11, 28), (15, 6), (2, 27), (17, 3), (22, 12), (3, 18), (6, 11), (18, 29), (32, 5), (9, 21), (27, 11), (21, 1), (12, 29), (10, 7), (11, 9), (0, 8), (30, 18), (15, 7), (12, 27), (20, 1), (21, 14), (24, 12), (25, 22), (30, 7), (23, 5), (21, 24), (25, 26), (30, 15), (5, 25), (13, 0), (10, 8), (31, 16), (24, 14), (4, 14), (18, 20), (10, 27), (23, 31), (31, 28), (22, 15), (6, 20), (3, 12), (28, 9), (1, 13), (18, 9), (2, 5), (18, 26), (7, 7), (13, 28), (15, 0), (32, 16), (0, 19), (6, 29), (22, 3), (31, 7), (15, 2), (12, 13), (7, 22), (2, 1), (7, 30), (16, 17), (16, 19), (5, 13), (32, 6), (15, 1), (12, 18), (11, 5), (22, 18), (18, 15), (9, 20), (2, 22), (2, 0), (8, 13), (30, 26), (16, 15), (14, 24), (12, 5), (15, 10), (14, 17), (13, 20), (30, 0), (23, 1), (7, 19), (12, 24), (20, 19), (21, 27), (30, 20), (28, 31), (5, 17), (19, 1), (22, 7), (5, 0), (9, 10), (30, 9), (19, 11), (7, 8), (5, 31), (7, 13), (15, 4), (9, 11), (11, 31), (27, 18), (15, 20), (14, 27), (25, 28), (3, 23), (6, 14), (32, 7), (6, 26), (26, 15), (11, 25), (24, 16), (23, 23), (13, 31), (24, 20), (25, 1), (16, 1), (13, 19), (20, 23), (9, 15), (13, 8), (26, 10), (7, 20), (30, 28), (3, 15), (11, 13), (11, 16), (13, 17), (24, 1), (12, 22), (30, 16), (3, 11), (1, 31), (19, 0), (21, 11), (31, 21), (5, 7), (23, 13), (23, 8), (9, 9), (13, 23), (27, 19), (10, 23), (32, 8), (3, 4), (29, 18), (13, 6), (15, 8), (17, 4), (20, 27), (20, 21), (20, 24), (4, 20), (25, 5), (15, 14), (12, 20), (23, 2), (23, 26), (26, 5), (17, 10), (8, 15), (26, 22), (0, 11), (31, 17), (25, 10), (16, 7), (9, 7), (5, 16), (26, 23), (14, 13), (22, 16), (30, 23), (1, 8), (18, 23), (23, 18), (25, 21), (16, 8), (24, 7), (25, 11), (1, 22), (4, 27), (6, 17), (32, 18), (19, 28), (3, 17), (28, 22), (19, 5), (25, 0), (9, 0), (31, 0), (31, 18), (30, 31), (19, 23), (20, 17), (11, 24), (22, 17), (23, 28), (27, 24), (2, 16), (0, 24), (2, 28), (25, 29), (6, 22), (26, 4), (1, 10), (29, 24), (20, 6), (23, 25), (12, 11), (7, 31), (30, 12), (4, 26), (2, 4), (26, 26), (15, 31), (29, 26), (27, 29), (21, 19), (22, 9), (20, 20), (17, 23), (6, 24), (12, 9), (21, 29), (28, 13), (32, 2), (13, 22), (11, 1), (31, 23), (7, 29), (16, 4), (26, 17), (3, 28), (28, 14), (1, 9), (15, 19), (30, 10), (25, 4), (30, 13), (2, 29), (30, 27), (4, 15), (30, 17), (17, 9), (6, 21), (4, 22), (28, 4), (31, 25), (21, 20), (31, 19), (29, 15), (2, 24), (23, 11), (7, 21), (16, 18), (6, 9), (26, 14), (23, 19), (1, 28), (24, 5), (21, 9), (11, 4), (12, 26), (25, 9), (15, 5), (3, 7), (29, 8), (13, 5), (16, 16), (15, 15), (30, 2), (2, 13), (5, 27), (27, 27), (10, 6), (15, 24), (32, 3), (24, 24), (12, 23), (29, 31), (15, 29), (27, 12), (20, 31), (20, 16), (4, 1), (27, 26), (0, 9), (30, 4), (18, 0), (14, 1), (13, 14), (2, 20), (31, 27), (10, 29), (15, 13), (4, 25), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "418320", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (26, 33), (16, 26), (0, 30), (21, 31), (9, 17), (3, 8), (6, 22), (2, 20), (26, 8), (12, 24), (24, 12), (31, 9), (3, 4), (31, 28), (20, 18), (15, 11), (18, 10), (5, 7), (0, 1), (17, 9), (28, 9), (28, 32), (20, 28), (31, 27), (4, 0), (15, 22), (16, 5), (20, 16), (10, 10), (14, 10), (9, 22), (9, 36), (10, 18), (21, 12), (30, 27), (1, 5), (4, 36), (21, 26), (7, 16), (8, 7), (8, 28), (3, 34), (10, 33), (31, 10), (27, 32), (5, 34), (26, 31), (12, 22), (19, 15), (19, 34), (6, 28), (7, 3), (7, 14), (25, 34), (12, 9), (20, 27), (21, 11), (24, 6), (18, 30), (1, 35), (7, 35), (28, 27), (28, 21), (19, 13), (12, 8), (29, 11), (27, 11), (14, 5), (5, 11), (15, 17), (5, 10), (25, 18), (28, 18), (3, 14), (23, 3), (28, 2), (18, 2), (14, 18), (23, 15), (12, 5), (11, 18), (9, 14), (2, 6), (0, 20), (4, 3), (8, 32), (11, 26), (24, 14), (23, 24), (18, 15), (14, 23), (27, 24), (7, 9), (9, 29), (10, 1), (23, 6), (31, 6), (23, 25), (12, 17), (14, 7), (16, 36), (29, 9), (16, 34), (0, 7), (10, 36), (17, 17), (16, 27), (14, 25), (20, 9), (18, 13), (27, 5), (0, 24), (12, 3), (22, 35), (9, 15), (13, 8), (28, 22), (1, 29), (6, 17), (20, 24), (19, 29), (29, 8), (25, 3), (11, 30), (18, 7), (28, 10), (10, 6), (6, 21), (18, 16), (17, 36), (27, 34), (26, 6), (25, 22), (1, 34), (4, 29), (15, 24), (7, 23), (23, 18), (22, 7), (21, 13), (20, 2), (5, 18), (14, 19), (27, 33), (23, 23), (10, 23), (29, 15), (1, 8), (14, 21), (31, 30), (27, 16), (30, 0), (12, 4), (10, 35), (28, 29), (12, 1), (12, 32), (10, 8), (14, 1), (19, 8), (4, 32), (15, 3), (10, 20), (28, 16), (22, 0), (12, 19), (15, 34), (6, 35), (20, 5), (7, 17), (11, 23), (16, 14), (16, 6), (3, 32), (6, 20), (29, 25), (25, 15), (9, 4), (7, 11), (28, 17), (7, 0), (11, 7), (4, 31), (4, 2), (2, 32), (18, 14), (25, 32), (7, 7), (11, 11), (23, 7), (1, 16), (5, 15), (7, 1), (14, 35), (7, 26), (5, 6), (24, 22), (2, 15), (19, 6), (0, 19), (26, 19), (25, 30), (8, 1), (17, 14), (29, 32), (26, 36), (26, 1), (7, 8), (6, 5), (29, 16), (30, 9), (17, 29), (28, 19), (21, 18), (12, 13), (26, 27), (12, 2), (17, 7), (13, 15), (25, 31), (12, 34), (5, 31), (8, 36), (9, 24), (26, 15), (22, 15), (5, 4), (10, 4), (10, 31), (3, 7), (27, 1), (3, 9), (27, 0), (9, 1), (21, 23), (11, 24), (29, 19), (4, 24), (8, 13), (25, 33), (29, 35), (4, 19), (14, 15), (9, 20), (23, 26), (11, 13), (0, 28), (2, 21), (24, 8), (21, 10), (31, 29), (12, 36), (4, 22), (25, 6), (16, 22), (21, 30), (18, 25), (18, 5), (9, 13), (7, 21), (7, 31), (22, 13), (29, 17), (4, 26), (24, 10), (17, 18), (16, 15), (18, 4), (30, 14), (4, 30), (18, 32), (9, 10), (8, 4), (14, 34), (27, 29), (14, 13), (19, 30), (21, 35), (2, 11), (30, 34), (20, 8), (15, 18), (0, 5), (29, 6), (22, 25), (28, 24), (15, 21), (24, 4), (22, 22), (13, 16), (22, 20), (22, 26), (30, 11), (19, 12), (28, 14), (11, 27), (9, 25), (11, 31), (25, 21), (3, 29), (23, 27), (18, 19), (23, 30), (8, 29), (22, 8), (17, 25), (24, 27), (26, 12), (1, 24), (14, 22), (6, 7), (2, 9), (3, 2), (25, 13), (31, 33), (8, 27), (27, 30), (0, 33), (5, 5), (20, 22), (13, 6), (20, 1), (3, 3), (30, 17), (3, 36), (7, 27), (5, 23), (27, 22), (23, 0), (16, 9), (8, 8), (22, 28), (22, 23), (9, 18), (3, 18), (27, 7), (0, 8), (9, 3), (20, 0), (12, 31), (14, 36), (30, 20), (28, 8), (21, 21), (6, 2), (17, 21), (20, 31), (0, 14), (9, 16), (11, 3), (27, 19), (7, 32), (1, 19), (30, 18), (17, 0), (13, 31), (12, 33), (17, 33), (24, 21), (23, 31), (20, 34), (22, 17), (20, 3), (1, 28), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613440", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), 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), (23, 10), (8, 33), (11, 0), (20, 24), (27, 18), (9, 19), (14, 3), (22, 5), (29, 12), (2, 7), (3, 16), (3, 2), (13, 22), (21, 35), (32, 21), (0, 13), (0, 27), (11, 1), (38, 26), (2, 4), (29, 28), (33, 34), (7, 9), (22, 9), (16, 4), (2, 3), (34, 19), (20, 25), (32, 7), (8, 25), (5, 14), (13, 5), (2, 20), (20, 27), (34, 21), (33, 8), (33, 10), (25, 22), (34, 13), (13, 23), (29, 32), (23, 30), (23, 1), (7, 16), (28, 34), (12, 3), (29, 16), (32, 4), (26, 20), (37, 15), (7, 1), (27, 31), (21, 17), (18, 26), (0, 30), (2, 28), (30, 18), (2, 24), (18, 8), (7, 18), (9, 22), (34, 3), (26, 11), (35, 14), (21, 33), (20, 21), (9, 9), (20, 13), (29, 6), (12, 29), (15, 34), (2, 14), (6, 27), (34, 24), (17, 32), (37, 1), (15, 23), (10, 29), (27, 10), (29, 30), (19, 13), (2, 30), (37, 28), (5, 26), (26, 16), (14, 31), (17, 20), (4, 0), (26, 34), (1, 29), (30, 35), (31, 8), (6, 9), (15, 2), (20, 5), (1, 23), (13, 11), (25, 35), (21, 24), (2, 23), (35, 5), (3, 21), (8, 16), (8, 19), (37, 25), (19, 4), (35, 27), (14, 29), (17, 21), (23, 6), (33, 28), (4, 35), (31, 0), (29, 13), (6, 20), (15, 0), (38, 29), (25, 29), (19, 15), (24, 10), (25, 34), (17, 19), (12, 6), (37, 20), (12, 25), (30, 6), (23, 9), (36, 2), (35, 17), (19, 5), (21, 14), (9, 30), (16, 31), (18, 7), (38, 5), (22, 25), (7, 30), (16, 26), (1, 21), (26, 14), (38, 31), (27, 35), (23, 0), (34, 5), (16, 17), (37, 10), (25, 19), (1, 9), (30, 1), (16, 25), (10, 31), (35, 23), (13, 27), (20, 26), (3, 14), (12, 4), (4, 12), (28, 12), (35, 15), (19, 34), (7, 22), (2, 5), (21, 4), (30, 28), (34, 32), (27, 34), (11, 15), (15, 19), (0, 21), (6, 7), (37, 13), (35, 4), (14, 6), (19, 24), (18, 33), (3, 11), (23, 33), (28, 21), (14, 30), (24, 19), (15, 21), (24, 34), (8, 17), (38, 20), (14, 20), (3, 4), (6, 29), (8, 23), (21, 13), (3, 18), (3, 24), (2, 21), (11, 7), (6, 21), (4, 11), (6, 5), (38, 32), (38, 16), (36, 15), (1, 22), (35, 25), (8, 11), (17, 9), (32, 23), (19, 26), (11, 35), (34, 9), (18, 13), (27, 13), (31, 13), (9, 6), (3, 12), (17, 33), (30, 16), (21, 32), (0, 33), (15, 11), (18, 31), (31, 7), (25, 24), (1, 31), (8, 15), (16, 7), (5, 15), (5, 8), (6, 10), (31, 27), (0, 15), (21, 9), (5, 0), (11, 25), (33, 22), (26, 8), (37, 0), (30, 5), (6, 4), (8, 13), (37, 32), (13, 32), (9, 16), (25, 11), (18, 18), (6, 32), (2, 0), (25, 0), (37, 22), (6, 17), (7, 25), (32, 15), (17, 5), (36, 33), (9, 5), (8, 1), (12, 34), (38, 9), (28, 17), (22, 34), (37, 8), (1, 15), (8, 14), (26, 35), (34, 1), (31, 26), (31, 17), (36, 3), (18, 27), (5, 7), (23, 11), (19, 9), (14, 17), (22, 19), (32, 10), (35, 35), (28, 6), (34, 20), (26, 0), (21, 25), (17, 29), (31, 31), (1, 18), (5, 11), (7, 34), (24, 18), (4, 13), (30, 32), (16, 3), (23, 16), (32, 1), (22, 1), (18, 3), (21, 3), (0, 23), (25, 21), (35, 33), (34, 0), (5, 2), (27, 3), (13, 14), (15, 33), (6, 35), (4, 19), (35, 31), (7, 6), (36, 32), (3, 25), (26, 19), (16, 28), (36, 28), (38, 13), (14, 1), (26, 23), (31, 23), (28, 28), (16, 1), (24, 0), (8, 24), (8, 20), (27, 19), (16, 21), (11, 22), (33, 32), (5, 9), (19, 18), (5, 20), (2, 15), (25, 14), (22, 12), (19, 30), (14, 23), (5, 21), (14, 16), (27, 14), (1, 33), (17, 23), (26, 31), (8, 10), (38, 4), (32, 34), (13, 19), (35, 12), (5, 17), (6, 12), (35, 28), (23, 27), (0, 2), (6, 33), (33, 6), (6, 34), (12, 31), (12, 1), (36, 4), (9, 31), (35, 3), (9, 23), (17, 30), (28, 32), (16, 35), (30, 13), (30, 3), (19, 1), (28, 19), (35, 6), (35, 10), (24, 3), (33, 16), (30, 11), (20, 35), (7, 14), (16, 11), (9, 32), (13, 4), (7, 8), (4, 25), (27, 25), (32, 30), (12, 23), (37, 2), (34, 23), (27, 30), (2, 19), (26, 25), (12, 14), (37, 7), (24, 17), (19, 28), (37, 5), (24, 26), (30, 19), (36, 12), (19, 2), (35, 24), (6, 31), (4, 31), (33, 20), (33, 0), (12, 19), (20, 7), (24, 1), (10, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432000", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), 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), (31, 5), (14, 1), (20, 7), (8, 13), (22, 7), (3, 6), (11, 21), (11, 33), (8, 26), (33, 8), (0, 9), (24, 31), (2, 13), (1, 16), (4, 33), (8, 9), (10, 11), (6, 30), (6, 13), (23, 17), (23, 14), (4, 34), (15, 32), (11, 29), (24, 24), (9, 35), (10, 12), (8, 16), (1, 31), (31, 2), (1, 3), (30, 30), (33, 7), (30, 26), (25, 10), (14, 22), (11, 7), (24, 6), (14, 2), (26, 4), (7, 15), (19, 30), (22, 21), (23, 20), (16, 22), (21, 17), (2, 26), (5, 6), (30, 1), (28, 25), (16, 13), (7, 6), (8, 17), (32, 29), (25, 31), (31, 22), (33, 24), (29, 15), (13, 34), (32, 16), (28, 30), (27, 17), (14, 24), (6, 14), (17, 31), (5, 33), (19, 18), (29, 28), (15, 16), (30, 7), (8, 11), (25, 11), (12, 0), (30, 16), (2, 21), (28, 3), (13, 14), (16, 3), (32, 8), (5, 19), (12, 16), (11, 5), (18, 16), (10, 27), (16, 18), (33, 9), (19, 14), (5, 22), (29, 2), (28, 27), (1, 33), (15, 18), (13, 10), (31, 11), (14, 9), (2, 11), (30, 9), (34, 33), (28, 9), (3, 29), (15, 29), (27, 23), (26, 3), (7, 32), (24, 25), (6, 3), (26, 7), (27, 15), (30, 2), (16, 21), (20, 22), (0, 35), (3, 31), (16, 4), (15, 1), (17, 16), (17, 30), (18, 20), (18, 25), (13, 6), (18, 24), (9, 5), (6, 27), (20, 17), (2, 28), (11, 4), (27, 7), (2, 25), (24, 29), (1, 20), (29, 19), (34, 13), (11, 24), (29, 8), (7, 26), (16, 16), (16, 1), (0, 3), (27, 5), (1, 1), (5, 16), (20, 19), (1, 6), (0, 23), (4, 5), (15, 12), (3, 34), (18, 19), (10, 15), (14, 19), (31, 16), (22, 35), (12, 21), (20, 11), (29, 35), (13, 4), (0, 25), (17, 23), (22, 2), (2, 17), (32, 28), (24, 22), (28, 17), (19, 27), (12, 1), (6, 24), (13, 25), (21, 27), (22, 25), (13, 12), (12, 15), (17, 0), (25, 5), (4, 0), (20, 20), (2, 30), (2, 29), (9, 0), (21, 31), (2, 5), (14, 28), (9, 21), (19, 1), (20, 24), (15, 24), (24, 7), (24, 27), (0, 20), (26, 2), (7, 7), (31, 15), (7, 0), (12, 11), (10, 34), (20, 21), (13, 18), (27, 20), (31, 33), (0, 21), (7, 10), (9, 26), (30, 4), (13, 21), (13, 20), (15, 6), (16, 17), (30, 10), (8, 14), (16, 8), (31, 1), (3, 3), (21, 30), (3, 11), (28, 15), (13, 16), (4, 13), (3, 15), (8, 31), (17, 22), (1, 24), (11, 14), (26, 27), (12, 5), (17, 13), (3, 22), (24, 23), (13, 27), (6, 6), (22, 19), (5, 31), (4, 4), (0, 7), (32, 20), (13, 26), (1, 35), (20, 18), (34, 26), (17, 10), (14, 30), (12, 9), (21, 12), (19, 6), (17, 28), (18, 26), (7, 4), (23, 3), (0, 29), (5, 25), (29, 13), (14, 26), (34, 30), (6, 12), (7, 23), (5, 24), (23, 22), (21, 20), (23, 11), (18, 21), (21, 22), (4, 6), (17, 6), (29, 26), (28, 10), (29, 27), (15, 8), (9, 2), (18, 34), (0, 16), (11, 9), (18, 1), (11, 12), (31, 30), (15, 3), (24, 20), (34, 22), (16, 35), (3, 26), (30, 12), (8, 1), (14, 29), (25, 25), (17, 17), (29, 33), (33, 0), (18, 6), (23, 15), (23, 32), (23, 1), (2, 22), (4, 20), (29, 20), (4, 24), (14, 20), (11, 19), (21, 10), (12, 13), (27, 28), (14, 7), (30, 19), (11, 10), (29, 5), (13, 8), (22, 16), (8, 25), (22, 9), (17, 32), (6, 16), (17, 34), (24, 2), (11, 31), (18, 12), (32, 27), (32, 31), (6, 15), (34, 6), (16, 24), (32, 2), (2, 35), (2, 6), (25, 28), (26, 9), (3, 28), (20, 16), (21, 4), (31, 18), (30, 23), (22, 34), (19, 13), (13, 1), (12, 20), (10, 10), (10, 5), (6, 11), (22, 32), (1, 19), (6, 4), (13, 9), (27, 6), (1, 10), (5, 5), (24, 5), (16, 6), (19, 21), (12, 24), (4, 12), (5, 30), (25, 8), (34, 12), (11, 3), (28, 22), (3, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239400", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), 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), (5, 15), (24, 6), (24, 14), (17, 24), (11, 12), (26, 11), (27, 26), (29, 2), (14, 12), (0, 34), (23, 31), (11, 13), (7, 14), (2, 6), (18, 12), (2, 3), (2, 30), (27, 2), (12, 27), (19, 18), (1, 13), (9, 10), (26, 12), (22, 10), (12, 26), (4, 3), (11, 1), (12, 17), (12, 32), (31, 5), (30, 28), (20, 4), (2, 12), (26, 29), (5, 14), (11, 16), (24, 34), (29, 24), (15, 2), (28, 15), (20, 20), (17, 22), (20, 17), (6, 28), (19, 29), (14, 20), (28, 29), (9, 22), (24, 16), (9, 7), (22, 29), (3, 5), (2, 33), (14, 26), (15, 16), (0, 26), (1, 33), (7, 1), (5, 9), (9, 29), (15, 20), (13, 31), (1, 18), (30, 25), (13, 13), (6, 18), (17, 10), (28, 30), (8, 20), (3, 20), (28, 18), (15, 19), (19, 33), (31, 7), (15, 25), (11, 8), (10, 28), (16, 7), (8, 9), (18, 2), (14, 9), (23, 16), (4, 34), (0, 12), (7, 12), (31, 4), (27, 21), (2, 0), (12, 23), (30, 29), (16, 11), (9, 17), (6, 13), (7, 21), (18, 10), (8, 5), (19, 16), (4, 8), (16, 3), (1, 11), (7, 26), (27, 22), (14, 33), (4, 11), (2, 26), (26, 19), (5, 6), (21, 2), (30, 2), (4, 14), (11, 14), (29, 22), (3, 15), (25, 7), (27, 4), (17, 19), (8, 25), (12, 20), (10, 21), (16, 32), (20, 22), (10, 1), (5, 32), (2, 8), (24, 15), (20, 15), (9, 26), (26, 1), (3, 27), (11, 26), (3, 28), (11, 20), (1, 24), (18, 8), (0, 1), (22, 14), (29, 15), (19, 20), (14, 7), (28, 4), (6, 6), (17, 34), (24, 13), (30, 16), (7, 0), (10, 33), (21, 33), (28, 11), (20, 26), (19, 7), (12, 0), (6, 19), (30, 27), (1, 26), (11, 10), (21, 30), (3, 32), (10, 16), (9, 24), (21, 29), (20, 14), (8, 11), (23, 21), (12, 8), (26, 27), (25, 29), (4, 5), (10, 27), (7, 34), (23, 28), (19, 26), (21, 6), (5, 24), (1, 20), (16, 1), (6, 24), (14, 15), (6, 20), (11, 31), (8, 2), (1, 27), (12, 30), (26, 33), (26, 20), (20, 9), (1, 10), (15, 33), (23, 2), (19, 21), (17, 33), (4, 28), (12, 7), (10, 24), (16, 5), (0, 18), (6, 1), (29, 18), (18, 23), (16, 17), (18, 26), (4, 12), (20, 32), (20, 16), (0, 2), (19, 31), (29, 1), (22, 9), (22, 20), (6, 17), (2, 5), (8, 13), (31, 0), (20, 7), (8, 32), (24, 12), (9, 30), (11, 7), (5, 25), (27, 32), (17, 29), (18, 11), (30, 12), (26, 9), (8, 8), (23, 34), (27, 16), (29, 5), (14, 24), (29, 34), (5, 21), (0, 22), (1, 19), (2, 23), (20, 19), (24, 28), (21, 0), (0, 3), (2, 24), (9, 2), (7, 22), (5, 23), (14, 28), (30, 23), (0, 16), (23, 14), (6, 32), (30, 21), (12, 4), (17, 6), (21, 21), (3, 2), (9, 18), (6, 34), (12, 28), (23, 8), (15, 32), (16, 26), (2, 17), (20, 34), (27, 10), (20, 21), (23, 5), (17, 0), (25, 18), (11, 17), (16, 2), (9, 32), (5, 20), (11, 34), (31, 32), (4, 2), (10, 13), (10, 10), (27, 14), (5, 4), (8, 17), (19, 19), (23, 27), (6, 10), (21, 5), (15, 11), (30, 3), (24, 0), (17, 31), (24, 25), (29, 29), (30, 34), (23, 18), (21, 28), (13, 24), (29, 14), (11, 5), (6, 22), (18, 0), (24, 21), (5, 8), (4, 15), (11, 0), (18, 31), (14, 18), (11, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "449820", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 28), (19, 6), (13, 1), (19, 0), (15, 23), (18, 22), (20, 21), (15, 27), (26, 18), (27, 2), (22, 22), (13, 2), (21, 28), (0, 20), (7, 23), (14, 11), (23, 26), (8, 1), (17, 8), (10, 3), (25, 7), (17, 18), (2, 11), (20, 0), (22, 0), (21, 22), (29, 17), (7, 10), (3, 22), (6, 4), (6, 1), (29, 21), (0, 24), (19, 2), (25, 3), (20, 19), (9, 13), (14, 4), (22, 21), (2, 15), (14, 8), (5, 18), (26, 26), (25, 20), (25, 6), (27, 28), (2, 25), (13, 21), (24, 28), (3, 8), (20, 28), (15, 30), (25, 16), (12, 13), (5, 27), (25, 27), (28, 7), (17, 21), (21, 18), (0, 28), (9, 21), (9, 30), (15, 12), (23, 11), (5, 12), (10, 12), (3, 24), (7, 17), (2, 1), (19, 5), (29, 5), (14, 13), (4, 12), (12, 28), (20, 4), (26, 29), (28, 13), (10, 20), (13, 3), (4, 18), (3, 19), (17, 26), (0, 5), (27, 16), (6, 10), (29, 8), (17, 1), (9, 27), (24, 9), (8, 21), (13, 10), (9, 23), (23, 2), (29, 3), (12, 10), (13, 20), (20, 13), (24, 25), (13, 6), (3, 13), (5, 21), (25, 23), (22, 18), (18, 24), (10, 19), (14, 30), (14, 15), (24, 8), (16, 13), (8, 10), (18, 6), (0, 8), (12, 9), (23, 4), (11, 6), (7, 20), (15, 10), (26, 3), (4, 26), (20, 27), (16, 6), (10, 9), (4, 2), (4, 8), (2, 29), (27, 8), (6, 18), (27, 7), (5, 26), (15, 28), (29, 26), (25, 30), (23, 27), (11, 29), (12, 19), (25, 22), (22, 20), (23, 6), (5, 13), (2, 10), (20, 15), (16, 2), (3, 20), (15, 9), (27, 9), (11, 7), (24, 19), (15, 29), (18, 28), (22, 7), (25, 5), (29, 28), (26, 24), (2, 12), (23, 16), (26, 9), (3, 15), (9, 24), (1, 5), (22, 10), (3, 17), (16, 17), (6, 27), (13, 15), (22, 26), (1, 6), (3, 2), (10, 23), (6, 25), (2, 26), (5, 5), (10, 1), (6, 8), (15, 22), (4, 19), (7, 12), (14, 17), (13, 18), (9, 4), (4, 17), (18, 18), (20, 2), (3, 30), (24, 18), (13, 14), (26, 27), (8, 15), (8, 14), (24, 10), (28, 11), (15, 2), (13, 9), (13, 7), (9, 10), (26, 4), (8, 16), (26, 7), (14, 5), (18, 13), (4, 5), (12, 18), (8, 4), (24, 17), (23, 21), (9, 2), (29, 10), (28, 2), (26, 1), (1, 27), (12, 27), (14, 9), (16, 24), (22, 6), (16, 26), (5, 17), (5, 6), (20, 5), (24, 6), (1, 1), (0, 9), (16, 21), (19, 13), (5, 16), (24, 13), (2, 14), (21, 23), (22, 28), (6, 23), (27, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "986776", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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), (0, 27), (16, 10), (18, 30), (3, 12), (26, 24), (34, 23), (7, 5), (24, 18), (7, 25), (24, 21), (22, 28), (6, 22), (21, 28), (16, 4), (13, 27), (27, 13), (34, 8), (18, 14), (11, 28), (1, 20), (24, 31), (11, 15), (14, 30), (29, 1), (1, 28), (27, 2), (5, 30), (12, 17), (31, 13), (33, 7), (30, 27), (16, 22), (2, 9), (28, 24), (21, 5), (11, 2), (28, 15), (12, 28), (10, 30), (30, 0), (13, 8), (10, 5), (13, 28), (33, 15), (21, 10), (2, 21), (31, 30), (32, 5), (3, 24), (0, 14), (27, 27), (3, 25), (19, 28), (28, 29), (0, 29), (21, 19), (22, 19), (21, 16), (32, 6), (4, 26), (1, 14), (32, 7), (14, 7), (3, 7), (18, 29), (15, 31), (19, 2), (31, 27), (10, 20), (14, 8), (10, 17), (13, 22), (29, 19), (5, 31), (23, 28), (14, 22), (11, 1), (18, 22), (32, 24), (7, 16), (28, 9), (16, 23), (30, 29), (29, 6), (2, 3), (11, 6), (20, 27), (9, 10), (10, 19), (7, 19), (2, 29), (19, 24), (14, 23), (0, 2), (2, 14), (21, 15), (14, 4), (0, 9), (10, 9), (26, 25), (23, 2), (32, 26), (34, 10), (30, 13), (2, 27), (31, 4), (7, 2), (18, 7), (31, 22), (2, 31), (6, 14), (28, 10), (30, 24), (4, 0), (20, 23), (29, 10), (1, 31), (12, 2), (27, 24), (32, 25), (18, 21), (12, 4), (5, 7), (9, 16), (25, 7), (5, 25), (31, 10), (1, 5), (10, 11), (22, 4), (1, 6), (8, 16), (22, 0), (33, 29), (34, 29), (8, 2), (15, 28), (33, 26), (33, 21), (34, 12), (24, 5), (34, 17), (6, 24), (32, 27), (1, 17), (5, 13), (32, 31), (3, 11), (14, 31), (3, 8), (25, 31), (29, 13), (5, 12), (18, 24), (0, 6), (25, 16), (10, 16), (13, 29), (22, 21), (20, 26), (34, 0), (2, 11), (17, 27), (33, 16), (19, 19), (0, 4), (20, 12), (2, 7), (2, 5), (34, 15), (2, 25), (4, 31), (33, 13), (26, 27), (16, 1), (4, 6), (23, 11), (32, 15), (34, 18), (23, 4), (22, 16), (2, 15), (30, 21), (25, 2), (25, 14), (10, 7), (7, 18), (14, 25), (21, 7), (10, 8), (11, 20), (16, 11), (9, 30), (29, 17), (27, 11), (34, 14), (14, 6), (6, 10), (26, 1), (9, 27), (3, 29), (26, 14), (22, 10), (33, 31), (28, 19), (19, 4), (20, 7), (15, 6), (31, 3), (4, 5), (15, 20), (5, 27), (0, 26), (20, 22), (27, 25), (19, 18), (4, 12), (4, 20), (13, 31), (28, 16), (14, 15), (26, 17), (9, 15), (25, 6), (12, 24), (28, 8), (15, 13), (5, 20), (16, 9), (12, 26), (7, 13), (32, 1), (15, 8), (24, 2), (6, 1), (17, 25), (18, 3), (4, 7), (23, 31), (13, 13), (20, 29), (19, 26), (23, 20), (19, 3), (22, 13), (2, 18), (2, 19), (33, 10), (28, 6), (18, 25), (13, 4), (21, 27), (11, 18), (31, 1), (12, 14), (12, 10), (24, 4), (10, 6), (20, 28), (2, 13), (8, 17), (21, 2), (4, 29), (4, 2), (4, 28), (10, 13), (6, 21), (4, 1), (29, 18), (23, 10), (19, 21), (13, 15), (26, 22), (12, 8), (1, 7), (6, 18), (18, 13), (33, 20), (30, 7), (5, 22), (18, 5), (29, 4), (29, 22), (32, 4), (25, 9), (4, 17), (29, 21), (8, 18), (24, 14), (5, 23), (29, 29), (20, 5), (27, 21), (30, 10), (19, 22), (22, 14), (8, 14), (22, 6), (14, 12), (34, 2), (2, 23), (6, 30), (28, 7), (17, 10), (34, 13), (3, 5), (1, 8), (1, 3), (34, 16), (17, 0), (11, 0), (17, 21), (25, 29), (4, 18), (18, 28), (5, 15), (9, 28), (20, 14), (19, 13), (27, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "666000", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), 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), (4, 9), (21, 1), (16, 12), (5, 25), (7, 15), (5, 18), (26, 22), (20, 10), (14, 8), (13, 29), (13, 22), (8, 6), (19, 18), (8, 16), (25, 18), (13, 24), (16, 24), (6, 11), (22, 26), (25, 12), (4, 11), (18, 29), (6, 13), (9, 20), (21, 0), (24, 26), (12, 30), (11, 20), (25, 8), (9, 16), (25, 27), (25, 22), (28, 29), (10, 0), (13, 15), (21, 24), (12, 26), (23, 10), (29, 17), (14, 0), (5, 23), (7, 13), (16, 26), (3, 14), (31, 18), (5, 26), (16, 8), (2, 23), (13, 27), (12, 2), (30, 7), (26, 16), (29, 29), (2, 0), (19, 9), (0, 25), (10, 19), (13, 12), (4, 4), (5, 22), (30, 22), (3, 28), (27, 21), (19, 0), (24, 10), (18, 19), (12, 0), (13, 0), (17, 3), (26, 29), (16, 7), (22, 11), (19, 3), (1, 29), (12, 10), (4, 24), (10, 8), (25, 4), (16, 17), (30, 6), (25, 7), (24, 0), (21, 23), (6, 29), (28, 3), (25, 30), (22, 10), (3, 11), (22, 18), (12, 3), (25, 13), (28, 4), (16, 11), (5, 6), (19, 7), (4, 20), (8, 11), (29, 21), (12, 12), (2, 26), (21, 15), (14, 12), (17, 0), (1, 27), (27, 18), (9, 25), (2, 2), (30, 20), (31, 25), (28, 11), (4, 22), (27, 8), (17, 19), (12, 21), (3, 7), (21, 2), (2, 27), (3, 29), (20, 17), (27, 7), (14, 23), (11, 9), (20, 27), (1, 12), (23, 14), (17, 4), (23, 18), (30, 14), (4, 6), (13, 6), (24, 4), (29, 27), (18, 4), (23, 17), (2, 16), (3, 20), (27, 15), (26, 14), (18, 6), (4, 23), (4, 15), (15, 3), (22, 0), (11, 1), (2, 6), (19, 20), (18, 5), (11, 3), (2, 18), (26, 23), (31, 13), (24, 7), (10, 17), (19, 24), (3, 27), (20, 25), (30, 16), (18, 20), (14, 24), (8, 0), (5, 29), (0, 10), (29, 13), (12, 5), (15, 12), (0, 12), (23, 5), (3, 3), (23, 2), (0, 7), (18, 2), (30, 21), (21, 12), (30, 23), (17, 1), (22, 1), (5, 13), (2, 15), (12, 22), (6, 14), (16, 0), (26, 8), (6, 28), (24, 12), (1, 3), (2, 7), (23, 15), (18, 10), (20, 20), (27, 4), (1, 9), (9, 26), (3, 25), (21, 26), (10, 24), (0, 29), (20, 26), (15, 19), (6, 0), (21, 10), (23, 20), (6, 5), (8, 7), (10, 25), (1, 25), (14, 25), (12, 24), (12, 15), (8, 4), (6, 23), (2, 4), (12, 29), (20, 8), (6, 22), (28, 0), (27, 5), (23, 21), (1, 18), (26, 11), (0, 30), (15, 29), (13, 9), (17, 21), (7, 4), (15, 15), (1, 17), (6, 7), (1, 4), (28, 9), (17, 29), (14, 15), (12, 16), (23, 25), (28, 17), (29, 5), (11, 25), (28, 20), (15, 21), (21, 27), (0, 11), (24, 9), (25, 15), (13, 26), (1, 23), (26, 1), (13, 14), (1, 28), (17, 18), (7, 19), (11, 29), (31, 20), (0, 8), (14, 19), (16, 2), (1, 10), (8, 18), (15, 30), (28, 13), (30, 17), (14, 27), (20, 23), (26, 13), (13, 23), (27, 25), (27, 24), (25, 20), (20, 14), (17, 23), (19, 5), (19, 12), (16, 16), (23, 22), (0, 27), (22, 19), (31, 11), (8, 25), (18, 9), (23, 28), (9, 24), (27, 19), (12, 13), (8, 13), (25, 11), (11, 18), (7, 1), (26, 18), (25, 2), (30, 25), (3, 24), (16, 13), (8, 10), (20, 6), (18, 12), (22, 30), (16, 14), (8, 19), (20, 15), (25, 5), (25, 16), (4, 13), (29, 28), (5, 15), (28, 14), (27, 14), (14, 13), (25, 9), (13, 4), (30, 30), (22, 9), (22, 25), (0, 21), (9, 5), (4, 26), (29, 0), (31, 10), (19, 29), (26, 15), (28, 21), (4, 27), (31, 3), (4, 1), (23, 26), (7, 0), (23, 8), (12, 4), (15, 28), (8, 15), (13, 20), (27, 11), (25, 6), (29, 10), (21, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315648", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), 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), (26, 17), (18, 24), (6, 4), (0, 26), (10, 15), (23, 9), (28, 9), (25, 20), (17, 21), (7, 14), (20, 0), (10, 30), (13, 21), (20, 9), (30, 12), (4, 26), (34, 5), (8, 15), (16, 12), (34, 20), (37, 10), (31, 6), (29, 15), (29, 19), (21, 30), (30, 23), (4, 22), (30, 18), (15, 27), (10, 3), (1, 16), (16, 14), (33, 8), (23, 18), (12, 24), (2, 15), (34, 1), (34, 26), (1, 23), (3, 9), (5, 9), (10, 18), (0, 29), (17, 26), (31, 20), (13, 28), (28, 30), (14, 23), (17, 27), (24, 5), (11, 32), (4, 2), (27, 13), (1, 18), (6, 15), (28, 23), (19, 17), (20, 31), (36, 15), (37, 31), (26, 11), (0, 9), (12, 4), (1, 7), (33, 24), (29, 23), (33, 22), (5, 21), (13, 1), (1, 30), (2, 12), (33, 28), (22, 7), (4, 6), (24, 21), (3, 19), (17, 22), (6, 22), (22, 24), (34, 8), (19, 16), (4, 28), (16, 9), (7, 24), (10, 8), (18, 12), (22, 16), (33, 15), (4, 25), (29, 16), (31, 26), (27, 30), (24, 6), (8, 32), (34, 17), (29, 0), (14, 14), (20, 22), (1, 2), (15, 3), (7, 17), (33, 5), (21, 21), (18, 27), (21, 26), (28, 10), (8, 19), (18, 0), (22, 12), (19, 15), (29, 28), (11, 20), (27, 33), (22, 14), (7, 27), (18, 30), (37, 21), (23, 29), (2, 32), (13, 2), (34, 13), (20, 21), (12, 12), (14, 3), (8, 4), (11, 27), (18, 10), (1, 32), (7, 33), (25, 6), (6, 20), (17, 17), (10, 13), (37, 11), (6, 29), (0, 6), (31, 4), (27, 11), (18, 1), (16, 2), (24, 0), (2, 24), (15, 6), (12, 22), (35, 0), (8, 8), (16, 18), (15, 31), (26, 32), (33, 33), (12, 33), (37, 7), (34, 27), (25, 27), (17, 12), (22, 11), (23, 22), (13, 20), (3, 4), (17, 24), (29, 1), (35, 30), (11, 23), (31, 22), (10, 28), (9, 7), (5, 31), (19, 3), (36, 18), (21, 22), (11, 11), (26, 20), (22, 23), (14, 27), (10, 22), (37, 20), (27, 8), (25, 9), (31, 25), (30, 8), (3, 32), (19, 21), (1, 26), (11, 19), (33, 30), (21, 32), (11, 5), (27, 4), (37, 12), (22, 21), (0, 20), (24, 27), (16, 10), (19, 26), (7, 19), (19, 19), (1, 15), (26, 12), (14, 22), (20, 28), (32, 17), (20, 29), (5, 3), (30, 22), (36, 16), (7, 13), (15, 16), (9, 21), (17, 1), (14, 9), (29, 30), (14, 6), (36, 32), (24, 11), (6, 2), (33, 18), (20, 1), (30, 14), (7, 21), (13, 15), (2, 33), (20, 25), (0, 31), (16, 4), (18, 21), (9, 27), (18, 22), (17, 6), (30, 17), (7, 5), (7, 26), (4, 20), (5, 6), (12, 23), (21, 0), (3, 20), (10, 26), (24, 7), (5, 13), (25, 18), (23, 25), (19, 31), (4, 13), (26, 8), (28, 33), (29, 13), (17, 3), (19, 20), (30, 11), (14, 24), (27, 23), (19, 29), (9, 16), (37, 1), (3, 31), (9, 17), (26, 24), (28, 1), (32, 8), (26, 27), (6, 17), (25, 24), (37, 13), (23, 6), (10, 33), (7, 11), (3, 1), (8, 22), (20, 17), (36, 31), (14, 13), (21, 16), (2, 16), (33, 19), (36, 29), (6, 25), (26, 21), (34, 14), (1, 14), (25, 19), (20, 33), (23, 13), (8, 25), (2, 5), (1, 13), (22, 6), (0, 22), (19, 32), (15, 8), (5, 0), (33, 3), (10, 9), (26, 19), (29, 9), (3, 11), (19, 8), (9, 3), (26, 25), (24, 26), (22, 15), (1, 9), (37, 0), (31, 15), (27, 24), (30, 20), (2, 7), (30, 15), (8, 20), (6, 6), (12, 0), (12, 14), (16, 0), (15, 11), (5, 25), (4, 29), (34, 9), (34, 24), (15, 21), (0, 5), (5, 29), (28, 11), (13, 8), (26, 9), (10, 12), (33, 29), (28, 6), (33, 20), (35, 23), (0, 24), (23, 0), (18, 8), (21, 9), (3, 28), (7, 31), (33, 23), (14, 31), (29, 29), (21, 31), (22, 19), (0, 16), (5, 2), (16, 26), (16, 28), (11, 10), (8, 27), (11, 21), (21, 14), (10, 23), (23, 14), (29, 6), (30, 5), (7, 8), (5, 20), (2, 13), (11, 22), (8, 10), (7, 12), (14, 16), (30, 16), (9, 33), (1, 4), (31, 9), (12, 27), (32, 6), (21, 18), (21, 27), (31, 14), (7, 18), (9, 2), (0, 33), (3, 17), (22, 28), (6, 26), (37, 5), (23, 16), (1, 17), (2, 10), (11, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249928", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), 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), (11, 5), (8, 29), (32, 29), (4, 26), (9, 6), (5, 28), (30, 7), (2, 11), (17, 9), (6, 2), (31, 23), (26, 2), (10, 5), (5, 8), (16, 1), (34, 2), (30, 9), (4, 5), (12, 11), (13, 21), (34, 19), (11, 9), (17, 27), (23, 26), (0, 18), (16, 28), (23, 21), (26, 12), (12, 22), (21, 2), (3, 0), (13, 14), (32, 8), (30, 18), (32, 21), (20, 28), (13, 11), (14, 5), (14, 16), (23, 18), (16, 22), (27, 23), (33, 22), (27, 16), (27, 2), (8, 21), (28, 0), (14, 3), (10, 27), (26, 23), (4, 28), (35, 10), (18, 24), (21, 22), (34, 25), (5, 3), (27, 5), (10, 26), (4, 27), (19, 5), (10, 8), (32, 3), (31, 27), (13, 4), (20, 26), (11, 1), (13, 12), (20, 24), (28, 1), (36, 8), (24, 29), (24, 18), (6, 24), (10, 23), (32, 26), (29, 27), (30, 15), (7, 8), (18, 2), (0, 8), (29, 7), (4, 6), (3, 28), (11, 27), (6, 17), (26, 27), (12, 20), (9, 0), (36, 13), (7, 4), (23, 13), (3, 22), (19, 24), (0, 2), (12, 29), (32, 28), (20, 22), (5, 0), (5, 24), (9, 26), (13, 7), (30, 21), (18, 11), (36, 1), (5, 5), (32, 25), (0, 7), (0, 29), (10, 22), (28, 7), (23, 14), (32, 27), (34, 6), (27, 1), (34, 12), (22, 20), (5, 2), (27, 22), (14, 19), (21, 25), (25, 27), (16, 10), (31, 5), (22, 4), (31, 0), (1, 12), (14, 9), (20, 21), (9, 5), (1, 27), (29, 14), (4, 9), (9, 18), (24, 22), (31, 29), (5, 16), (1, 28), (24, 15), (33, 18), (31, 4), (30, 23), (13, 29), (36, 18), (17, 6), (18, 21), (20, 16), (18, 29), (35, 20), (20, 17), (31, 16), (7, 14), (23, 12), (23, 17), (13, 25), (29, 17), (32, 4), (3, 5), (15, 13), (31, 15), (26, 19), (11, 7), (22, 12), (34, 13), (7, 12), (17, 19), (28, 6), (5, 1), (19, 17), (26, 28), (27, 9), (2, 4), (29, 5), (15, 28), (10, 14), (36, 26), (33, 13), (16, 9), (5, 20), (19, 29), (3, 11), (12, 24), (3, 12), (28, 10), (34, 24), (14, 20), (24, 27), (11, 29), (1, 11), (28, 18), (18, 26), (0, 20), (23, 2), (35, 24), (28, 25), (27, 20), (5, 14), (6, 29), (10, 17), (35, 1), (36, 10), (33, 8), (21, 0), (1, 26), (30, 5), (8, 7), (32, 12), (17, 11), (28, 20), (22, 7), (14, 26), (20, 6), (10, 24), (30, 13), (9, 4), (14, 25), (22, 16), (27, 21), (26, 15), (30, 26), (32, 1), (21, 8), (13, 5), (33, 11), (30, 17), (4, 23), (33, 4), (8, 26), (14, 7), (25, 2), (7, 20), (18, 28), (17, 2), (22, 13), (0, 13), (20, 19), (32, 6), (9, 21), (17, 4), (18, 23), (20, 27), (7, 28), (14, 0), (15, 17), (31, 11), (12, 19), (4, 29), (17, 20), (9, 12), (20, 10), (35, 23), (0, 3), (20, 13), (13, 0), (20, 23), (27, 15), (17, 24), (10, 3), (4, 1), (16, 5), (24, 4), (25, 21), (30, 4), (22, 25), (7, 7), (25, 10), (36, 19), (23, 8), (15, 0), (10, 2), (25, 7), (15, 27), (10, 18), (13, 27), (8, 3), (22, 23), (15, 22), (33, 7), (36, 3), (19, 19), (33, 10), (9, 8), (1, 18), (30, 2), (22, 0), (2, 6), (21, 29), (1, 23), (33, 21), (17, 12), (25, 11), (14, 14), (5, 17), (5, 26), (20, 14), (27, 17), (13, 20), (34, 11), (3, 7), (2, 12), (8, 4), (22, 26), (31, 8), (11, 12), (2, 27), (25, 26), (32, 17), (1, 0), (18, 20), (16, 29), (10, 21), (16, 6), (5, 12), (6, 8), (16, 27), (27, 10), (1, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897579", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), 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), (12, 23), (2, 4), (2, 22), (1, 14), (25, 2), (24, 6), (9, 25), (26, 32), (15, 15), (13, 14), (28, 20), (15, 18), (27, 22), (17, 8), (13, 18), (17, 10), (11, 23), (1, 5), (28, 3), (25, 27), (36, 22), (22, 7), (19, 10), (31, 22), (3, 1), (18, 23), (29, 13), (23, 8), (20, 30), (24, 11), (5, 6), (12, 27), (32, 25), (35, 6), (12, 7), (24, 12), (35, 7), (29, 6), (15, 28), (34, 33), (3, 22), (6, 8), (13, 4), (28, 1), (35, 22), (19, 11), (32, 9), (33, 20), (2, 31), (35, 21), (30, 23), (32, 12), (11, 9), (5, 0), (11, 20), (26, 15), (35, 30), (27, 24), (3, 19), (26, 22), (3, 8), (31, 10), (29, 5), (13, 27), (21, 14), (26, 28), (7, 10), (26, 16), (5, 15), (18, 5), (21, 26), (0, 5), (33, 12), (7, 19), (4, 1), (4, 3), (1, 28), (9, 8), (9, 13), (5, 30), (0, 8), (2, 6), (23, 3), (18, 33), (24, 8), (11, 4), (24, 29), (17, 6), (10, 28), (12, 8), (9, 19), (12, 9), (7, 31), (2, 13), (27, 11), (9, 28), (15, 30), (28, 24), (25, 0), (16, 16), (15, 12), (0, 15), (17, 1), (25, 17), (21, 24), (15, 13), (4, 31), (36, 32), (18, 32), (20, 22), (13, 13), (6, 19), (22, 21), (23, 4), (4, 9), (8, 16), (34, 6), (23, 16), (25, 4), (29, 4), (2, 0), (16, 0), (29, 8), (2, 12), (34, 19), (36, 19), (5, 27), (2, 9), (16, 7), (5, 21), (15, 31), (19, 27), (12, 33), (20, 8), (4, 13), (17, 11), (34, 7), (19, 31), (19, 5), (22, 0), (34, 20), (14, 32), (30, 31), (32, 19), (25, 25), (2, 28), (8, 30), (6, 3), (3, 15), (1, 6), (15, 16), (33, 7), (27, 18), (16, 4), (30, 5), (25, 31), (28, 30), (11, 24), (20, 2), (2, 8), (4, 27), (15, 23), (10, 17), (30, 28), (15, 17), (0, 31), (32, 26), (14, 29), (31, 30), (28, 7), (21, 9), (28, 14), (26, 2), (0, 22), (21, 25), (31, 24), (22, 5), (12, 14), (35, 24), (16, 28), (20, 28), (7, 6), (23, 12), (34, 27), (15, 33), (5, 25), (1, 3), (27, 5), (20, 33), (22, 16), (33, 32), (26, 12), (4, 14), (3, 7), (25, 20), (3, 18), (12, 5), (21, 12), (20, 12), (21, 32), (18, 16), (6, 26), (9, 14), (14, 1), (29, 24), (27, 15), (5, 29), (33, 27), (13, 10), (4, 7), (11, 6), (14, 22), (3, 0), (32, 8), (0, 30), (22, 19), (24, 25), (32, 30), (36, 5), (11, 32), (7, 14), (34, 26), (19, 9), (10, 5), (30, 18), (11, 1), (1, 30), (0, 28), (17, 7), (27, 4), (23, 32), (6, 10), (32, 13), (32, 11), (34, 5), (20, 10), (10, 2), (24, 31), (25, 7), (11, 26), (10, 30), (22, 2), (24, 10), (23, 24), (15, 27), (8, 19), (8, 1), (2, 26), (22, 11), (12, 19), (33, 18), (21, 23), (32, 14), (1, 27), (12, 11), (20, 3), (15, 1), (19, 32), (10, 9), (30, 20), (11, 25), (26, 19), (19, 30), (1, 24), (3, 14), (17, 0), (31, 12), (24, 15), (28, 21), (25, 3), (8, 28), (32, 33), (11, 31), (28, 33), (36, 6), (8, 12), (36, 7), (11, 10), (16, 31), (29, 16), (35, 11), (30, 17), (2, 1), (12, 6), (1, 7), (28, 12), (15, 32), (25, 24), (31, 28), (29, 7), (7, 20), (28, 2), (18, 25), (23, 13), (31, 8), (27, 25), (32, 24), (16, 11), (22, 24), (18, 21), (16, 2), (17, 29), (36, 2), (21, 17), (3, 10), (6, 7), (17, 18), (20, 16), (23, 6), (31, 20), (25, 32), (36, 30), (10, 0), (5, 31), (22, 31), (20, 0), (32, 16), (14, 19), (34, 11), (23, 10), (16, 5), (5, 12), (17, 5), (7, 23), (26, 31), (21, 18), (0, 25), (0, 4), (8, 6), (24, 1), (30, 30), (24, 2), (21, 22), (18, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "885168", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 8), (4, 27), (17, 15), (22, 0), (20, 16), (7, 9), (29, 21), (8, 21), (1, 13), (2, 9), (27, 3), (19, 10), (18, 2), (4, 28), (17, 18), (11, 1), (2, 16), (27, 22), (18, 16), (17, 26), (8, 15), (17, 0), (11, 9), (28, 24), (4, 22), (14, 7), (3, 9), (10, 27), (8, 29), (1, 18), (12, 14), (19, 9), (12, 10), (17, 9), (13, 14), (27, 7), (16, 18), (11, 30), (1, 19), (0, 8), (25, 27), (11, 5), (18, 27), (9, 19), (16, 29), (5, 22), (19, 1), (14, 4), (11, 25), (2, 26), (16, 5), (9, 2), (12, 27), (9, 25), (5, 16), (4, 5), (9, 4), (11, 21), (16, 26), (25, 28), (9, 5), (15, 6), (1, 20), (29, 27), (11, 18), (15, 25), (29, 17), (25, 24), (19, 3), (17, 2), (27, 14), (19, 17), (16, 6), (3, 27), (27, 12), (8, 14), (12, 5), (3, 23), (4, 1), (3, 11), (23, 2), (12, 20), (3, 26), (27, 8), (7, 15), (14, 15), (2, 13), (3, 5), (24, 16), (19, 13), (11, 17), (7, 29), (14, 13), (27, 16), (23, 13), (11, 7), (22, 1), (2, 6), (29, 10), (25, 11), (25, 4), (10, 15), (5, 1), (4, 21), (14, 17), (6, 23), (5, 21), (4, 17), (29, 11), (28, 12), (9, 11), (21, 25), (20, 1), (25, 15), (13, 29), (0, 7), (14, 3), (24, 4), (16, 9), (17, 22), (23, 16), (26, 18), (11, 10), (6, 17), (20, 4), (15, 10), (23, 21), (2, 1), (27, 24), (15, 13), (21, 19), (14, 8), (1, 28), (28, 13), (11, 2), (14, 16), (22, 4), (24, 11), (27, 29), (22, 5), (27, 1), (23, 11), (14, 18), (7, 26), (24, 21), (10, 11), (23, 24), (8, 22), (20, 12), (26, 14), (10, 16), (23, 0), (10, 0), (15, 23), (26, 25), (5, 15), (1, 3), (29, 20), (29, 23), (12, 4), (3, 8), (12, 16), (17, 1), (13, 16), (24, 3), (29, 12), (27, 25), (15, 17), (29, 8), (10, 20), (13, 27), (23, 18), (3, 13), (22, 12), (18, 19), (2, 27), (22, 3), (11, 15), (26, 28), (29, 9), (7, 5), (0, 13), (8, 28), (25, 1), (23, 30), (8, 27), (17, 3), (25, 7), (20, 22), (22, 17), (20, 27), (20, 13), (10, 2), (15, 5), (29, 0), (19, 29), (24, 26), (5, 28), (14, 19), (11, 27), (1, 24), (13, 7), (16, 13), (25, 17), (28, 15), (11, 3), (9, 17), (13, 6), (1, 6), (24, 1), (15, 2), (11, 28), (10, 13), (27, 21), (24, 15), (15, 9), (10, 12), (4, 9), (20, 10), (5, 0), (27, 18), (21, 14), (2, 20), (25, 0), (26, 29), (24, 0), (17, 12), (2, 23), (8, 1), (17, 5), (23, 23), (14, 2), (21, 29), (17, 8), (15, 15), (1, 29), (18, 0), (8, 10), (21, 20), (4, 29), (19, 24), (4, 7), (20, 0), (25, 14), (20, 29), (23, 14), (23, 28), (3, 19), (28, 11), (13, 4), (26, 11), (27, 5), (18, 18), (16, 22), (5, 23), (0, 6), (4, 26), (15, 4), (6, 28), (16, 15), (1, 15), (8, 9), (18, 12), (16, 8), (9, 1), (7, 17), (6, 10), (2, 25), (0, 29), (23, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672660", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 27), (10, 6), (32, 24), (16, 7), (17, 13), (24, 33), (18, 13), (24, 18), (7, 1), (20, 3), (3, 3), (1, 34), (19, 6), (30, 10), (8, 34), (8, 0), (4, 13), (13, 23), (6, 16), (14, 14), (7, 4), (33, 21), (14, 8), (26, 22), (11, 9), (21, 26), (28, 4), (28, 27), (24, 2), (16, 22), (6, 1), (23, 2), (15, 6), (22, 5), (19, 15), (17, 28), (25, 0), (16, 13), (28, 6), (26, 29), (27, 5), (6, 21), (9, 33), (28, 14), (18, 26), (3, 13), (3, 26), (6, 12), (0, 25), (19, 11), (5, 19), (0, 31), (29, 4), (13, 2), (12, 2), (32, 22), (23, 9), (11, 14), (11, 22), (33, 26), (8, 11), (21, 18), (17, 4), (31, 2), (4, 3), (17, 14), (19, 1), (16, 24), (22, 19), (26, 1), (2, 27), (11, 31), (28, 24), (17, 30), (13, 34), (14, 25), (27, 13), (24, 19), (29, 29), (10, 18), (11, 2), (5, 32), (4, 4), (31, 22), (10, 15), (0, 15), (26, 16), (5, 31), (33, 25), (31, 11), (18, 22), (2, 34), (24, 1), (27, 23), (15, 30), (14, 0), (4, 5), (28, 32), (31, 0), (0, 5), (27, 18), (3, 1), (32, 2), (2, 33), (27, 9), (24, 21), (21, 13), (33, 3), (1, 27), (9, 23), (20, 19), (24, 28), (18, 7), (15, 10), (10, 20), (25, 24), (28, 34), (31, 24), (8, 5), (0, 9), (11, 4), (4, 2), (15, 8), (1, 10), (22, 28), (26, 33), (31, 5), (20, 34), (6, 24), (19, 19), (1, 2), (10, 22), (16, 2), (1, 19), (8, 6), (19, 32), (2, 23), (24, 9), (32, 25), (8, 3), (32, 23), (6, 5), (7, 10), (31, 17), (1, 20), (14, 7), (12, 12), (11, 18), (25, 16), (8, 15), (27, 33), (17, 26), (24, 17), (22, 10), (25, 19), (0, 32), (23, 23), (12, 17), (23, 32), (10, 0), (18, 16), (0, 20), (15, 26), (23, 12), (0, 6), (29, 5), (16, 16), (26, 24), (31, 7), (21, 25), (22, 26), (28, 23), (20, 30), (32, 20), (23, 8), (25, 18), (27, 10), (13, 10), (6, 31), (24, 3), (29, 13), (16, 4), (22, 11), (12, 1), (30, 0), (22, 0), (17, 34), (26, 5), (32, 1), (5, 3), (11, 0), (31, 30), (29, 30), (10, 13), (4, 27), (2, 29), (19, 16), (31, 25), (9, 21), (21, 28), (19, 8), (11, 33), (6, 15), (32, 6), (7, 2), (24, 5), (29, 23), (2, 16), (15, 23), (21, 34), (14, 2), (21, 7), (22, 33), (8, 17), (28, 0), (27, 11), (10, 30), (32, 13), (33, 0), (25, 9), (28, 15), (8, 12), (14, 20), (33, 29), (5, 17), (11, 10), (29, 15), (2, 1), (30, 25), (29, 28), (5, 12), (17, 1), (13, 21), (14, 26), (26, 7), (20, 7), (19, 34), (8, 30), (18, 15), (28, 28), (20, 8), (30, 5), (25, 14), (16, 27), (3, 18), (10, 19), (1, 30), (23, 1), (9, 9), (12, 31), (14, 21), (4, 17), (21, 16), (27, 6), (29, 10), (21, 31), (18, 31), (27, 8), (25, 30), (33, 7), (4, 28), (4, 23), (4, 30), (10, 34), (5, 0), (15, 29), (9, 4), (26, 28), (21, 23), (5, 33), (33, 22), (25, 28), (33, 19), (13, 32), (11, 21), (25, 8), (10, 5), (2, 0), (15, 3), (21, 1), (30, 2), (17, 3), (29, 14), (25, 34), (6, 27), (19, 10), (2, 31), (5, 14), (5, 4), (12, 34), (1, 0), (8, 28), (33, 12), (18, 30), (6, 20), (8, 9), (13, 25), (32, 26), (33, 31), (27, 32), (26, 18), (12, 6), (8, 8), (26, 21), (3, 22), (27, 22), (22, 34), (7, 34), (23, 17), (23, 3), (12, 32), (0, 27), (27, 27), (4, 34), (14, 3), (14, 22), (27, 19), (2, 7), (8, 26), (30, 11), (16, 9), (20, 28), (32, 8), (3, 4), (1, 6), (19, 29), (23, 20), (0, 21), (5, 26), (21, 8), (17, 29), (21, 32), (31, 16), (20, 29), (4, 6), (8, 29), (28, 1), (3, 10), (10, 24), (18, 21), (31, 15), (23, 21), (28, 5), (1, 32), (12, 22), (2, 13), (16, 11), (29, 2), (11, 5), (29, 16), (9, 22), (33, 9), (19, 12), (15, 1), (13, 7), (20, 20), (30, 1), (28, 22), (3, 30), (12, 29), (30, 24), (9, 0), (30, 27), (7, 31), (5, 7), (16, 29), (13, 15), (5, 1), (12, 33), (14, 16), (27, 20), (26, 25), (12, 3), (12, 25), (10, 25), (23, 19), (16, 26), (32, 17), (33, 30), (26, 20), (17, 21), (30, 12), (7, 29), (25, 4), (20, 31), (6, 34), (29, 1), (11, 23), (33, 15), (20, 26), (4, 12), (28, 2), (3, 17), (12, 18), (32, 0), (29, 25), (12, 8), (7, 25), (6, 8), (0, 28), (16, 32), (25, 12), (3, 0), (22, 12), (25, 3), (7, 0), (21, 27), (3, 34), (12, 19), (4, 9), (6, 32), (23, 6), (31, 10), (25, 13), (31, 33), (17, 2), (1, 1), (14, 30), (32, 33), (2, 26), (15, 0), (8, 1), (0, 14), (9, 17), (27, 29), (18, 12), (20, 24), (16, 14), (3, 5), (12, 27), (29, 11), (4, 16), (14, 31), (26, 27), (4, 31), (16, 34), (22, 21), (8, 22), (30, 18), (24, 10), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "617760", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), 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), (21, 9), (12, 29), (32, 23), (11, 5), (1, 37), (6, 21), (3, 24), (24, 6), (19, 27), (26, 10), (26, 23), (29, 4), (28, 19), (22, 15), (16, 36), (0, 35), (27, 22), (13, 5), (11, 12), (34, 36), (29, 33), (0, 17), (21, 0), (11, 6), (30, 15), (18, 21), (34, 11), (3, 38), (24, 13), (0, 1), (10, 34), (7, 33), (11, 27), (32, 30), (33, 16), (26, 28), (20, 37), (7, 24), (0, 2), (36, 22), (6, 36), (20, 27), (31, 23), (21, 36), (35, 11), (5, 19), (35, 3), (27, 28), (11, 15), (0, 19), (28, 35), (0, 16), (12, 14), (32, 37), (3, 2), (8, 28), (16, 1), (14, 27), (5, 17), (16, 12), (2, 18), (5, 37), (0, 5), (20, 19), (31, 9), (28, 33), (26, 6), (23, 14), (14, 22), (27, 25), (10, 32), (9, 17), (8, 35), (8, 1), (5, 6), (10, 9), (13, 6), (11, 28), (29, 20), (24, 38), (35, 20), (18, 20), (24, 23), (18, 10), (9, 1), (11, 1), (35, 28), (32, 4), (3, 25), (2, 22), (16, 4), (18, 11), (34, 24), (2, 35), (11, 26), (21, 12), (2, 27), (23, 6), (21, 23), (35, 35), (35, 2), (25, 33), (30, 19), (22, 36), (21, 31), (4, 0), (10, 20), (8, 34), (33, 29), (19, 32), (36, 17), (25, 30), (23, 27), (29, 17), (21, 19), (0, 30), (18, 16), (10, 1), (36, 0), (9, 38), (29, 34), (29, 18), (23, 38), (25, 24), (31, 15), (33, 37), (6, 22), (8, 24), (16, 31), (14, 6), (6, 33), (34, 32), (13, 15), (17, 9), (7, 26), (12, 23), (28, 12), (22, 38), (29, 0), (2, 29), (1, 24), (3, 12), (24, 19), (28, 13), (22, 9), (3, 31), (28, 24), (7, 38), (4, 25), (4, 27), (8, 29), (3, 1), (21, 8), (18, 12), (24, 34), (35, 7), (16, 21), (27, 3), (26, 35), (10, 28), (25, 27), (36, 24), (11, 19), (5, 20), (4, 9), (31, 2), (7, 9), (27, 23), (32, 29), (2, 6), (36, 27), (6, 26), (31, 16), (1, 6), (23, 5), (12, 11), (35, 34), (35, 25), (23, 26), (16, 26), (4, 21), (14, 10), (6, 14), (28, 3), (33, 14), (32, 0), (3, 37), (18, 1), (12, 19), (16, 8), (18, 13), (17, 29), (32, 25), (12, 20), (15, 1), (27, 21), (15, 7), (18, 23), (16, 27), (29, 27), (36, 4), (29, 8), (0, 9), (29, 2), (4, 18), (1, 35), (17, 12), (6, 38), (7, 36), (26, 33), (34, 5), (17, 6), (28, 20), (29, 11), (21, 13), (4, 16), (20, 15), (13, 36), (15, 36), (20, 38), (0, 8), (1, 29), (30, 21), (17, 4), (28, 6), (18, 19), (20, 8), (9, 32), (20, 21), (26, 13), (21, 27), (14, 8), (17, 34), (17, 35), (22, 24), (19, 12), (4, 12), (33, 5), (12, 37), (32, 27), (35, 14), (26, 17), (28, 1), (12, 6), (13, 30), (27, 16), (34, 1), (20, 24), (11, 4), (27, 30), (16, 38), (36, 7), (6, 3), (8, 14), (2, 37), (32, 13), (18, 0), (32, 38), (6, 2), (22, 2), (14, 35), (6, 6), (27, 36), (32, 2), (2, 1), (22, 37), (30, 9), (30, 16), (30, 10), (15, 4), (2, 30), (2, 15), (21, 32), (12, 33), (7, 2), (18, 35), (5, 4), (6, 37), (14, 25), (20, 6), (35, 32), (20, 2), (23, 28), (34, 35), (29, 28), (0, 4), (1, 8), (26, 11), (31, 22), (18, 33), (4, 26), (5, 16), (21, 6), (33, 15), (11, 36), (0, 11), (21, 18), (30, 24), (3, 18), (5, 23), (9, 21), (15, 16), (25, 34), (9, 4), (31, 30), (6, 35), (20, 4), (18, 37), (25, 3), (25, 19), (35, 36), (26, 29), (12, 7), (30, 5), (19, 36), (30, 23), (33, 33), (31, 36), (7, 18), (1, 13), (12, 0), (27, 14), (13, 25), (16, 35), (29, 5), (22, 30), (25, 9), (20, 22), (10, 8), (19, 5), (24, 37), (20, 20), (1, 26), (4, 28), (32, 18), (19, 31), (32, 15), (22, 33), (13, 18), (1, 25), (20, 23), (27, 5), (34, 4), (3, 9), (36, 15), (20, 28), (9, 22), (21, 30), (23, 32), (34, 12), (9, 8), (13, 32), (25, 20), (29, 25), (15, 22), (22, 7), (9, 14), (14, 19), (13, 14), (3, 4), (23, 8), (21, 15), (33, 13), (20, 36), (19, 15), (22, 17), (26, 24), (5, 13), (4, 29), (29, 32), (7, 30), (11, 38), (29, 7), (15, 15), (0, 37), (28, 32), (6, 5), (31, 1), (35, 12), (28, 7), (16, 19), (22, 28), (22, 32), (23, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842400", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 25), (0, 4), (2, 21), (7, 4), (8, 24), (27, 11), (33, 3), (20, 22), (25, 1), (9, 17), (30, 0), (33, 8), (9, 12), (1, 16), (32, 6), (32, 15), (15, 19), (31, 15), (23, 28), (5, 5), (5, 0), (15, 9), (1, 7), (10, 10), (33, 6), (4, 22), (32, 12), (31, 19), (23, 26), (20, 18), (9, 29), (18, 14), (13, 11), (23, 6), (16, 12), (4, 1), (2, 20), (17, 3), (15, 21), (27, 2), (28, 5), (6, 7), (4, 27), (5, 6), (28, 3), (20, 6), (1, 10), (23, 12), (24, 11), (8, 16), (30, 9), (8, 0), (10, 22), (10, 15), (23, 15), (16, 11), (10, 9), (20, 16), (10, 20), (21, 14), (24, 8), (18, 1), (13, 20), (4, 17), (2, 17), (14, 11), (5, 7), (32, 7), (24, 26), (21, 7), (0, 5), (7, 11), (13, 18), (1, 18), (10, 18), (1, 12), (5, 14), (4, 20), (13, 19), (18, 2), (0, 26), (5, 29), (13, 21), (23, 13), (14, 15), (8, 28), (29, 23), (8, 18), (32, 13), (15, 20), (28, 2), (5, 11), (33, 23), (33, 4), (14, 20), (30, 12), (13, 1), (30, 13), (19, 29), (17, 10), (21, 25), (26, 1), (24, 12), (9, 23), (16, 26), (31, 21), (9, 1), (12, 22), (24, 4), (26, 20), (16, 3), (21, 16), (16, 6), (25, 6), (13, 14), (3, 26), (21, 26), (2, 15), (12, 26), (30, 10), (17, 6), (19, 23), (2, 4), (30, 18), (22, 26), (7, 27), (6, 23), (33, 17), (30, 17), (31, 24), (15, 14), (25, 22), (11, 10), (17, 16), (14, 24), (16, 1), (4, 2), (1, 2), (20, 27), (23, 23), (24, 1), (1, 6), (32, 11), (3, 0), (21, 9), (7, 12), (25, 27), (7, 21), (12, 28), (23, 1), (7, 7), (24, 3), (33, 27), (29, 19), (26, 12), (25, 4), (11, 14), (3, 24), (23, 14), (13, 27), (14, 3), (15, 0), (12, 5), (10, 1), (24, 16), (7, 26), (21, 23), (19, 17), (10, 13), (0, 27), (12, 15), (30, 5), (2, 9), (12, 19), (22, 5), (31, 4), (17, 29), (28, 8), (6, 18), (21, 6), (15, 29), (6, 16), (15, 18), (5, 21), (4, 4), (24, 9), (4, 10), (1, 8), (12, 0), (17, 24), (8, 5), (2, 24), (23, 21), (5, 16), (14, 12), (33, 13), (19, 13), (25, 15), (7, 2), (12, 16), (7, 1), (17, 9), (0, 14), (13, 26), (27, 5), (15, 25), (29, 18), (16, 0), (3, 6), (20, 19), (9, 8), (14, 13), (2, 22), (14, 6), (11, 4), (5, 28), (10, 5), (18, 29), (26, 10), (33, 16), (15, 3), (12, 17), (3, 10), (8, 13), (27, 12), (29, 21), (10, 21), (30, 2), (7, 19), (32, 1), (18, 8), (15, 7), (7, 13), (8, 27), (15, 26), (12, 3), (0, 18), (33, 28), (24, 18), (13, 24), (30, 3), (33, 7), (28, 21), (22, 27), (3, 2), (13, 4), (4, 6), (31, 26), (3, 19), (31, 12), (21, 22), (8, 4), (25, 16), (2, 23), (21, 27), (20, 14), (25, 18), (1, 28), (32, 19), (20, 1), (18, 16), (28, 29), (0, 12), (6, 0), (11, 7), (11, 16), (17, 15), (27, 19), (32, 8), (10, 3), (19, 5), (9, 22), (12, 12), (14, 8), (5, 19), (19, 11), (10, 6), (10, 26), (5, 18), (22, 29), (5, 24), (11, 29), (19, 16), (32, 22), (32, 21), (26, 19), (18, 22), (19, 6), (4, 14), (18, 10), (21, 4), (24, 27), (17, 4), (6, 9), (5, 27), (21, 21), (30, 1), (4, 24), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22816", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 24), (20, 29), (21, 6), (20, 26), (0, 34), (24, 3), (10, 32), (29, 30), (4, 20), (8, 24), (16, 20), (2, 3), (26, 0), (29, 21), (5, 21), (3, 2), (29, 17), (8, 9), (27, 16), (17, 27), (12, 3), (27, 34), (24, 13), (8, 28), (0, 9), (23, 11), (14, 10), (22, 25), (22, 17), (4, 35), (7, 6), (15, 35), (24, 18), (26, 19), (0, 3), (14, 34), (18, 18), (27, 20), (22, 15), (20, 31), (20, 13), (28, 2), (17, 7), (20, 17), (16, 15), (14, 0), (19, 25), (23, 35), (28, 29), (19, 24), (10, 23), (6, 25), (23, 34), (11, 4), (29, 32), (10, 31), (24, 24), (25, 29), (18, 2), (3, 33), (27, 23), (5, 25), (26, 24), (29, 28), (0, 32), (16, 34), (19, 20), (3, 35), (6, 17), (13, 11), (21, 16), (27, 4), (19, 11), (9, 25), (5, 26), (26, 1), (24, 7), (0, 13), (4, 15), (15, 9), (4, 21), (26, 16), (29, 9), (7, 17), (26, 8), (1, 2), (3, 10), (21, 31), (16, 35), (10, 19), (13, 3), (8, 31), (3, 7), (23, 4), (29, 4), (18, 5), (15, 0), (6, 4), (13, 17), (21, 21), (16, 9), (26, 4), (23, 6), (21, 35), (13, 14), (26, 12), (18, 10), (12, 1), (1, 16), (9, 20), (2, 11), (22, 22), (14, 5), (25, 26), (28, 3), (29, 5), (16, 19), (1, 20), (15, 14), (10, 8), (1, 9), (28, 4), (1, 1), (21, 29), (24, 14), (5, 9), (10, 1), (24, 2), (19, 16), (5, 8), (0, 33), (26, 15), (8, 23), (8, 21), (6, 10), (14, 11), (22, 19), (8, 33), (2, 9), (9, 11), (12, 27), (22, 12), (22, 13), (4, 30), (20, 22), (0, 4), (20, 21), (8, 6), (11, 15), (9, 8), (28, 34), (7, 31), (22, 21), (20, 15), (20, 14), (28, 22), (0, 14), (19, 32), (12, 23), (3, 17), (22, 3), (23, 17), (19, 7), (24, 6), (11, 26), (20, 9), (7, 11), (21, 4), (4, 5), (29, 25), (3, 1), (6, 34), (8, 17), (6, 21), (13, 1), (7, 20), (10, 29), (8, 4), (9, 18), (24, 19), (28, 21), (16, 1), (29, 29), (11, 29), (9, 0), (29, 16), (5, 12), (24, 35), (7, 3), (25, 20), (1, 23), (2, 33), (25, 14), (2, 26), (12, 15), (10, 4), (24, 30), (6, 23), (29, 2), (27, 21), (19, 19), (11, 35), (24, 8), (3, 20), (18, 29), (16, 32), (6, 5), (16, 28), (11, 8), (11, 7), (24, 11), (12, 31), (8, 32), (0, 1), (8, 1), (13, 26), (2, 32), (22, 10), (2, 30), (18, 25), (10, 11), (2, 5), (9, 23), (13, 33), (1, 12), (7, 24), (7, 26), (26, 18), (23, 19), (9, 34), (22, 33), (26, 33), (7, 29), (4, 22), (22, 4), (2, 7), (15, 15), (15, 34), (1, 11), (20, 0), (23, 18), (28, 6), (11, 16), (6, 3), (4, 26), (6, 12), (10, 6), (23, 16), (25, 4), (16, 4), (2, 31), (19, 27), (24, 23), (4, 29), (24, 5), (28, 15), (15, 2), (16, 5), (21, 19), (10, 33), (25, 19), (2, 16), (22, 18), (14, 24), (0, 27), (28, 25), (21, 28), (24, 20), (9, 30), (9, 21), (13, 8), (3, 28), (24, 33), (27, 33), (28, 9), (18, 0), (13, 35), (6, 18), (20, 5), (18, 34), (12, 25), (15, 27), (11, 12), (18, 14), (29, 7), (17, 34), (29, 23), (11, 28), (19, 23), (20, 33), (18, 19), (19, 5), (17, 24), (3, 6), (11, 6), (25, 15), (11, 5), (19, 1), (2, 15), (1, 29), (3, 25), (23, 10), (25, 17), (26, 3), (18, 30), (24, 17), (12, 17), (18, 17), (17, 14), (19, 12), (9, 10), (17, 11), (20, 28), (0, 22), (17, 3), (28, 16), (2, 4), (10, 25), (25, 10), (16, 24), (4, 32), (20, 27), (27, 26), (25, 6), (22, 23), (22, 7), (13, 18), (23, 14), (2, 6), (14, 22), (27, 10), (27, 35), (3, 24), (23, 29), (0, 20), (13, 12), (7, 35), (16, 29), (25, 1), (12, 35), (15, 7), (11, 10), (10, 3), (10, 26), (13, 19), (21, 27), (1, 26), (28, 31), (19, 3), (8, 8), (9, 4), (5, 28), (17, 23), (7, 28), (26, 25), (3, 19), (18, 3), (17, 5), (28, 14), (12, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "823020", "dataset": "MATH"}
{"messages": [{"content": "In a 35x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 35), (16, 5), (28, 18), (27, 10), (0, 30), (14, 9), (28, 13), (22, 37), (21, 10), (12, 6), (22, 27), (33, 31), (11, 9), (17, 30), (22, 28), (28, 20), (31, 31), (1, 25), (16, 32), (25, 24), (3, 15), (2, 35), (18, 4), (28, 24), (33, 4), (8, 36), (8, 12), (30, 2), (30, 32), (20, 32), (12, 3), (6, 28), (13, 29), (21, 23), (26, 1), (27, 12), (21, 38), (14, 1), (29, 25), (23, 1), (20, 15), (34, 8), (24, 6), (19, 37), (13, 36), (15, 31), (31, 7), (7, 26), (2, 2), (15, 32), (34, 1), (8, 37), (33, 34), (31, 1), (4, 30), (17, 3), (28, 6), (27, 33), (8, 1), (21, 4), (24, 19), (25, 18), (6, 23), (30, 3), (19, 4), (22, 31), (32, 19), (11, 38), (16, 25), (27, 29), (28, 11), (30, 14), (12, 10), (8, 16), (21, 36), (27, 26), (25, 0), (22, 30), (9, 23), (20, 9), (29, 0), (6, 33), (24, 26), (34, 19), (16, 6), (33, 11), (9, 14), (15, 21), (26, 18), (25, 38), (24, 16), (12, 28), (12, 23), (10, 11), (17, 20), (16, 0), (20, 26), (19, 19), (33, 3), (21, 35), (7, 23), (7, 13), (20, 7), (33, 32), (29, 4), (29, 22), (33, 20), (29, 31), (28, 36), (31, 17), (11, 35), (12, 24), (33, 25), (28, 35), (34, 12), (4, 13), (0, 35), (20, 1), (26, 26), (3, 8), (16, 19), (6, 38), (23, 4), (19, 33), (32, 12), (17, 15), (15, 37), (34, 29), (7, 30), (23, 3), (10, 7), (10, 38), (16, 22), (10, 18), (1, 35), (20, 0), (25, 17), (26, 35), (30, 31), (15, 38), (15, 23), (28, 0), (11, 15), (32, 16), (18, 15), (9, 12), (7, 4), (5, 25), (7, 2), (3, 12), (8, 28), (5, 32), (3, 2), (2, 12), (14, 13), (18, 16), (22, 12), (31, 25), (18, 28), (31, 11), (8, 38), (29, 19), (17, 5), (24, 5), (27, 16), (17, 21), (33, 17), (9, 19), (5, 0), (17, 9), (15, 22), (9, 9), (31, 18), (30, 18), (8, 30), (24, 12), (32, 35), (30, 37), (6, 32), (1, 27), (25, 23), (34, 21), (26, 16), (22, 0), (9, 6), (26, 4), (3, 14), (5, 18), (13, 8), (7, 31), (2, 23), (17, 16), (30, 9), (14, 22), (25, 33), (9, 7), (31, 28), (7, 0), (34, 7), (4, 35), (2, 20), (18, 25), (1, 32), (15, 24), (27, 2), (12, 5), (12, 30), (1, 7), (2, 14), (32, 36), (19, 27), (20, 21), (29, 10), (0, 31), (26, 20), (21, 1), (9, 1), (17, 28), (9, 38), (17, 0), (10, 0), (4, 24), (32, 5), (0, 9), (30, 12), (21, 11), (23, 16), (7, 29), (8, 2), (6, 36), (10, 15), (17, 29), (4, 22), (2, 31), (14, 21), (16, 34), (31, 37), (26, 6), (13, 9), (24, 9), (0, 13), (23, 15), (5, 33), (28, 16), (16, 18), (12, 18), (15, 29), (8, 22), (11, 30), (21, 30), (7, 9), (9, 8), (13, 2), (13, 24), (17, 37), (33, 26), (10, 5), (0, 12), (19, 15), (16, 29), (27, 8), (7, 8), (13, 5), (26, 19), (33, 21), (23, 8), (8, 13), (29, 7), (13, 33), (7, 20), (18, 35), (14, 29), (7, 36), (5, 4), (17, 2), (2, 3), (2, 19), (24, 30), (29, 36), (10, 13), (15, 33), (27, 37), (23, 36), (8, 35), (11, 24), (1, 2), (28, 32), (8, 7), (23, 28), (22, 2), (4, 7), (18, 38), (31, 14), (14, 34), (30, 26), (6, 16), (31, 6), (10, 29), (31, 9), (2, 5), (13, 0), (32, 30), (19, 12), (21, 29), (15, 1), (30, 28), (24, 24), (1, 3), (5, 12), (34, 13), (28, 38), (18, 22), (9, 20), (26, 34), (33, 33), (19, 38), (12, 35), (24, 18), (13, 12), (10, 36), (20, 29), (25, 6), (8, 3), (23, 18), (3, 9), (13, 14), (25, 26), (26, 23), (17, 11), (17, 18), (6, 29), (12, 17), (15, 19), (30, 29), (23, 27), (3, 24), (5, 27), (13, 27), (10, 9), (32, 17), (30, 33), (31, 16), (14, 36), (12, 15), (29, 11), (5, 23), (7, 35), (2, 13), (6, 35), (18, 37), (29, 12), (0, 19), (24, 33), (11, 10), (19, 31), (23, 32), (13, 1), (21, 15), (19, 20), (26, 24), (7, 5), (29, 15), (32, 26), (24, 37), (24, 23), (23, 17), (10, 32), (31, 30), (17, 26), (8, 23), (11, 6), (29, 16), (21, 32), (11, 0), (8, 19), (18, 29), (14, 7), (34, 3), (15, 6), (32, 3), (30, 8), (22, 7), (3, 10), (3, 25), (11, 33), (10, 4), (11, 3), (15, 15), (24, 25), (16, 10), (13, 18), (24, 14), (26, 3), (11, 1), (17, 6), (29, 38), (8, 14), (14, 23), (17, 36), (14, 30), (15, 13), (22, 1), (31, 24), (27, 27), (23, 11), (19, 11), (34, 9), (8, 33), (2, 27), (33, 23), (1, 23), (2, 29), (23, 31), (29, 14), (2, 0), (6, 22), (21, 19), (27, 17), (34, 6), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "824448", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (9, 5), (26, 22), (2, 32), (26, 2), (28, 32), (18, 33), (33, 34), (29, 13), (5, 29), (11, 31), (29, 3), (16, 21), (26, 31), (1, 3), (19, 5), (18, 24), (13, 7), (3, 9), (18, 32), (25, 35), (33, 8), (11, 16), (33, 20), (20, 9), (24, 0), (4, 13), (32, 4), (33, 3), (20, 27), (9, 13), (13, 4), (4, 26), (25, 15), (27, 7), (0, 28), (16, 35), (31, 29), (22, 11), (16, 4), (22, 32), (21, 20), (2, 23), (27, 25), (30, 11), (30, 27), (17, 4), (17, 12), (28, 29), (0, 18), (1, 15), (31, 7), (2, 28), (5, 6), (32, 14), (10, 25), (2, 4), (22, 16), (24, 33), (28, 12), (12, 32), (0, 26), (14, 27), (29, 35), (7, 26), (10, 20), (7, 0), (24, 6), (12, 1), (9, 15), (25, 26), (8, 18), (13, 15), (23, 18), (10, 16), (12, 10), (18, 18), (4, 16), (23, 17), (25, 21), (19, 12), (14, 12), (20, 20), (18, 14), (2, 21), (9, 21), (4, 0), (16, 9), (18, 30), (2, 34), (32, 30), (8, 13), (0, 24), (1, 2), (3, 20), (14, 8), (26, 1), (26, 14), (13, 3), (1, 25), (22, 15), (14, 30), (16, 33), (4, 2), (0, 8), (10, 29), (8, 24), (20, 3), (32, 23), (13, 34), (1, 23), (25, 16), (3, 22), (27, 14), (11, 15), (3, 29), (24, 10), (10, 33), (18, 31), (33, 24), (5, 24), (8, 30), (15, 30), (29, 16), (14, 29), (19, 1), (8, 3), (33, 33), (30, 15), (3, 0), (9, 33), (19, 11), (19, 9), (18, 17), (13, 17), (30, 34), (6, 34), (31, 8), (9, 35), (2, 27), (26, 32), (9, 22), (7, 16), (27, 10), (7, 34), (20, 24), (7, 17), (13, 13), (8, 14), (26, 27), (7, 31), (1, 34), (19, 27), (2, 12), (8, 0), (11, 24), (15, 23), (33, 21), (14, 15), (1, 31), (20, 32), (28, 0), (31, 17), (2, 5), (5, 31), (3, 10), (13, 32), (21, 28), (9, 0), (29, 26), (16, 28), (8, 20), (1, 12), (23, 27), (10, 34), (19, 32), (29, 21), (21, 11), (9, 1), (14, 6), (9, 24), (1, 24), (26, 8), (11, 26), (12, 17), (17, 17), (31, 23), (18, 26), (9, 4), (15, 16), (6, 11), (14, 23), (25, 14), (33, 18), (8, 8), (33, 2), (8, 16), (14, 10), (21, 16), (15, 20), (2, 18), (24, 28), (12, 7), (6, 33), (9, 29), (8, 10), (20, 14), (4, 25), (3, 4), (20, 22), (30, 35), (15, 3), (3, 21), (6, 21), (33, 14), (18, 3), (1, 27), (6, 32), (20, 8), (8, 17), (28, 21), (5, 32), (26, 10), (18, 8), (22, 19), (28, 17), (3, 11), (33, 17), (8, 31), (24, 30), (3, 19), (15, 9), (11, 11), (20, 11), (14, 20), (7, 2), (2, 22), (30, 19), (18, 6), (23, 33), (16, 10), (7, 28), (21, 2), (8, 27), (19, 35), (6, 1), (6, 13), (21, 23), (1, 17), (16, 19), (6, 22), (15, 27), (17, 28), (1, 1), (17, 2), (5, 0), (0, 27), (33, 25), (8, 34), (32, 32), (1, 20), (19, 26), (21, 19), (1, 28), (3, 25), (6, 12), (11, 30), (26, 35), (27, 24), (7, 19), (29, 12), (30, 28), (9, 20), (17, 20), (12, 20), (28, 16), (23, 9), (23, 1), (13, 25), (9, 6), (15, 17), (17, 9), (20, 10), (9, 9), (19, 14), (2, 10), (33, 15), (7, 8), (10, 13), (4, 7), (15, 35), (8, 1), (8, 35), (16, 1), (27, 2), (21, 26), (19, 10), (23, 30), (1, 35), (24, 23), (28, 30), (5, 30), (6, 19), (24, 7), (18, 23), (22, 29), (10, 28), (28, 19), (7, 3), (27, 29), (4, 4), (32, 12), (13, 6), (27, 20), (2, 25), (13, 5), (26, 23), (20, 25), (2, 0), (22, 3), (7, 21), (6, 8), (14, 13), (24, 16), (26, 15), (22, 14), (11, 35), (10, 12), (9, 30), (5, 27), (16, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "896805", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 27), (11, 5), (10, 9), (27, 17), (9, 23), (8, 9), (30, 22), (27, 10), (2, 23), (16, 16), (3, 5), (8, 10), (8, 11), (5, 22), (26, 2), (2, 24), (17, 9), (20, 27), (6, 13), (20, 1), (15, 27), (9, 0), (24, 5), (8, 0), (24, 21), (16, 19), (9, 4), (8, 3), (15, 17), (1, 14), (0, 27), (1, 27), (18, 6), (8, 23), (20, 14), (2, 22), (5, 21), (4, 2), (8, 20), (29, 18), (29, 6), (30, 6), (6, 14), (17, 7), (1, 19), (30, 19), (6, 17), (5, 34), (24, 15), (25, 17), (25, 8), (10, 6), (21, 27), (28, 30), (19, 15), (28, 34), (10, 31), (17, 21), (12, 15), (17, 11), (1, 33), (31, 27), (8, 12), (2, 3), (10, 3), (22, 33), (12, 28), (14, 22), (7, 20), (21, 13), (22, 34), (4, 1), (11, 25), (8, 26), (27, 3), (28, 14), (27, 29), (17, 34), (4, 6), (21, 30), (16, 18), (28, 5), (11, 22), (0, 5), (12, 16), (21, 1), (21, 7), (3, 26), (13, 18), (8, 25), (3, 17), (5, 30), (23, 20), (9, 29), (5, 10), (21, 29), (10, 12), (31, 14), (28, 31), (23, 24), (4, 5), (20, 16), (26, 20), (26, 28), (2, 21), (13, 2), (4, 17), (1, 17), (24, 34), (14, 8), (4, 22), (20, 22), (16, 8), (31, 31), (24, 22), (21, 20), (31, 4), (15, 23), (26, 30), (17, 18), (7, 32), (19, 22), (10, 11), (14, 34), (19, 0), (26, 23), (25, 24), (11, 9), (3, 18), (4, 30), (8, 19), (22, 2), (8, 21), (31, 7), (29, 0), (3, 34), (20, 6), (20, 12), (31, 24), (29, 32), (4, 19), (20, 4), (15, 18), (27, 11), (23, 21), (24, 20), (7, 3), (21, 3), (2, 16), (17, 22), (23, 16), (27, 26), (25, 10), (5, 14), (17, 2), (9, 28), (20, 34), (11, 20), (9, 7), (19, 25), (5, 24), (9, 5), (21, 4), (3, 29), (18, 10), (28, 33), (17, 15), (1, 30), (26, 11), (7, 24), (30, 23), (13, 26), (7, 2), (3, 0), (22, 21), (29, 10), (18, 24), (16, 13), (26, 21), (6, 32), (7, 14), (27, 4), (12, 27), (22, 19), (1, 12), (7, 19), (21, 14), (3, 15), (23, 6), (26, 8), (17, 31), (8, 30), (6, 5), (3, 12), (23, 15), (22, 9), (8, 28), (25, 26), (5, 20), (1, 29), (5, 17), (5, 1), (4, 10), (19, 34), (31, 29), (24, 7), (17, 14), (20, 20), (0, 1), (12, 6), (17, 17), (25, 34), (16, 31), (29, 17), (27, 33), (19, 11), (27, 1), (7, 5), (14, 26), (9, 24), (5, 12), (30, 11), (28, 11), (16, 11), (10, 17), (18, 15), (26, 6), (9, 26), (27, 24), (31, 2), (28, 0), (7, 26), (21, 0), (18, 7), (31, 3), (4, 29), (10, 32), (0, 14), (16, 7), (20, 25), (14, 31), (10, 5), (11, 11), (7, 18), (0, 32), (17, 25), (27, 19), (17, 6), (16, 2), (12, 26), (5, 9), (8, 27), (15, 0), (10, 4), (26, 1), (22, 10), (0, 22), (12, 17), (13, 8), (29, 21), (5, 16), (11, 13), (0, 23), (20, 2), (18, 1), (13, 15), (26, 33), (30, 13), (21, 6), (31, 17), (26, 12), (19, 18), (17, 32), (0, 16), (0, 4), (24, 0), (2, 12), (6, 21), (8, 29), (12, 13), (6, 1), (29, 20), (6, 15), (25, 30), (6, 18), (30, 29), (26, 24), (30, 18), (31, 33), (14, 28), (19, 21), (21, 28), (28, 26), (18, 31), (11, 14), (13, 29), (13, 21), (1, 25), (12, 4), (25, 1), (24, 24), (0, 15), (24, 18), (22, 22), (18, 16), (16, 34), (15, 6), (13, 6), (5, 4), (0, 24), (25, 28), (7, 4), (13, 27), (25, 29), (20, 15), (12, 20), (20, 18), (15, 4), (31, 13), (30, 20), (8, 17), (25, 31), (7, 17), (8, 15), (3, 13), (26, 14), (18, 29), (23, 9), (14, 19), (19, 13), (21, 11), (4, 24), (25, 21), (2, 26), (11, 29), (25, 20), (24, 11), (0, 34), (2, 32), (24, 26), (20, 32), (2, 18), (14, 4), (3, 28), (11, 17), (9, 1), (6, 0), (14, 5), (16, 5), (10, 10), (16, 24), (21, 16), (31, 21), (5, 32), (23, 10), (5, 26), (12, 10), (5, 6), (8, 22), (15, 25), (22, 12), (31, 16), (24, 4), (26, 34), (18, 2), (31, 30), (27, 13), (17, 3), (4, 32), (20, 21), (19, 30), (23, 26), (3, 30), (13, 30), (7, 23), (15, 26), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959616", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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), (31, 0), (11, 23), (28, 4), (29, 28), (13, 12), (2, 7), (14, 26), (7, 7), (6, 22), (4, 17), (27, 24), (22, 9), (7, 29), (17, 10), (15, 4), (23, 6), (18, 28), (11, 4), (9, 11), (15, 3), (8, 17), (13, 18), (6, 23), (33, 6), (25, 22), (16, 18), (27, 10), (7, 27), (0, 15), (24, 5), (22, 14), (6, 25), (0, 3), (22, 11), (24, 14), (17, 31), (34, 5), (1, 30), (19, 19), (16, 6), (8, 27), (31, 17), (14, 16), (5, 2), (14, 29), (10, 3), (29, 23), (9, 28), (15, 6), (6, 3), (34, 24), (16, 23), (12, 26), (19, 30), (30, 6), (1, 24), (14, 24), (1, 28), (21, 6), (33, 3), (34, 17), (23, 17), (8, 8), (18, 31), (12, 12), (33, 2), (0, 17), (2, 17), (4, 0), (34, 22), (10, 30), (19, 9), (13, 27), (24, 2), (21, 4), (18, 19), (27, 15), (18, 17), (3, 28), (24, 6), (34, 23), (17, 0), (8, 1), (16, 5), (5, 5), (23, 26), (23, 9), (27, 21), (11, 28), (34, 29), (19, 8), (16, 9), (22, 26), (27, 6), (23, 24), (18, 20), (8, 30), (29, 27), (25, 18), (9, 14), (30, 8), (11, 12), (10, 22), (20, 22), (5, 3), (21, 5), (7, 10), (16, 15), (31, 9), (27, 17), (28, 3), (30, 30), (14, 4), (28, 29), (15, 2), (0, 1), (12, 30), (10, 1), (18, 27), (26, 23), (23, 25), (4, 30), (17, 5), (25, 31), (4, 28), (21, 19), (5, 6), (6, 12), (28, 18), (9, 0), (29, 9), (11, 13), (32, 0), (18, 1), (2, 21), (8, 31), (15, 23), (13, 28), (15, 24), (18, 12), (21, 10), (12, 0), (33, 25), (5, 24), (11, 25), (0, 5), (33, 18), (2, 6), (9, 18), (5, 18), (0, 16), (26, 4), (26, 11), (13, 4), (32, 2), (3, 4), (4, 29), (31, 26), (30, 19), (31, 25), (26, 3), (29, 16), (29, 4), (30, 13), (13, 8), (23, 2), (1, 26), (33, 5), (14, 21), (17, 7), (34, 20), (4, 8), (5, 30), (26, 5), (19, 18), (13, 15), (33, 26), (7, 19), (28, 6), (23, 19), (1, 31), (26, 15), (28, 27), (28, 30), (19, 28), (15, 16), (7, 8), (23, 28), (24, 0), (21, 8), (4, 26), (24, 20), (26, 24), (23, 1), (20, 17), (7, 28), (28, 11), (34, 9), (27, 9), (20, 16), (10, 13), (1, 15), (11, 14), (9, 10), (2, 30), (9, 4), (34, 28), (19, 22), (9, 7), (12, 19), (24, 3), (33, 7), (14, 14), (14, 22), (26, 1), (24, 1), (34, 6), (20, 10), (28, 16), (18, 23), (20, 28), (11, 30), (30, 18), (33, 28), (6, 0), (18, 25), (30, 15), (34, 14), (17, 9), (7, 17), (31, 2), (5, 16), (15, 20), (25, 5), (13, 31), (20, 23), (5, 20), (23, 16), (8, 26), (21, 21), (1, 3), (12, 5), (34, 19), (21, 17), (31, 1), (29, 3), (25, 7), (25, 17), (5, 17), (16, 7), (30, 22), (3, 11), (9, 9), (25, 14), (10, 6), (4, 27), (25, 27), (11, 2), (19, 7), (33, 22), (3, 30), (26, 2), (31, 13), (22, 30), (8, 4), (27, 4), (18, 7), (14, 23), (7, 21), (4, 16), (27, 12), (23, 23), (23, 22), (8, 25), (2, 5), (1, 23), (29, 17), (11, 24), (8, 13), (34, 25), (12, 11), (21, 28), (34, 18), (31, 27), (12, 18), (12, 8), (5, 0), (34, 3), (24, 9), (27, 31), (6, 16), (25, 25), (0, 12), (4, 15), (20, 27), (29, 12), (17, 19), (12, 20), (3, 2), (21, 30), (24, 23), (21, 9), (22, 29), (22, 23), (11, 29), (23, 12), (14, 12), (8, 18), (27, 13), (0, 25), (2, 14), (22, 27), (10, 16), (24, 15), (8, 16), (16, 13), (21, 11), (0, 18), (13, 24), (31, 3), (21, 27), (29, 25), (27, 20), (22, 28), (14, 30), (26, 17), (27, 16), (20, 26), (1, 11), (20, 2), (27, 7), (19, 6), (29, 31), (2, 3), (21, 22), (33, 17), (2, 11), (1, 8), (2, 24), (24, 11), (5, 25), (29, 7), (2, 0), (33, 20), (5, 9), (9, 20), (16, 17), (20, 25), (32, 16), (8, 19), (21, 16), (4, 3), (11, 15), (6, 15), (27, 30), (2, 13), (21, 31), (24, 16), (4, 4), (17, 1), (15, 10), (2, 12), (11, 17), (2, 20), (31, 11), (8, 2), (13, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "807696", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (19, 0), (15, 18), (1, 8), (35, 29), (11, 36), (22, 18), (14, 27), (17, 3), (26, 10), (29, 7), (2, 9), (20, 9), (6, 24), (17, 17), (9, 0), (23, 7), (19, 4), (22, 37), (13, 12), (27, 24), (15, 29), (24, 35), (10, 10), (1, 37), (37, 33), (33, 12), (4, 18), (20, 33), (36, 4), (23, 38), (7, 20), (27, 19), (7, 36), (30, 19), (16, 25), (32, 37), (37, 18), (5, 5), (35, 25), (6, 19), (9, 7), (38, 6), (29, 26), (5, 33), (26, 22), (34, 7), (10, 31), (20, 29), (2, 21), (1, 28), (37, 5), (0, 15), (11, 26), (27, 0), (23, 11), (27, 9), (23, 15), (18, 15), (18, 11), (6, 14), (6, 13), (8, 37), (33, 36), (31, 9), (8, 0), (20, 14), (19, 13), (24, 17), (6, 7), (11, 18), (1, 4), (34, 30), (13, 20), (19, 29), (20, 35), (13, 30), (31, 17), (18, 28), (25, 31), (9, 19), (32, 5), (16, 10), (28, 4), (35, 11), (11, 3), (21, 3), (26, 27), (37, 21), (6, 22), (36, 12), (15, 22), (13, 15), (14, 35), (30, 0), (21, 13), (37, 35), (11, 37), (9, 8), (12, 12), (24, 32), (12, 29), (12, 35), (16, 28), (4, 37), (14, 18), (30, 18), (21, 19), (29, 9), (12, 9), (9, 1), (11, 38), (28, 1), (2, 26), (9, 22), (35, 7), (31, 22), (3, 7), (14, 26), (6, 11), (22, 28), (7, 4), (21, 21), (18, 32), (12, 38), (12, 3), (22, 13), (32, 11), (0, 26), (31, 6), (20, 31), (15, 20), (13, 11), (21, 18), (21, 14), (4, 21), (0, 28), (4, 9), (31, 11), (38, 35), (22, 29), (2, 28), (5, 21), (10, 7), (3, 25), (30, 11), (7, 0), (28, 6), (30, 15), (34, 4), (11, 5), (27, 21), (4, 13), (1, 13), (38, 16), (22, 10), (21, 37), (36, 27), (18, 23), (23, 8), (38, 24), (18, 19), (5, 6), (30, 21), (6, 1), (17, 34), (1, 3), (21, 38), (33, 23), (31, 8), (34, 5), (18, 13), (32, 13), (12, 6), (11, 32), (12, 26), (29, 35), (11, 20), (5, 35), (37, 38), (12, 30), (33, 6), (10, 19), (24, 33), (23, 4), (20, 15), (3, 38), (14, 22), (12, 20), (36, 22), (34, 19), (34, 2), (8, 16), (19, 26), (3, 18), (15, 13), (18, 34), (31, 37), (0, 24), (17, 31), (10, 14), (5, 7), (16, 35), (26, 15), (12, 15), (6, 31), (35, 13), (8, 24), (8, 22), (25, 9), (21, 11), (20, 23), (33, 35), (11, 33), (2, 23), (7, 22), (16, 2), (7, 2), (31, 4), (15, 19), (0, 17), (4, 11), (33, 28), (37, 36), (18, 0), (30, 13), (4, 1), (19, 8), (23, 13), (18, 2), (0, 29), (13, 5), (36, 1), (13, 25), (24, 30), (8, 18), (9, 31), (17, 27), (18, 25), (21, 8), (29, 28), (23, 3), (1, 35), (11, 28), (12, 16), (31, 0), (28, 29), (3, 3), (22, 19), (8, 2), (5, 15), (16, 19), (26, 23), (25, 8), (20, 24), (15, 17), (6, 6), (17, 25), (3, 35), (35, 5), (10, 16), (26, 9), (17, 0), (28, 26), (7, 37), (11, 7), (0, 1), (21, 20), (4, 6), (6, 28), (38, 31), (34, 17), (11, 0), (2, 11), (24, 13), (35, 19), (18, 16), (3, 33), (24, 7), (17, 14), (10, 2), (9, 11), (32, 22), (12, 36), (31, 7), (12, 0), (36, 8), (18, 36), (5, 34), (26, 30), (38, 2), (3, 0), (5, 1), (9, 32), (22, 24), (13, 29), (2, 34), (22, 8), (24, 27), (8, 33), (11, 4), (27, 34), (38, 36), (30, 6), (30, 34), (30, 28), (35, 10), (5, 18), (26, 20), (31, 26), (24, 9), (21, 6), (24, 21), (2, 22), (35, 31), (23, 18), (7, 21), (0, 38), (11, 16), (17, 11), (36, 23), (38, 18), (22, 23), (33, 30), (8, 10), (28, 28), (33, 34), (10, 20), (33, 27), (32, 20), (29, 22), (29, 14), (0, 7), (33, 8), (20, 16), (25, 7), (16, 17), (6, 33), (21, 27), (9, 37), (37, 34), (32, 35), (24, 12), (9, 23), (35, 17), (32, 25), (5, 12), (14, 0), (15, 16), (8, 13), (26, 29), (21, 7), (6, 21), (22, 4), (35, 1), (18, 1), (4, 23), (3, 34), (28, 14), (20, 30), (17, 6), (37, 29), (20, 22), (32, 12), (14, 21), (4, 31), (0, 36), (14, 36), (5, 19), (16, 14), (35, 37), (25, 37), (24, 2), (10, 15), (14, 7), (10, 18), (15, 23), (3, 14), (36, 17), (32, 1), (1, 22), (13, 26), (5, 0), (19, 7), (35, 21), (28, 22), (7, 30), (3, 31), (27, 18), (26, 11), (22, 11), (18, 26), (36, 24), (27, 26), (9, 26), (26, 18), (4, 19), (26, 33), (28, 16), (22, 26), (5, 14), (10, 17), (27, 4), (17, 15), (1, 20), (10, 5), (14, 17), (20, 38), (14, 8), (13, 24), (35, 14), (25, 32), (0, 3), (0, 14), (20, 37), (31, 33), (14, 6), (18, 37), (27, 36), (27, 31), (14, 20), (28, 15), (37, 19), (1, 30), (20, 12), (32, 3), (14, 10), (23, 28), (5, 3), (28, 9), (0, 27), (29, 20), (35, 36), (15, 9), (35, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "413440", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 35), (11, 3), (14, 28), (11, 21), (14, 13), (22, 34), (17, 21), (14, 29), (18, 9), (15, 15), (12, 8), (16, 34), (4, 29), (5, 9), (28, 29), (25, 21), (25, 18), (8, 0), (23, 26), (3, 2), (29, 35), (3, 32), (23, 29), (1, 16), (19, 18), (6, 1), (3, 17), (7, 30), (16, 38), (18, 6), (13, 38), (27, 30), (27, 32), (0, 26), (2, 3), (17, 1), (10, 22), (10, 28), (22, 6), (18, 32), (8, 9), (28, 11), (23, 8), (2, 34), (24, 13), (18, 8), (14, 32), (12, 29), (28, 21), (1, 18), (0, 33), (13, 33), (2, 33), (15, 24), (11, 35), (4, 34), (21, 20), (12, 15), (11, 13), (29, 20), (20, 6), (24, 1), (15, 0), (16, 18), (15, 6), (12, 37), (9, 28), (27, 35), (2, 21), (13, 4), (24, 37), (19, 1), (18, 24), (10, 4), (21, 0), (19, 35), (6, 34), (3, 21), (8, 35), (24, 24), (21, 19), (14, 18), (28, 14), (19, 6), (24, 14), (27, 29), (19, 22), (18, 35), (1, 25), (29, 1), (17, 2), (17, 26), (10, 5), (11, 4), (7, 24), (23, 9), (5, 30), (14, 9), (2, 24), (1, 36), (23, 23), (11, 12), (24, 9), (26, 20), (13, 30), (10, 8), (5, 25), (27, 13), (0, 34), (16, 2), (18, 28), (16, 28), (26, 34), (6, 28), (27, 37), (9, 31), (24, 28), (9, 11), (20, 35), (29, 6), (15, 2), (21, 32), (16, 35), (1, 23), (9, 33), (19, 19), (15, 23), (13, 18), (24, 16), (11, 28), (22, 14), (3, 26), (21, 7), (2, 29), (10, 6), (28, 4), (10, 9), (19, 28), (14, 30), (20, 20), (28, 28), (22, 38), (16, 4), (6, 12), (11, 19), (10, 16), (26, 27), (23, 17), (21, 14), (15, 38), (0, 20), (11, 1), (25, 7), (26, 13), (0, 30), (12, 32), (4, 36), (6, 35), (8, 38), (28, 15), (19, 26), (13, 25), (9, 6), (20, 19), (18, 26), (5, 33), (24, 27), (7, 25), (12, 7), (8, 31), (26, 6), (29, 33), (21, 13), (29, 14), (2, 35), (11, 2), (7, 0), (7, 19), (12, 2), (10, 27), (8, 17), (0, 17), (25, 34), (14, 21), (15, 32), (11, 34), (6, 24), (4, 35), (13, 34), (10, 24), (25, 9), (20, 4), (18, 25), (2, 9), (10, 17), (7, 12), (8, 29), (19, 27), (21, 3), (23, 14), (26, 32), (22, 23), (19, 8), (16, 8), (7, 7), (1, 3), (27, 24), (0, 3), (4, 24), (7, 22), (20, 34), (16, 30), (25, 36), (25, 26), (26, 26), (22, 11), (25, 13), (23, 24), (9, 17), (3, 13), (1, 11), (3, 37), (12, 25), (9, 9), (29, 19), (25, 37), (17, 23), (10, 20), (19, 33), (0, 11), (21, 17), (6, 16), (6, 5), (14, 27), (14, 8), (16, 17), (16, 27), (10, 14), (29, 24), (26, 1), (12, 5), (11, 10), (8, 19), (22, 15), (20, 2), (2, 17), (9, 25), (21, 34), (19, 14), (25, 8), (15, 3), (29, 7), (17, 30), (13, 24), (24, 5), (13, 1), (6, 13), (11, 30), (6, 21), (24, 25), (25, 2), (17, 3), (24, 2), (5, 17), (9, 5), (25, 31), (5, 16), (1, 38), (20, 36), (4, 11), (8, 18), (1, 4), (11, 16), (16, 11), (10, 29), (18, 30), (14, 33), (29, 28), (25, 27), (27, 22), (15, 33), (26, 36), (7, 5), (10, 33), (20, 27), (24, 32), (20, 32), (5, 28), (13, 5), (26, 31), (9, 34), (2, 4), (29, 25), (12, 23), (19, 32), (27, 11), (27, 36), (19, 31), (8, 37), (23, 6), (5, 26), (12, 12), (28, 37), (27, 20), (1, 33), (15, 9), (23, 20), (15, 5), (6, 30), (6, 17), (28, 0), (4, 12), (11, 20), (15, 14), (1, 35), (15, 4), (0, 27), (8, 34), (17, 28), (9, 38), (7, 16), (12, 36), (25, 17), (13, 35), (18, 33), (12, 35), (26, 35), (12, 30), (1, 21), (14, 35), (19, 23), (9, 18), (28, 32), (5, 20), (25, 28), (13, 32), (26, 5), (3, 35), (17, 7), (2, 14), (17, 24), (21, 10), (24, 23), (0, 25), (23, 2), (20, 9), (10, 1), (17, 31), (6, 23), (27, 8), (19, 29), (17, 14), (27, 18), (5, 15), (21, 36), (29, 4), (9, 20), (19, 7), (10, 3), (10, 2), (10, 12), (26, 2), (24, 36), (7, 14), (11, 29), (27, 15), (6, 4), (28, 2), (10, 0), (25, 0), (17, 11), (7, 38), (13, 8), (1, 26), (11, 8), (20, 3), (25, 25), (13, 3), (17, 18), (2, 30), (15, 22), (6, 32), (14, 34), (14, 11), (22, 36), (23, 4), (18, 4), (9, 23), (4, 33), (2, 37), (3, 16), (3, 27), (14, 23), (1, 29), (1, 12), (28, 26), (21, 23), (23, 38), (13, 37), (27, 38), (16, 33), (29, 29), (17, 34), (18, 36), (13, 7), (4, 26), (20, 33), (4, 37), (26, 9), (8, 30), (22, 8), (4, 19), (15, 28), (26, 29), (27, 31), (19, 3), (2, 27), (20, 25), (20, 14), (12, 34), (3, 12), (24, 15), (1, 32), (7, 35), (15, 20), (1, 2), (18, 12), (3, 29), (10, 21), (13, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530348", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), 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, 23), (6, 14), (22, 1), (36, 5), (27, 10), (26, 24), (1, 30), (8, 13), (6, 8), (18, 33), (1, 6), (22, 13), (21, 16), (25, 21), (11, 9), (26, 4), (23, 0), (15, 0), (20, 19), (20, 30), (28, 24), (35, 6), (32, 4), (5, 22), (2, 34), (27, 27), (1, 14), (38, 20), (29, 11), (22, 24), (20, 14), (5, 1), (9, 11), (25, 18), (23, 5), (0, 25), (27, 13), (30, 18), (38, 31), (1, 34), (7, 30), (13, 15), (3, 12), (18, 22), (31, 4), (34, 27), (13, 34), (11, 10), (9, 7), (7, 15), (16, 28), (9, 33), (36, 30), (23, 17), (18, 30), (6, 5), (29, 25), (9, 9), (37, 26), (31, 10), (32, 15), (15, 28), (5, 28), (33, 1), (6, 26), (1, 17), (20, 18), (29, 23), (12, 1), (4, 29), (14, 20), (24, 1), (7, 12), (28, 12), (33, 31), (23, 12), (10, 17), (18, 2), (9, 15), (11, 30), (21, 15), (11, 14), (37, 17), (30, 31), (28, 30), (9, 34), (6, 0), (29, 16), (3, 3), (2, 30), (7, 34), (14, 14), (7, 27), (11, 17), (32, 23), (30, 7), (15, 12), (6, 23), (9, 29), (33, 18), (34, 14), (35, 27), (10, 32), (20, 7), (26, 1), (6, 3), (29, 32), (14, 9), (29, 22), (37, 27), (13, 9), (25, 14), (16, 19), (37, 28), (10, 11), (28, 4), (7, 20), (20, 23), (1, 29), (3, 14), (18, 28), (12, 8), (38, 16), (23, 30), (1, 23), (22, 12), (12, 14), (30, 9), (38, 12), (34, 17), (32, 27), (4, 32), (23, 7), (9, 32), (13, 22), (11, 13), (38, 14), (29, 24), (7, 31), (22, 25), (14, 5), (8, 10), (32, 9), (6, 15), (36, 0), (14, 27), (30, 1), (33, 28), (38, 26), (16, 32), (16, 23), (2, 14), (28, 8), (17, 19), (17, 21), (34, 8), (23, 25), (19, 3), (9, 16), (22, 17), (1, 33), (10, 26), (6, 6), (26, 22), (14, 13), (32, 3), (21, 8), (38, 22), (8, 24), (3, 26), (9, 22), (6, 32), (37, 3), (29, 10), (32, 34), (33, 9), (35, 19), (37, 11), (26, 16), (1, 22), (2, 6), (17, 29), (18, 17), (38, 21), (16, 31), (27, 29), (14, 8), (19, 13), (9, 17), (25, 9), (9, 3), (15, 11), (10, 1), (19, 21), (8, 6), (8, 15), (35, 34), (15, 29), (12, 34), (6, 27), (22, 3), (14, 34), (29, 9), (28, 28), (0, 16), (19, 32), (14, 12), (32, 18), (36, 8), (2, 2), (4, 26), (23, 13), (33, 7), (35, 28), (29, 33), (24, 6), (13, 10), (26, 10), (8, 9), (34, 15), (31, 34), (10, 22), (21, 22), (36, 25), (35, 17), (14, 19), (8, 19), (29, 0), (31, 14), (38, 24), (26, 3), (12, 20), (18, 27), (16, 22), (22, 31), (17, 25), (9, 0), (16, 13), (1, 25), (36, 10), (19, 27), (2, 33), (19, 29), (4, 12), (27, 30), (27, 0), (22, 15), (22, 23), (5, 8), (27, 21), (27, 12), (3, 25), (16, 20), (32, 16), (30, 11), (13, 19), (6, 16), (11, 6), (34, 11), (10, 27), (9, 12), (8, 21), (32, 33), (38, 27), (12, 19), (16, 4), (10, 20), (13, 30), (4, 30), (5, 0), (30, 4), (26, 33), (2, 18), (3, 4), (8, 25), (35, 0), (36, 6), (10, 15), (33, 16), (31, 31), (32, 25), (36, 22), (16, 29), (15, 2), (33, 12), (11, 29), (24, 33), (15, 17), (18, 32), (20, 17), (23, 34), (7, 19), (24, 13), (31, 20), (11, 20), (27, 4), (2, 31), (11, 0), (10, 8), (12, 6), (7, 22), (12, 27), (3, 34), (4, 10), (38, 33), (9, 13), (32, 2), (3, 30), (11, 4), (20, 1), (36, 28), (5, 9), (16, 10), (36, 15), (9, 31), (33, 22), (27, 7), (11, 24), (9, 26), (7, 33), (21, 26), (19, 25), (0, 1), (10, 4), (6, 21), (21, 29), (26, 12), (32, 6), (26, 27), (14, 16), (21, 18), (35, 1), (25, 16), (28, 10), (25, 28), (11, 31), (20, 21), (0, 22), (3, 9), (32, 7), (31, 1), (36, 11), (22, 21), (18, 34), (35, 25), (6, 24), (9, 2), (8, 4), (3, 11), (4, 1), (35, 30), (23, 11), (37, 22), (32, 28), (3, 8), (17, 5), (33, 13), (35, 8), (34, 1), (34, 16), (17, 34), (4, 24), (29, 13), (38, 0), (14, 26), (25, 8), (12, 24), (21, 5), (38, 18), (35, 29), (31, 32), (2, 23), (8, 14), (35, 18), (17, 13), (32, 31), (23, 23), (11, 2), (27, 32), (25, 0), (28, 29), (24, 4), (26, 21), (20, 9), (22, 27), (25, 29), (38, 30), (12, 4), (32, 20), (12, 29), (8, 28), (22, 30), (19, 6), (3, 28), (32, 24), (26, 15), (13, 32), (4, 33), (5, 34), (19, 17), (24, 19), (20, 3), (20, 4), (29, 19), (17, 9), (23, 28), (14, 3), (0, 4), (37, 6), (33, 24), (29, 21), (14, 31), (29, 17), (4, 8), (38, 3), (27, 34), (15, 3), (34, 5), (26, 0), (14, 24), (31, 33), (17, 8), (29, 7), (3, 0), (20, 29), (15, 20), (32, 10), (32, 30), (4, 34), (28, 25), (2, 0), (7, 25), (20, 0), (7, 1), (37, 18), (30, 19), (20, 24), (28, 16), (30, 22), (27, 28), (10, 29), (13, 29), (37, 8), (18, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866304", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 16), (18, 22), (0, 9), (18, 4), (7, 20), (31, 17), (14, 8), (29, 27), (26, 19), (4, 7), (25, 7), (3, 17), (0, 3), (10, 11), (26, 6), (9, 13), (8, 0), (16, 15), (14, 5), (19, 10), (20, 10), (31, 8), (18, 24), (13, 22), (31, 18), (22, 4), (24, 20), (28, 18), (23, 25), (26, 11), (6, 28), (8, 11), (0, 10), (21, 7), (19, 4), (24, 27), (24, 21), (20, 30), (8, 18), (2, 4), (27, 19), (19, 21), (25, 13), (18, 21), (6, 14), (24, 6), (24, 22), (23, 27), (17, 28), (26, 13), (5, 5), (2, 8), (10, 30), (27, 12), (12, 11), (10, 19), (24, 24), (29, 2), (24, 3), (0, 4), (28, 26), (1, 4), (3, 20), (10, 0), (21, 1), (7, 22), (16, 4), (29, 0), (16, 13), (6, 18), (12, 0), (21, 30), (13, 17), (8, 26), (6, 19), (1, 5), (13, 26), (23, 0), (20, 26), (19, 19), (27, 1), (5, 7), (28, 15), (25, 8), (10, 26), (13, 8), (3, 24), (25, 30), (5, 24), (27, 27), (31, 19), (16, 5), (7, 26), (20, 25), (6, 0), (5, 3), (17, 14), (5, 19), (29, 16), (1, 7), (28, 22), (20, 9), (8, 10), (28, 9), (29, 23), (0, 28), (16, 14), (30, 10), (29, 10), (17, 24), (21, 22), (10, 15), (24, 14), (3, 30), (11, 22), (15, 8), (21, 0), (22, 7), (28, 7), (8, 9), (9, 29), (14, 26), (15, 15), (11, 12), (2, 10), (30, 0), (21, 14), (10, 1), (21, 28), (9, 18), (28, 27), (7, 12), (28, 11), (22, 6), (31, 6), (27, 24), (12, 21), (14, 22), (11, 28), (14, 11), (17, 6), (21, 27), (0, 17), (11, 30), (1, 23), (13, 28), (8, 16), (13, 23), (3, 23), (1, 10), (25, 28), (31, 28), (9, 21), (9, 19), (18, 19), (7, 27), (22, 27), (14, 30), (31, 25), (22, 23), (24, 0), (6, 21), (14, 17), (30, 16), (10, 20), (17, 0), (16, 1), (15, 21), (18, 11), (7, 9), (21, 6), (14, 15), (14, 2), (2, 6), (12, 27), (22, 17), (3, 0), (5, 21), (17, 23), (2, 18), (8, 3), (19, 6), (3, 1), (9, 3), (31, 23), (22, 16), (2, 13), (10, 17), (17, 1), (29, 18), (10, 7), (9, 28), (20, 4), (29, 28), (15, 18), (10, 23), (24, 8), (19, 3), (25, 21), (26, 18), (15, 17), (23, 14), (25, 0), (17, 29), (31, 21), (14, 10), (11, 14), (7, 18), (30, 3), (0, 7), (15, 30), (18, 20), (0, 1), (0, 18), (5, 1), (24, 17), (3, 4), (5, 18), (9, 24), (25, 27), (18, 5), (5, 6), (7, 3), (20, 20), (19, 27), (22, 20), (2, 29), (7, 11), (22, 13), (22, 22), (27, 9), (4, 30), (24, 29), (0, 26), (30, 14), (18, 14), (31, 7), (1, 17), (16, 8), (13, 18), (22, 1), (11, 23), (30, 6), (4, 27), (27, 11), (14, 7), (12, 8), (6, 27), (5, 10), (30, 21), (29, 4), (30, 12), (29, 17), (31, 0), (8, 22), (0, 22), (13, 4), (6, 29), (29, 26), (11, 17), (2, 25), (3, 2), (9, 30), (8, 5), (1, 2), (15, 16), (24, 19), (30, 5), (17, 22), (10, 3), (15, 2), (26, 21), (7, 14), (13, 15), (7, 23), (13, 21), (22, 28), (12, 14), (5, 13), (27, 5), (8, 14), (29, 13), (1, 29), (12, 26), (19, 26), (28, 23), (3, 9), (23, 30), (31, 26), (19, 12), (14, 3), (28, 1), (1, 9), (16, 27), (11, 15), (5, 12), (6, 5), (13, 10), (6, 22), (7, 6), (18, 9), (18, 26), (7, 29), (30, 26), (2, 7), (1, 16), (15, 11), (2, 11), (9, 9), (18, 15), (28, 12), (28, 19), (29, 21), (22, 25), (15, 26), (5, 8), (17, 3), (27, 18), (14, 18), (24, 18), (30, 29), (16, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876960", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), 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), (0, 5), (23, 1), (16, 25), (16, 32), (6, 2), (26, 31), (8, 3), (35, 33), (6, 26), (1, 6), (29, 25), (5, 5), (19, 27), (34, 13), (21, 28), (21, 20), (19, 32), (10, 17), (13, 34), (7, 6), (11, 22), (25, 20), (15, 19), (31, 27), (32, 20), (0, 7), (7, 34), (22, 31), (37, 31), (36, 19), (26, 17), (1, 26), (1, 33), (27, 7), (3, 30), (29, 20), (16, 30), (9, 29), (25, 33), (4, 1), (20, 27), (27, 0), (13, 21), (14, 11), (24, 2), (26, 13), (20, 5), (25, 5), (16, 26), (22, 9), (1, 7), (20, 34), (7, 25), (31, 5), (14, 8), (23, 17), (0, 18), (36, 10), (8, 29), (37, 16), (27, 25), (29, 21), (17, 1), (18, 34), (29, 18), (5, 15), (1, 21), (24, 7), (18, 25), (15, 3), (21, 13), (0, 14), (21, 11), (16, 21), (28, 33), (16, 10), (13, 15), (17, 26), (25, 21), (4, 26), (19, 11), (37, 27), (12, 6), (26, 2), (4, 11), (32, 15), (11, 29), (13, 9), (29, 7), (32, 10), (33, 3), (28, 24), (5, 19), (14, 6), (36, 8), (21, 6), (12, 2), (5, 14), (1, 5), (2, 27), (20, 0), (34, 18), (31, 23), (7, 24), (27, 26), (22, 3), (23, 4), (2, 30), (17, 22), (27, 31), (21, 33), (4, 22), (15, 9), (16, 27), (7, 7), (27, 9), (32, 16), (4, 9), (23, 16), (34, 27), (14, 12), (11, 19), (4, 7), (18, 22), (24, 32), (31, 9), (18, 6), (30, 25), (27, 30), (37, 23), (33, 22), (13, 25), (4, 5), (28, 27), (26, 9), (10, 25), (33, 23), (23, 24), (2, 7), (33, 27), (25, 22), (25, 1), (36, 15), (26, 33), (18, 11), (6, 21), (19, 2), (14, 4), (7, 1), (31, 28), (37, 18), (15, 25), (29, 23), (6, 6), (4, 31), (19, 21), (8, 16), (10, 9), (8, 5), (30, 18), (10, 10), (12, 14), (8, 30), (5, 18), (8, 13), (23, 34), (34, 8), (5, 23), (27, 19), (5, 10), (20, 10), (21, 1), (33, 7), (26, 12), (16, 28), (32, 14), (1, 25), (27, 33), (3, 21), (1, 0), (25, 7), (21, 12), (36, 25), (33, 33), (29, 12), (32, 32), (3, 28), (7, 8), (30, 14), (19, 23), (1, 11), (0, 33), (15, 29), (16, 20), (16, 9), (18, 18), (21, 22), (6, 19), (20, 2), (29, 1), (28, 7), (9, 24), (0, 21), (11, 31), (5, 16), (20, 32), (10, 5), (10, 14), (5, 20), (28, 4), (35, 14), (28, 3), (33, 13), (15, 30), (13, 0), (30, 8), (31, 2), (23, 5), (24, 17), (7, 22), (8, 12), (19, 22), (21, 8), (14, 14), (21, 5), (14, 25), (20, 19), (33, 21), (12, 4), (29, 16), (36, 29), (29, 5), (36, 1), (11, 28), (35, 27), (19, 9), (35, 9), (13, 4), (29, 26), (29, 31), (18, 13), (28, 20), (0, 13), (30, 29), (5, 26), (31, 0), (32, 6), (12, 10), (29, 3), (31, 1), (19, 16), (35, 6), (7, 32), (0, 15), (10, 2), (22, 10), (7, 31), (0, 4), (37, 4), (14, 22), (0, 29), (34, 11), (31, 19), (27, 28), (15, 6), (1, 23), (10, 16), (36, 20), (18, 27), (3, 9), (25, 19), (32, 21), (17, 7), (9, 20), (18, 19), (27, 22), (33, 18), (28, 34), (20, 17), (7, 20), (1, 34), (25, 6), (24, 23), (31, 18), (14, 20), (15, 18), (10, 18), (30, 11), (36, 26), (7, 15), (26, 16), (35, 28), (17, 29), (9, 11), (1, 4), (0, 34), (1, 27), (35, 3), (24, 6), (34, 34), (26, 27), (25, 2), (28, 8), (26, 1), (19, 3), (15, 2), (22, 17), (31, 26), (33, 29), (16, 7), (31, 14), (26, 22), (19, 17), (12, 5), (36, 28), (9, 8), (34, 28), (33, 17), (0, 6), (13, 30), (5, 12), (24, 19), (34, 21), (23, 26), (17, 3), (8, 9), (4, 6), (24, 9), (37, 7), (21, 24), (4, 19), (10, 30), (16, 14), (1, 8), (21, 9), (15, 4), (6, 22), (35, 19), (37, 6), (12, 29), (14, 3), (33, 24), (21, 25), (21, 29), (20, 7), (25, 12), (11, 12), (34, 5), (26, 8), (15, 16), (22, 2), (4, 10), (2, 3), (33, 26), (19, 29), (31, 32), (7, 3), (14, 32), (29, 24), (20, 26), (2, 31), (9, 17), (7, 26), (10, 21), (17, 15), (3, 20), (1, 2), (10, 15), (13, 19), (25, 26), (33, 14), (30, 6), (22, 26), (0, 17), (29, 13), (21, 0), (5, 0), (28, 32), (18, 14), (37, 20), (8, 33), (10, 28), (25, 18), (30, 0), (33, 2), (1, 31), (17, 19), (35, 22), (35, 0), (23, 31), (31, 8), (1, 18), (18, 29), (3, 22), (30, 1), (19, 14), (4, 21), (30, 23), (6, 27), (10, 27), (18, 31), (31, 3), (35, 11), (25, 3), (15, 1), (1, 28), (24, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "806112", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), 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), (28, 5), (8, 2), (25, 32), (0, 4), (20, 0), (29, 3), (2, 4), (29, 21), (17, 9), (4, 18), (4, 11), (2, 23), (28, 36), (7, 18), (21, 12), (8, 23), (9, 12), (14, 25), (30, 16), (0, 23), (32, 24), (23, 30), (13, 16), (17, 28), (8, 4), (8, 36), (6, 8), (21, 13), (30, 20), (6, 28), (6, 7), (12, 14), (4, 24), (5, 21), (32, 1), (6, 16), (13, 27), (28, 26), (13, 38), (4, 34), (11, 27), (12, 36), (15, 34), (17, 12), (4, 19), (19, 35), (3, 35), (11, 11), (10, 23), (22, 3), (21, 34), (32, 28), (26, 35), (21, 33), (27, 37), (25, 33), (15, 12), (27, 15), (23, 21), (10, 9), (11, 14), (17, 24), (20, 36), (21, 19), (2, 36), (14, 30), (2, 11), (1, 27), (8, 31), (3, 0), (16, 1), (14, 36), (28, 8), (22, 24), (18, 33), (15, 8), (28, 12), (12, 31), (29, 24), (4, 16), (23, 27), (15, 4), (2, 3), (23, 31), (16, 18), (19, 21), (26, 17), (3, 3), (2, 1), (16, 38), (26, 32), (11, 20), (21, 9), (11, 34), (7, 34), (20, 25), (14, 38), (17, 27), (17, 35), (18, 8), (1, 5), (23, 19), (3, 37), (11, 22), (4, 21), (25, 10), (22, 35), (17, 32), (15, 22), (2, 24), (30, 3), (5, 36), (13, 29), (16, 4), (13, 17), (19, 29), (2, 31), (8, 35), (20, 5), (4, 6), (2, 0), (28, 23), (16, 10), (21, 6), (9, 9), (16, 20), (32, 3), (24, 32), (27, 28), (11, 35), (13, 7), (14, 10), (21, 4), (28, 34), (5, 32), (24, 27), (29, 22), (8, 32), (6, 2), (31, 25), (20, 16), (4, 30), (12, 11), (10, 0), (12, 12), (6, 14), (31, 30), (29, 19), (6, 0), (26, 33), (8, 27), (6, 25), (4, 9), (10, 5), (22, 11), (1, 33), (7, 25), (22, 21), (17, 15), (31, 4), (5, 26), (2, 18), (0, 26), (16, 2), (1, 22), (3, 15), (28, 13), (17, 18), (32, 4), (27, 5), (32, 30), (17, 33), (32, 35), (21, 15), (4, 28), (18, 4), (16, 28), (27, 8), (1, 32), (23, 38), (19, 23), (31, 10), (17, 31), (23, 18), (4, 38), (21, 1), (20, 32), (21, 35), (26, 30), (4, 33), (0, 20), (5, 29), (10, 33), (10, 8), (22, 9), (26, 29), (15, 16), (27, 19), (5, 14), (25, 28), (9, 18), (24, 16), (25, 7), (24, 11), (30, 15), (30, 5), (11, 28), (23, 14), (14, 4), (3, 24), (30, 4), (23, 0), (12, 20), (24, 24), (8, 13), (23, 13), (27, 22), (3, 8), (32, 20), (0, 3), (22, 32), (26, 12), (3, 17), (9, 28), (24, 36), (18, 26), (19, 15), (12, 24), (1, 23), (29, 5), (4, 29), (27, 16), (17, 0), (1, 25), (30, 30), (19, 9), (23, 23), (8, 16), (13, 21), (19, 6), (8, 10), (31, 23), (24, 21), (10, 24), (20, 8), (12, 3), (18, 32), (24, 17), (18, 29), (13, 9), (27, 34), (28, 11), (18, 15), (15, 21), (10, 31), (11, 0), (28, 22), (6, 22), (1, 36), (24, 2), (1, 28), (11, 10), (20, 11), (7, 3), (2, 34), (12, 35), (16, 24), (12, 30), (3, 22), (13, 33), (24, 38), (29, 38), (5, 12), (12, 15), (2, 27), (9, 1), (6, 12), (30, 7), (23, 5), (4, 15), (11, 3), (24, 26), (28, 14), (14, 29), (8, 6), (3, 1), (4, 23), (24, 33), (15, 17), (4, 12), (26, 10), (23, 33), (13, 37), (23, 28), (30, 0), (5, 24), (11, 24), (31, 2), (30, 13), (23, 20), (22, 6), (22, 23), (0, 31), (10, 10), (29, 37), (14, 22), (22, 33), (0, 10), (5, 3), (14, 28), (25, 34), (26, 22), (5, 37), (15, 0), (27, 9), (2, 19), (27, 35), (17, 23), (5, 30), (25, 38), (14, 17), (8, 34), (2, 35), (12, 28), (7, 21), (28, 16), (32, 6), (29, 30), (22, 27), (0, 5), (32, 37), (0, 15), (11, 4), (28, 2), (8, 22), (31, 36), (15, 15), (10, 7), (2, 22), (14, 15), (24, 10), (21, 26), (3, 6), (29, 26), (24, 25), (5, 19), (7, 12), (17, 11), (12, 9), (7, 13), (14, 33), (29, 29), (9, 10), (10, 26), (7, 20), (15, 25), (14, 3), (30, 6), (32, 27), (24, 3), (14, 16), (25, 35), (11, 19), (20, 29), (25, 29), (14, 2), (30, 25), (30, 24), (19, 32), (12, 16), (8, 17), (11, 37), (32, 32), (28, 0), (3, 18), (30, 11), (18, 25), (9, 22), (13, 34), (14, 14), (28, 38), (29, 27), (25, 24), (23, 16), (27, 26), (0, 34), (13, 12), (5, 11), (22, 19), (25, 13), (6, 36), (17, 14), (25, 25), (31, 9), (13, 6), (7, 17), (30, 2), (21, 28), (30, 23), (13, 13), (15, 36), (18, 1), (20, 18), (18, 21), (27, 33), (26, 5), (3, 28), (5, 2), (24, 13), (28, 15), (21, 37), (4, 17), (10, 27), (6, 37), (24, 7), (25, 21), (7, 0), (25, 20), (5, 31), (23, 26), (6, 19), (18, 9), (1, 10), (30, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278784", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), 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), (23, 3), (28, 2), (35, 22), (15, 14), (21, 16), (33, 5), (33, 27), (37, 23), (17, 19), (11, 20), (2, 3), (9, 22), (26, 21), (13, 25), (8, 17), (28, 15), (37, 22), (7, 13), (0, 20), (13, 18), (14, 9), (4, 7), (22, 4), (3, 7), (18, 26), (5, 11), (22, 19), (22, 1), (14, 20), (31, 8), (32, 19), (31, 15), (21, 7), (10, 17), (9, 20), (25, 4), (2, 10), (19, 5), (22, 21), (36, 1), (25, 24), (30, 9), (35, 23), (12, 15), (31, 27), (15, 28), (3, 4), (7, 16), (12, 19), (8, 6), (6, 23), (30, 16), (1, 19), (2, 7), (10, 0), (19, 26), (25, 26), (35, 15), (1, 25), (19, 25), (31, 18), (27, 6), (5, 6), (4, 20), (36, 8), (1, 6), (2, 22), (9, 4), (15, 6), (20, 28), (8, 20), (21, 8), (36, 15), (8, 22), (11, 2), (1, 20), (2, 4), (21, 29), (13, 11), (5, 18), (34, 6), (16, 9), (7, 4), (24, 15), (21, 0), (28, 29), (25, 27), (34, 23), (15, 29), (12, 1), (26, 0), (17, 26), (16, 27), (26, 23), (28, 24), (7, 2), (28, 12), (13, 24), (11, 6), (0, 28), (11, 15), (34, 7), (13, 21), (17, 13), (17, 28), (0, 9), (28, 5), (30, 23), (26, 6), (21, 26), (17, 5), (27, 5), (11, 3), (34, 18), (34, 16), (21, 12), (12, 22), (15, 0), (27, 7), (6, 2), (14, 1), (33, 10), (30, 20), (16, 12), (4, 8), (0, 8), (10, 4), (27, 1), (15, 12), (10, 29), (11, 12), (32, 14), (12, 17), (20, 24), (3, 1), (3, 24), (32, 20), (30, 13), (35, 7), (3, 0), (10, 19), (19, 4), (11, 10), (5, 4), (24, 26), (18, 0), (20, 29), (27, 16), (14, 0), (37, 0), (15, 23), (16, 14), (33, 22), (10, 6), (7, 20), (7, 21), (24, 28), (32, 6), (16, 13), (19, 6), (32, 28), (34, 20), (34, 29), (3, 26), (15, 2), (4, 13), (32, 23), (35, 11), (28, 20), (36, 9), (18, 10), (37, 25), (24, 27), (26, 26), (14, 24), (17, 7), (2, 26), (36, 0), (13, 22), (1, 24), (18, 11), (0, 11), (1, 22), (10, 7), (6, 18), (21, 9), (17, 24), (8, 4), (8, 29), (2, 18), (2, 16), (9, 29), (0, 5), (19, 8), (14, 13), (18, 25), (15, 19), (4, 6), (1, 8), (26, 20), (7, 23), (29, 14), (36, 11), (34, 27), (6, 10), (22, 26), (34, 13), (3, 22), (31, 23), (15, 1), (30, 12), (26, 5), (31, 0), (6, 3), (26, 19), (30, 3), (19, 14), (33, 18), (13, 13), (8, 23), (36, 27), (15, 7), (29, 28), (25, 28), (25, 29), (8, 2), (21, 17), (30, 4), (17, 11), (6, 22), (11, 21), (21, 21), (34, 17), (31, 12), (12, 18), (34, 25), (27, 28), (17, 8), (3, 12), (14, 16), (14, 5), (6, 8), (13, 2), (7, 7), (12, 28), (26, 9), (34, 19), (1, 29), (12, 10), (22, 15), (29, 0), (16, 2), (18, 16), (4, 11), (31, 20), (16, 4), (28, 3), (32, 27), (16, 10), (11, 18), (10, 27), (10, 16), (34, 4), (37, 14), (4, 23), (34, 5), (11, 7), (20, 2), (22, 20), (16, 17), (11, 29), (9, 11), (10, 1), (25, 9), (7, 27), (22, 18), (23, 28), (28, 26), (7, 24), (36, 13), (17, 0), (5, 17), (31, 16), (37, 18), (3, 9), (30, 7), (12, 3), (13, 12), (13, 8), (0, 15), (10, 20), (36, 24), (6, 25), (33, 26), (3, 20), (19, 11), (3, 25), (34, 14), (35, 6), (27, 27), (18, 24), (2, 9), (18, 1), (28, 9), (32, 0), (32, 17), (3, 23), (22, 23), (8, 10), (29, 21), (6, 15), (18, 29), (21, 13), (18, 5), (3, 21), (4, 10), (11, 16), (17, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "416160", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (25, 28), (8, 16), (18, 30), (1, 26), (24, 17), (21, 31), (25, 13), (19, 25), (2, 19), (22, 3), (12, 20), (22, 5), (19, 23), (19, 5), (6, 9), (11, 24), (26, 5), (9, 29), (20, 16), (12, 11), (20, 24), (7, 29), (22, 8), (19, 15), (26, 30), (17, 29), (1, 8), (20, 5), (17, 12), (16, 28), (10, 31), (1, 20), (28, 24), (20, 18), (9, 16), (12, 30), (12, 28), (26, 15), (1, 5), (21, 23), (20, 12), (5, 1), (6, 15), (27, 3), (10, 5), (26, 29), (23, 28), (23, 8), (9, 14), (9, 30), (5, 5), (30, 22), (24, 9), (27, 15), (21, 10), (16, 1), (26, 12), (13, 20), (3, 13), (2, 3), (17, 27), (15, 0), (18, 13), (29, 21), (21, 14), (13, 15), (15, 5), (14, 13), (24, 18), (18, 31), (1, 29), (8, 17), (10, 30), (15, 20), (17, 4), (14, 5), (8, 4), (2, 16), (18, 7), (28, 8), (30, 2), (9, 22), (4, 28), (9, 27), (23, 11), (25, 17), (27, 20), (23, 19), (26, 11), (15, 17), (10, 7), (13, 7), (6, 27), (6, 29), (14, 31), (6, 7), (7, 19), (22, 26), (20, 13), (27, 30), (11, 29), (5, 4), (16, 17), (28, 7), (16, 22), (20, 6), (24, 3), (8, 23), (21, 24), (0, 15), (13, 22), (0, 18), (30, 28), (21, 20), (18, 17), (25, 30), (17, 25), (13, 25), (7, 25), (4, 7), (30, 30), (6, 12), (16, 4), (9, 8), (22, 9), (12, 14), (16, 13), (8, 6), (28, 4), (27, 16), (17, 5), (7, 14), (21, 11), (2, 9), (10, 11), (11, 2), (22, 14), (14, 4), (18, 2), (8, 29), (6, 31), (25, 21), (8, 26), (27, 4), (17, 11), (9, 11), (17, 22), (18, 6), (10, 13), (26, 23), (27, 8), (19, 7), (27, 18), (21, 12), (12, 26), (29, 0), (2, 29), (12, 12), (1, 2), (25, 5), (24, 15), (27, 9), (20, 2), (21, 21), (9, 1), (20, 15), (25, 24), (30, 13), (6, 2), (0, 11), (12, 22), (18, 24), (14, 17), (30, 15), (11, 17), (3, 22), (9, 18), (25, 11), (19, 12), (20, 20), (30, 29), (14, 18), (10, 2), (16, 23), (27, 22), (11, 19), (5, 20), (10, 29), (21, 22), (15, 24), (1, 24), (24, 2), (24, 27), (17, 8), (30, 6), (11, 28), (5, 14), (16, 3), (1, 14), (25, 10), (19, 19), (18, 21), (19, 14), (21, 9), (22, 18), (0, 8), (29, 15), (20, 27), (22, 4), (12, 31), (26, 21), (0, 30), (21, 3), (19, 13), (29, 22), (10, 10), (24, 23), (28, 3), (3, 24), (2, 10), (26, 6), (25, 3), (1, 13), (2, 6), (1, 27), (9, 19), (3, 31), (19, 16), (9, 13), (16, 9), (29, 10), (16, 31), (25, 29), (3, 15), (19, 6), (30, 27), (8, 24), (7, 2), (13, 16), (21, 30), (3, 28), (6, 13), (5, 22), (26, 3), (16, 24), (15, 6), (15, 11), (16, 30), (1, 12), (30, 14), (16, 27), (12, 5), (11, 9), (11, 12), (15, 8), (18, 14), (29, 20), (17, 1), (15, 21), (15, 10), (30, 23), (4, 17), (4, 1), (4, 11), (27, 12), (8, 18), (24, 30), (12, 15), (14, 16), (17, 28), (2, 27), (28, 18), (26, 14), (11, 3), (9, 31), (20, 11), (28, 17), (10, 8), (1, 15), (26, 10), (3, 17), (11, 21), (14, 0), (6, 5), (20, 4), (13, 12), (5, 6), (22, 19), (13, 26), (23, 2), (15, 1), (17, 15), (8, 1), (30, 11), (4, 25), (22, 22), (11, 23), (19, 29), (27, 25), (10, 14), (7, 22), (4, 16), (15, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369792", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), 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), (21, 10), (29, 17), (0, 18), (12, 8), (27, 7), (0, 14), (25, 14), (3, 33), (16, 16), (28, 13), (12, 6), (20, 4), (34, 32), (35, 8), (23, 13), (36, 10), (10, 9), (1, 13), (34, 35), (13, 9), (20, 20), (10, 6), (38, 30), (6, 31), (29, 14), (6, 19), (1, 20), (13, 6), (36, 26), (27, 19), (38, 18), (3, 1), (21, 2), (32, 21), (33, 18), (38, 21), (17, 20), (14, 27), (31, 27), (38, 26), (6, 1), (26, 21), (23, 1), (19, 5), (0, 2), (13, 5), (6, 26), (8, 9), (14, 0), (34, 25), (31, 14), (25, 4), (32, 30), (16, 23), (23, 17), (15, 11), (15, 21), (35, 1), (19, 4), (37, 12), (2, 13), (30, 26), (37, 29), (29, 13), (15, 14), (21, 3), (34, 8), (3, 27), (17, 11), (11, 6), (22, 16), (24, 15), (12, 4), (31, 15), (5, 25), (33, 25), (9, 17), (28, 30), (1, 7), (16, 31), (38, 0), (17, 27), (18, 1), (26, 4), (36, 17), (11, 3), (7, 7), (14, 4), (35, 17), (36, 11), (35, 19), (3, 29), (6, 11), (25, 21), (6, 3), (20, 29), (36, 21), (7, 4), (19, 11), (10, 2), (20, 8), (8, 27), (17, 29), (28, 33), (16, 9), (24, 26), (29, 35), (1, 0), (3, 20), (4, 20), (37, 35), (34, 19), (15, 33), (13, 22), (10, 28), (2, 24), (31, 35), (11, 22), (20, 11), (10, 13), (34, 9), (4, 17), (1, 3), (10, 35), (25, 33), (35, 25), (7, 31), (29, 12), (20, 15), (31, 4), (14, 14), (10, 11), (12, 22), (37, 5), (23, 4), (37, 10), (1, 12), (32, 2), (29, 3), (23, 6), (8, 19), (32, 19), (8, 10), (3, 26), (24, 23), (15, 15), (37, 0), (24, 2), (27, 35), (4, 35), (11, 11), (9, 24), (19, 17), (12, 14), (33, 31), (18, 31), (11, 21), (35, 18), (15, 27), (32, 20), (6, 10), (28, 8), (13, 23), (24, 22), (2, 22), (7, 34), (32, 1), (4, 28), (28, 5), (25, 15), (21, 4), (17, 22), (23, 24), (5, 19), (30, 14), (35, 26), (5, 32), (0, 12), (5, 34), (12, 12), (20, 31), (26, 35), (10, 1), (17, 9), (3, 22), (31, 34), (26, 32), (37, 24), (37, 18), (26, 1), (11, 34), (19, 21), (34, 30), (18, 24), (31, 16), (17, 2), (23, 12), (0, 26), (38, 33), (37, 20), (30, 15), (28, 12), (26, 0), (12, 2), (36, 24), (13, 13), (33, 20), (3, 32), (3, 25), (27, 3), (29, 22), (17, 24), (38, 28), (21, 23), (8, 15), (1, 21), (6, 23), (24, 10), (34, 5), (0, 29), (4, 10), (2, 18), (3, 5), (36, 1), (20, 12), (4, 23), (23, 28), (33, 2), (22, 4), (12, 19), (12, 21), (17, 21), (1, 25), (8, 22), (3, 12), (26, 24), (0, 6), (5, 13), (14, 2), (38, 1), (0, 13), (33, 26), (23, 15), (9, 27), (19, 33), (36, 27), (28, 7), (16, 22), (27, 18), (36, 31), (34, 0), (17, 19), (17, 15), (33, 16), (27, 27), (37, 1), (36, 7), (31, 8), (35, 0), (2, 3), (11, 24), (13, 0), (29, 11), (8, 26), (16, 11), (25, 35), (13, 21), (3, 19), (6, 27), (11, 27), (4, 4), (11, 17), (17, 16), (16, 17), (38, 32), (23, 2), (7, 20), (18, 7), (23, 32), (35, 21), (21, 22), (2, 20), (1, 33), (21, 19), (32, 22), (0, 27), (14, 28), (29, 30), (9, 15), (13, 20), (29, 4), (32, 35), (3, 18), (14, 15), (21, 20), (38, 4), (9, 12), (33, 15), (28, 24), (18, 20), (19, 14), (11, 4), (30, 1), (30, 35), (3, 30), (37, 19), (35, 5), (26, 6), (22, 5), (28, 11), (24, 31), (23, 20), (20, 17), (10, 23), (36, 16), (27, 32), (30, 0), (22, 25), (4, 3), (16, 33), (16, 4), (1, 15), (15, 1), (28, 2), (37, 23), (6, 34), (0, 8), (34, 31), (11, 20), (7, 33), (6, 7), (4, 9), (23, 29), (35, 4), (15, 3), (35, 29), (16, 34), (29, 5), (24, 20), (22, 19), (33, 29), (22, 35), (16, 25), (11, 2), (14, 7), (21, 27), (0, 11), (23, 26), (18, 22), (27, 17), (10, 29), (22, 3), (34, 24), (3, 4), (28, 20), (18, 19), (2, 28), (18, 17), (19, 25), (24, 28), (24, 24), (20, 33), (34, 13), (11, 31), (10, 16), (7, 8), (27, 10), (0, 9), (13, 33), (10, 21), (34, 22), (31, 0), (29, 34), (14, 26), (29, 23), (15, 24), (35, 11), (31, 25), (29, 6), (15, 0), (27, 31), (11, 15), (19, 15), (22, 22), (23, 5), (29, 29), (10, 34), (3, 13), (13, 28), (29, 0), (0, 32), (2, 0), (11, 35), (14, 30), (36, 6), (15, 9), (16, 35), (35, 9), (17, 12), (25, 28), (33, 8), (15, 10), (9, 28), (26, 27), (29, 27), (22, 32), (19, 12), (3, 3), (1, 2), (19, 26), (12, 24), (25, 32), (5, 28), (18, 14), (24, 3), (14, 5), (13, 16), (24, 7), (12, 27), (2, 6), (14, 16), (29, 9), (7, 19), (10, 8), (9, 6), (6, 5), (26, 7), (5, 21), (22, 12), (15, 34), (28, 21), (1, 8), (9, 4), (35, 16), (0, 24), (12, 3), (34, 7), (30, 32), (9, 30), (18, 0), (17, 34), (29, 26), (18, 18), (10, 31), (36, 15), (25, 8), (29, 19), (31, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476280", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 31), (26, 5), (37, 6), (15, 13), (33, 7), (28, 22), (4, 5), (18, 5), (21, 0), (23, 25), (18, 14), (15, 28), (2, 1), (1, 24), (22, 28), (37, 28), (5, 6), (20, 21), (13, 13), (33, 24), (17, 9), (4, 24), (6, 9), (11, 10), (37, 24), (6, 31), (29, 8), (24, 23), (22, 25), (13, 21), (26, 26), (14, 4), (27, 17), (24, 3), (30, 10), (34, 18), (34, 16), (16, 5), (7, 6), (32, 32), (20, 29), (34, 3), (31, 5), (21, 27), (12, 16), (4, 2), (27, 16), (2, 26), (6, 10), (11, 12), (30, 9), (15, 29), (35, 15), (24, 27), (29, 29), (10, 22), (21, 26), (29, 5), (9, 14), (10, 0), (25, 22), (33, 5), (21, 2), (1, 29), (37, 16), (18, 10), (2, 3), (14, 13), (17, 13), (27, 8), (16, 15), (16, 1), (15, 27), (35, 8), (8, 8), (20, 15), (19, 13), (21, 25), (9, 16), (37, 13), (9, 28), (29, 30), (5, 12), (15, 26), (0, 27), (27, 1), (30, 1), (6, 32), (32, 15), (7, 19), (6, 26), (20, 32), (25, 27), (22, 5), (25, 14), (23, 14), (24, 15), (34, 12), (34, 1), (5, 5), (23, 30), (28, 2), (25, 26), (3, 32), (34, 21), (13, 2), (29, 12), (13, 32), (28, 24), (31, 9), (4, 26), (12, 3), (26, 6), (21, 4), (14, 29), (36, 14), (9, 25), (13, 18), (0, 7), (24, 17), (11, 25), (10, 19), (19, 27), (6, 11), (13, 9), (6, 19), (14, 24), (13, 3), (29, 19), (8, 9), (33, 2), (4, 12), (13, 20), (37, 0), (1, 22), (10, 17), (21, 30), (28, 29), (2, 13), (33, 12), (5, 20), (19, 8), (36, 26), (27, 32), (23, 26), (10, 25), (19, 19), (32, 26), (11, 11), (3, 6), (2, 8), (22, 11), (12, 13), (12, 19), (17, 22), (9, 10), (37, 3), (32, 4), (25, 25), (27, 21), (14, 25), (14, 3), (19, 26), (36, 1), (10, 8), (14, 17), (34, 25), (28, 32), (15, 7), (12, 31), (30, 12), (28, 26), (27, 19), (4, 30), (24, 11), (5, 2), (1, 30), (22, 17), (21, 14), (21, 7), (17, 26), (4, 20), (16, 3), (3, 19), (1, 20), (29, 21), (32, 12), (7, 28), (24, 16), (2, 25), (37, 4), (37, 29), (28, 23), (3, 26), (35, 11), (26, 16), (36, 11), (2, 6), (32, 30), (27, 26), (35, 17), (11, 30), (7, 13), (12, 18), (7, 3), (13, 29), (18, 25), (2, 30), (26, 22), (35, 31), (9, 3), (2, 31), (4, 22), (17, 16), (22, 12), (31, 7), (6, 27), (25, 12), (7, 1), (4, 23), (15, 22), (34, 24), (2, 11), (27, 18), (17, 1), (14, 27), (11, 7), (8, 12), (32, 20), (26, 2), (32, 10), (13, 25), (22, 29), (33, 0), (26, 7), (6, 1), (34, 13), (36, 10), (22, 20), (1, 12), (10, 32), (25, 20), (36, 22), (25, 4), (19, 18), (2, 22), (21, 23), (16, 21), (30, 22), (35, 13), (19, 23), (7, 10), (16, 25), (25, 29), (33, 10), (8, 16), (34, 32), (27, 27), (19, 2), (37, 9), (18, 29), (26, 17), (30, 27), (28, 10), (6, 22), (32, 18), (1, 26), (20, 3), (13, 16), (0, 25), (27, 20), (34, 17), (37, 23), (7, 29), (26, 14), (13, 8), (11, 15), (26, 19), (32, 6), (9, 2), (30, 18), (25, 9), (6, 7), (6, 29), (31, 32), (6, 28), (2, 12), (28, 16), (3, 28), (13, 11), (21, 1), (10, 3), (3, 15), (5, 16), (17, 0), (13, 19), (28, 1), (17, 10), (33, 13), (27, 7), (22, 3), (18, 31), (35, 29), (20, 8), (30, 4), (20, 25), (27, 12), (17, 17), (20, 23), (9, 6), (5, 13), (2, 23), (7, 24), (6, 3), (8, 26), (23, 23), (11, 9), (9, 11), (36, 24), (32, 21), (21, 32), (26, 20), (16, 16), (25, 32), (25, 5), (0, 16), (30, 15), (20, 0), (20, 18), (18, 16), (30, 16), (9, 23), (30, 19), (5, 27), (34, 7), (36, 28), (5, 28), (23, 20), (32, 13), (1, 13), (4, 4), (16, 8), (16, 10), (18, 19), (25, 28), (33, 3), (14, 32), (7, 7), (1, 23), (16, 14), (20, 2), (8, 30), (15, 20), (2, 29), (31, 2), (19, 5), (32, 9), (12, 26), (3, 9), (15, 1), (31, 11), (24, 2), (18, 23), (6, 0), (16, 19), (10, 18), (9, 29), (9, 13), (14, 31), (13, 0), (37, 5), (7, 11), (16, 9), (20, 7), (9, 22), (14, 8), (13, 22), (3, 11), (5, 30), (16, 6), (18, 27), (15, 15), (37, 17), (20, 20), (29, 7), (33, 8), (10, 23), (32, 0), (8, 19), (35, 28), (36, 29), (37, 21), (36, 5), (0, 15), (15, 10), (26, 18), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "698976", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 28), (0, 33), (22, 33), (29, 35), (18, 15), (30, 17), (19, 7), (12, 22), (9, 22), (14, 28), (23, 6), (13, 22), (36, 28), (35, 12), (32, 22), (18, 2), (7, 37), (7, 2), (23, 36), (8, 23), (27, 36), (36, 1), (3, 32), (10, 6), (10, 16), (22, 3), (26, 15), (14, 23), (16, 30), (28, 9), (15, 25), (27, 26), (1, 26), (14, 8), (1, 17), (25, 31), (5, 17), (10, 5), (25, 17), (26, 30), (17, 1), (15, 32), (8, 10), (27, 2), (24, 17), (38, 7), (9, 2), (10, 35), (2, 18), (28, 13), (10, 14), (28, 18), (32, 35), (32, 3), (16, 37), (15, 6), (19, 13), (19, 25), (14, 3), (15, 10), (34, 3), (0, 26), (32, 32), (23, 26), (35, 18), (27, 9), (33, 30), (34, 30), (24, 32), (11, 34), (33, 22), (4, 35), (4, 12), (2, 35), (2, 16), (21, 37), (36, 24), (15, 24), (18, 11), (7, 23), (19, 30), (16, 35), (3, 27), (35, 23), (19, 8), (28, 7), (32, 34), (36, 20), (23, 7), (14, 0), (30, 36), (8, 6), (12, 25), (13, 20), (12, 16), (24, 2), (14, 1), (31, 6), (19, 36), (31, 27), (5, 25), (32, 31), (4, 27), (37, 31), (37, 5), (12, 11), (0, 27), (20, 37), (16, 31), (38, 15), (15, 27), (32, 7), (17, 34), (12, 27), (19, 2), (26, 27), (33, 2), (25, 13), (14, 12), (19, 18), (6, 33), (2, 32), (31, 12), (16, 16), (13, 17), (12, 31), (38, 9), (22, 21), (6, 35), (2, 17), (13, 29), (3, 19), (37, 6), (36, 21), (14, 24), (5, 13), (6, 25), (3, 13), (19, 3), (11, 29), (33, 20), (12, 3), (36, 6), (23, 20), (12, 34), (33, 19), (23, 30), (32, 1), (1, 12), (26, 14), (33, 6), (32, 10), (32, 11), (7, 24), (3, 33), (1, 6), (23, 22), (20, 0), (34, 31), (27, 34), (29, 20), (18, 21), (16, 9), (35, 30), (5, 22), (37, 23), (1, 14), (12, 18), (20, 6), (4, 11), (30, 22), (37, 19), (26, 26), (1, 27), (24, 3), (17, 2), (33, 10), (28, 29), (8, 7), (16, 18), (32, 26), (7, 11), (19, 23), (23, 12), (26, 16), (14, 4), (2, 6), (9, 33), (25, 2), (23, 10), (27, 16), (22, 10), (16, 1), (10, 32), (25, 29), (16, 0), (17, 24), (18, 19), (38, 25), (30, 28), (27, 15), (29, 10), (31, 18), (34, 20), (28, 33), (10, 28), (35, 6), (5, 31), (7, 27), (38, 26), (38, 27), (26, 20), (34, 33), (20, 3), (38, 1), (22, 27), (9, 6), (8, 18), (12, 9), (35, 25), (26, 28), (32, 27), (22, 30), (11, 35), (17, 22), (31, 1), (27, 1), (36, 33), (1, 9), (24, 21), (4, 24), (7, 30), (37, 20), (29, 25), (5, 24), (24, 27), (38, 18), (12, 13), (31, 7), (17, 18), (34, 37), (21, 25), (13, 3), (1, 7), (24, 10), (12, 15), (30, 27), (10, 20), (18, 9), (30, 3), (10, 10), (6, 34), (28, 23), (29, 2), (36, 0), (27, 35), (30, 16), (34, 19), (1, 23), (6, 24), (35, 20), (20, 28), (5, 6), (2, 21), (0, 2), (31, 19), (19, 21), (2, 3), (35, 34), (0, 28), (4, 15), (23, 8), (12, 26), (23, 21), (14, 36), (30, 20), (19, 15), (8, 32), (22, 31), (3, 29), (19, 4), (7, 16), (35, 7), (28, 30), (18, 26), (32, 28), (34, 0), (31, 26), (30, 10), (0, 31), (11, 32), (30, 31), (13, 7), (14, 15), (32, 36), (14, 7), (14, 5), (38, 32), (19, 5), (9, 29), (6, 5), (27, 17), (30, 24), (34, 28), (29, 3), (3, 2), (29, 5), (34, 35), (7, 26), (3, 21), (6, 3), (29, 19), (11, 3), (8, 2), (31, 34), (25, 34), (21, 5), (25, 3), (28, 20), (36, 17), (38, 13), (5, 9), (31, 9), (0, 35), (11, 25), (9, 23), (14, 25), (3, 12), (36, 35), (34, 5), (33, 13), (26, 0), (17, 0), (21, 31), (37, 10), (0, 1), (12, 21), (0, 32), (28, 17), (36, 12), (32, 13), (31, 10), (26, 33), (1, 8), (30, 29), (22, 2), (36, 36), (4, 37), (19, 1), (15, 12), (26, 12), (37, 22), (19, 34), (17, 4), (6, 21), (14, 11), (11, 13), (8, 27), (25, 25), (18, 10), (16, 13), (22, 34), (3, 23), (13, 19), (0, 14), (35, 33), (18, 35), (3, 20), (16, 22), (28, 8), (15, 14), (3, 35), (13, 34), (22, 9), (28, 36), (22, 24), (7, 19), (22, 5), (13, 36), (0, 13), (9, 24), (21, 16), (31, 0), (5, 10), (16, 14), (4, 34), (28, 27), (26, 2), (35, 24), (5, 26), (11, 22), (15, 18), (23, 0), (21, 22), (32, 16), (14, 27), (25, 18), (22, 7), (16, 2), (11, 6), (37, 34), (16, 15), (9, 17), (14, 29), (0, 10), (6, 16), (19, 9), (11, 12), (2, 2), (27, 14), (17, 9), (25, 7), (24, 36), (32, 0), (20, 32), (35, 26), (9, 9), (6, 0), (36, 14), (35, 27), (32, 17), (18, 6), (30, 15), (11, 8), (21, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "405408", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 8), (5, 14), (5, 25), (19, 23), (17, 16), (1, 10), (7, 0), (19, 21), (11, 17), (18, 22), (29, 20), (28, 9), (15, 21), (13, 1), (16, 12), (17, 20), (9, 4), (23, 14), (14, 1), (14, 28), (7, 13), (26, 3), (15, 26), (7, 8), (5, 26), (7, 5), (2, 6), (10, 7), (30, 18), (2, 17), (18, 15), (16, 1), (22, 21), (1, 12), (14, 15), (8, 1), (20, 21), (24, 14), (27, 6), (23, 2), (6, 28), (6, 20), (19, 17), (18, 2), (0, 23), (7, 1), (27, 19), (15, 20), (25, 27), (15, 19), (9, 8), (25, 26), (28, 5), (12, 11), (5, 7), (13, 7), (2, 19), (29, 27), (4, 13), (24, 21), (13, 5), (9, 12), (11, 24), (24, 12), (6, 7), (24, 1), (19, 13), (11, 22), (30, 14), (18, 20), (17, 13), (28, 0), (13, 20), (30, 4), (4, 19), (16, 16), (30, 1), (9, 16), (9, 20), (13, 16), (22, 7), (27, 1), (3, 24), (0, 5), (21, 27), (28, 26), (3, 25), (24, 22), (1, 2), (8, 19), (11, 29), (16, 29), (3, 20), (27, 8), (29, 11), (5, 4), (6, 11), (23, 21), (7, 12), (5, 11), (23, 25), (30, 5), (22, 3), (30, 13), (4, 2), (27, 21), (2, 26), (12, 1), (23, 12), (12, 12), (18, 13), (27, 28), (8, 23), (29, 16), (29, 10), (4, 1), (4, 28), (11, 28), (0, 14), (21, 20), (23, 29), (17, 3), (9, 24), (17, 7), (12, 18), (8, 17), (29, 1), (3, 19), (6, 6), (10, 12), (24, 9), (21, 19), (16, 9), (5, 21), (3, 29), (25, 24), (3, 9), (7, 20), (4, 20), (11, 4), (22, 18), (9, 19), (5, 28), (23, 23), (23, 15), (11, 23), (20, 4), (3, 16), (28, 17), (5, 27), (6, 17), (11, 9), (8, 16), (22, 4), (10, 19), (22, 16), (2, 13), (11, 1), (3, 23), (3, 7), (14, 29), (9, 3), (19, 6), (15, 15), (20, 20), (19, 27), (15, 10), (22, 8), (26, 29), (21, 9), (19, 28), (17, 12), (13, 12), (29, 22), (4, 4), (12, 16), (7, 9), (22, 2), (3, 18), (2, 15), (20, 0), (19, 16), (25, 0), (26, 9), (9, 15), (30, 23), (8, 27), (18, 7), (21, 3), (2, 9), (0, 20), (26, 15), (27, 27), (7, 22), (9, 23), (11, 0), (18, 5), (15, 7), (5, 6), (4, 3), (21, 10), (6, 15), (26, 4), (18, 1), (1, 5), (20, 22), (28, 13), (2, 18), (22, 14), (6, 14), (16, 17), (14, 22), (1, 19), (3, 11), (19, 15), (21, 12), (23, 26), (14, 21), (22, 25), (25, 1), (30, 10), (20, 5), (25, 10), (7, 25), (4, 12), (11, 27), (22, 27), (22, 13), (28, 1), (10, 28), (6, 1), (22, 0), (17, 26), (1, 6), (19, 19), (5, 17), (25, 29), (17, 6), (19, 20), (6, 8), (20, 26), (30, 15), (6, 24), (27, 18), (11, 2), (21, 24), (26, 10), (7, 6), (21, 14), (10, 24), (17, 15), (14, 12), (6, 19), (26, 18), (14, 11), (30, 0), (29, 5), (5, 2), (2, 24), (25, 4), (10, 21), (3, 1), (2, 10), (2, 7), (6, 3), (0, 6), (28, 10), (15, 6), (23, 24), (22, 22), (10, 23), (16, 19), (17, 19), (23, 6), (8, 29), (20, 17), (4, 9), (16, 28), (12, 14), (14, 9), (16, 2), (10, 25), (3, 21), (0, 1), (4, 15), (20, 9), (6, 27), (13, 22), (2, 21), (8, 3), (19, 9), (26, 8), (8, 4), (29, 14), (12, 19), (18, 26), (12, 29), (11, 11), (19, 22), (14, 8), (3, 28), (0, 25), (15, 5), (5, 15), (18, 12), (16, 18), (25, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "704512", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 28), (23, 15), (23, 1), (4, 25), (28, 1), (14, 14), (15, 12), (28, 8), (13, 2), (6, 8), (4, 28), (6, 24), (0, 29), (23, 29), (5, 25), (22, 23), (20, 25), (9, 20), (18, 35), (0, 25), (27, 16), (10, 10), (31, 10), (23, 19), (4, 7), (24, 37), (26, 14), (13, 29), (2, 24), (18, 12), (18, 32), (25, 19), (1, 37), (2, 4), (12, 38), (16, 18), (3, 17), (28, 28), (24, 19), (15, 5), (1, 34), (22, 36), (2, 33), (10, 38), (5, 15), (11, 30), (17, 35), (26, 25), (20, 15), (19, 38), (22, 9), (32, 20), (32, 35), (8, 23), (4, 35), (17, 33), (13, 17), (17, 17), (17, 5), (10, 22), (8, 6), (1, 32), (13, 9), (20, 30), (7, 31), (29, 10), (6, 6), (13, 0), (18, 26), (16, 2), (25, 21), (27, 22), (27, 33), (13, 38), (0, 36), (4, 34), (24, 36), (9, 23), (31, 18), (32, 18), (18, 10), (18, 11), (3, 4), (0, 1), (10, 1), (7, 25), (14, 8), (23, 7), (5, 10), (33, 33), (26, 10), (2, 27), (11, 13), (16, 30), (8, 36), (17, 10), (17, 31), (23, 25), (27, 10), (23, 3), (7, 13), (29, 19), (18, 21), (25, 1), (12, 17), (14, 0), (2, 29), (8, 5), (15, 22), (22, 28), (6, 37), (32, 5), (9, 14), (14, 19), (26, 12), (32, 28), (15, 1), (14, 2), (12, 32), (27, 31), (7, 15), (27, 38), (12, 8), (5, 34), (7, 30), (11, 1), (8, 38), (1, 31), (28, 26), (29, 4), (17, 30), (33, 23), (31, 17), (1, 19), (25, 11), (17, 27), (10, 27), (3, 26), (8, 4), (28, 37), (24, 14), (9, 18), (31, 22), (28, 9), (8, 8), (6, 23), (4, 30), (12, 34), (7, 12), (25, 14), (32, 24), (21, 29), (12, 20), (11, 2), (18, 29), (9, 9), (9, 2), (16, 24), (1, 22), (17, 0), (32, 7), (18, 36), (30, 3), (30, 14), (12, 18), (6, 36), (8, 13), (16, 23), (18, 31), (3, 19), (27, 13), (4, 8), (9, 5), (12, 24), (24, 22), (8, 27), (11, 8), (0, 22), (31, 35), (27, 17), (10, 26), (21, 11), (25, 29), (24, 11), (1, 29), (23, 10), (15, 15), (9, 35), (4, 20), (18, 6), (0, 18), (27, 12), (33, 30), (29, 38), (24, 28), (6, 17), (16, 29), (26, 26), (15, 0), (8, 21), (1, 13), (13, 23), (10, 3), (29, 14), (9, 33), (17, 14), (1, 15), (9, 12), (11, 5), (4, 6), (19, 28), (32, 15), (12, 35), (17, 21), (12, 5), (25, 2), (5, 2), (9, 8), (1, 25), (1, 18), (22, 5), (11, 11), (21, 28), (2, 16), (19, 16), (7, 14), (0, 6), (24, 10), (5, 11), (7, 35), (17, 26), (0, 13), (12, 15), (20, 6), (14, 9), (7, 36), (5, 29), (3, 10), (11, 32), (8, 3), (11, 31), (5, 18), (14, 32), (19, 19), (32, 14), (16, 36), (31, 6), (1, 7), (12, 22), (9, 25), (2, 28), (26, 3), (28, 4), (26, 0), (16, 35), (17, 12), (22, 18), (17, 3), (31, 26), (30, 6), (31, 1), (7, 32), (2, 2), (30, 34), (26, 31), (24, 35), (33, 0), (13, 3), (19, 15), (31, 9), (24, 38), (20, 1), (30, 15), (17, 24), (32, 12), (19, 22), (28, 35), (29, 6), (27, 24), (15, 30), (2, 14), (22, 24), (29, 32), (25, 25), (26, 19), (4, 31), (5, 12), (27, 25), (19, 2), (8, 31), (27, 19), (5, 0), (25, 3), (1, 3), (0, 37), (22, 2), (22, 27), (4, 3), (4, 9), (0, 9), (32, 27), (26, 11), (2, 6), (28, 25), (27, 3), (13, 13), (20, 35), (23, 20), (0, 30), (27, 5), (9, 4), (6, 0), (24, 27), (18, 27), (9, 29), (24, 9), (20, 26), (29, 25), (27, 8), (14, 5), (30, 11), (31, 31), (0, 33), (23, 26), (30, 0), (17, 23), (30, 25), (17, 25), (2, 10), (23, 27), (9, 0), (9, 36), (21, 7), (3, 22), (32, 37), (10, 12), (25, 15), (14, 23), (22, 14), (12, 37), (8, 0), (33, 20), (1, 11), (3, 12), (8, 32), (31, 24), (9, 27), (20, 2), (28, 10), (6, 20), (5, 33), (31, 15), (12, 31), (12, 3), (30, 37), (33, 28), (18, 5), (28, 17), (30, 2), (31, 4), (13, 15), (12, 11), (15, 18), (24, 32), (15, 16), (23, 6), (14, 7), (18, 17), (19, 36), (32, 10), (11, 19), (3, 20), (1, 20), (31, 13), (29, 22), (29, 26), (8, 33), (23, 14), (1, 10), (33, 12), (23, 9), (3, 25), (32, 34), (32, 25), (27, 27), (21, 4), (30, 24), (24, 4), (19, 17), (26, 6), (32, 30), (22, 26), (12, 16), (17, 28), (26, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501760", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 27), (2, 25), (25, 5), (21, 27), (17, 3), (26, 13), (7, 1), (23, 6), (29, 9), (0, 14), (28, 6), (32, 4), (33, 2), (11, 10), (24, 5), (32, 31), (15, 15), (6, 13), (16, 0), (9, 31), (23, 8), (24, 18), (7, 18), (12, 4), (31, 8), (18, 17), (17, 24), (5, 11), (16, 20), (17, 10), (21, 21), (3, 25), (32, 28), (19, 14), (11, 30), (25, 8), (11, 9), (0, 11), (24, 7), (24, 11), (19, 5), (32, 8), (20, 8), (13, 28), (0, 10), (21, 7), (7, 8), (1, 7), (8, 21), (12, 29), (18, 12), (32, 29), (29, 27), (0, 21), (14, 23), (14, 22), (18, 27), (17, 5), (1, 27), (10, 19), (30, 21), (26, 25), (6, 0), (22, 12), (30, 1), (20, 7), (21, 10), (15, 17), (2, 17), (16, 14), (25, 0), (14, 14), (23, 10), (26, 30), (17, 17), (30, 31), (20, 31), (17, 7), (20, 4), (14, 13), (15, 10), (20, 26), (18, 31), (4, 24), (14, 5), (3, 17), (23, 28), (20, 22), (22, 31), (8, 15), (33, 21), (8, 6), (25, 24), (17, 29), (11, 3), (11, 16), (10, 4), (6, 11), (5, 4), (28, 11), (33, 26), (7, 25), (30, 8), (6, 26), (9, 24), (3, 28), (17, 13), (22, 17), (21, 17), (0, 1), (14, 18), (27, 23), (25, 10), (23, 12), (24, 1), (11, 20), (17, 23), (19, 30), (5, 2), (11, 29), (4, 27), (24, 14), (18, 21), (19, 1), (15, 13), (29, 16), (0, 31), (12, 30), (25, 18), (32, 13), (24, 20), (28, 25), (27, 12), (18, 10), (2, 31), (5, 21), (23, 21), (18, 6), (25, 13), (10, 18), (21, 22), (25, 15), (24, 26), (23, 11), (23, 27), (11, 6), (9, 2), (5, 5), (5, 15), (29, 26), (6, 22), (24, 17), (28, 10), (19, 19), (32, 16), (23, 26), (11, 1), (3, 15), (26, 8), (27, 4), (2, 3), (15, 30), (21, 30), (24, 31), (1, 5), (27, 6), (11, 11), (13, 31), (21, 13), (22, 9), (10, 16), (25, 20), (16, 27), (31, 3), (11, 19), (31, 2), (13, 24), (28, 8), (21, 4), (12, 8), (15, 19), (25, 26), (30, 17), (2, 23), (13, 10), (27, 30), (6, 30), (10, 31), (0, 12), (26, 5), (6, 20), (22, 20), (21, 2), (29, 5), (27, 26), (4, 9), (33, 3), (11, 0), (9, 9), (32, 20), (0, 30), (13, 0), (32, 26), (33, 9), (15, 27), (12, 0), (10, 26), (31, 7), (27, 16), (25, 27), (9, 30), (18, 9), (7, 26), (1, 13), (24, 9), (4, 12), (31, 19), (16, 4), (17, 27), (1, 15), (29, 17), (26, 1), (0, 17), (7, 5), (14, 25), (0, 15), (2, 7), (6, 2), (22, 11), (21, 14), (16, 7), (6, 21), (1, 3), (14, 26), (7, 23), (13, 12), (12, 14), (28, 28), (5, 8), (27, 22), (0, 26), (7, 14), (26, 7), (26, 17), (10, 3), (8, 25), (5, 7), (29, 4), (10, 30), (29, 15), (4, 18), (26, 31), (9, 21), (12, 21), (23, 16), (14, 29), (3, 18), (31, 27), (32, 7), (21, 26), (7, 17), (17, 30), (16, 2), (28, 29), (18, 20), (18, 5), (27, 25), (2, 11), (18, 24), (5, 16), (12, 17), (20, 20), (16, 23), (23, 20), (24, 21), (23, 1), (28, 4), (12, 1), (20, 11), (12, 20), (20, 10), (0, 7), (10, 6), (12, 16), (26, 10), (17, 11), (7, 28), (11, 17), (33, 5), (27, 18), (33, 19), (2, 2), (9, 17), (31, 22), (22, 27), (15, 18), (15, 9), (5, 0), (9, 0), (25, 2), (31, 18), (13, 23), (15, 1), (32, 6), (0, 25), (23, 13), (17, 0), (9, 23), (26, 14), (7, 13), (22, 13), (16, 11), (7, 30), (8, 17), (28, 7), (6, 23), (16, 18), (17, 15), (9, 8), (29, 3), (30, 2), (28, 15), (13, 14), (26, 21), (18, 25), (23, 29), (18, 18), (33, 20), (12, 11), (7, 4), (22, 3), (0, 4), (30, 19), (19, 26), (20, 3), (9, 20), (6, 27), (32, 14), (4, 29), (2, 4), (26, 6), (1, 28), (21, 9), (24, 3), (10, 27), (25, 14), (23, 30), (1, 29), (20, 2), (31, 20), (25, 11), (5, 10), (33, 10), (9, 11), (27, 27), (4, 10), (33, 18), (8, 28), (29, 20), (30, 4), (33, 11), (28, 20), (5, 17), (31, 29), (26, 11), (1, 17), (17, 18), (33, 22), (33, 1), (2, 6), (29, 8), (8, 1), (5, 13), (21, 0), (6, 10), (6, 15), (6, 5), (10, 11), (30, 12), (9, 5), (28, 17), (29, 6), (14, 27), (13, 19), (33, 25), (16, 25), (13, 7), (13, 5), (9, 6), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "711360", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 25), (5, 8), (30, 19), (21, 10), (2, 18), (4, 8), (10, 0), (9, 30), (21, 6), (12, 10), (16, 16), (20, 9), (28, 2), (8, 18), (9, 12), (5, 4), (3, 12), (10, 28), (28, 14), (29, 28), (24, 9), (25, 30), (1, 31), (3, 1), (25, 27), (12, 14), (28, 7), (24, 24), (17, 11), (6, 10), (20, 11), (13, 20), (25, 16), (9, 20), (11, 12), (21, 28), (24, 7), (13, 22), (14, 26), (14, 3), (24, 11), (6, 11), (5, 24), (10, 29), (11, 28), (16, 8), (21, 22), (13, 21), (19, 17), (11, 21), (19, 27), (9, 31), (15, 20), (16, 28), (2, 23), (5, 6), (20, 22), (25, 2), (3, 0), (5, 20), (19, 11), (20, 5), (28, 20), (29, 8), (18, 28), (28, 27), (8, 9), (26, 6), (25, 12), (24, 28), (15, 7), (21, 0), (17, 31), (22, 9), (27, 0), (16, 24), (0, 2), (29, 6), (8, 0), (12, 16), (14, 0), (30, 8), (5, 11), (12, 26), (9, 1), (14, 4), (2, 27), (0, 6), (30, 17), (20, 14), (25, 8), (13, 5), (27, 11), (20, 29), (29, 21), (2, 15), (28, 25), (13, 1), (9, 8), (14, 16), (17, 17), (15, 5), (9, 29), (30, 21), (30, 11), (17, 3), (7, 7), (6, 17), (0, 8), (29, 13), (1, 6), (16, 13), (30, 22), (7, 11), (20, 27), (24, 22), (21, 9), (8, 19), (3, 17), (11, 8), (15, 29), (23, 29), (27, 25), (0, 25), (25, 10), (25, 0), (16, 30), (11, 4), (0, 31), (30, 1), (24, 14), (11, 20), (10, 24), (10, 20), (28, 8), (12, 12), (18, 12), (14, 7), (18, 6), (5, 2), (13, 18), (27, 12), (28, 13), (7, 31), (10, 11), (27, 29), (14, 29), (9, 27), (10, 18), (9, 28), (17, 9), (22, 19), (2, 26), (6, 5), (7, 16), (10, 7), (7, 23), (19, 23), (22, 4), (19, 9), (21, 12), (0, 3), (19, 25), (11, 0), (29, 3), (28, 10), (6, 28), (6, 9), (6, 15), (14, 21), (26, 20), (11, 30), (10, 21), (25, 17), (10, 15), (25, 29), (3, 25), (25, 23), (24, 15), (6, 14), (7, 30), (17, 2), (10, 6), (28, 11), (6, 7), (28, 1), (15, 15), (5, 18), (3, 8), (15, 9), (15, 6), (20, 8), (25, 11), (2, 3), (27, 21), (13, 23), (8, 11), (16, 3), (6, 29), (0, 4), (17, 27), (14, 5), (27, 18), (22, 18), (20, 26), (11, 31), (6, 8), (28, 6), (22, 7), (9, 19), (6, 20), (5, 13), (24, 3), (0, 11), (1, 1), (22, 10), (13, 4), (2, 30), (29, 12), (17, 23), (2, 12), (6, 12), (1, 23), (25, 25), (17, 8), (28, 24), (16, 29), (24, 23), (8, 22), (4, 14), (3, 7), (0, 12), (0, 19), (29, 29), (1, 5), (5, 15), (12, 24), (27, 17), (14, 24), (12, 19), (24, 0), (0, 27), (22, 11), (24, 30), (23, 25), (19, 4), (0, 26), (24, 4), (23, 6), (22, 16), (7, 21), (30, 7), (30, 30), (18, 0), (20, 4), (1, 22), (28, 29), (26, 3), (4, 7), (4, 31), (15, 14), (0, 10), (12, 6), (2, 4), (5, 16), (5, 29), (13, 30), (15, 27), (15, 24), (26, 23), (22, 12), (4, 23), (27, 4), (3, 14), (27, 3), (25, 1), (17, 14), (0, 14), (15, 30), (19, 22), (0, 18), (21, 31), (30, 29), (26, 12), (8, 7), (4, 11), (17, 7), (1, 9), (3, 16), (9, 16), (13, 3), (22, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271320", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 25), (23, 21), (14, 11), (29, 10), (20, 32), (8, 14), (27, 31), (17, 20), (22, 30), (17, 1), (6, 13), (11, 4), (24, 31), (16, 28), (4, 1), (0, 15), (15, 28), (11, 17), (9, 8), (10, 0), (35, 5), (12, 21), (23, 26), (21, 3), (24, 10), (3, 3), (12, 14), (15, 1), (24, 2), (23, 31), (25, 33), (30, 15), (5, 22), (4, 31), (26, 25), (16, 20), (3, 23), (4, 2), (25, 9), (21, 10), (7, 18), (12, 9), (2, 11), (1, 30), (5, 23), (27, 10), (14, 12), (23, 15), (7, 29), (6, 25), (22, 31), (35, 10), (2, 13), (33, 10), (33, 0), (12, 33), (19, 20), (8, 13), (4, 7), (13, 7), (28, 22), (24, 20), (28, 31), (19, 27), (15, 15), (11, 12), (1, 20), (2, 25), (16, 11), (3, 14), (35, 8), (13, 26), (27, 5), (25, 19), (11, 5), (15, 29), (9, 5), (10, 14), (10, 17), (7, 32), (18, 9), (25, 1), (32, 23), (32, 22), (9, 14), (35, 6), (9, 13), (10, 15), (22, 10), (6, 23), (32, 3), (20, 33), (13, 20), (9, 16), (31, 31), (23, 18), (15, 14), (6, 12), (33, 6), (11, 10), (32, 10), (22, 22), (24, 24), (34, 26), (21, 0), (9, 22), (35, 19), (11, 14), (20, 19), (17, 17), (34, 6), (15, 3), (27, 18), (13, 2), (24, 32), (3, 17), (8, 5), (22, 17), (20, 30), (18, 2), (4, 14), (23, 6), (25, 28), (8, 26), (11, 33), (21, 18), (26, 15), (30, 21), (3, 28), (11, 0), (18, 22), (3, 20), (15, 27), (34, 27), (30, 25), (26, 11), (2, 23), (35, 18), (33, 15), (35, 21), (18, 0), (6, 30), (2, 5), (16, 27), (20, 13), (17, 16), (0, 27), (35, 9), (23, 14), (6, 6), (14, 1), (27, 2), (29, 27), (4, 33), (4, 20), (22, 3), (12, 0), (27, 25), (31, 33), (19, 5), (27, 1), (4, 3), (22, 28), (34, 25), (14, 21), (33, 27), (22, 2), (17, 0), (21, 12), (18, 7), (17, 25), (14, 20), (7, 28), (16, 24), (1, 12), (11, 11), (29, 20), (27, 33), (25, 26), (16, 16), (31, 22), (30, 26), (23, 5), (32, 2), (26, 8), (26, 20), (7, 15), (31, 30), (26, 33), (12, 20), (35, 3), (1, 6), (27, 20), (12, 5), (14, 18), (29, 32), (3, 9), (31, 4), (34, 14), (17, 33), (6, 8), (8, 3), (6, 26), (19, 17), (34, 18), (18, 16), (23, 1), (24, 4), (27, 17), (25, 25), (4, 30), (16, 6), (31, 2), (2, 31), (0, 13), (13, 1), (18, 26), (11, 9), (33, 9), (16, 8), (21, 2), (5, 28), (28, 9), (17, 10), (4, 5), (12, 19), (8, 15), (27, 28), (18, 15), (23, 3), (1, 8), (31, 23), (24, 8), (22, 20), (6, 9), (9, 31), (14, 32), (26, 30), (30, 23), (33, 22), (6, 11), (17, 7), (5, 12), (10, 10), (27, 3), (28, 29), (5, 24), (21, 32), (2, 28), (28, 0), (30, 5), (2, 19), (32, 33), (14, 3), (29, 9), (35, 17), (33, 30), (11, 25), (31, 18), (29, 30), (31, 26), (35, 14), (19, 0), (29, 12), (9, 26), (22, 12), (19, 11), (9, 2), (4, 29), (29, 5), (4, 11), (34, 28), (20, 16), (28, 13), (19, 14), (0, 18), (28, 14), (7, 17), (17, 24), (34, 11), (19, 30), (31, 12), (2, 8), (25, 30), (17, 18), (16, 7), (1, 11), (35, 27), (29, 19), (2, 32), (9, 27), (6, 22), (12, 23), (3, 18), (19, 4), (0, 29), (9, 29), (9, 20), (17, 13), (24, 0), (23, 28), (4, 26), (11, 24), (33, 18), (14, 30), (1, 25), (14, 27), (2, 15), (33, 26), (33, 20), (4, 12), (17, 23), (25, 14), (22, 32), (16, 9), (1, 21), (25, 32), (19, 9), (6, 4), (14, 23), (10, 6), (13, 5), (4, 9), (24, 13), (15, 5), (1, 26), (29, 0), (20, 2), (29, 22), (7, 8), (28, 4), (25, 22), (34, 33), (2, 27), (32, 11), (29, 11), (9, 32), (20, 14), (13, 17), (32, 25), (7, 2), (27, 24), (10, 3), (32, 7), (12, 7), (22, 18), (1, 15), (27, 23), (33, 8), (13, 15), (26, 29), (9, 33), (26, 9), (26, 32), (26, 22), (7, 23), (28, 6), (10, 19), (4, 10), (16, 25), (25, 17), (32, 28), (12, 2), (6, 18), (14, 10), (35, 1), (8, 4), (35, 30), (16, 5), (13, 22), (16, 29), (16, 30), (33, 16), (26, 3), (13, 3), (16, 26), (30, 18), (27, 30), (25, 0), (4, 16), (13, 21), (6, 2), (12, 12), (19, 3), (26, 10), (9, 12), (27, 12), (30, 30), (21, 23), (23, 2), (30, 29), (7, 4), (32, 6), (6, 19), (18, 30), (5, 18), (17, 30), (27, 13), (5, 19), (26, 31), (7, 9), (24, 17), (13, 29), (21, 31), (14, 29), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159984", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), 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), (30, 16), (30, 32), (27, 3), (2, 35), (29, 20), (3, 20), (3, 10), (24, 34), (23, 15), (32, 13), (6, 8), (15, 6), (22, 21), (6, 14), (9, 30), (9, 14), (16, 22), (2, 27), (3, 11), (9, 6), (5, 5), (25, 37), (20, 29), (11, 11), (16, 8), (2, 31), (17, 30), (15, 17), (31, 28), (0, 25), (1, 32), (21, 17), (15, 2), (12, 7), (27, 32), (16, 17), (20, 30), (15, 34), (16, 35), (27, 23), (14, 6), (27, 14), (14, 36), (27, 36), (26, 26), (22, 6), (12, 0), (30, 36), (21, 7), (12, 4), (16, 3), (31, 21), (31, 16), (23, 6), (19, 3), (21, 27), (16, 7), (16, 30), (4, 24), (0, 10), (11, 23), (32, 17), (9, 28), (13, 17), (29, 1), (30, 11), (31, 25), (4, 13), (17, 29), (19, 5), (6, 21), (11, 30), (0, 3), (25, 18), (28, 13), (26, 16), (2, 37), (23, 23), (27, 21), (9, 17), (14, 2), (1, 2), (8, 18), (17, 36), (4, 4), (25, 26), (20, 1), (17, 7), (30, 30), (8, 12), (10, 4), (9, 33), (30, 9), (32, 24), (24, 6), (25, 30), (20, 16), (11, 12), (24, 16), (12, 31), (2, 36), (30, 29), (1, 33), (4, 14), (11, 22), (21, 24), (16, 32), (0, 37), (27, 17), (24, 7), (25, 14), (2, 17), (6, 1), (9, 16), (7, 9), (18, 13), (31, 3), (27, 22), (21, 12), (5, 0), (27, 6), (12, 19), (7, 35), (11, 36), (21, 11), (16, 23), (16, 0), (21, 2), (15, 27), (25, 27), (18, 21), (16, 33), (29, 2), (13, 5), (15, 7), (22, 12), (11, 24), (23, 19), (0, 15), (28, 4), (0, 12), (21, 25), (11, 31), (31, 23), (7, 10), (31, 26), (14, 26), (5, 15), (5, 31), (29, 23), (13, 21), (9, 24), (17, 27), (7, 29), (27, 31), (29, 34), (26, 3), (28, 2), (25, 24), (23, 10), (26, 11), (18, 1), (17, 12), (1, 0), (20, 14), (14, 30), (18, 35), (26, 8), (27, 8), (4, 35), (24, 10), (27, 37), (13, 31), (22, 27), (11, 6), (15, 29), (14, 11), (31, 2), (20, 35), (3, 3), (24, 27), (21, 6), (6, 26), (25, 10), (32, 4), (25, 11), (22, 15), (16, 14), (18, 37), (28, 27), (32, 31), (19, 19), (10, 12), (15, 32), (20, 25), (11, 7), (7, 36), (22, 29), (13, 20), (27, 33), (27, 30), (8, 2), (31, 32), (29, 15), (10, 2), (20, 5), (9, 34), (24, 15), (17, 2), (21, 0), (0, 28), (29, 5), (12, 29), (30, 24), (25, 33), (12, 34), (4, 9), (21, 4), (27, 13), (20, 24), (11, 15), (28, 23), (30, 31), (19, 24), (23, 12), (14, 17), (3, 27), (22, 13), (20, 19), (16, 6), (23, 25), (11, 33), (22, 8), (18, 10), (28, 30), (20, 31), (15, 9), (28, 22), (14, 34), (13, 24), (30, 0), (3, 13), (27, 0), (3, 30), (3, 9), (4, 2), (17, 16), (9, 7), (2, 21), (8, 36), (5, 28), (5, 22), (25, 35), (3, 14), (17, 26), (5, 3), (1, 26), (10, 6), (19, 25), (25, 17), (23, 36), (25, 29), (2, 14), (13, 19), (31, 37), (8, 24), (25, 19), (0, 27), (8, 10), (10, 32), (21, 14), (3, 22), (14, 25), (25, 16), (25, 22), (9, 27), (10, 31), (7, 0), (21, 16), (1, 19), (7, 12), (23, 26), (24, 1), (10, 14), (2, 32), (6, 6), (10, 23), (23, 35), (16, 34), (30, 13), (10, 19), (12, 15), (26, 9), (2, 12), (7, 28), (21, 15), (31, 17), (15, 37), (18, 7), (0, 33), (20, 8), (6, 19), (8, 11), (13, 25), (6, 3), (24, 24), (28, 17), (16, 20), (26, 18), (21, 37), (22, 10), (17, 3), (21, 31), (10, 13), (2, 6), (28, 6), (25, 23), (2, 24), (4, 10), (6, 2), (21, 5), (28, 16), (14, 29), (8, 7), (17, 18), (8, 26), (7, 13), (20, 4), (10, 5), (26, 28), (6, 34), (29, 28), (28, 26), (31, 8), (3, 19), (23, 14), (24, 13), (18, 16), (22, 7), (12, 16), (14, 8), (8, 20), (29, 8), (24, 32), (16, 1), (20, 27), (8, 13), (19, 7), (19, 32), (10, 29), (4, 30), (8, 31), (16, 2), (26, 12), (30, 25), (30, 23), (29, 10), (30, 21), (14, 5), (32, 11), (11, 3), (13, 27), (29, 12), (15, 19), (26, 17), (22, 37), (1, 3), (21, 34), (7, 31), (2, 9), (29, 27), (18, 14), (11, 21), (2, 8), (3, 26), (5, 35), (19, 35), (17, 5), (5, 37), (32, 25), (19, 1), (32, 5), (11, 25), (31, 5), (20, 3), (16, 27), (22, 24), (2, 29), (12, 37), (31, 33), (14, 21), (31, 4), (10, 22), (10, 8), (2, 28), (29, 26), (14, 37), (17, 10), (26, 10), (28, 24), (15, 36), (11, 28), (6, 27), (0, 30), (9, 36), (10, 33), (30, 17), (9, 29), (1, 8), (27, 35), (15, 30), (25, 3), (1, 7), (14, 15), (2, 5), (0, 2), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 29), (23, 15), (34, 15), (31, 26), (10, 4), (20, 0), (15, 31), (24, 24), (36, 34), (38, 26), (8, 3), (15, 34), (29, 2), (27, 33), (18, 3), (18, 7), (6, 30), (34, 22), (12, 26), (22, 29), (35, 34), (26, 33), (30, 29), (8, 11), (20, 23), (7, 6), (28, 23), (37, 20), (9, 23), (7, 29), (11, 25), (36, 24), (20, 10), (10, 3), (15, 26), (17, 34), (5, 28), (6, 21), (37, 21), (21, 8), (18, 25), (8, 18), (14, 30), (11, 7), (29, 9), (24, 23), (33, 14), (6, 9), (15, 13), (8, 21), (22, 5), (22, 10), (27, 21), (35, 3), (9, 1), (10, 26), (7, 23), (15, 21), (23, 11), (7, 16), (18, 0), (13, 34), (11, 31), (23, 13), (2, 5), (11, 17), (1, 18), (34, 1), (11, 15), (9, 11), (23, 0), (19, 3), (27, 12), (33, 13), (14, 5), (31, 12), (15, 1), (20, 15), (5, 27), (35, 10), (29, 15), (28, 29), (35, 17), (12, 28), (35, 11), (1, 8), (14, 12), (2, 32), (19, 6), (2, 3), (12, 2), (23, 28), (29, 29), (22, 20), (36, 15), (26, 1), (36, 23), (37, 34), (27, 2), (19, 34), (12, 23), (14, 26), (0, 25), (27, 1), (11, 3), (36, 1), (21, 2), (34, 6), (20, 27), (16, 27), (7, 17), (32, 22), (37, 25), (10, 18), (21, 0), (25, 9), (7, 30), (24, 32), (31, 19), (13, 13), (20, 24), (12, 24), (30, 22), (30, 13), (14, 10), (7, 20), (30, 21), (0, 16), (2, 1), (0, 12), (1, 29), (13, 15), (4, 19), (17, 29), (4, 8), (9, 26), (23, 26), (29, 19), (4, 4), (25, 1), (10, 25), (16, 22), (17, 14), (3, 28), (23, 21), (0, 15), (9, 32), (36, 22), (28, 28), (25, 24), (6, 20), (6, 26), (24, 7), (0, 9), (3, 17), (8, 0), (17, 24), (29, 28), (37, 0), (9, 22), (12, 30), (8, 4), (4, 20), (16, 12), (33, 15), (5, 10), (14, 9), (19, 29), (18, 24), (23, 10), (26, 5), (31, 29), (30, 20), (12, 29), (1, 24), (12, 33), (35, 32), (5, 13), (23, 1), (31, 10), (36, 30), (0, 13), (13, 19), (2, 25), (34, 11), (6, 32), (17, 17), (25, 20), (16, 6), (32, 10), (19, 9), (27, 15), (18, 32), (0, 32), (28, 20), (25, 18), (4, 3), (12, 18), (29, 11), (36, 32), (3, 4), (14, 28), (31, 32), (23, 7), (26, 2), (4, 15), (34, 25), (16, 8), (37, 3), (38, 31), (21, 31), (22, 17), (36, 8), (16, 32), (34, 10), (2, 11), (14, 16), (11, 21), (26, 22), (20, 29), (4, 21), (27, 16), (16, 19), (34, 2), (3, 23), (29, 5), (24, 20), (11, 26), (24, 31), (37, 11), (0, 27), (11, 11), (19, 21), (31, 7), (30, 10), (14, 1), (27, 8), (32, 6), (5, 2), (9, 15), (38, 23), (13, 27), (16, 9), (27, 26), (22, 23), (38, 16), (22, 8), (4, 32), (7, 32), (29, 25), (10, 15), (9, 27), (25, 21), (19, 8), (6, 23), (34, 31), (25, 11), (26, 20), (0, 5), (17, 3), (0, 4), (30, 23), (12, 4), (26, 8), (37, 27), (23, 23), (21, 34), (33, 21), (27, 11), (33, 29), (3, 11), (19, 2), (21, 4), (15, 2), (7, 28), (25, 28), (21, 9), (14, 7), (17, 9), (6, 8), (11, 19), (24, 26), (9, 33), (37, 24), (22, 11), (35, 27), (36, 18), (10, 12), (21, 24), (17, 12), (38, 14), (14, 2), (28, 27), (4, 16), (27, 14), (32, 32), (2, 6), (10, 14), (20, 17), (1, 1), (24, 19), (7, 22), (2, 31), (29, 21), (38, 1), (18, 6), (11, 29), (14, 20), (36, 14), (13, 7), (33, 19), (0, 31), (25, 32), (13, 17), (28, 18), (30, 30), (21, 6), (3, 14), (18, 28), (34, 30), (11, 24), (6, 18), (23, 18), (10, 16), (33, 5), (0, 33), (17, 25), (37, 32), (11, 22), (27, 27), (8, 10), (21, 22), (14, 24), (38, 2), (30, 12), (28, 17), (5, 9), (22, 34), (35, 21), (7, 9), (29, 18), (10, 9), (13, 20), (26, 29), (1, 7), (6, 0), (31, 15), (18, 15), (25, 16), (20, 20), (18, 4), (16, 13), (34, 34), (11, 10), (12, 20), (4, 0), (8, 33), (2, 33), (17, 31), (25, 27), (28, 12), (28, 26), (2, 13), (36, 5), (14, 22), (12, 9), (28, 33), (7, 15), (36, 10), (13, 5), (6, 4), (35, 18), (9, 12), (32, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399042", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 26), (20, 30), (25, 2), (21, 5), (14, 0), (31, 0), (17, 0), (13, 19), (3, 10), (6, 1), (24, 18), (22, 16), (2, 10), (27, 0), (11, 31), (32, 23), (28, 19), (19, 26), (7, 10), (8, 5), (22, 23), (11, 32), (13, 22), (32, 3), (6, 30), (30, 21), (15, 9), (20, 17), (8, 6), (0, 22), (13, 13), (32, 29), (13, 24), (30, 12), (30, 0), (27, 17), (7, 7), (31, 1), (22, 8), (12, 16), (5, 22), (30, 14), (25, 1), (27, 8), (4, 28), (18, 35), (1, 26), (16, 15), (9, 6), (15, 32), (14, 34), (4, 19), (12, 12), (13, 30), (1, 27), (29, 35), (13, 15), (16, 30), (26, 34), (27, 29), (4, 6), (28, 2), (13, 21), (7, 4), (6, 29), (29, 17), (2, 16), (0, 35), (19, 9), (11, 2), (20, 13), (0, 34), (20, 11), (19, 7), (22, 22), (24, 6), (16, 24), (0, 32), (30, 7), (6, 23), (23, 28), (12, 9), (13, 20), (15, 4), (28, 10), (6, 26), (21, 7), (19, 19), (2, 23), (20, 14), (20, 16), (6, 11), (30, 19), (25, 25), (7, 21), (0, 29), (32, 28), (4, 5), (8, 14), (30, 13), (6, 15), (19, 24), (22, 18), (2, 31), (0, 10), (11, 7), (30, 22), (13, 17), (14, 29), (15, 5), (0, 27), (9, 4), (26, 17), (21, 0), (23, 10), (29, 29), (30, 18), (6, 14), (2, 4), (7, 6), (17, 33), (26, 1), (4, 24), (20, 31), (16, 26), (30, 10), (24, 34), (23, 22), (20, 34), (5, 13), (25, 24), (21, 31), (26, 21), (3, 25), (17, 16), (16, 17), (12, 25), (1, 33), (4, 25), (9, 27), (26, 28), (0, 16), (25, 7), (25, 28), (23, 4), (12, 31), (18, 6), (4, 23), (10, 28), (12, 35), (12, 2), (24, 35), (25, 31), (14, 10), (29, 1), (31, 6), (10, 11), (32, 12), (19, 15), (22, 13), (23, 14), (20, 19), (2, 12), (4, 21), (1, 14), (20, 9), (25, 14), (30, 35), (27, 26), (22, 30), (7, 31), (22, 31), (30, 30), (30, 24), (11, 34), (1, 13), (32, 20), (21, 21), (19, 27), (13, 3), (18, 20), (9, 1), (13, 12), (24, 14), (21, 2), (24, 23), (12, 8), (0, 18), (27, 16), (23, 15), (5, 23), (4, 35), (27, 34), (17, 6), (20, 27), (30, 31), (2, 17), (23, 13), (4, 4), (16, 33), (7, 28), (14, 24), (0, 20), (20, 35), (27, 15), (1, 35), (19, 29), (7, 25), (23, 0), (6, 16), (26, 27), (14, 27), (11, 20), (3, 35), (29, 25), (0, 17), (28, 31), (4, 29), (12, 5), (11, 30), (21, 14), (26, 11), (14, 28), (29, 5), (0, 13), (29, 30), (26, 12), (30, 3), (3, 4), (26, 24), (6, 4), (7, 8), (31, 7), (18, 13), (17, 7), (8, 17), (4, 9), (27, 21), (10, 34), (30, 23), (26, 13), (27, 10), (18, 12), (20, 29), (2, 19), (24, 31), (9, 30), (29, 26), (9, 16), (4, 18), (32, 27), (19, 34), (30, 2), (30, 11), (28, 1), (8, 16), (8, 28), (11, 11), (2, 0), (3, 14), (11, 29), (17, 1), (7, 13), (31, 15), (18, 7), (1, 29), (5, 7), (24, 25), (5, 24), (31, 21), (26, 4), (11, 19), (9, 31), (9, 24), (3, 33), (32, 9), (26, 0), (18, 22), (4, 32), (5, 12), (16, 13), (25, 9), (2, 20), (23, 1), (11, 28), (7, 5), (24, 27), (14, 25), (6, 0), (17, 21), (11, 35), (9, 22), (6, 17), (23, 12), (10, 7), (4, 8), (11, 10), (13, 4), (30, 9), (5, 6), (17, 12), (1, 23), (14, 9), (8, 25), (0, 3), (11, 12), (21, 15), (8, 27), (28, 22), (16, 14), (9, 14), (15, 14), (11, 25), (2, 3), (14, 4), (15, 29), (31, 2), (0, 30), (14, 17), (8, 29), (29, 10), (22, 19), (11, 16), (21, 13), (13, 5), (25, 21), (7, 3), (1, 10), (27, 3), (23, 34), (4, 13), (4, 15), (14, 3), (31, 17), (17, 2), (22, 4), (15, 23), (28, 28), (0, 11), (3, 16), (23, 25), (19, 8), (15, 8), (20, 22), (12, 3), (30, 15), (24, 11), (25, 12), (22, 10), (22, 27), (7, 14), (15, 24), (2, 32), (6, 3), (6, 25), (25, 32), (30, 33), (0, 7), (10, 4), (14, 19), (27, 12), (31, 22), (18, 24), (20, 23), (17, 10), (2, 26), (32, 30), (14, 15), (9, 25), (27, 9), (31, 32), (17, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734103", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 1), (17, 15), (32, 27), (23, 21), (9, 16), (17, 8), (36, 10), (12, 11), (36, 13), (28, 23), (34, 23), (28, 6), (8, 6), (19, 8), (18, 22), (6, 0), (37, 7), (2, 18), (11, 8), (13, 8), (11, 16), (9, 2), (14, 23), (26, 22), (7, 12), (6, 10), (13, 2), (37, 20), (9, 10), (33, 11), (16, 8), (0, 21), (27, 4), (5, 14), (23, 15), (25, 6), (37, 1), (20, 25), (21, 24), (6, 11), (27, 0), (36, 16), (11, 4), (13, 12), (30, 16), (24, 25), (33, 12), (29, 28), (0, 3), (6, 2), (12, 19), (21, 4), (11, 11), (10, 26), (6, 25), (5, 1), (18, 26), (12, 3), (25, 9), (5, 2), (15, 1), (15, 19), (26, 4), (15, 18), (15, 7), (28, 7), (22, 19), (15, 10), (6, 4), (29, 5), (15, 0), (26, 5), (34, 10), (13, 19), (34, 26), (23, 5), (4, 27), (9, 13), (22, 20), (11, 2), (23, 2), (19, 29), (7, 6), (11, 21), (23, 9), (10, 0), (10, 11), (26, 12), (36, 9), (34, 19), (32, 28), (33, 23), (18, 19), (31, 15), (6, 1), (34, 16), (31, 23), (18, 14), (17, 16), (26, 1), (3, 27), (0, 29), (35, 12), (16, 25), (37, 8), (21, 16), (29, 19), (19, 22), (37, 11), (26, 29), (1, 0), (12, 12), (36, 28), (2, 22), (9, 7), (3, 12), (5, 10), (23, 8), (26, 28), (29, 26), (17, 9), (23, 4), (31, 28), (16, 22), (2, 17), (22, 6), (9, 17), (28, 0), (29, 2), (12, 25), (21, 9), (25, 7), (23, 12), (1, 20), (23, 28), (29, 16), (33, 17), (22, 15), (10, 22), (1, 13), (14, 8), (17, 13), (32, 29), (2, 29), (7, 11), (8, 15), (6, 29), (26, 19), (25, 15), (2, 21), (10, 20), (34, 27), (28, 26), (32, 24), (32, 26), (23, 20), (3, 22), (26, 27), (25, 16), (1, 26), (5, 3), (23, 17), (14, 14), (9, 20), (0, 13), (8, 28), (18, 17), (22, 1), (35, 29), (9, 25), (3, 29), (18, 24), (7, 13), (1, 4), (36, 2), (36, 11), (8, 27), (2, 10), (33, 5), (19, 3), (4, 13), (28, 13), (22, 14), (20, 7), (22, 0), (22, 16), (30, 24), (33, 29), (17, 14), (18, 21), (30, 3), (25, 0), (29, 8), (12, 10), (16, 19), (27, 1), (17, 26), (21, 28), (28, 3), (14, 21), (20, 23), (10, 1), (31, 1), (16, 2), (27, 28), (29, 3), (14, 28), (12, 13), (17, 24), (9, 0), (14, 20), (3, 26), (22, 18), (23, 26), (6, 26), (11, 15), (31, 4), (7, 20), (22, 8), (31, 12), (8, 26), (13, 22), (14, 19), (25, 19), (5, 9), (24, 14), (10, 19), (17, 17), (28, 21), (26, 3), (31, 26), (23, 14), (25, 25), (20, 26), (12, 18), (4, 23), (21, 11), (7, 14), (32, 7), (28, 4), (16, 27), (15, 11), (13, 17), (3, 10), (12, 9), (2, 13), (0, 11), (35, 2), (35, 27), (19, 19), (35, 24), (24, 28), (33, 25), (21, 14), (33, 10), (33, 2), (4, 11), (29, 13), (28, 19), (5, 15), (6, 24), (8, 25), (34, 2), (24, 9), (18, 18), (8, 10), (8, 8), (29, 15), (16, 4), (25, 12), (11, 12), (3, 4), (18, 0), (7, 22), (2, 9), (0, 16), (36, 21), (2, 25), (12, 2), (20, 12), (13, 20), (14, 22), (13, 9), (35, 26), (16, 14), (15, 6), (19, 23), (33, 19), (21, 8), (30, 26), (21, 29), (9, 27), (18, 8), (37, 13), (9, 28), (30, 8), (30, 13), (14, 9), (26, 17), (31, 9), (21, 1), (17, 10), (9, 12), (24, 27), (34, 3), (11, 10), (27, 11), (2, 26), (24, 6), (5, 17), (15, 23), (11, 23), (3, 13), (23, 25), (11, 24), (3, 24), (3, 18), (35, 10), (20, 9), (3, 15), (20, 1), (29, 20), (27, 10), (30, 14), (37, 16), (3, 16), (35, 5), (4, 21), (34, 1), (6, 17), (13, 14), (28, 1), (13, 21), (1, 29), (26, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898128", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), 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), (25, 0), (14, 14), (1, 10), (7, 4), (7, 25), (27, 23), (22, 5), (14, 23), (12, 5), (4, 13), (2, 29), (30, 23), (14, 2), (5, 0), (6, 10), (1, 29), (16, 25), (11, 0), (12, 7), (6, 19), (13, 17), (6, 24), (0, 8), (21, 16), (10, 11), (32, 1), (11, 21), (7, 24), (14, 21), (21, 12), (19, 18), (30, 3), (31, 14), (22, 17), (1, 12), (11, 10), (21, 15), (24, 25), (20, 26), (24, 15), (16, 22), (25, 25), (21, 7), (13, 21), (33, 28), (6, 7), (17, 2), (23, 26), (11, 1), (16, 11), (14, 11), (31, 12), (24, 1), (10, 21), (10, 20), (19, 26), (3, 23), (21, 9), (20, 20), (28, 5), (19, 7), (1, 14), (18, 23), (10, 5), (26, 16), (33, 6), (13, 13), (8, 0), (26, 17), (23, 16), (7, 18), (3, 19), (19, 28), (14, 28), (25, 22), (6, 14), (0, 25), (9, 15), (19, 22), (3, 20), (20, 29), (20, 3), (32, 2), (18, 10), (26, 4), (5, 1), (33, 26), (4, 23), (33, 8), (6, 18), (24, 21), (6, 1), (7, 9), (30, 11), (23, 15), (2, 8), (29, 0), (29, 27), (18, 6), (2, 1), (8, 19), (23, 1), (0, 2), (9, 13), (22, 8), (16, 20), (2, 25), (28, 25), (29, 4), (6, 13), (29, 29), (2, 3), (22, 25), (12, 23), (30, 1), (9, 5), (0, 7), (0, 1), (10, 29), (26, 2), (6, 28), (12, 27), (13, 16), (28, 22), (22, 28), (10, 0), (17, 21), (2, 11), (0, 12), (24, 9), (16, 2), (27, 5), (23, 6), (18, 13), (4, 10), (22, 1), (12, 6), (27, 26), (24, 11), (8, 20), (25, 5), (17, 14), (14, 27), (5, 12), (31, 0), (17, 5), (10, 6), (32, 5), (23, 12), (14, 12), (19, 24), (5, 19), (31, 25), (24, 23), (17, 28), (25, 7), (32, 13), (12, 15), (23, 4), (29, 6), (7, 6), (27, 7), (32, 4), (21, 14), (15, 15), (0, 17), (27, 21), (27, 8), (9, 29), (18, 14), (31, 16), (11, 5), (18, 7), (16, 1), (4, 14), (30, 4), (3, 8), (31, 24), (31, 20), (30, 24), (17, 10), (28, 17), (26, 9), (30, 27), (12, 1), (14, 5), (4, 29), (7, 10), (30, 8), (17, 15), (24, 24), (12, 4), (17, 17), (1, 18), (9, 3), (24, 16), (16, 18), (25, 10), (1, 8), (22, 10), (18, 27), (5, 16), (15, 8), (12, 8), (16, 10), (20, 7), (4, 28), (9, 1), (29, 17), (13, 2), (3, 6), (15, 17), (6, 15), (18, 17), (21, 3), (17, 20), (33, 0), (1, 25), (2, 2), (31, 3), (10, 23), (16, 6), (33, 1), (5, 9), (1, 27), (24, 22), (32, 26), (8, 11), (28, 3), (10, 1), (15, 4), (32, 22), (24, 10), (31, 7), (23, 24), (31, 17), (27, 15), (16, 19), (15, 10), (26, 12), (29, 21), (6, 12), (24, 19), (17, 29), (17, 19), (19, 5), (6, 23), (24, 12), (29, 11), (26, 8), (22, 24), (19, 1), (29, 18), (14, 0), (15, 27), (17, 12), (27, 22), (9, 25), (4, 3), (30, 25), (33, 19), (9, 28), (4, 6), (2, 15), (29, 7), (0, 28), (11, 15), (23, 2), (28, 13), (18, 9), (14, 19), (13, 22), (12, 17), (8, 7), (8, 26), (25, 4), (16, 23), (2, 13), (23, 21), (29, 10), (18, 2), (17, 24), (16, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882096", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 3), (27, 26), (3, 5), (5, 7), (23, 17), (8, 15), (14, 15), (16, 30), (19, 0), (34, 5), (14, 29), (16, 34), (7, 17), (32, 10), (3, 0), (9, 12), (32, 36), (27, 37), (1, 11), (8, 34), (31, 38), (32, 26), (4, 17), (20, 11), (28, 0), (7, 20), (15, 33), (19, 7), (10, 9), (28, 13), (10, 16), (9, 31), (23, 36), (20, 25), (14, 34), (17, 30), (29, 19), (10, 2), (26, 15), (4, 34), (26, 1), (18, 21), (5, 13), (35, 2), (23, 35), (23, 5), (6, 34), (1, 21), (5, 34), (1, 36), (15, 0), (1, 8), (4, 20), (28, 6), (19, 18), (31, 37), (19, 6), (21, 0), (27, 27), (36, 20), (0, 11), (27, 0), (30, 32), (23, 4), (8, 32), (0, 23), (25, 16), (13, 37), (29, 35), (1, 6), (7, 23), (17, 33), (25, 13), (13, 19), (25, 0), (9, 4), (4, 35), (29, 17), (6, 23), 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"469440", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (0, 2), (22, 28), (19, 31), (21, 16), (11, 0), (17, 8), (5, 17), (28, 33), (29, 9), (30, 30), (28, 30), (23, 0), (33, 6), (28, 6), (18, 26), (13, 25), (19, 19), (11, 28), (5, 26), (9, 31), (26, 0), (31, 15), (23, 2), (5, 6), (11, 4), (31, 34), (24, 3), (24, 8), (25, 19), (30, 10), (25, 28), (29, 18), (8, 31), (1, 22), (23, 24), (11, 12), (2, 1), (20, 2), (9, 23), (31, 28), (0, 15), (15, 26), (29, 21), (28, 12), (25, 1), (25, 24), (10, 16), (5, 8), (14, 29), (35, 22), (13, 22), (5, 31), (22, 27), (17, 17), (31, 17), (29, 13), (6, 23), (22, 22), (17, 1), (31, 0), (33, 17), (4, 18), (11, 15), (35, 11), (28, 13), (19, 6), (21, 27), (28, 8), (33, 8), (8, 15), (0, 9), (8, 1), (28, 11), (16, 20), (21, 9), (1, 11), (26, 30), (26, 25), (11, 34), (15, 31), (20, 30), (32, 34), (22, 25), (23, 22), (21, 14), (9, 8), (23, 8), (22, 31), (12, 0), (30, 1), (9, 12), (33, 19), (19, 29), (14, 4), (7, 14), (2, 20), (24, 5), (31, 22), (11, 24), (21, 32), (35, 6), (26, 23), (9, 4), (1, 23), (11, 10), (33, 4), (17, 32), (22, 16), (0, 28), (23, 18), (20, 28), (33, 34), (26, 27), (10, 23), (27, 5), (28, 23), (7, 6), (32, 19), (0, 20), (32, 2), (13, 8), (28, 9), (19, 5), (34, 32), (18, 6), (17, 0), (2, 33), (5, 18), (34, 2), (8, 21), (7, 2), (28, 26), (22, 6), (4, 23), (10, 19), (15, 33), (10, 20), (33, 22), (10, 8), (5, 10), (27, 33), (28, 0), (35, 29), (2, 17), (35, 3), (13, 33), (10, 5), (22, 24), (26, 2), (33, 30), (9, 1), (35, 17), (6, 16), (8, 10), (28, 18), (3, 9), (11, 21), (27, 24), (32, 8), (4, 20), (3, 2), (23, 1), (26, 12), (12, 5), (12, 34), (31, 13), (2, 24), (25, 2), (9, 19), (24, 17), (4, 1), (27, 19), (11, 2), (22, 20), (29, 20), (28, 16), (30, 32), (31, 24), (7, 33), (24, 11), (7, 10), (4, 10), (9, 24), (23, 30), (29, 11), (11, 5), (16, 24), (23, 28), (18, 16), (19, 14), (3, 5), (17, 14), (4, 14), (8, 3), (33, 24), (32, 29), (30, 34), (11, 18), (26, 3), (18, 3), (3, 7), (25, 5), (14, 27), (34, 8), (13, 5), (27, 28), (35, 33), (30, 6), (30, 3), (8, 34), (15, 8), (4, 32), (31, 26), (31, 33), (30, 7), (0, 16), (7, 13), (25, 9), (7, 21), (27, 26), (6, 32), (17, 3), (7, 20), (20, 12), (29, 31), (13, 30), (28, 28), (3, 18), (24, 29), (12, 9), (20, 26), (23, 19), (23, 26), (3, 16), (11, 32), (17, 21), (6, 24), (1, 9), (12, 27), (11, 6), (33, 23), (4, 24), (0, 22), (16, 12), (5, 27), (32, 5), (10, 3), (15, 34), (35, 25), (32, 26), (20, 25), (4, 31), (7, 24), (18, 31), (34, 12), (26, 10), (16, 6), (25, 33), (10, 34), (15, 28), (7, 11), (15, 16), (35, 14), (8, 28), (26, 15), (29, 12), (22, 11), (14, 24), (25, 20), (13, 18), (34, 10), (20, 34), (30, 9), (16, 22), (9, 10), (10, 7), (28, 10), (1, 16), (1, 25), (13, 6), (7, 19), (17, 23), (3, 32), (34, 29), (10, 14), (13, 21), (5, 29), (19, 15), (32, 21), (20, 3), (22, 30), (17, 22), (32, 10), (0, 30), (12, 11), (28, 32), (4, 26), (12, 18), (13, 24), (25, 23), (23, 7), (22, 14), (6, 17), (0, 25), (33, 15), (11, 27), (25, 11), (0, 3), (6, 29), (6, 9), (11, 8), (7, 12), (16, 23), (28, 34), (25, 14), (3, 0), (25, 32), (27, 12), (14, 2), (29, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206336", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 24), (21, 19), (35, 31), (9, 22), (11, 1), (18, 5), (23, 9), (24, 27), (7, 23), (2, 18), (26, 30), (10, 11), (5, 25), (14, 15), (1, 10), (4, 10), (2, 23), (34, 7), (22, 9), (21, 29), (36, 23), (16, 14), (11, 25), (18, 18), (33, 8), (6, 9), (33, 17), (16, 0), (12, 2), (5, 4), (7, 13), (8, 14), (5, 11), (20, 29), (3, 8), (4, 0), (32, 23), (8, 4), (31, 23), (35, 9), (13, 12), (12, 6), (13, 1), (32, 26), (30, 6), (6, 6), (5, 5), (14, 27), (32, 5), (26, 8), (7, 2), (15, 25), (3, 28), (24, 19), (22, 2), (22, 31), (14, 30), (29, 22), (19, 15), (25, 0), (3, 0), (31, 27), (27, 6), (18, 23), (25, 3), (10, 20), (4, 20), (12, 13), (0, 19), (24, 22), (31, 17), (6, 20), (0, 1), (30, 2), (17, 13), (32, 31), (21, 20), (27, 26), (8, 26), (22, 1), (13, 5), (19, 12), (29, 14), (4, 25), (1, 6), (5, 26), (7, 24), (9, 19), (25, 4), (19, 10), (0, 31), (25, 19), (16, 30), (17, 8), (18, 22), (25, 8), (0, 7), (29, 6), (31, 26), (21, 16), (35, 7), (13, 29), (34, 14), (19, 17), (3, 11), (2, 31), (10, 15), (5, 13), (13, 20), (27, 20), (22, 4), (16, 15), (33, 6), (5, 16), (10, 12), (17, 21), (19, 1), (11, 13), (13, 31), (29, 15), (30, 22), (6, 27), (0, 14), (14, 11), (12, 26), (21, 8), (21, 13), (17, 16), (8, 6), (26, 18), (28, 1), (2, 30), (2, 5), (10, 10), (8, 8), (34, 30), (20, 0), (5, 29), (34, 4), (35, 24), (26, 20), (30, 14), (34, 8), (2, 19), (14, 26), (3, 23), (20, 25), (3, 27), (5, 31), (13, 15), (21, 22), (6, 30), (36, 9), (34, 31), (8, 2), (27, 9), (16, 3), (33, 5), (15, 1), (8, 29), (1, 27), (18, 9), (19, 20), (11, 5), (27, 10), (27, 1), (32, 14), (7, 28), (4, 17), (12, 18), (25, 6), (23, 2), (15, 9), (3, 29), (19, 23), (4, 31), (15, 13), (6, 4), (14, 20), (1, 31), (7, 22), (13, 22), (21, 14), (6, 8), (23, 5), (0, 9), (15, 28), (27, 4), (31, 1), (18, 28), (17, 5), (27, 2), (21, 28), (33, 20), (22, 6), (13, 16), (11, 22), (7, 10), (4, 26), (12, 28), (7, 11), (29, 5), (24, 21), (2, 24), (25, 21), (23, 1), (21, 27), (22, 30), (17, 31), (13, 10), (29, 17), (9, 0), (35, 21), (15, 31), (23, 22), (1, 23), (20, 26), (23, 12), (8, 25), (14, 25), (5, 9), (25, 29), (4, 14), (18, 8), (22, 15), (21, 12), (35, 15), (19, 30), (16, 29), (26, 1), (10, 29), (34, 15), (23, 31), (29, 7), (19, 4), (18, 16), (5, 14), (0, 22), (8, 31), (36, 5), (4, 18), (12, 5), (32, 30), (25, 17), (24, 0), (2, 8), (26, 22), (33, 0), (12, 3), (12, 4), (7, 0), (5, 28), (1, 16), (3, 24), (25, 25), (23, 24), (32, 18), (32, 9), (11, 12), (24, 11), (4, 22), (26, 19), (12, 20), (35, 30), (4, 29), (31, 7), (32, 4), (23, 13), (35, 20), (22, 16), (36, 3), (31, 28), (22, 29), (5, 22), (17, 14), (9, 29), (3, 26), (28, 9), (21, 25), (32, 16), (15, 29), (10, 18), (15, 4), (19, 6), (32, 3), (26, 13), (14, 28), (15, 20), (23, 20), (8, 19), (27, 16), (12, 0), (26, 0), (22, 28), (9, 17), (22, 18), (20, 5), (8, 18), (26, 21), (29, 25), (8, 13), (2, 22), (28, 19), (35, 3), (27, 31), (1, 25), (23, 19), (22, 17), (13, 11), (0, 15), (30, 3), (21, 17), (33, 11), (9, 5), (8, 12), (13, 27), (7, 31), (36, 24), (2, 9), (36, 16), (30, 20), (12, 19), (5, 21), (13, 13), (35, 18), (1, 28), (15, 10), (14, 17), (36, 22), (5, 17), (22, 22), (11, 24), (5, 30), (8, 9), (10, 23), (20, 7), (10, 3), (12, 22), (22, 12), (6, 16), (21, 2), (5, 23), (9, 3), (33, 15), (5, 24), (33, 7), (2, 1), (10, 31), (34, 10), (10, 7), (12, 17), (12, 9), (3, 31), (33, 12), (32, 13), (21, 3), (1, 20), (20, 12), (22, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "893760", "dataset": "MATH"}
{"messages": [{"content": "In a 38x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 1), (11, 24), (15, 10), (30, 2), (24, 8), (14, 2), (25, 14), (5, 0), (33, 0), (23, 31), (2, 16), (4, 27), (1, 15), (28, 12), (10, 7), (27, 23), (22, 20), (17, 15), (23, 13), (9, 30), (28, 13), (23, 0), (25, 20), (14, 0), (16, 22), (37, 12), (29, 5), (23, 20), (4, 26), (28, 23), (27, 21), (3, 21), (5, 16), (14, 4), (17, 10), (6, 0), (7, 6), (19, 5), (24, 19), (31, 7), (4, 15), (13, 1), (19, 19), (16, 19), (2, 8), (23, 9), (29, 12), (23, 8), (7, 25), (12, 21), (13, 20), (36, 28), (27, 20), (35, 13), (16, 14), (18, 29), (29, 11), (3, 4), (26, 28), (19, 27), (18, 22), (19, 20), (25, 11), (7, 7), (1, 16), (9, 29), (16, 18), (3, 16), (24, 0), (15, 4), (25, 18), (0, 17), (14, 27), (13, 19), (25, 4), (28, 3), (29, 14), (15, 29), (18, 24), (18, 10), (33, 8), (16, 28), (15, 1), (37, 28), (17, 6), (6, 4), (22, 2), (26, 25), (33, 9), (24, 11), (17, 23), (11, 10), (8, 23), (25, 21), (16, 9), (30, 5), (34, 5), (25, 12), (2, 14), (12, 12), (9, 3), (12, 17), (14, 10), (1, 22), (34, 12), (14, 28), (30, 21), (9, 22), (2, 21), (22, 0), (30, 22), (9, 13), (14, 30), (24, 28), (29, 13), (8, 4), (10, 0), (29, 20), (14, 29), (10, 26), (16, 21), (25, 26), (9, 2), (5, 14), (20, 26), (37, 22), (25, 15), (15, 20), (4, 13), (37, 30), (4, 22), (28, 1), (26, 30), (22, 16), (21, 8), (17, 8), (8, 21), (10, 24), (35, 8), (13, 5), (0, 14), (36, 11), (27, 12), (5, 4), (8, 12), (35, 10), (7, 1), (16, 15), (35, 0), (2, 30), (10, 15), (15, 18), (17, 7), (30, 7), (35, 1), (37, 10), (37, 19), (18, 27), (5, 3), (16, 27), (23, 4), (33, 27), (10, 30), (27, 27), (13, 27), (34, 0), (34, 22), (0, 29), (35, 18), (17, 1), (36, 16), (33, 7), (36, 15), (36, 1), (22, 7), (33, 26), (19, 8), (23, 5), (19, 12), (8, 20), (23, 17), (14, 9), (31, 9), (27, 11), (18, 30), (32, 18), (18, 26), (3, 11), (28, 16), (12, 14), (31, 18), (34, 16), (35, 27), (32, 5), (35, 20), (12, 27), (19, 29), (18, 14), (13, 17), (14, 7), (0, 9), (12, 18), (2, 4), (18, 6), (14, 22), (32, 29), (20, 24), (4, 14), (21, 27), (17, 3), (25, 28), (7, 13), (33, 19), (3, 14), (8, 18), (25, 3), (11, 0), (22, 10), (22, 19), (21, 4), (26, 11), (7, 18), (1, 18), (26, 2), (14, 25), (7, 19), (30, 6), (21, 28), (36, 3), (1, 8), (0, 6), (19, 3), (13, 23), (1, 19), (34, 23), (2, 6), (10, 10), (15, 11), (32, 21), (33, 5), (13, 21), (23, 26), (18, 19), (16, 4), (0, 18), (2, 1), (8, 10), (26, 12), (19, 22), (32, 17), (36, 10), (32, 2), (8, 30), (27, 4), (10, 22), (24, 25), (29, 31), (34, 2), (22, 5), (6, 8), (25, 25), (32, 26), (19, 10), (27, 19), (11, 23), (21, 3), (1, 31), (3, 30), (27, 5), (8, 22), (3, 20), (14, 15), (6, 6), (15, 7), (0, 23), (6, 10), (36, 14), (19, 30), (15, 31), (34, 8), (20, 27), (5, 10), (7, 8), (0, 4), (10, 31), (19, 28), (20, 31), (30, 29), (18, 18), (12, 23), (14, 11), (34, 18), (12, 4), (33, 3), (25, 16), (3, 29), (30, 19), (1, 12), (29, 9), (27, 29), (4, 4), (10, 19), (9, 25), (21, 15), (2, 2), (9, 15), (2, 11), (18, 25), (35, 3), (7, 3), (32, 15), (20, 14), (5, 25), (15, 30), (19, 17), (32, 27), (3, 2), (3, 9), (0, 28), (5, 18), (32, 30), (33, 28), (16, 16), (6, 30), (8, 17), (21, 21), (34, 25), (8, 28), (37, 5), (25, 6), (37, 20), (20, 10), (26, 23), (10, 12), (24, 12), (12, 30), (26, 24), (26, 19), (1, 9), (25, 1), (6, 1), (29, 10), (15, 16), (28, 9), (22, 18), (26, 15), (22, 12), (14, 5), (20, 20), (26, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129720", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (37, 10), (9, 25), (8, 9), (36, 11), (28, 3), (2, 25), (34, 21), (31, 3), (37, 8), (28, 5), (20, 26), (19, 27), (19, 19), (8, 7), (12, 9), (18, 9), (30, 15), (28, 11), (29, 31), (21, 2), (24, 5), (7, 0), (3, 10), (32, 14), (15, 20), (13, 7), (37, 24), (35, 12), (22, 4), (3, 1), (17, 32), (7, 28), (13, 12), (21, 14), (17, 13), (26, 20), (11, 28), (34, 22), (32, 0), (32, 16), (1, 12), (9, 8), (2, 13), (25, 9), (14, 4), (34, 2), (34, 7), (13, 25), (23, 27), (35, 32), (0, 24), (4, 16), (27, 14), (1, 32), (28, 4), (15, 2), (22, 0), (20, 17), (16, 0), (30, 25), (22, 10), (18, 30), (16, 32), (30, 32), (29, 9), (26, 9), (6, 19), (16, 24), (33, 6), (36, 32), (13, 27), (6, 16), (15, 1), (25, 16), (24, 0), (0, 20), (21, 1), (26, 7), (23, 29), (31, 27), (28, 6), (19, 10), (31, 17), (13, 23), (21, 18), (14, 21), (35, 2), (11, 0), (20, 0), (13, 13), (11, 14), (11, 19), (29, 16), (34, 0), (14, 27), (2, 21), (0, 10), (16, 25), (21, 17), (7, 25), (0, 29), (4, 8), (31, 5), (37, 29), (21, 6), (5, 26), (25, 18), (31, 30), (34, 26), (8, 28), (2, 7), (11, 26), (9, 23), (3, 31), (14, 16), (3, 5), (0, 19), (0, 22), (24, 16), (32, 2), (26, 31), (19, 22), (24, 6), (34, 13), (26, 5), (4, 4), (27, 20), (19, 20), (20, 23), (29, 18), (7, 12), (28, 0), (28, 26), (7, 16), (6, 32), (19, 11), (26, 30), (18, 0), (23, 30), (27, 18), (6, 0), (6, 27), (27, 23), (15, 0), (0, 23), (35, 18), (30, 19), (1, 11), (3, 17), (12, 7), (17, 19), (30, 17), (3, 2), (5, 17), (32, 25), (14, 32), (9, 13), (3, 23), (3, 26), (13, 21), (27, 10), (12, 32), (30, 10), (10, 6), (27, 31), (35, 7), (0, 3), (37, 11), (7, 14), (19, 29), (23, 25), (31, 8), (14, 12), (27, 5), (11, 30), (27, 7), (5, 15), (19, 14), (1, 18), (19, 12), (35, 24), (9, 10), (32, 26), (6, 2), (3, 4), (0, 25), (26, 12), (33, 13), (0, 16), (17, 24), (23, 32), (14, 24), (18, 8), (27, 8), (9, 2), (10, 31), (20, 12), (28, 10), (29, 2), (12, 1), (30, 26), (18, 24), (15, 29), (8, 13), (3, 21), (3, 29), (5, 11), (37, 23), (16, 19), (2, 31), (21, 8), (1, 10), (7, 27), (36, 4), (6, 14), (13, 9), (14, 0), (13, 2), (8, 2), (34, 1), (15, 27), (34, 30), (16, 16), (23, 8), (1, 25), (35, 19), (7, 18), (33, 31), (24, 9), (7, 17), (19, 3), (21, 5), (14, 14), (22, 6), (37, 18), (9, 24), (21, 13), (23, 3), (16, 8), (26, 14), (37, 25), (29, 7), (14, 17), (32, 10), (27, 25), (28, 21), (19, 18), (9, 4), (14, 18), (21, 26), (26, 29), (12, 12), (33, 16), (10, 19), (2, 27), (15, 17), (7, 32), (18, 25), (21, 24), (12, 18), (30, 27), (30, 4), (7, 7), (4, 7), (28, 24), (14, 8), (13, 26), (24, 22), (0, 15), (2, 24), (9, 14), (21, 10), (17, 1), (33, 15), (14, 10), (6, 25), (8, 30), (11, 16), (35, 6), (5, 29), (10, 23), (1, 27), (24, 12), (11, 3), (9, 28), (33, 1), (4, 25), (15, 26), (22, 7), (22, 27), (32, 20), (29, 20), (36, 7), (25, 20), (7, 31), (33, 28), (12, 31), (26, 23), (25, 21), (1, 6), (11, 15), (27, 30), (0, 1), (6, 22), (20, 9), (24, 13), (5, 19), (5, 18), (5, 24), (16, 27), (16, 30), (29, 26), (4, 22), (37, 4), (17, 11), (4, 21), (10, 10), (19, 25), (10, 24), (26, 4), (30, 21), (9, 22), (34, 15), (12, 14), (36, 3), (33, 0), (5, 1), (9, 15), (29, 10), (15, 15), (34, 8), (19, 1), (23, 11), (4, 5), (4, 17), (14, 1), (17, 12), (6, 7), (18, 2), (11, 12), (6, 23), (11, 6), (8, 32), (20, 27), (13, 0), (14, 3), (4, 0), (9, 21), (23, 14), (12, 24), (35, 25), (29, 30), (0, 18), (32, 30), (17, 7), (9, 29), (26, 11), (0, 13), (24, 2), (25, 32), (13, 24), (1, 14), (9, 26), (3, 27), (33, 32), (12, 26), (31, 4), (37, 6), (34, 28), (24, 21), (11, 17), (26, 27), (13, 3), (6, 11), (13, 15), (17, 3), (22, 8), (15, 4), (2, 3), (8, 8), (32, 5), (17, 25), (8, 18), (22, 19), (29, 15), (25, 23), (2, 12), (13, 16), (20, 5), (37, 26), (12, 10), (30, 29), (4, 24), (9, 18), (37, 16), (19, 0), (20, 14), (24, 19), (23, 22), (17, 9), (31, 21), (6, 28), (7, 8), (21, 15), (30, 23), (36, 30), (14, 15), (27, 15), (33, 26), (2, 16), (0, 6), (7, 4), (0, 30), (10, 26), (31, 20), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384048", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), 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), (14, 15), (8, 11), (29, 8), (14, 19), (3, 32), (12, 13), (15, 7), (18, 16), (14, 21), (13, 18), (25, 7), (27, 29), (17, 7), (11, 34), (27, 30), (17, 10), (10, 20), (0, 7), (18, 7), (18, 6), (15, 10), (23, 4), (15, 16), (19, 27), (21, 27), (1, 26), (10, 10), (8, 29), (11, 19), (24, 34), (9, 7), (14, 24), (23, 25), (11, 27), (15, 6), (27, 26), (26, 32), (5, 6), (5, 12), (1, 10), (26, 31), (27, 21), (28, 9), (7, 6), (23, 0), (29, 3), (2, 3), (10, 34), (27, 6), (29, 19), (2, 8), (7, 21), (19, 21), (22, 10), (9, 23), (15, 2), (21, 18), (20, 15), (30, 9), (20, 9), (0, 23), (13, 6), (18, 34), (24, 3), (13, 20), (14, 25), (3, 7), (9, 6), (25, 29), (14, 2), (20, 6), (3, 28), (6, 34), (22, 34), (23, 20), (3, 25), (0, 9), (28, 22), (18, 21), (30, 27), (27, 27), (21, 2), (22, 33), (3, 22), (29, 1), (0, 12), (15, 28), (6, 22), (26, 34), (7, 27), (14, 29), (12, 19), (14, 28), (8, 31), (21, 0), (25, 5), (23, 5), (17, 16), (7, 15), (16, 11), (4, 29), (20, 4), (4, 32), (27, 22), (17, 11), (0, 6), (29, 6), (10, 5), (26, 27), (13, 28), (29, 16), (9, 9), (7, 5), (8, 0), (26, 13), (7, 10), (28, 5), (15, 12), (3, 21), (1, 4), (25, 26), (8, 19), (16, 32), (18, 22), (14, 13), (19, 2), (7, 23), (12, 34), (8, 18), (26, 33), (17, 24), (26, 14), (21, 20), (28, 8), (12, 0), (30, 0), (21, 25), (18, 5), (20, 11), (19, 15), (18, 24), (3, 2), (7, 0), (11, 29), (14, 33), (2, 10), (4, 10), (17, 21), (14, 31), (0, 32), (3, 23), (4, 3), (2, 11), (6, 3), (27, 11), (4, 8), (30, 14), (25, 11), (13, 9), (3, 10), (8, 5), (27, 25), (14, 7), (28, 18), (1, 23), (6, 23), (11, 3), (12, 25), (9, 28), (7, 11), (3, 16), (0, 8), (22, 18), (1, 6), (17, 1), (23, 22), (9, 31), (10, 14), (4, 13), (15, 18), (23, 29), (23, 33), (19, 31), (27, 13), (15, 11), (10, 4), (25, 30), (13, 25), (9, 2), (17, 23), (3, 12), (11, 24), (17, 22), (10, 24), (0, 13), (3, 30), (6, 25), (22, 3), (2, 7), (6, 4), (24, 23), (17, 19), (9, 1), (23, 1), (3, 1), (20, 13), (0, 25), (19, 5), (28, 31), (7, 7), (29, 4), (14, 0), (2, 9), (0, 31), (16, 26), (8, 23), (27, 17), (25, 25), (29, 26), (25, 34), (6, 16), (4, 27), (15, 25), (27, 18), (10, 33), (8, 2), (0, 24), (11, 23), (0, 33), (20, 20), (0, 27), (9, 30), (13, 21), (29, 2), (3, 34), (15, 21), (27, 10), (5, 11), (29, 23), (0, 20), (25, 32), (10, 13), (13, 5), (19, 8), (26, 30), (3, 14), (9, 26), (4, 14), (10, 31), (6, 24), (9, 27), (21, 28), (11, 11), (3, 15), (26, 1), (11, 12), (13, 0), (5, 7), (5, 26), (24, 1), (24, 7), (7, 14), (26, 26), (5, 9), (13, 10), (17, 3), (28, 34), (7, 24), (29, 14), (24, 16), (11, 20), (17, 26), (17, 2), (29, 28), (18, 13), (28, 11), (25, 15), (21, 6), (19, 23), (30, 8), (20, 19), (1, 12), (20, 32), (18, 10), (23, 27), (13, 33), (22, 13), (22, 32), (19, 7), (9, 12), (20, 28), (26, 28), (20, 7), (19, 33), (25, 4), (1, 27), (28, 20), (30, 1), (19, 4), (2, 31), (0, 2), (5, 28), (25, 13), (7, 4), (15, 8), (25, 2), (19, 11), (6, 2), (11, 32), (26, 0), (21, 23), (10, 26), (23, 23), (21, 24), (5, 14), (2, 29), (13, 14), (16, 22), (23, 31), (14, 32), (23, 32), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84942", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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), (10, 5), (18, 15), (33, 6), (7, 3), (15, 0), (31, 6), (4, 9), (0, 6), (12, 13), (7, 8), (6, 18), (2, 30), (15, 27), (20, 2), (31, 3), (20, 9), (21, 1), (18, 23), (3, 4), (7, 16), (27, 29), (22, 3), (6, 15), (26, 19), (19, 5), (5, 2), (25, 16), (28, 15), (23, 6), (22, 29), (32, 3), (12, 22), (26, 5), (26, 22), (0, 20), (4, 22), (10, 8), (15, 28), (19, 28), (2, 16), (5, 24), (21, 10), (0, 1), (13, 9), (17, 18), (12, 6), (23, 12), (15, 8), (14, 14), (6, 8), (19, 4), (30, 1), (16, 18), (12, 7), (8, 8), (30, 13), (27, 1), (17, 5), (11, 4), (1, 28), (25, 9), (33, 8), (20, 16), (5, 19), (1, 17), (17, 20), (28, 27), (23, 15), (17, 16), (23, 25), (8, 28), (30, 12), (11, 12), (13, 24), (15, 14), (28, 5), (23, 20), (8, 23), (5, 1), (33, 10), (5, 18), (9, 5), (6, 25), (29, 28), (6, 4), (31, 4), (27, 10), (24, 13), (21, 12), (33, 3), (31, 16), (17, 26), (29, 1), (0, 12), (24, 28), (5, 30), (20, 25), (27, 23), (32, 17), (31, 14), (31, 10), (15, 21), (24, 11), (20, 21), (19, 13), (32, 6), (14, 13), (2, 23), (7, 12), (16, 16), (20, 8), (1, 18), (28, 2), (11, 30), (21, 7), (21, 0), (22, 14), (7, 0), (17, 28), (9, 10), (10, 17), (30, 11), (1, 11), (6, 20), (14, 15), (25, 20), (5, 20), (12, 20), (29, 18), (0, 22), (9, 30), (0, 16), (20, 28), (31, 5), (0, 2), (31, 23), (9, 7), (33, 2), (5, 14), (19, 1), (4, 12), (1, 20), (7, 20), (25, 27), (3, 23), (13, 30), (25, 5), (10, 26), (17, 17), (28, 30), (13, 19), (1, 2), (24, 6), (2, 19), (6, 11), (8, 1), (19, 6), (29, 10), (0, 9), (14, 19), (25, 13), (3, 29), (13, 5), (0, 11), (4, 7), (15, 30), (15, 6), (16, 25), (31, 25), (6, 26), (10, 25), (32, 22), (23, 21), (11, 6), (26, 0), (8, 10), (8, 14), (2, 14), (22, 2), (32, 21), (11, 17), (23, 13), (30, 10), (19, 18), (30, 6), (11, 9), (19, 19), (1, 3), (29, 0), (0, 27), (1, 14), (21, 8), (23, 14), (20, 27), (26, 27), (33, 29), (11, 5), (24, 0), (22, 28), (31, 1), (11, 16), (13, 0), (24, 2), (3, 25), (9, 18), (15, 16), (21, 20), (29, 24), (6, 5), (5, 3), (4, 28), (7, 4), (17, 23), (5, 28), (30, 26), (19, 9), (14, 9), (30, 21), (5, 7), (28, 18), (20, 4), (27, 12), (3, 5), (28, 3), (21, 11), (8, 5), (16, 19), (22, 22), (9, 13), (1, 21), (22, 26), (27, 14), (25, 22), (17, 0), (23, 1), (9, 23), (29, 23), (12, 19), (5, 22), (11, 23), (26, 23), (16, 7), (11, 3), (15, 9), (32, 15), (4, 25), (3, 2), (31, 26), (7, 9), (25, 14), (28, 23), (33, 17), (23, 11), (6, 9), (12, 11), (12, 23), (20, 19), (12, 9), (17, 15), (15, 4), (20, 3), (9, 21), (29, 16), (14, 25), (17, 3), (6, 29), (18, 19), (32, 18), (22, 30), (28, 21), (33, 21), (31, 8), (16, 26), (4, 29), (33, 5), (23, 10), (16, 12), (28, 0), (15, 2), (32, 2), (22, 12), (26, 3), (3, 10), (29, 30), (3, 18), (21, 24), (16, 15), (30, 16), (27, 7), (23, 22), (3, 1), (30, 7), (31, 24), (29, 15), (27, 18), (1, 27), (24, 27), (21, 22), (25, 11), (18, 28), (2, 7), (4, 6), (2, 9), (16, 5), (17, 9), (8, 25), (9, 14), (0, 25), (17, 25), (28, 11), (12, 17), (19, 14), (13, 21), (32, 19), (0, 19), (18, 25), (26, 14), (32, 5), (14, 10), (24, 12), (27, 0), (10, 29), (7, 7), (33, 24), (8, 4), (17, 27), (25, 1), (10, 30), (16, 24), (2, 24), (16, 0), (28, 14), (26, 9), (22, 5), (9, 24), (30, 9), (31, 28), (4, 10), (32, 1), (32, 24), (7, 30), (29, 13), (14, 27), (4, 17), (31, 22), (22, 27), (11, 29), (12, 16), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "596160", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (14, 34), (15, 21), (4, 19), (24, 36), (9, 30), (20, 27), (8, 15), (9, 25), (18, 32), (9, 18), (6, 33), (7, 3), (6, 22), (32, 19), (28, 24), (1, 28), (12, 26), (5, 34), (20, 35), (12, 29), (14, 23), (7, 21), (32, 7), (3, 13), (6, 34), (26, 33), (26, 18), (2, 28), (19, 5), (26, 0), (22, 27), (11, 14), (14, 21), (22, 31), (24, 11), (3, 32), (1, 34), (5, 7), (2, 23), (6, 32), (12, 24), (27, 21), (5, 10), (28, 13), (8, 3), (28, 23), (11, 20), (7, 7), (19, 20), (15, 14), (16, 14), (17, 36), (3, 21), (7, 4), (19, 17), (25, 34), (17, 23), (24, 24), (24, 21), (17, 12), (7, 13), (15, 20), (21, 19), (15, 0), (7, 31), (33, 10), (5, 2), (12, 6), (6, 19), (5, 35), (19, 32), (10, 30), (9, 14), (10, 26), (24, 12), (4, 12), (29, 21), (1, 12), (31, 29), (23, 8), (30, 33), (24, 32), (18, 6), (13, 28), (26, 5), (3, 17), (9, 24), (8, 9), (12, 32), (30, 36), (12, 18), (4, 1), (29, 26), (28, 19), (32, 22), (11, 25), (9, 33), (2, 27), (9, 11), (20, 8), (20, 19), (3, 8), (29, 33), (16, 28), (23, 34), (7, 14), (2, 1), (4, 30), (32, 26), (27, 4), (9, 3), (13, 9), (1, 29), (24, 29), (26, 15), (15, 5), (16, 31), (12, 15), (20, 12), (13, 5), (13, 24), (0, 16), (15, 25), (25, 27), (4, 23), (22, 6), (27, 0), (16, 21), (31, 24), (20, 4), (15, 13), (22, 5), (31, 9), (5, 21), (26, 25), (2, 4), (17, 27), (20, 25), (2, 30), (29, 23), (19, 7), (3, 35), (21, 24), (10, 24), (33, 31), (19, 28), (26, 16), (21, 26), (13, 2), (21, 22), (6, 23), (0, 32), (19, 35), (28, 10), (10, 21), (13, 25), (25, 23), (5, 5), (0, 17), (1, 26), (13, 33), (7, 32), (5, 31), (23, 1), (25, 24), (0, 24), (3, 15), (9, 29), (2, 26), (18, 19), (4, 17), (17, 16), (29, 9), (25, 29), (0, 28), (21, 23), (27, 34), (18, 30), (26, 29), (6, 1), (8, 33), (5, 19), (15, 27), (24, 16), (23, 27), (28, 7), (9, 36), (33, 12), (14, 36), (15, 2), (12, 30), (33, 8), (32, 5), (21, 11), (12, 12), (0, 10), (33, 27), (10, 23), (1, 21), (29, 25), (14, 15), (5, 6), (17, 25), (16, 12), (13, 22), (19, 13), (18, 23), (8, 6), (25, 20), (16, 34), (17, 18), (9, 2), (20, 0), (16, 3), (1, 10), (18, 8), (24, 7), (16, 1), (3, 1), (18, 17), (21, 20), (2, 21), (16, 35), (21, 5), (0, 21), (3, 20), (32, 30), (27, 3), (32, 35), (15, 36), (19, 15), (20, 28), (29, 27), (30, 14), (30, 29), (30, 12), (21, 34), (27, 9), (27, 13), (5, 4), (12, 3), (3, 11), (20, 15), (29, 13), (16, 11), (31, 6), (26, 34), (11, 32), (31, 32), (19, 30), (0, 26), (31, 10), (0, 33), (6, 35), (25, 5), (30, 22), (2, 11), (30, 21), (22, 20), (4, 32), (9, 34), (24, 27), (1, 2), (28, 16), (18, 9), (5, 22), (0, 6), (12, 23), (29, 36), (30, 0), (19, 0), (22, 0), (22, 24), (3, 33), (9, 6), (16, 0), (24, 17), (14, 35), (1, 32), (22, 13), (29, 1), (2, 12), (12, 14), (13, 0), (23, 28), (22, 34), (5, 28), (7, 2), (23, 20), (28, 21), (6, 16), (3, 4), (2, 3), (13, 15), (30, 5), (3, 36), (23, 11), (33, 15), (11, 36), (11, 26), (17, 0), (9, 32), (19, 31), (11, 27), (20, 34), (31, 34), (8, 17), (33, 32), (13, 19), (24, 28), (24, 20), (8, 8), (32, 13), (17, 26), (13, 30), (9, 0), (24, 23), (6, 10), (18, 7), (22, 16), (4, 11), (1, 13), (15, 4), (5, 33), (15, 34), (1, 15), (22, 22), (32, 1), (22, 25), (33, 28), (9, 12), (16, 36), (1, 3), (29, 16), (21, 35), (21, 15), (4, 8), (4, 9), (29, 6), (10, 8), (13, 29), (30, 8), (19, 22), (12, 5), (27, 1), (21, 3), (3, 10), (10, 2), (25, 26), (31, 0), (4, 3), (23, 7), (21, 31), (31, 3), (30, 20), (29, 35), (32, 36), (14, 5), (7, 1), (30, 1), (7, 35), (26, 2), (7, 9), (17, 7), (18, 34), (17, 13), (28, 22), (23, 16), (25, 10), (29, 4), (25, 25), (1, 18), (2, 22), (12, 33), (29, 10), (18, 5), (27, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209880", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 27), (4, 21), (5, 33), (7, 34), (18, 36), (11, 11), (30, 28), (6, 28), (9, 22), (6, 5), (5, 25), (33, 9), (8, 4), (31, 18), (24, 2), (31, 24), (4, 27), (13, 10), (5, 22), (25, 30), (11, 24), (19, 20), (11, 36), (2, 36), (25, 3), (33, 30), (13, 37), (29, 5), (8, 25), (5, 8), (7, 0), (21, 37), (5, 30), (4, 31), (10, 26), (15, 12), (16, 9), (6, 20), (20, 1), (5, 19), (24, 9), (5, 1), (27, 14), (19, 0), (18, 6), (12, 32), (2, 34), (2, 9), (28, 14), (18, 3), (9, 20), (13, 11), (27, 10), (10, 35), (19, 30), (30, 27), (18, 9), (6, 0), (21, 33), (23, 22), (17, 33), (23, 15), (27, 29), (33, 25), (29, 2), (3, 7), (19, 22), (11, 9), (32, 23), (23, 16), (0, 36), (25, 5), (9, 33), (18, 17), (25, 19), (24, 30), (8, 6), (24, 23), (30, 8), (11, 33), (18, 19), (16, 29), (23, 14), (12, 22), (33, 16), (12, 13), (1, 28), (23, 21), (29, 33), (33, 20), (22, 24), (6, 4), (19, 19), (27, 9), (4, 0), (22, 12), (15, 29), (11, 18), (18, 37), (2, 7), (27, 28), (21, 19), (2, 17), (28, 6), (19, 28), (5, 4), (31, 31), (6, 14), (22, 32), (3, 15), (25, 31), (9, 21), (7, 25), (21, 9), (15, 31), (12, 5), (8, 31), (2, 26), (6, 15), (19, 10), (32, 14), (31, 12), (22, 11), (1, 32), (10, 2), (6, 25), (11, 19), (4, 35), (11, 34), (10, 27), (12, 24), (17, 4), (6, 13), (8, 19), (12, 12), (30, 30), (13, 3), (15, 14), (21, 20), (31, 37), (28, 0), (14, 28), (20, 22), (28, 35), (21, 8), (33, 18), (8, 16), (0, 30), (13, 6), (21, 27), (29, 16), (28, 36), (27, 23), (16, 21), (28, 24), (0, 13), (1, 36), (24, 14), (23, 7), (31, 28), (2, 32), (21, 6), (14, 14), (14, 25), (13, 33), (24, 15), (14, 16), (0, 32), (30, 0), (6, 19), (8, 24), (19, 29), (0, 7), (16, 10), (12, 31), (16, 12), (10, 28), (32, 31), (20, 35), (19, 32), (8, 14), (16, 17), (7, 13), (0, 23), (24, 21), (28, 34), (8, 34), (2, 30), (22, 13), (22, 26), (11, 16), (7, 4), (10, 11), (8, 29), (5, 18), (20, 15), (29, 22), (5, 29), (0, 22), (23, 19), (33, 0), (28, 26), (12, 8), (12, 17), (2, 31), (8, 8), (4, 34), (25, 9), (3, 13), (5, 20), (28, 8), (6, 18), (28, 3), (31, 7), (30, 12), (19, 8), (32, 9), (33, 27), (8, 23), (3, 36), (7, 9), (23, 25), (20, 12), (16, 16), (22, 31), (8, 18), (22, 15), (32, 5), (14, 2), (17, 14), (5, 5), (30, 6), (18, 2), (26, 27), (17, 12), (19, 3), (26, 14), (30, 18), (4, 24), (9, 28), (24, 19), (18, 35), (4, 37), (23, 30), (25, 26), (25, 8), (13, 17), (9, 8), (32, 15), (8, 5), (31, 36), (1, 3), (14, 32), (25, 11), (3, 37), (21, 26), (0, 1), (17, 9), (24, 5), (21, 21), (30, 37), (14, 6), (0, 24), (3, 4), (21, 28), (4, 36), (2, 23), (8, 32), (24, 28), (16, 8), (4, 3), (17, 24), (24, 6), (6, 30), (15, 16), (10, 18), (24, 33), (15, 36), (5, 12), (20, 26), (27, 15), (22, 0), (15, 32), (25, 24), (25, 27), (28, 23), (14, 24), (4, 33), (26, 11), (16, 2), (15, 10), (5, 37), (19, 27), (32, 36), (7, 5), (12, 23), (10, 17), (31, 23), (8, 7), (2, 37), (6, 7), (12, 28), (27, 24), (30, 9), (10, 12), (3, 0), (33, 17), (5, 23), (10, 36), (27, 4), (32, 18), (11, 2), (10, 0), (3, 28), (19, 16), (25, 16), (22, 14), (1, 5), (12, 35), (19, 15), (4, 13), (18, 28), (24, 13), (4, 15), (24, 4), (8, 11), (2, 1), (15, 21), (11, 1), (28, 5), (13, 0), (17, 31), (10, 5), (4, 19), (27, 17), (6, 36), (19, 23), (6, 9), (8, 21), (1, 4), (30, 33), (18, 16), (9, 30), (12, 9), (33, 29), (22, 36), (22, 17), (14, 9), (12, 7), (28, 4), (14, 22), (9, 3), (27, 7), (18, 34), (29, 14), (18, 15), (10, 24), (3, 16), (19, 5), (24, 16), (1, 7), (25, 33), (10, 29), (5, 0), (26, 12), (13, 20), (14, 7), (9, 36), (26, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224640", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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), (28, 38), (24, 37), (6, 19), (19, 28), (2, 26), (21, 20), (2, 19), (10, 36), (11, 23), (8, 10), (19, 25), (3, 19), (11, 6), (7, 17), (0, 9), (20, 17), (5, 20), (8, 12), (16, 12), (28, 0), (6, 12), (16, 28), (8, 8), (18, 27), (11, 3), (27, 2), (20, 9), (26, 35), (12, 3), (19, 32), (22, 20), (6, 25), (6, 26), (16, 20), (1, 24), (1, 30), (22, 36), (19, 7), (28, 3), (19, 34), (18, 37), (21, 33), (23, 24), (0, 12), (13, 11), (5, 7), (26, 7), (15, 0), (6, 38), (5, 10), (15, 35), (11, 35), (10, 17), (28, 34), (25, 20), (25, 5), (17, 9), (19, 8), (0, 6), (16, 3), (13, 31), (7, 15), (30, 0), (8, 17), (30, 4), (10, 22), (5, 13), (3, 14), (6, 4), (7, 6), (12, 37), (25, 17), (3, 37), (17, 10), (28, 13), (24, 7), (22, 30), (11, 32), (10, 0), (20, 0), (10, 20), (8, 25), (18, 21), (15, 12), (8, 18), (3, 18), (23, 8), (18, 24), (5, 31), (2, 37), (7, 9), (14, 22), (28, 2), (0, 16), (16, 31), (29, 20), (30, 12), (14, 36), (19, 3), (29, 19), (11, 15), (28, 25), (7, 12), (21, 10), (1, 5), (26, 8), (19, 36), (0, 25), (15, 15), (30, 2), (26, 27), (25, 4), (4, 11), (16, 9), (28, 29), (25, 10), (23, 1), (26, 14), (27, 12), (11, 17), (26, 25), (1, 32), (18, 30), (18, 19), (7, 25), (18, 33), (27, 27), (7, 38), (24, 30), (14, 23), (2, 11), (20, 28), (15, 23), (6, 2), (25, 34), (11, 30), (10, 14), (16, 34), (29, 27), (24, 1), (12, 0), (8, 37), (5, 18), (27, 24), (4, 37), (16, 11), (13, 6), (13, 12), (0, 38), (13, 25), (13, 18), (21, 5), (1, 0), (24, 21), (7, 23), (10, 15), (22, 26), (21, 32), (13, 0), (12, 5), (12, 22), (17, 15), (21, 21), (3, 3), (28, 23), (28, 31), (8, 38), (8, 26), (25, 35), (19, 38), (19, 6), (12, 6), (24, 12), (30, 16), (1, 2), (18, 13), (12, 18), (13, 1), (22, 19), (17, 31), (4, 22), (9, 34), (13, 15), (17, 19), (13, 37), (15, 1), (6, 29), (24, 28), (27, 20), (12, 19), (6, 6), (21, 37), (26, 5), (1, 35), (2, 10), (0, 26), (17, 26), (30, 28), (16, 1), (21, 30), (19, 31), (0, 34), (29, 10), (30, 36), (22, 35), (19, 13), (29, 7), (6, 27), (5, 4), (1, 9), (14, 37), (30, 10), (21, 31), (25, 21), (30, 5), (15, 27), (17, 18), (26, 18), (22, 16), (14, 34), (22, 4), (24, 27), (25, 29), (13, 34), (17, 8), (22, 38), (6, 7), (10, 4), (12, 35), (26, 6), (5, 24), (29, 25), (0, 13), (19, 17), (28, 18), (15, 25), (18, 9), (8, 0), (24, 4), (12, 10), (25, 37), (0, 28), (21, 4), (8, 6), (30, 13), (24, 22), (2, 38), (20, 23), (26, 33), (30, 33), (1, 6), (18, 22), (30, 34), (5, 38), (6, 36), (22, 11), (30, 3), (18, 12), (20, 6), (7, 37), (23, 10), (24, 19), (11, 7), (8, 19), (23, 9), (19, 14), (24, 33), (27, 1), (10, 9), (24, 6), (7, 16), (3, 2), (26, 17), (27, 4), (14, 29), (24, 3), (1, 17), (3, 4), (28, 11), (11, 4), (5, 19), (5, 9), (6, 28), (13, 22), (29, 3), (20, 15), (20, 20), (22, 27), (29, 4), (0, 27), (28, 10), (5, 28), (28, 27), (14, 15), (21, 0), (2, 3), (4, 18), (3, 28), (9, 24), (1, 11), (2, 23), (24, 20), (21, 17), (6, 14), (5, 14), (19, 23), (20, 8), (15, 17), (24, 26), (6, 9), (15, 34), (24, 5), (1, 14), (7, 7), (2, 35), (15, 6), (15, 10), (0, 4), (14, 28), (1, 36), (14, 25), (18, 35), (26, 23), (20, 26), (29, 5), (30, 15), (12, 21), (30, 22), (22, 14), (15, 13), (14, 13), (1, 33), (6, 17), (8, 4), (22, 32), (5, 36), (16, 2), (20, 13), (10, 11), (15, 30), (5, 30), (15, 38), (12, 23), (23, 4), (24, 8), (23, 26), (20, 31), (9, 15), (21, 18), (0, 8), (16, 38), (12, 1), (4, 25), (28, 22), (12, 7), (17, 27), (3, 1), (14, 9), (23, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "311640", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (21, 26), (25, 19), (22, 2), (14, 0), (25, 4), (16, 20), (16, 2), (23, 7), (18, 7), (4, 4), (26, 1), (6, 6), (0, 28), (14, 6), (23, 22), (13, 20), (16, 29), (1, 23), (26, 29), (27, 28), (2, 12), (8, 4), (10, 13), (17, 14), (11, 9), (12, 2), (3, 21), (10, 5), (21, 5), (24, 29), (1, 2), (6, 1), (19, 14), (0, 18), (3, 23), (7, 3), (10, 15), (4, 6), (20, 15), (2, 8), (3, 8), (5, 5), (25, 28), (3, 27), (14, 19), (5, 28), (8, 21), (8, 7), (7, 22), (7, 18), (29, 24), (9, 15), (4, 15), (20, 7), (9, 18), (13, 21), (15, 28), (24, 9), (15, 17), (16, 1), (7, 21), (13, 29), (0, 10), (30, 22), (23, 4), (29, 4), (19, 11), (30, 10), (5, 24), (27, 29), (3, 10), (16, 23), (15, 5), (26, 6), (25, 8), (25, 12), (6, 9), (7, 17), (1, 25), (9, 5), (8, 6), (8, 20), (21, 27), (1, 1), (17, 12), (5, 11), (29, 13), (18, 1), (22, 10), (11, 25), (8, 3), (7, 2), (10, 19), (18, 8), (11, 12), (4, 3), (24, 21), (16, 19), (7, 24), (26, 12), (13, 7), (9, 6), (12, 16), (30, 23), (15, 27), (14, 28), (24, 11), (2, 15), (1, 20), (28, 1), (2, 25), (3, 22), (19, 24), (1, 24), (3, 20), (13, 18), (3, 3), (1, 3), (0, 7), (21, 10), (23, 3), (23, 5), (15, 0), (11, 14), (11, 23), (25, 14), (23, 25), (1, 6), (15, 1), (12, 22), (5, 8), (12, 27), (0, 22), (29, 20), (6, 19), (17, 26), (23, 17), (29, 0), (18, 5), (24, 4), (15, 23), (28, 25), (7, 26), (17, 2), (30, 7), (20, 8), (18, 14), (8, 10), (1, 12), (16, 16), (9, 17), (7, 4), (0, 9), (7, 7), (4, 10), (13, 16), (19, 4), (5, 23), (15, 18), (29, 19), (20, 28), (16, 24), (3, 12), (25, 23), (5, 16), (21, 7), (1, 19), (11, 5), (6, 3), (10, 28), (14, 16), (28, 17), (11, 11), (21, 21), (21, 19), (6, 8), (30, 14), (14, 2), (24, 1), (10, 10), (20, 27), (16, 22), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "248400", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (7, 8), (11, 18), (17, 13), (21, 11), (24, 19), (12, 8), (19, 9), (22, 17), (16, 13), (16, 0), (29, 17), (30, 27), (17, 26), (14, 23), (24, 23), (10, 2), (12, 7), (27, 12), (29, 10), (3, 5), (10, 21), (4, 21), (21, 7), (18, 7), (16, 4), (22, 25), (19, 20), (12, 4), (12, 17), (3, 16), (14, 5), (11, 19), (8, 18), (21, 4), (31, 25), (1, 10), (8, 23), (7, 24), (23, 14), (5, 21), (26, 28), (2, 25), (1, 17), (11, 27), (12, 12), (10, 20), (31, 27), (4, 29), (12, 9), (14, 8), (16, 2), (23, 19), (3, 7), (15, 27), (27, 24), (31, 12), (25, 0), (4, 15), (25, 2), (16, 28), (26, 11), (16, 23), (15, 19), (19, 15), (6, 10), (21, 23), (21, 20), (26, 1), (5, 25), (7, 4), (9, 25), (24, 25), (4, 26), (8, 4), (18, 15), (23, 20), (27, 0), (7, 16), (0, 27), (24, 6), (17, 5), (7, 12), (6, 6), (3, 22), (22, 9), (4, 19), (16, 12), (9, 27), (30, 26), (0, 9), (12, 15), (13, 19), (25, 7), (8, 2), (29, 16), (7, 11), (3, 26), (20, 8), (11, 6), (28, 7), (23, 3), (24, 12), (16, 18), (0, 17), (9, 2), (15, 29), (30, 8), (23, 16), (20, 28), (4, 14), (27, 5), (30, 1), (21, 0), (3, 17), (16, 6), (11, 17), (6, 5), (1, 11), (5, 24), (2, 28), (27, 17), (5, 9), (28, 23), (18, 28), (25, 28), (26, 27), (30, 14), (17, 25), (12, 18), (5, 6), (26, 12), (2, 18), (21, 25), (11, 1), (22, 15), (4, 1), (29, 0), (2, 22), (13, 29), (30, 9), (24, 16), (22, 4), (0, 5), (27, 14), (20, 21), (13, 15), (31, 18), (29, 8), (19, 2), (11, 13), (18, 3), (24, 22), (0, 4), (1, 12), (1, 5), (20, 7), (15, 10), (12, 20), (5, 4), (17, 20), (21, 26), (24, 21), (21, 28), (22, 18), (18, 26), (4, 10), (5, 27), (4, 27), (28, 0), (28, 10), (10, 16), (18, 19), (18, 20), (5, 23), (19, 22), (10, 11), (19, 29), (4, 11), (5, 0), (14, 17), (29, 24), (6, 18), (28, 28), (25, 19), (22, 16), (22, 5), (4, 13), (4, 23), (19, 23), (12, 29), (27, 21), (7, 22), (17, 21), (7, 20), (12, 26), (20, 20), (5, 12), (9, 26), (6, 20), (11, 4), (6, 4), (28, 19), (14, 4), (30, 11), (11, 26), (11, 11), (30, 22), (29, 26), (7, 18), (9, 4), (15, 20), (29, 15), (9, 29), (6, 23), (13, 27), (12, 13), (13, 14), (18, 16), (11, 21), (12, 3), (6, 28), (8, 11), (2, 16), (22, 13), (23, 1), (11, 0), (19, 14), (17, 4), (28, 24), (12, 25), (25, 27), (18, 2), (14, 14), (31, 14), (31, 28), (29, 5), (15, 22), (21, 16), (19, 21), (22, 21), (10, 1), (18, 9), (15, 8), (15, 11), (25, 29), (13, 5), (28, 3), (8, 20), (13, 26), (27, 16), (11, 20), (11, 14), (29, 7), (2, 12), (13, 18), (6, 8), (21, 18), (18, 27), (24, 10), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159120", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 31), (22, 10), (16, 29), (25, 8), (30, 19), (10, 23), (25, 16), (31, 15), (28, 29), (15, 0), (0, 19), (23, 16), (23, 14), (10, 10), (28, 28), (5, 19), (17, 7), (27, 21), (29, 25), (0, 1), (22, 32), (8, 4), (12, 25), (15, 9), (18, 15), (17, 17), (25, 25), (30, 4), (20, 3), (17, 29), (19, 26), (12, 24), (15, 4), (5, 12), (0, 18), (17, 5), (22, 12), (5, 26), (31, 2), (31, 3), (1, 5), (0, 5), (3, 1), (4, 7), (2, 32), (12, 31), (16, 5), (12, 16), (22, 26), (31, 14), (11, 17), (24, 5), (15, 16), (20, 14), (14, 14), (23, 25), (10, 22), (21, 28), (21, 25), (31, 20), (15, 32), (8, 0), (6, 22), (30, 7), (3, 11), (9, 14), (29, 17), (9, 13), (7, 9), (24, 24), (13, 8), (0, 23), (14, 31), (3, 28), (26, 13), (8, 3), (16, 14), (13, 23), (5, 28), (10, 30), (23, 27), (6, 29), (14, 18), (11, 26), (9, 27), (6, 6), (18, 10), (16, 8), (0, 30), (7, 8), (21, 4), (2, 10), (22, 28), (27, 9), (20, 4), (14, 8), (23, 3), (25, 7), (11, 11), (16, 19), (24, 23), (28, 6), (15, 19), (25, 28), (16, 24), (5, 16), (25, 1), (29, 4), (0, 25), (15, 24), (31, 4), (31, 28), (10, 29), (25, 22), (22, 23), (4, 13), (2, 22), (24, 7), (20, 28), (8, 14), (24, 18), (7, 23), (19, 27), (28, 0), (0, 13), (24, 8), (26, 5), (21, 31), (26, 20), (25, 3), (12, 19), (19, 20), (28, 22), (29, 22), (21, 11), (0, 10), (20, 12), (20, 10), (14, 17), (31, 23), (18, 24), (0, 7), (31, 8), (11, 14), (22, 18), (3, 24), (21, 14), (27, 28), (19, 9), (9, 0), (7, 2), (15, 14), (4, 6), (1, 10), (19, 1), (16, 27), (14, 4), (2, 2), (21, 9), (6, 27), (12, 28), (28, 1), (22, 29), (1, 6), (11, 21), (3, 0), (1, 30), (19, 8), (25, 15), (29, 20), (0, 4), (24, 1), (2, 16), (2, 15), (2, 28), (31, 12), (28, 31), (11, 6), (28, 7), (1, 12), (18, 31), (29, 12), (24, 29), (21, 6), (1, 25), (30, 14), (5, 11), (15, 18), (27, 15), (18, 26), (21, 1), (16, 10), (22, 0), (9, 1), (23, 18), (2, 11), (13, 5), (27, 1), (7, 15), (17, 14), (1, 27), (20, 32), (15, 20), (16, 15), (6, 8), (3, 32), (7, 17), (12, 21), (21, 17), (13, 22), (24, 31), (30, 2), (10, 9), (18, 16), (21, 21), (7, 21), (10, 28), (4, 29), (2, 13), (14, 23), (28, 24), (31, 22), (15, 25), (17, 23), (7, 12), (16, 7), (23, 0), (18, 5), (19, 22), (13, 19), (22, 5), (22, 6), (15, 6), (31, 24), (26, 25), (28, 8), (10, 7), (31, 21), (7, 25), (6, 7), (24, 26), (31, 6), (13, 15), (20, 22), (26, 11), (29, 28), (21, 15), (27, 17), (16, 11), (30, 21), (9, 32), (5, 14), (2, 19), (6, 21), (9, 23), (25, 19), (17, 13), (29, 13), (0, 17), (16, 17), (23, 9), (8, 10), (19, 24), (8, 17), (15, 30), (24, 6), (12, 2), (3, 30), (18, 12), (29, 3), (20, 13), (22, 19), (24, 25), (29, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510300", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (8, 33), (14, 22), (7, 28), (16, 6), (29, 8), (19, 18), (9, 16), (15, 0), (24, 5), (1, 10), (22, 33), (19, 6), (32, 21), (3, 27), (6, 18), (19, 4), (0, 11), (27, 13), (15, 13), (6, 22), (2, 3), (16, 29), (7, 19), (8, 4), (16, 2), (10, 21), (4, 16), (32, 34), (22, 11), (29, 28), (24, 29), (0, 1), (5, 25), (9, 27), (32, 4), (32, 2), (11, 17), (24, 4), (8, 1), (7, 33), (7, 13), (23, 19), (25, 29), (21, 12), (12, 18), (16, 13), (16, 30), (20, 12), (3, 26), (25, 12), (9, 10), (12, 14), (19, 31), (31, 24), (1, 7), (3, 21), (10, 31), (9, 29), (15, 30), (17, 9), (23, 30), (21, 33), (7, 25), (17, 19), (31, 10), (13, 4), (17, 21), (26, 1), (20, 18), (7, 5), (1, 33), (18, 15), (15, 1), (27, 27), (30, 13), (25, 21), (29, 9), (33, 5), (9, 11), (13, 15), (22, 3), (13, 30), (21, 19), (26, 14), (32, 7), (13, 18), (26, 0), (29, 1), (5, 6), (33, 24), (10, 12), (21, 23), (5, 20), (1, 29), (3, 7), (25, 0), (30, 20), (28, 24), (8, 30), (1, 9), (0, 23), (2, 16), (30, 11), (3, 18), (15, 26), (10, 34), (15, 5), (1, 32), (30, 17), (15, 9), (4, 19), (33, 12), (11, 3), (24, 13), (25, 17), (4, 1), (24, 34), (6, 15), (27, 19), (21, 4), (5, 21), (26, 33), (1, 4), (31, 30), (0, 18), (13, 19), (21, 14), (5, 18), (10, 28), (30, 34), (8, 32), (25, 22), (21, 8), (18, 31), (32, 18), (5, 26), (31, 28), (20, 14), (4, 31), (32, 9), (6, 13), (1, 16), (1, 13), (28, 17), (10, 14), (17, 23), (23, 11), (0, 8), (5, 14), (32, 0), (21, 18), (24, 27), (25, 15), (31, 31), (5, 10), (28, 4), (19, 8), (25, 10), (10, 17), (14, 11), (15, 2), (22, 7), (24, 3), (2, 0), (1, 31), (15, 12), (10, 4), (25, 6), (11, 18), (21, 10), (27, 8), (25, 34), (17, 10), (25, 30), (18, 14), (10, 33), (3, 13), (23, 32), (16, 20), (3, 16), (21, 34), (18, 18), (29, 16), (15, 24), (2, 21), (3, 4), (21, 25), (30, 16), (6, 16), (6, 9), (27, 2), (24, 14), (26, 27), (27, 10), (11, 8), (23, 29), (0, 16), (18, 0), (13, 20), (22, 28), (29, 6), (6, 28), (22, 1), (2, 20), (27, 33), (2, 12), (15, 22), (22, 20), (20, 28), (4, 22), (18, 2), (26, 9), (5, 15), (13, 11), (8, 9), (30, 28), (14, 32), (27, 18), (33, 6), (6, 12), (28, 33), (8, 27), (5, 8), (13, 23), (6, 10), (23, 33), (26, 25), (21, 13), (27, 22), (9, 0), (24, 33), (10, 11), (9, 6), (2, 15), (12, 15), (18, 17), (32, 23), (15, 11), (18, 32), (24, 8), (12, 31), (10, 10), (24, 2), (0, 25), (20, 17), (5, 0), (29, 20), (14, 0), (20, 33), (13, 33), (17, 27), (16, 23), (2, 33), (25, 33), (30, 5), (7, 0), (9, 30), (16, 10), (12, 21), (8, 22), (30, 32), (21, 32), (15, 31), (8, 21), (21, 20), (28, 18), (25, 16), (15, 28), (7, 17), (14, 16), (0, 21), (4, 27), (0, 29), (30, 14), (29, 34), (32, 17), (20, 23), (2, 19), (22, 4), (30, 7), (25, 8), (11, 14), (30, 18), (4, 26), (7, 24), (4, 32), (4, 23), (0, 6), (10, 9), (27, 4), (11, 7), (25, 19), (29, 11), (24, 9), (9, 19), (9, 9), (19, 15), (15, 15), (14, 28), (31, 11), (18, 19), (5, 7), (18, 25), (11, 23), (18, 22), (20, 13), (20, 11), (22, 17), (23, 9), (6, 6), (11, 4), (29, 17), (28, 25), (32, 32), (17, 7), (24, 32), (10, 20), (14, 5), (17, 26), (28, 21), (24, 11), (0, 5), (14, 6), (20, 32), (23, 21), (7, 21), (15, 4), (19, 34), (19, 23), (15, 17), (9, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "920079", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (18, 16), (5, 19), (16, 18), (8, 18), (4, 22), (23, 9), (10, 29), (18, 27), (19, 22), (10, 5), (3, 3), (11, 4), (8, 27), (6, 19), (17, 24), (23, 25), (6, 14), (3, 26), (1, 16), (24, 16), (9, 3), (27, 14), (13, 8), (9, 18), (22, 23), (0, 4), (26, 20), (0, 23), (3, 0), (4, 3), (3, 14), (15, 18), (12, 24), (29, 5), (23, 28), (24, 25), (4, 18), (12, 25), (23, 13), (1, 15), (8, 1), (1, 11), (3, 21), (22, 3), (8, 23), (20, 27), (7, 13), (20, 13), (10, 2), (3, 7), (12, 20), (8, 25), (25, 5), (3, 2), (20, 29), (12, 11), (21, 0), (19, 4), (3, 9), (10, 10), (21, 7), (28, 24), (29, 24), (7, 22), (18, 6), (26, 8), (0, 26), (14, 10), (8, 17), (14, 2), (2, 5), (4, 27), (25, 16), (27, 13), (3, 11), (6, 29), (6, 3), (14, 17), (28, 27), (26, 13), (4, 20), (20, 19), (27, 12), (29, 4), (24, 29), (28, 3), (0, 22), (28, 0), (18, 20), (27, 6), (29, 15), (2, 20), (8, 28), (7, 9), (12, 13), (24, 0), (6, 22), (15, 3), (29, 28), (18, 25), (25, 26), (15, 4), (16, 10), (0, 15), (5, 2), (5, 17), (4, 7), (18, 22), (10, 19), (18, 7), (12, 28), (4, 1), (13, 21), (18, 8), (1, 0), (10, 25), (27, 23), (0, 21), (8, 5), (14, 26), (4, 16), (15, 8), (18, 2), (5, 26), (23, 4), (22, 2), (7, 14), (23, 21), (19, 5), (11, 19), (1, 29), (16, 21), (9, 28), (1, 25), (1, 7), (13, 12), (25, 14), (7, 23), (10, 4), (0, 28), (6, 13), (29, 13), (15, 0), (21, 6), (15, 22), (28, 1), (7, 24), (27, 17), (25, 22), (20, 18), (29, 14), (3, 16), (11, 5), (29, 22), (6, 15), (7, 12), (0, 12), (14, 29), (2, 26), (1, 17), (22, 14), (2, 11), (28, 26), (6, 18), (28, 23), (26, 16), (26, 26), (10, 9), (29, 18), (15, 11), (22, 12), (16, 12), (17, 5), (2, 18), (23, 24), (21, 28), (26, 1), (7, 1), (6, 24), (25, 1), (11, 11), (0, 5), (8, 4), (13, 16), (16, 7), (19, 3), (11, 3), (9, 11), (2, 29), (9, 10), (9, 9), (21, 9), (9, 17), (19, 0), (0, 10), (2, 28), (26, 15), (27, 11), (21, 26), (21, 12), (0, 20), (11, 20), (24, 2), (4, 6), (9, 7), (20, 22), (7, 18), (12, 23), (27, 27), (27, 9), (3, 18), (12, 14), (12, 5), (3, 13), (3, 17), (2, 7), (17, 17), (28, 21), (2, 16), (25, 23), (28, 17), (20, 6), (15, 28), (16, 1), (27, 7), (4, 4), (26, 12), (16, 14), (6, 10), (15, 16), (23, 12), (22, 22), (10, 14), (5, 27), (22, 21), (17, 12), (14, 22), (19, 19), (2, 3), (1, 2), (20, 10), (5, 8), (19, 25), (4, 0), (17, 28), (24, 1), (26, 25), (7, 16), (14, 3), (27, 2), (12, 22), (29, 27), (11, 6), (6, 17), (29, 11), (24, 4), (23, 23), (16, 29), (26, 10), (4, 23), (9, 15), (29, 3), (24, 3), (26, 3), (12, 4), (29, 8), (20, 11), (8, 14), (25, 10), (23, 7), (19, 10), (9, 8), (3, 1), (28, 5), (10, 28), (24, 24), (24, 22), (19, 12), (28, 15), (17, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800712", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), 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), (9, 26), (6, 10), (29, 23), (28, 11), (24, 21), (25, 26), (24, 0), (0, 30), (1, 26), (17, 14), (23, 2), (17, 2), (22, 25), (2, 17), (18, 7), (2, 23), (22, 23), (25, 32), (21, 23), (6, 7), (30, 14), (21, 7), (26, 26), (25, 18), (13, 3), (28, 24), (17, 23), (10, 14), (19, 27), (17, 6), (9, 24), (27, 21), (14, 1), (30, 0), (13, 18), (19, 11), (21, 10), (3, 17), (9, 5), (11, 24), (8, 22), (10, 21), (30, 25), (28, 29), (21, 3), (8, 7), (29, 24), (4, 23), (5, 1), (9, 0), (9, 25), (7, 0), (31, 5), (23, 14), (3, 19), (1, 11), (21, 9), (10, 11), (31, 30), (16, 10), (1, 30), (3, 8), (19, 9), (16, 14), (27, 30), (3, 32), (24, 17), (20, 16), (27, 13), (27, 31), (8, 5), (28, 18), (30, 12), (30, 23), (31, 14), (3, 13), (19, 6), (17, 24), (23, 28), (0, 18), (8, 4), (8, 9), (28, 0), (14, 30), (24, 16), (6, 31), (12, 5), (4, 0), (18, 12), (9, 9), (5, 17), (14, 20), (14, 31), (17, 19), (27, 8), (22, 0), (23, 27), (31, 6), (30, 4), (6, 3), (30, 1), (10, 0), (6, 24), (26, 5), (13, 10), (28, 10), (6, 30), (10, 7), (25, 9), (25, 8), (13, 14), (14, 5), (4, 5), (10, 23), (25, 11), (8, 19), (13, 23), (9, 21), (5, 21), (3, 2), (13, 21), (28, 7), (16, 25), (2, 22), (27, 2), (18, 10), (20, 31), (17, 7), (13, 8), (19, 8), (20, 10), (14, 9), (6, 16), (19, 23), (19, 26), (9, 8), (22, 8), (5, 16), (1, 18), (11, 23), (15, 7), (1, 14), (16, 29), (8, 24), (0, 9), (0, 29), (23, 15), (4, 4), (31, 2), (21, 8), (17, 21), (13, 26), (1, 9), (26, 30), (2, 31), (18, 2), (2, 13), (16, 3), (15, 14), (11, 13), (3, 27), (24, 29), (2, 19), (15, 19), (28, 25), (29, 8), (25, 17), (16, 15), (12, 9), (10, 22), (21, 17), (16, 16), (10, 30), (22, 31), (24, 22), (23, 31), (12, 3), (4, 6), (31, 1), (31, 7), (2, 32), (31, 23), (13, 24), (30, 5), (13, 2), (30, 30), (21, 27), (25, 25), (28, 16), (14, 12), (11, 10), (4, 22), (6, 22), (3, 11), (9, 31), (30, 7), (28, 12), (16, 11), (9, 28), (31, 13), (19, 14), (4, 8), (2, 26), (2, 30), (0, 22), (21, 26), (28, 23), (18, 14), (3, 10), (28, 21), (22, 22), (13, 1), (26, 31), (0, 19), (20, 26), (21, 14), (19, 2), (12, 27), (11, 25), (22, 15), (7, 27), (21, 5), (9, 2), (29, 21), (16, 22), (20, 22), (3, 25), (19, 3), (29, 1), (21, 32), (9, 19), (2, 29), (22, 13), (10, 3), (31, 16), (0, 26), (24, 23), (26, 2), (0, 23), (15, 4), (27, 11), (6, 2), (7, 32), (21, 4), (12, 4), (14, 6), (9, 18), (6, 14), (5, 25), (12, 18), (21, 18), (1, 13), (20, 24), (11, 19), (8, 31), (28, 2), (12, 31), (11, 16), (14, 19), (31, 22), (1, 0), (5, 29), (27, 3), (20, 2), (21, 25), (12, 19), (0, 10), (29, 5), (3, 28), (6, 25), (26, 1), (10, 17), (24, 24), (20, 23), (15, 22), (15, 18), (31, 9), (5, 22), (29, 15), (27, 9), (22, 7), (9, 29), (0, 20), (14, 26), (14, 2), (15, 28), (31, 3), (5, 5), (25, 7), (12, 20), (18, 1), (22, 3), (2, 24), (2, 21), (13, 13), (27, 12), (4, 7), (29, 12), (15, 16), (26, 9), (11, 32), (30, 29), (15, 12), (10, 26), (20, 29), (26, 0), (30, 3), (24, 15), (1, 3), (28, 13), (19, 24), (0, 27), (4, 29), (20, 11), (16, 5), (29, 3), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882090", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 20), (12, 11), (16, 12), (31, 1), (14, 5), (6, 27), (37, 13), (7, 10), (9, 25), (30, 7), (26, 2), (22, 29), (21, 27), (11, 21), (20, 25), (1, 13), (19, 29), (3, 28), (35, 18), (24, 25), (0, 5), (20, 24), (28, 25), (1, 25), (37, 9), (23, 12), (16, 21), (26, 28), (12, 4), (11, 10), (30, 14), (25, 24), (13, 3), (11, 25), (29, 2), (34, 9), (4, 24), (13, 26), (36, 7), (15, 8), (12, 1), (4, 0), (36, 16), (14, 6), (36, 23), (35, 20), (18, 19), (14, 28), (16, 18), (25, 8), (28, 9), (20, 10), (24, 21), (5, 13), (4, 6), (30, 29), (26, 9), (21, 13), (10, 28), (27, 1), (26, 22), (26, 26), (13, 14), (27, 12), (19, 2), (9, 10), (2, 16), (29, 6), (18, 22), (20, 7), (4, 25), (35, 23), (21, 17), (6, 0), (5, 24), (12, 16), (21, 4), (7, 19), (9, 20), (7, 6), (28, 20), (2, 12), (6, 4), (34, 26), (5, 8), (18, 3), (10, 21), (30, 18), (32, 28), (35, 11), (17, 12), (11, 29), (22, 26), (36, 12), (7, 14), (27, 19), (8, 26), (21, 30), (23, 23), (4, 28), (24, 18), (34, 19), (24, 22), (21, 29), (17, 10), (2, 9), (1, 23), (6, 30), (16, 23), (1, 19), (1, 7), (20, 29), (25, 28), (18, 14), (37, 27), (25, 6), (14, 30), (36, 11), (9, 6), (19, 10), (20, 16), (35, 22), (7, 2), (32, 20), (5, 19), (13, 6), (27, 22), (16, 7), (20, 9), (25, 21), (25, 20), (6, 12), (16, 5), (16, 2), (27, 26), (23, 5), (10, 6), (34, 27), (4, 12), (2, 10), (12, 29), (8, 8), (5, 17), (36, 6), (12, 27), (15, 24), (34, 7), (26, 5), (7, 0), (20, 27), (17, 11), (15, 23), (12, 3), (15, 1), (32, 13), (20, 20), (19, 19), (26, 19), (16, 3), (16, 17), (23, 24), (15, 13), (16, 19), (31, 16), (9, 5), (11, 19), (30, 1), (18, 23), (16, 10), (6, 18), (13, 18), (17, 13), (28, 7), (26, 6), (20, 28), (28, 2), (13, 5), (28, 21), (23, 16), (24, 10), (6, 15), (7, 7), (3, 4), (2, 13), (27, 17), (19, 26), (5, 26), (26, 29), (18, 7), (13, 4), (26, 12), (25, 25), (22, 13), (12, 22), (21, 7), (7, 5), (5, 16), (15, 3), (36, 1), (30, 8), (35, 1), (35, 26), (23, 13), (35, 4), (29, 14), (24, 13), (32, 3), (13, 7), (18, 5), (32, 16), (31, 7), (14, 7), (19, 23), (1, 1), (14, 8), (20, 19), (12, 23), (37, 3), (13, 20), (23, 8), (24, 9), (25, 3), (16, 20), (28, 3), (9, 21), (15, 11), (32, 2), (10, 23), (24, 0), (31, 8), (7, 28), (4, 22), (25, 11), (12, 20), (27, 4), (27, 25), (25, 12), (2, 7), (30, 30), (36, 10), (16, 30), (6, 5), (26, 27), (34, 22), (36, 30), (31, 18), (35, 14), (37, 4), (29, 8), (6, 13), (1, 5), (1, 12), (28, 16), (10, 12), (13, 21), (6, 9), (12, 17), (20, 5), (25, 22), (22, 12), (3, 21), (6, 11), (31, 23), (23, 6), (32, 5), (4, 10), (30, 11), (37, 18), (9, 1), (31, 25), (29, 21), (10, 14), (3, 20), (2, 19), (30, 24), (23, 9), (4, 29), (8, 9), (4, 11), (22, 20), (26, 10), (19, 21), (37, 2), (14, 27), (24, 29), (29, 30), (26, 17), (3, 16), (15, 14), (32, 18), (17, 24), (11, 20), (34, 16), (10, 18), (21, 12), (28, 22), (10, 26), (19, 22), (35, 27), (1, 0), (17, 14), (18, 2), (6, 10), (29, 23), (25, 4), (22, 17), (14, 1), (16, 25), (3, 2), (13, 10), (17, 7), (24, 1), (24, 30), (17, 27), (15, 19), (5, 23), (34, 1), (30, 2), (23, 1), (20, 17), (3, 27), (35, 17), (15, 30), (37, 15), (0, 26), (15, 16), (2, 17), (2, 29), (37, 14), (9, 28), (3, 22), (6, 1), (3, 9), (32, 9), (12, 9), (14, 0), (1, 17), (2, 23), (12, 18), (11, 8), (33, 0), (27, 14), (5, 30), (18, 10), (28, 0), (30, 15), (25, 26), (22, 3), (29, 4), (33, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950796", "dataset": "MATH"}
{"messages": [{"content": "In a 35x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 9), (16, 23), (29, 12), (17, 37), (7, 22), (25, 3), (33, 31), (12, 22), (12, 29), (24, 30), (6, 28), (21, 16), (16, 7), (2, 27), (33, 22), (21, 14), (13, 9), (6, 15), (5, 5), (1, 26), (9, 1), (30, 26), (6, 34), (22, 33), (16, 0), (18, 3), (15, 7), (23, 13), (19, 15), (14, 1), (30, 12), (11, 20), (0, 1), (1, 5), (2, 15), (25, 10), (18, 33), (18, 35), (1, 6), (28, 6), (33, 23), (30, 31), (23, 35), (33, 8), (10, 3), (34, 37), (13, 0), (11, 16), (24, 25), (17, 29), (30, 11), (4, 8), (4, 10), (21, 4), (21, 25), (0, 18), (9, 25), (8, 35), (9, 15), (3, 23), (32, 10), (22, 4), (21, 1), (1, 16), (34, 14), (22, 0), (2, 35), (23, 24), (2, 24), (24, 3), (34, 33), (12, 0), (17, 30), (28, 38), (9, 13), (22, 30), (34, 22), (4, 27), (20, 0), (22, 22), (1, 17), (23, 37), (15, 36), (2, 28), (33, 26), (26, 3), (30, 6), (20, 25), (30, 14), (7, 2), (0, 2), (25, 32), (1, 37), (18, 16), (17, 32), (25, 7), (17, 21), (0, 17), (3, 29), (17, 31), (32, 37), (15, 26), (13, 2), (26, 1), (2, 31), (2, 9), (6, 38), (16, 14), (11, 7), (24, 10), (14, 15), (5, 35), (0, 13), (3, 37), (8, 38), (24, 32), (1, 36), (13, 10), (7, 29), (11, 33), (12, 37), (3, 12), (27, 30), (13, 13), (3, 18), (34, 28), (16, 33), (3, 15), (2, 23), (6, 18), (0, 37), (29, 33), (20, 29), (7, 16), (24, 5), (19, 31), (20, 6), (31, 35), (19, 0), (33, 33), (15, 29), (34, 6), (19, 35), (29, 29), (4, 17), (26, 8), (16, 22), (7, 6), (18, 23), (26, 23), (33, 0), (3, 2), (8, 34), (25, 28), (28, 8), (18, 30), (33, 35), (7, 7), (7, 17), (15, 18), (16, 27), (14, 16), (26, 14), (0, 9), (22, 16), (24, 19), (24, 0), (4, 35), (24, 21), (3, 4), (26, 17), (25, 16), (19, 18), (29, 18), (0, 5), (11, 3), (12, 19), (20, 4), (5, 18), (28, 31), (32, 12), (6, 13), (20, 15), (26, 11), (21, 3), (19, 22), (32, 38), (14, 17), (34, 3), (28, 12), (9, 3), (18, 28), (9, 31), (4, 33), (5, 11), (4, 3), (34, 5), (2, 37), (1, 2), (17, 33), (22, 9), (27, 29), (3, 30), (29, 10), (24, 23), (16, 3), (29, 19), (5, 21), (16, 19), (13, 3), (11, 37), (5, 25), (0, 24), (34, 29), (21, 12), (26, 4), (5, 27), (11, 27), (2, 18), (10, 2), (7, 14), (30, 10), (22, 10), (1, 23), (22, 38), (27, 32), (23, 27), (4, 15), (21, 13), (17, 27), (14, 21), (4, 21), (3, 8), (24, 20), (15, 25), (6, 37), (20, 21), (8, 31), (30, 24), (29, 34), (13, 22), (10, 33), (9, 10), (7, 12), (21, 18), (27, 7), (2, 29), (31, 15), (24, 24), (9, 30), (17, 17), (10, 26), (20, 18), (5, 33), (32, 16), (29, 23), (28, 26), (28, 30), (17, 1), (21, 32), (21, 38), (7, 3), (6, 14), (26, 9), (25, 27), (17, 38), (13, 20), (22, 26), (0, 6), (2, 6), (11, 15), (27, 13), (7, 19), (17, 16), (9, 11), (12, 35), (28, 5), (26, 2), (23, 32), (5, 10), (24, 29), (27, 10), (21, 36), (6, 11), (19, 3), (0, 7), (8, 29), (30, 28), (6, 33), (7, 9), (20, 35), (32, 31), (31, 11), (4, 38), (0, 10), (11, 28), (23, 29), (33, 24), (17, 8), (17, 26), (8, 13), (15, 28), (10, 37), (2, 14), (12, 12), (1, 21), (1, 13), (22, 1), (17, 23), (19, 32), (2, 1), (18, 31), (6, 22), (33, 18), (28, 21), (28, 23), (11, 13), (11, 21), (28, 32), (2, 3), (14, 11), (29, 20), (12, 17), (12, 38), (0, 19), (33, 13), (31, 20), (4, 26), (9, 8), (3, 38), (18, 6), (21, 26), (16, 17), (16, 6), (28, 9), (16, 21), (33, 21), (10, 7), (2, 2), (25, 23), (30, 34), (29, 25), (34, 13), (15, 22), (16, 18), (5, 0), (26, 38), (11, 25), (15, 33), (5, 34), (0, 33), (33, 3), (30, 38), (26, 34), (13, 15), (33, 12), (18, 15), (28, 27), (15, 6), (2, 16), (16, 37), (20, 30), (7, 5), (16, 16), (20, 13), (27, 38), (13, 24), (5, 38), (8, 32), (32, 0), (6, 30), (17, 13), (10, 11), (1, 11), (5, 19), (10, 20), (17, 10), (34, 12), (23, 10), (22, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26448", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 22), (23, 28), (3, 12), (6, 31), (33, 11), (15, 17), (1, 30), (3, 16), (16, 29), (24, 6), (8, 20), (25, 18), (1, 18), (25, 14), (26, 4), (11, 30), (8, 23), (18, 3), (27, 14), (9, 5), (27, 26), (4, 18), (28, 3), (17, 11), (5, 28), (6, 24), (20, 20), (1, 2), (28, 18), (27, 24), (8, 30), (1, 19), (23, 31), (12, 8), (27, 20), (24, 10), (6, 8), (2, 7), (26, 20), (21, 15), (28, 14), (2, 5), (3, 28), (1, 28), (13, 3), (21, 1), (11, 15), (32, 18), (24, 20), (19, 29), (27, 13), (0, 19), (15, 5), (25, 29), (20, 14), (32, 29), (5, 20), (31, 8), (15, 13), (3, 7), (2, 25), (13, 30), (18, 7), (14, 9), (21, 3), (32, 0), (8, 16), (22, 2), (20, 29), (21, 6), (24, 7), (30, 2), (15, 24), (28, 30), (15, 16), (1, 14), (13, 10), (33, 21), (13, 4), (28, 29), (8, 14), (27, 21), (3, 27), (0, 24), (6, 27), (29, 9), (31, 10), (21, 14), (2, 2), (15, 3), (3, 26), (19, 5), (4, 11), (5, 15), (15, 8), (15, 25), (23, 29), (31, 14), (0, 18), (10, 29), (10, 16), (18, 30), (0, 25), (0, 3), (25, 20), (14, 7), (32, 22), (23, 8), (23, 22), (14, 30), (30, 8), (13, 14), (2, 12), (22, 16), (6, 21), (10, 7), (27, 15), (24, 14), (19, 23), (21, 4), (2, 14), (6, 10), (24, 1), (2, 15), (11, 23), (23, 27), (1, 20), (0, 23), (29, 26), (21, 16), (16, 7), (1, 16), (24, 31), (7, 23), (28, 16), (3, 20), (5, 4), (27, 25), (22, 0), (18, 29), (14, 16), (1, 1), (21, 25), (11, 22), (29, 10), (25, 9), (28, 13), (31, 19), (4, 7), (32, 5), (18, 11), (31, 5), (25, 12), (21, 9), (33, 1), (13, 15), (1, 10), (4, 27), (0, 11), (3, 14), (7, 0), (4, 16), (23, 19), (4, 25), (3, 22), (5, 10), (14, 3), (2, 27), (11, 10), (25, 5), (24, 16), (5, 14), (17, 14), (32, 8), (0, 15), (28, 24), (26, 29), (8, 5), (9, 24), (28, 19), (18, 26), (26, 0), (33, 24), (4, 28), (15, 9), (32, 20), (27, 12), (16, 1), (10, 19), (13, 28), (8, 12), (25, 27), (33, 13), (27, 27), (30, 5), (23, 2), (31, 27), (33, 10), (23, 16), (20, 4), (17, 30), (9, 6), (11, 31), (12, 20), (30, 6), (32, 21), (11, 2), (30, 21), (14, 5), (5, 5), (21, 0), (28, 6), (6, 3), (26, 30), (7, 18), (8, 13), (5, 8), (16, 23), (32, 7), (19, 31), (22, 13), (23, 14), (27, 3), (13, 8), (10, 0), (16, 28), (29, 6), (33, 30), (9, 28), (8, 9), (26, 10), (29, 1), (14, 27), (7, 9), (19, 12), (8, 15), (12, 30), (6, 11), (8, 25), (15, 12), (32, 3), (12, 1), (0, 9), (13, 24), (16, 4), (31, 24), (26, 5), (30, 17), (32, 28), (22, 19), (29, 29), (13, 1), (0, 1), (13, 5), (20, 17), (1, 13), (1, 15), (23, 0), (18, 27), (18, 0), (8, 26), (31, 2), (10, 22), (30, 11), (1, 26), (4, 5), (7, 12), (31, 18), (24, 26), (18, 16), (0, 28), (6, 16), (15, 20), (8, 10), (5, 23), (14, 17), (21, 18), (17, 22), (28, 1), (29, 4), (12, 4), (17, 21), (20, 7), (4, 24), (32, 13), (33, 29), (22, 23), (24, 30), (23, 1), (28, 10), (12, 28), (7, 10), (32, 10), (18, 28), (9, 17), (33, 27), (31, 11), (30, 30), (29, 5), (21, 23), (28, 8), (17, 7), (2, 8), (14, 11), (22, 28), (14, 18), (9, 16), (8, 3), (7, 19), (15, 21), (5, 21), (31, 9), (31, 31), (28, 7), (33, 3), (24, 25), (28, 28), (19, 22), (24, 13), (24, 15), (12, 11), (28, 5), (1, 11), (27, 0), (27, 29), (24, 9), (22, 15), (19, 14), (7, 16), (8, 2), (24, 18), (21, 11), (8, 11), (5, 7), (1, 24), (27, 1), (7, 11), (19, 7), (10, 17), (20, 26), (9, 12), (2, 3), (17, 8), (15, 10), (13, 18), (21, 8), (17, 24), (19, 15), (5, 3), (1, 29), (10, 23), (9, 25), (29, 17), (20, 3), (8, 29), (9, 30), (31, 28), (5, 13), (12, 24), (27, 6), (7, 26), (32, 19), (33, 6), (3, 15), (33, 28), (12, 27), (24, 0), (29, 3), (28, 4), (6, 6), (19, 3), (23, 11), (13, 9), (26, 21), (17, 1), (8, 27), (17, 18), (30, 19), (30, 0), (0, 12), (18, 25), (12, 14), (15, 28), (11, 4), (24, 17), (11, 6), (14, 21), (15, 14), (13, 19), (23, 5), (5, 22), (25, 2), (6, 13), (2, 30), (14, 1), (33, 22), (11, 11), (1, 9), (3, 3), (33, 12), (9, 15), (24, 24), (2, 16), (13, 6), (9, 9), (9, 27), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465500", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (2, 23), (22, 25), (23, 4), (12, 26), (4, 18), (25, 2), (17, 11), (28, 4), (23, 22), (16, 8), (22, 6), (1, 9), (13, 15), (24, 8), (24, 1), (30, 2), (8, 17), (18, 3), (30, 5), (30, 27), (8, 12), (0, 7), (26, 28), (7, 30), (17, 16), (24, 28), (26, 7), (7, 29), (32, 28), (0, 18), (25, 24), (13, 8), (27, 16), (19, 24), (10, 18), (15, 20), (9, 13), (20, 10), (23, 24), (25, 7), (11, 7), (17, 5), (29, 11), (2, 20), (28, 5), (13, 3), (15, 14), (8, 10), (11, 10), (19, 29), (12, 29), (9, 26), (10, 24), (20, 27), (11, 8), (19, 13), (14, 18), (21, 7), (32, 6), (25, 14), (16, 21), (21, 14), (8, 20), (28, 6), (0, 25), (17, 22), (0, 4), (21, 30), (8, 26), (23, 29), (19, 11), (21, 4), (3, 11), (5, 29), (2, 7), (7, 7), (22, 26), (21, 20), (0, 8), (2, 6), (31, 14), (26, 2), (31, 13), (32, 27), (0, 26), (3, 0), (18, 20), (31, 24), (31, 16), (15, 21), (8, 27), (16, 22), (18, 10), (28, 3), (16, 10), (28, 14), (19, 17), (9, 29), (24, 4), (20, 3), (26, 8), (22, 1), (12, 3), (3, 29), (23, 20), (18, 4), (2, 17), (21, 28), (23, 30), (32, 17), (7, 3), (5, 28), (17, 19), (11, 4), (24, 24), (2, 21), (22, 19), (6, 18), (3, 13), (1, 6), (18, 28), (9, 16), (32, 23), (26, 23), (24, 3), (4, 2), (6, 5), (2, 9), (8, 14), (14, 24), (14, 15), (30, 1), (21, 21), (30, 26), (10, 7), (26, 10), (4, 6), (24, 26), (16, 4), (11, 6), (29, 24), (8, 15), (11, 2), (28, 13), (6, 25), (16, 20), (21, 2), (4, 9), (32, 2), (27, 17), (12, 19), (2, 14), (6, 24), (16, 13), (6, 22), (5, 15), (4, 17), (5, 1), (29, 29), (14, 2), (17, 6), (30, 17), (24, 16), (25, 26), (22, 15), (6, 10), (15, 4), (19, 0), (15, 9), (12, 0), (13, 26), (30, 29), (20, 29), (26, 19), (5, 2), (3, 3), (23, 9), (6, 4), (8, 22), (0, 28), (15, 0), (10, 2), (4, 3), (11, 25), (6, 26), (19, 16), (28, 26), (6, 0), (13, 2), (6, 21), (17, 18), (21, 24), (14, 7), (25, 1), (3, 22), (11, 27), (28, 25), (19, 21), (4, 15), (25, 6), (12, 17), (15, 17), (12, 12), (6, 7), (19, 30), (23, 21), (0, 17), (28, 12), (13, 16), (1, 2), (31, 21), (13, 0), (12, 27), (24, 17), (20, 22), (4, 13), (21, 25), (32, 21), (19, 19), (29, 9), (18, 8), (3, 9), (17, 0), (29, 30), (31, 23), (29, 7), (32, 7), (8, 19), (28, 2), (1, 17), (29, 4), (32, 3), (15, 10), (3, 30), (28, 1), (5, 27), (0, 15), (5, 26), (28, 11), (6, 29), (3, 26), (12, 2), (28, 10), (12, 5), (21, 6), (27, 0), (29, 22), (8, 9), (20, 14), (18, 0), (20, 25), (1, 29), (2, 22), (32, 9), (14, 21), (1, 13), (13, 18), (32, 14), (27, 5), (1, 16), (22, 20), (19, 10), (25, 30), (15, 18), (17, 20), (27, 20), (13, 28), (31, 12), (12, 6), (0, 11), (16, 18), (25, 0), (6, 17), (10, 3), (29, 19), (20, 2), (32, 20), (10, 21), (1, 28), (4, 12), (30, 7), (27, 29), (8, 4), (25, 16), (13, 13), (32, 18), (16, 0), (17, 1), (30, 3), (23, 0), (16, 24), (19, 27), (10, 9), (22, 2), (1, 5), (6, 12), (23, 15), (8, 30), (7, 18), (31, 25), (5, 19), (17, 4), (4, 22), (1, 18), (22, 14), (31, 3), (12, 30), (32, 24), (18, 27), (13, 11), (31, 1), (12, 28), (28, 23), (8, 3), (27, 8), (5, 16), (12, 22), (8, 8), (28, 18), (20, 15), (31, 22), (16, 26), (28, 24), (4, 1), (9, 14), (19, 7), (13, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276000", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 9), (9, 0), (20, 33), (13, 1), (29, 24), (30, 31), (36, 29), (17, 13), (18, 32), (16, 16), (3, 11), (3, 15), (30, 10), (21, 20), (35, 2), (1, 22), (4, 27), (33, 23), (20, 21), (25, 23), (30, 14), (4, 3), (17, 19), (23, 20), (4, 18), (17, 29), (30, 24), (27, 2), (3, 28), (18, 7), (31, 25), (32, 11), (7, 33), (21, 3), (26, 20), (20, 18), (13, 4), (11, 17), (35, 20), (26, 3), (2, 15), (27, 32), (11, 21), (30, 12), (32, 6), (18, 3), (21, 23), (19, 7), (3, 33), (25, 1), (11, 14), (19, 28), (23, 23), (20, 9), (18, 27), (32, 25), (25, 10), (23, 24), (17, 2), (34, 8), (2, 27), (35, 16), (33, 11), (13, 15), (35, 21), (20, 22), (5, 22), (10, 25), (0, 9), (7, 27), (2, 30), (13, 18), (22, 5), (10, 32), (16, 28), (21, 19), (35, 27), (9, 10), (0, 8), (18, 22), (25, 0), (8, 32), (8, 30), (19, 8), (9, 6), (32, 16), (0, 4), (29, 17), (8, 3), (28, 1), (2, 2), (8, 6), (33, 20), (26, 32), (5, 29), (35, 0), (34, 10), (31, 14), (3, 17), (3, 13), (3, 2), (17, 25), (18, 25), (22, 21), (7, 10), (17, 6), (31, 24), (24, 11), (12, 5), (0, 15), (7, 1), (33, 15), (30, 3), (18, 19), (6, 19), (20, 7), (3, 32), (15, 22), (20, 29), (7, 12), (19, 15), (32, 32), (17, 14), (22, 26), (0, 17), (13, 29), (1, 17), (3, 6), (21, 0), (2, 0), (25, 34), (0, 32), (16, 8), (7, 29), (23, 12), (34, 24), (23, 10), (18, 9), (10, 7), (4, 22), (2, 4), (29, 8), (16, 1), (2, 24), (4, 7), (30, 5), (33, 6), (29, 10), (2, 33), (0, 25), (4, 25), (36, 31), (35, 28), (27, 20), (21, 33), (28, 3), (12, 7), (35, 22), (16, 32), (13, 12), (25, 14), (8, 17), (4, 15), (10, 2), (7, 13), (0, 24), (13, 8), (1, 34), (35, 17), (19, 24), (28, 0), (4, 0), (3, 4), (26, 6), (1, 13), (6, 34), (29, 12), (28, 17), (6, 11), (33, 0), (35, 12), (6, 33), (1, 18), (36, 15), (31, 20), (17, 0), (3, 26), (10, 23), (29, 32), (17, 30), (36, 5), (3, 14), (19, 5), (14, 10), (10, 15), (8, 13), (28, 31), (20, 32), (31, 29), (18, 18), (10, 6), (23, 8), (3, 27), (3, 10), (12, 3), (12, 20), (21, 30), (28, 19), (14, 9), (7, 18), (22, 8), (13, 30), (23, 4), (3, 16), (18, 20), (33, 7), (7, 2), (11, 23), (15, 16), (35, 1), (6, 6), (32, 31), (26, 19), (17, 10), (26, 21), (13, 0), (9, 27), (19, 26), (16, 22), (31, 1), (9, 3), (14, 4), (21, 16), (7, 11), (22, 14), (36, 21), (28, 14), (8, 5), (29, 31), (10, 20), (6, 25), (24, 32), (30, 0), (31, 26), (8, 28), (21, 6), (31, 8), (24, 5), (20, 24), (12, 19), (34, 23), (7, 34), (20, 12), (1, 6), (3, 34), (20, 3), (33, 29), (20, 0), (10, 4), (27, 26), (1, 7), (21, 12), (33, 5), (36, 13), (28, 16), (8, 29), (31, 33), (9, 8), (32, 30), (36, 16), (24, 27), (11, 22), (10, 31), (3, 8), (28, 28), (16, 14), (27, 28), (34, 26), (4, 30), (26, 4), (33, 25), (16, 23), (10, 11), (13, 2), (36, 17), (31, 16), (27, 13), (24, 20), (27, 9), (33, 28), (15, 23), (25, 31), (31, 13), (2, 32), (26, 15), (10, 9), (21, 29), (4, 19), (19, 22), (22, 15), (15, 24), (24, 34), (23, 32), (18, 10), (11, 5), (0, 21), (35, 10), (10, 27), (19, 10), (34, 9), (7, 5), (22, 28), (34, 19), (13, 32), (25, 21), (15, 32), (8, 34), (14, 20), (33, 8), (34, 15), (35, 6), (1, 21), (15, 4), (5, 11), (30, 18), (32, 2), (23, 2), (1, 14), (26, 14), (1, 15), (13, 26), (5, 30), (26, 5), (7, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474240", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 31), (2, 8), (23, 29), (7, 5), (6, 33), (2, 18), (8, 23), (20, 31), (21, 13), (20, 19), (10, 28), (1, 26), (19, 3), (1, 20), (13, 19), (3, 34), (18, 36), (11, 1), (6, 19), (24, 7), (26, 38), (25, 22), (15, 26), (23, 14), (12, 9), (7, 16), (30, 25), (6, 14), (8, 9), (0, 36), (24, 15), (14, 23), (24, 20), (1, 4), (30, 13), (29, 6), (15, 2), (8, 32), (7, 33), (27, 14), (8, 34), (24, 18), (18, 7), (17, 18), (12, 1), (2, 27), (25, 25), (29, 17), (3, 25), (11, 19), (15, 38), (19, 4), (19, 34), (30, 23), (25, 31), (23, 7), (2, 2), (13, 36), (30, 22), (11, 16), (23, 9), (3, 27), (5, 22), (16, 30), (25, 21), (30, 26), (22, 13), (24, 25), (14, 19), (12, 8), (20, 6), (21, 15), (8, 13), (2, 35), (16, 1), (28, 2), (29, 29), (26, 18), (3, 11), (15, 18), (1, 38), (12, 15), (29, 3), (22, 1), (26, 32), (11, 2), (10, 10), (19, 18), (7, 2), (22, 26), (10, 18), (30, 14), (13, 6), (13, 35), (22, 21), (10, 19), (17, 38), (29, 7), (13, 27), (2, 31), (20, 28), (1, 34), (7, 4), (18, 26), (11, 17), (24, 28), (5, 15), (11, 36), (28, 23), (24, 3), (3, 0), (18, 28), (13, 31), (13, 29), (2, 26), (20, 36), (12, 13), (0, 2), (23, 35), (16, 36), (8, 16), (23, 30), (13, 21), (21, 35), (22, 0), (24, 13), (5, 36), (26, 1), (13, 12), (23, 24), (17, 3), (18, 29), (6, 35), (22, 29), (25, 18), (29, 8), (8, 5), (14, 10), (15, 10), (4, 29), (19, 16), (0, 18), (25, 8), (10, 14), (21, 32), (15, 23), (13, 33), (24, 30), (16, 10), (22, 6), (19, 38), (23, 13), (0, 25), (13, 5), (26, 20), (15, 33), (19, 20), (27, 20), (14, 24), (24, 5), (4, 26), (0, 1), (16, 23), (10, 23), (15, 9), (25, 24), (22, 38), (20, 21), (10, 11), (14, 16), (20, 10), (18, 27), (16, 28), (19, 23), (15, 31), (7, 35), (11, 11), (24, 24), (30, 28), (20, 23), (3, 38), (15, 37), (29, 9), (19, 13), (2, 29), (7, 3), (26, 17), (10, 5), (29, 33), (22, 28), (13, 28), (18, 33), (27, 33), (1, 1), (23, 15), (17, 2), (18, 4), (20, 12), (22, 9), (19, 6), (5, 32), (25, 29), (6, 26), (9, 29), (19, 29), (24, 11), (6, 38), (28, 25), (15, 15), (13, 37), (16, 38), (4, 4), (3, 15), (17, 4), (21, 28), (30, 27), (20, 16), (25, 38), (23, 19), (2, 24), (10, 0), (8, 14), (21, 8), (2, 17), (16, 3), (15, 29), (22, 11), (18, 3), (6, 10), (18, 19), (22, 22), (8, 37), (9, 24), (4, 1), (5, 27), (9, 28), (24, 29), (13, 10), (13, 23), (27, 29), (14, 36), (24, 38), (22, 37), (18, 18), (25, 3), (16, 15), (12, 38), (28, 19), (8, 35), (3, 4), (5, 38), (0, 35), (7, 18), (25, 6), (13, 4), (29, 38), (19, 30), (1, 7), (18, 12), (21, 18), (23, 4), (10, 35), (28, 7), (21, 0), (8, 3), (1, 15), (28, 30), (24, 33), (6, 18), (27, 0), (11, 5), (5, 13), (18, 22), (13, 26), (28, 8), (26, 3), (11, 8), (2, 23), (9, 18), (17, 13), (25, 32), (28, 16), (22, 15), (19, 37), (21, 3), (8, 29), (15, 24), (25, 13), (10, 8), (27, 10), (29, 28), (21, 6), (1, 11), (9, 10), (13, 22), (27, 27), (7, 8), (17, 22), (29, 18), (7, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425160", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (10, 29), (28, 17), (19, 20), (27, 25), (20, 27), (0, 27), (28, 31), (14, 28), (34, 31), (11, 14), (20, 18), (14, 14), (14, 9), (8, 15), (20, 21), (11, 1), (33, 0), (23, 2), (35, 13), (12, 33), (28, 24), (2, 29), (25, 11), (12, 4), (15, 21), (1, 2), (24, 31), (21, 34), (35, 3), (28, 13), (2, 11), (13, 6), (20, 20), (10, 4), (31, 33), (35, 7), (15, 17), (29, 16), (29, 7), (25, 12), (29, 20), (21, 31), (13, 23), (26, 16), (6, 29), (35, 20), (8, 6), (19, 0), (33, 33), (21, 14), (25, 0), (19, 27), (7, 11), (8, 27), (32, 0), (35, 6), (31, 30), (21, 6), (3, 14), (14, 32), (7, 18), (5, 11), (17, 8), (6, 5), (21, 5), (30, 34), (15, 12), (9, 7), (14, 5), (29, 22), (20, 32), (18, 28), (5, 7), (33, 16), (13, 2), (13, 19), (27, 1), (23, 18), (30, 10), (33, 15), (3, 33), (31, 13), (18, 20), (22, 33), (22, 20), (28, 11), (17, 28), (23, 33), (23, 34), (28, 21), (2, 33), (1, 7), (31, 9), (30, 30), (26, 13), (20, 25), (15, 27), (31, 4), (25, 32), (24, 19), (32, 5), (26, 17), (0, 22), (35, 28), (1, 19), (1, 10), (9, 15), (1, 25), (34, 13), (23, 24), (21, 30), (10, 11), (14, 17), (28, 12), (6, 28), (0, 11), (2, 3), (8, 2), (34, 15), (1, 11), (29, 31), (8, 31), (28, 2), (21, 7), (23, 29), (21, 26), (30, 2), (9, 27), (30, 6), (12, 12), (6, 16), (5, 34), (18, 34), (3, 19), (16, 18), (12, 11), (14, 0), (4, 17), (21, 19), (31, 26), (30, 11), (2, 12), (25, 17), (17, 19), (3, 24), (20, 3), (31, 0), (4, 24), (17, 23), (33, 27), (34, 16), (12, 31), (28, 10), (35, 14), (22, 7), (2, 27), (15, 11), (9, 21), (32, 24), (9, 1), (16, 20), (5, 0), (4, 25), (4, 16), (35, 18), (19, 13), (22, 11), (8, 19), (6, 34), (1, 12), (33, 20), (18, 14), (15, 8), (25, 10), (15, 22), (18, 2), (32, 1), (30, 32), (5, 25), (6, 17), (13, 21), (21, 17), (24, 1), (21, 15), (31, 31), (24, 16), (15, 4), (1, 33), (4, 7), (12, 28), (12, 9), (5, 8), (5, 31), (15, 30), (30, 25), (5, 18), (6, 32), (15, 13), (22, 5), (26, 29), (11, 16), (17, 15), (19, 21), (12, 17), (4, 13), (5, 13), (23, 11), (1, 30), (8, 14), (18, 18), (12, 19), (3, 25), (34, 22), (23, 30), (7, 4), (23, 16), (33, 13), (17, 22), (14, 10), (0, 25), (29, 3), (24, 17), (1, 17), (24, 26), (13, 16), (9, 32), (23, 17), (29, 5), (6, 10), (33, 3), (2, 31), (32, 19), (25, 30), (11, 22), (14, 6), (4, 30), (25, 13), (13, 0), (21, 29), (9, 11), (18, 13), (23, 21), (14, 26), (12, 22), (8, 29), (25, 21), (17, 32), (30, 4), (7, 23), (11, 10), (13, 11), (2, 21), (5, 33), (21, 18), (29, 33), (26, 20), (12, 29), (34, 24), (19, 7), (23, 7), (17, 20), (16, 27), (27, 8), (11, 9), (27, 12), (27, 7), (24, 34), (21, 4), (25, 6), (2, 28), (33, 7), (33, 29), (31, 25), (27, 13), (33, 30), (14, 20), (15, 2), (7, 21), (29, 13), (24, 0), (25, 9), (8, 16), (9, 8), (34, 21), (30, 14), (20, 4), (28, 6), (14, 3), (18, 17), (3, 7), (8, 12), (13, 14), (2, 6), (19, 31), (4, 4), (25, 28), (19, 29), (19, 9), (10, 16), (33, 31), (23, 3), (8, 30), (10, 6), (2, 5), (8, 8), (22, 8), (6, 19), (10, 13), (17, 33), (6, 8), (17, 3), (3, 10), (7, 25), (3, 27), (35, 22), (12, 15), (3, 31), (27, 32), (20, 17), (26, 2), (12, 5), (28, 1), (24, 20), (35, 2), (27, 10), (4, 26), (25, 1), (9, 0), (32, 32), (27, 4), (32, 12), (35, 11), (16, 4), (9, 5), (30, 9), (5, 30), (18, 30), (1, 29), (19, 23), (18, 8), (3, 0), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "131040", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 26), (28, 29), (19, 12), (11, 22), (15, 24), (3, 21), (33, 31), (22, 1), (5, 16), (25, 8), (32, 7), (23, 5), (29, 19), (32, 11), (25, 20), (22, 22), (30, 10), (14, 8), (0, 2), (33, 25), (31, 26), (10, 9), (4, 33), (30, 17), (15, 17), (24, 20), (15, 10), (4, 4), (2, 20), (27, 1), (12, 17), (29, 4), (18, 21), (30, 9), (28, 11), (5, 10), (4, 34), (19, 6), (5, 9), (12, 14), (29, 32), (9, 5), (9, 33), (4, 12), (17, 13), (16, 19), (7, 30), (33, 20), (9, 8), (25, 27), (25, 33), (10, 0), (6, 30), (32, 20), (6, 11), (8, 34), (12, 23), (26, 29), (26, 4), (1, 31), (23, 0), (23, 33), (21, 0), (2, 25), (13, 5), (15, 32), (0, 10), (27, 32), (6, 28), (25, 22), (4, 15), (8, 3), (19, 0), (5, 19), (2, 12), (26, 17), (22, 4), (24, 17), (18, 27), (16, 29), (0, 8), (20, 11), (25, 13), (9, 20), (6, 7), (4, 13), (11, 5), (12, 21), (22, 9), (20, 2), (27, 16), (16, 24), (14, 24), (9, 22), (22, 8), (22, 19), (4, 0), (15, 33), (10, 25), (0, 6), (11, 20), (19, 5), (27, 0), (19, 29), (5, 32), (0, 27), (7, 10), (15, 26), (5, 0), (1, 2), (24, 15), (11, 11), (15, 12), (33, 19), (30, 14), (11, 33), (28, 30), (23, 17), (25, 32), (7, 7), (31, 17), (26, 18), (12, 20), (27, 8), (26, 6), (32, 6), (31, 28), (26, 5), (4, 6), (19, 3), (32, 2), (2, 3), (1, 16), (20, 9), (10, 32), (15, 34), (8, 9), (5, 34), (20, 1), (19, 18), (9, 9), (14, 32), (3, 7), (12, 29), (22, 25), (29, 34), (31, 9), (13, 13), (32, 30), (8, 6), (18, 25), (4, 28), (16, 5), (14, 18), (33, 5), (13, 19), (27, 24), (28, 21), (28, 23), (19, 8), (14, 14), (14, 28), (13, 26), (5, 18), (5, 15), (31, 5), (30, 19), (24, 24), (16, 34), (5, 8), (8, 8), (13, 0), (29, 13), (26, 3), (15, 19), (10, 10), (16, 6), (21, 10), (33, 0), (9, 3), (31, 10), (0, 24), (26, 30), (25, 9), (4, 31), (18, 13), (9, 0), (28, 2), (17, 3), (27, 31), (10, 33), (14, 10), (17, 7), (3, 22), (4, 5), (28, 32), (22, 6), (16, 33), (1, 29), (24, 22), (6, 18), (11, 10), (19, 11), (15, 14), (7, 20), (7, 4), (32, 22), (1, 22), (10, 3), (19, 16), (22, 34), (23, 15), (6, 3), (23, 26), (9, 27), (17, 14), (19, 22), (5, 23), (9, 31), (29, 25), (12, 13), (18, 19), (30, 2), (30, 26), (14, 6), (21, 14), (14, 33), (5, 3), (0, 4), (17, 12), (1, 9), (31, 18), (2, 33), (29, 16), (0, 13), (1, 1), (2, 34), (28, 22), (1, 13), (28, 10), (10, 34), (7, 33), (27, 9), (3, 2), (4, 22), (21, 21), (28, 5), (23, 31), (13, 16), (12, 34), (11, 2), (8, 33), (11, 26), (10, 5), (14, 7), (3, 11), (20, 24), (20, 22), (28, 6), (29, 27), (2, 26), (24, 6), (9, 2), (0, 32), (23, 11), (32, 9), (13, 2), (27, 25), (21, 27), (13, 34), (13, 24), (2, 32), (27, 18), (20, 32), (9, 30), (21, 30), (32, 10), (10, 18), (32, 19), (23, 14), (30, 31), (5, 14), (28, 33), (29, 2), (33, 21), (20, 28), (8, 24), (33, 1), (31, 4), (32, 32), (14, 25), (27, 21), (27, 4), (1, 4), (21, 19), (18, 28), (9, 14), (28, 19), (33, 6), (2, 13), (5, 26), (7, 15), (31, 6), (11, 27), (19, 14), (10, 17), (18, 22), (32, 34), (32, 29), (15, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "857200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 30), (19, 13), (12, 18), (28, 22), (32, 24), (15, 10), (7, 31), (28, 25), (7, 23), (9, 18), (21, 22), (27, 9), (14, 11), (9, 4), (31, 29), (17, 19), (1, 1), (21, 9), (23, 0), (19, 29), (13, 34), (21, 33), (14, 9), (14, 18), (31, 19), (29, 12), (15, 31), (23, 21), (24, 21), (7, 9), (18, 29), (23, 23), (12, 15), (13, 15), (21, 1), (26, 20), (6, 5), (27, 26), (4, 6), (27, 22), (4, 34), (25, 18), (7, 15), (20, 31), (17, 28), (11, 6), (24, 18), (32, 33), (17, 9), (11, 14), (22, 3), (5, 4), (15, 23), (20, 10), (0, 31), (29, 3), (23, 28), (17, 29), (21, 6), (13, 10), (26, 2), (3, 4), (29, 34), (28, 20), (30, 32), (11, 21), (13, 11), (19, 25), (25, 11), (19, 17), (8, 22), (1, 11), (29, 10), (26, 23), (1, 5), (6, 14), (30, 13), (20, 1), (12, 16), (1, 15), (8, 17), (15, 16), (27, 27), (8, 15), (19, 27), (30, 26), (2, 19), (12, 22), (25, 6), (21, 32), (3, 29), (5, 3), (19, 6), (20, 15), (26, 16), (11, 24), (17, 27), (17, 11), (20, 20), (14, 4), (10, 18), (12, 31), (32, 14), (19, 16), (6, 16), (19, 9), (11, 31), (14, 0), (19, 10), (21, 19), (23, 5), (12, 9), (8, 0), (1, 33), (0, 21), (12, 26), (27, 15), (17, 25), (23, 32), (25, 20), (15, 9), (14, 10), (4, 28), (26, 7), (32, 26), (29, 17), (5, 5), (13, 9), (9, 10), (6, 3), (27, 0), (24, 27), (9, 27), (11, 33), (7, 22), (16, 22), (31, 31), (20, 21), (16, 32), (2, 1), (5, 19), (12, 12), (24, 6), (4, 27), (18, 28), (14, 27), (32, 8), (13, 4), (9, 11), (3, 6), (30, 1), (2, 22), (19, 8), (8, 28), (18, 18), (17, 16), (17, 4), (4, 21), (11, 7), (7, 25), (28, 5), (25, 32), (27, 33), (22, 7), (2, 33), (20, 18), (20, 2), (25, 5), (18, 16), (19, 31), (0, 30), (1, 30), (32, 30), (4, 23), (11, 4), (22, 15), (10, 28), (26, 17), (2, 8), (16, 0), (24, 4), (0, 10), (25, 14), (28, 21), (30, 27), (12, 11), (1, 12), (23, 12), (25, 23), (5, 23), (31, 8), (14, 16), (7, 6), (3, 32), (18, 7), (27, 18), (24, 8), (1, 2), (0, 18), (22, 31), (12, 20), (5, 11), (21, 24), (3, 23), (9, 13), (27, 7), (29, 7), (26, 15), (13, 29), (8, 25), (25, 12), (13, 6), (22, 27), (30, 29), (11, 18), (7, 14), (17, 13), (14, 31), (20, 22), (6, 6), (4, 8), (29, 8), (8, 23), (1, 26), (27, 4), (11, 29), (16, 1), (18, 26), (20, 23), (30, 5), (32, 31), (23, 6), (13, 12), (6, 29), (12, 24), (4, 2), (0, 14), (16, 8), (25, 21), (32, 10), (26, 14), (27, 14), (10, 19), (14, 13), (2, 25), (17, 34), (11, 16), (22, 19), (9, 9), (27, 1), (22, 21), (16, 9), (23, 27), (6, 20), (13, 18), (12, 25), (28, 24), (21, 10), (25, 26), (6, 28), (4, 12), (26, 33), (29, 0), (21, 26), (0, 34), (32, 15), (32, 21), (32, 19), (27, 11), (17, 23), (20, 5), (22, 16), (7, 18), (30, 12), (26, 26), (15, 12), (20, 30), (16, 19), (19, 21), (25, 10), (12, 30), (8, 11), (7, 8), (32, 12), (13, 28), (26, 27), (14, 25), (27, 30), (7, 11), (27, 23), (5, 28), (5, 30), (16, 21), (10, 1), (8, 30), (9, 31), (0, 9), (14, 22), (22, 26), (4, 18), (28, 17), (24, 14), (24, 29), (4, 25), (6, 25), (11, 25), (9, 15), (13, 33), (13, 14), (7, 4), (2, 0), (23, 3), (25, 34), (3, 17), (14, 17), (15, 30), (7, 7), (4, 13), (15, 0), (31, 2), (28, 12), (10, 6), (22, 13), (29, 32), (6, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37440", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (17, 0), (28, 7), (8, 28), (18, 18), (29, 4), (0, 31), (23, 33), (29, 21), (4, 21), (10, 8), (0, 12), (32, 8), (4, 33), (27, 30), (25, 23), (19, 22), (15, 23), (3, 5), (17, 28), (31, 4), (9, 1), (23, 14), (14, 14), (20, 17), (24, 15), (16, 22), (5, 16), (17, 10), (24, 11), (8, 33), (1, 7), (27, 27), (9, 10), (7, 1), (18, 7), (26, 10), (31, 24), (23, 28), (17, 11), (22, 23), (26, 20), (19, 4), (11, 6), (6, 33), (32, 23), (17, 15), (13, 21), (9, 27), (2, 2), (14, 0), (31, 26), (32, 32), (1, 27), (6, 22), (2, 33), (1, 0), (10, 4), (0, 16), (14, 15), (17, 3), (7, 12), (11, 25), (31, 22), (19, 21), (2, 20), (19, 12), (26, 32), (15, 29), (18, 12), (1, 4), (19, 25), (11, 2), (25, 8), (24, 31), (0, 17), (9, 7), (3, 17), (21, 32), (1, 14), (8, 27), (0, 25), (4, 14), (32, 0), (8, 14), (9, 20), (30, 18), (11, 18), (20, 33), (29, 26), (13, 24), (13, 1), (20, 12), (17, 4), (8, 9), (9, 28), (20, 0), (25, 26), (6, 3), (0, 2), (28, 24), (28, 28), (29, 15), (23, 17), (31, 15), (12, 32), (13, 15), (32, 7), (30, 13), (4, 15), (29, 19), (2, 31), (26, 28), (10, 20), (28, 12), (31, 7), (13, 12), (17, 7), (32, 28), (4, 23), (22, 4), (27, 17), (5, 31), (9, 0), (32, 4), (18, 15), (12, 25), (8, 6), (9, 25), (15, 24), (15, 27), (32, 14), (15, 1), (2, 27), (30, 19), (18, 14), (23, 32), (25, 20), (11, 33), (26, 8), (29, 10), (25, 32), (8, 4), (31, 21), (8, 8), (14, 3), (21, 28), (3, 26), (21, 30), (23, 12), (18, 0), (12, 4), (4, 24), (31, 12), (27, 31), (29, 33), (5, 13), (10, 3), (9, 4), (27, 21), (31, 2), (1, 20), (10, 17), (15, 22), (6, 10), (6, 5), (11, 5), (5, 3), (20, 8), (8, 13), (19, 6), (9, 26), (14, 17), (21, 4), (24, 25), (10, 27), (29, 11), (32, 11), (21, 22), (30, 5), (7, 11), (13, 27), (22, 33), (18, 8), (2, 14), (31, 32), (5, 2), (12, 23), (30, 16), (6, 29), (4, 20), (25, 10), (21, 12), (19, 20), (26, 25), (13, 7), (1, 24), (14, 11), (6, 18), (15, 2), (25, 15), (10, 11), (29, 0), (2, 24), (0, 28), (5, 30), (18, 21), (3, 31), (32, 27), (5, 28), (3, 4), (23, 16), (25, 16), (20, 15), (24, 3), (9, 21), (11, 8), (28, 29), (9, 33), (13, 20), (28, 14), (9, 16), (17, 6), (23, 21), (4, 8), (21, 5), (25, 19), (21, 15), (20, 23), (14, 7), (9, 9), (10, 6), (29, 6), (24, 29), (22, 19), (9, 2), (10, 26), (24, 33), (20, 13), (17, 24), (27, 26), (12, 31), (30, 1), (5, 8), (20, 2), (16, 19), (18, 33), (21, 20), (3, 14), (18, 10), (9, 24), (7, 14), (18, 28), (0, 8), (6, 28), (4, 6), (26, 22), (13, 22), (27, 23), (30, 24), (5, 20), (26, 7), (15, 33), (30, 22), (9, 30), (12, 21), (20, 16), (8, 11), (15, 13), (28, 22), (26, 14), (21, 26), (29, 14), (30, 3), (30, 15), (29, 3), (22, 30), (6, 0), (27, 11), (26, 17), (9, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954408", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (19, 3), (17, 2), (13, 22), (6, 29), (9, 35), (4, 29), (5, 10), (10, 16), (22, 27), (17, 35), (26, 24), (23, 5), (18, 0), (24, 11), (7, 7), (32, 7), (3, 33), (13, 12), (8, 16), (8, 35), (15, 31), (28, 12), (13, 20), (31, 29), (16, 1), (28, 18), (22, 21), (24, 12), (8, 14), (23, 20), (24, 15), (10, 8), (26, 29), (23, 13), (22, 4), (15, 28), (13, 26), (17, 12), (22, 34), (24, 27), (16, 11), (7, 17), (3, 12), (32, 26), (19, 18), (24, 30), (29, 6), (3, 6), (7, 16), (32, 3), (17, 34), (30, 28), (26, 9), (19, 5), (23, 7), (12, 29), (16, 22), (29, 24), (16, 19), (27, 16), (20, 8), (20, 19), (19, 30), (15, 14), (32, 14), (30, 18), (29, 23), (15, 16), (17, 23), (23, 22), (21, 14), (5, 35), (0, 27), (13, 10), (31, 5), (7, 19), (32, 28), (32, 9), (29, 0), (21, 30), (12, 8), (26, 22), (11, 22), (32, 8), (18, 33), (2, 34), (20, 2), (20, 29), (20, 6), (5, 14), (27, 27), (32, 13), (22, 12), (17, 29), (20, 14), (3, 8), (1, 19), (12, 6), (21, 16), (8, 11), (16, 4), (5, 24), (26, 32), (9, 3), (12, 18), (16, 7), (13, 30), (31, 19), (25, 5), (12, 2), (7, 8), (2, 7), (31, 4), (23, 26), (18, 10), (13, 24), (14, 30), (10, 4), (24, 17), (9, 19), (13, 29), (31, 16), (12, 23), (8, 2), (20, 0), (8, 9), (15, 11), (18, 31), (25, 33), (15, 26), (7, 6), (5, 23), (9, 18), (24, 7), (20, 35), (32, 21), (15, 17), (5, 12), (3, 23), (1, 14), (32, 6), (13, 9), (29, 18), (18, 18), (8, 27), (5, 8), (32, 20), (4, 6), (9, 20), (9, 21), (22, 22), (3, 4), (7, 34), (25, 23), (29, 29), (7, 12), (28, 6), (12, 26), (23, 24), (12, 27), (29, 25), (22, 32), (11, 10), (27, 2), (27, 0), (23, 15), (10, 15), (21, 6), (0, 11), (2, 31), (26, 27), (22, 8), (16, 15), (19, 1), (14, 13), (6, 23), (21, 29), (17, 0), (4, 16), (5, 7), (21, 17), (11, 2), (10, 24), (1, 7), (13, 34), (1, 30), (16, 30), (0, 24), (2, 8), (26, 33), (7, 4), (13, 27), (3, 10), (12, 17), (31, 3), (26, 15), (30, 6), (30, 16), (9, 13), (22, 25), (3, 18), (23, 9), (30, 8), (6, 16), (23, 30), (2, 18), (24, 0), (22, 28), (22, 13), (28, 24), (19, 19), (14, 22), (14, 8), (11, 24), (23, 35), (23, 6), (28, 3), (18, 28), (22, 16), (26, 19), (25, 32), (9, 34), (29, 2), (1, 12), (6, 14), (29, 27), (5, 16), (0, 10), (30, 29), (28, 28), (1, 5), (30, 22), (24, 29), (18, 12), (24, 18), (0, 5), (19, 26), (27, 26), (7, 26), (6, 22), (15, 25), (28, 25), (29, 20), (14, 5), (20, 34), (28, 4), (26, 7), (30, 13), (3, 7), (16, 28), (27, 13), (2, 10), (10, 13), (13, 17), (20, 18), (26, 14), (7, 33), (4, 33), (28, 11), (25, 29), (7, 23), (30, 7), (14, 12), (2, 28), (15, 3), (18, 19), (25, 10), (22, 15), (0, 29), (15, 2), (1, 18), (5, 15), (10, 30), (1, 35), (17, 3), (16, 27), (19, 6), (4, 22), (11, 1), (4, 25), (9, 11), (9, 24), (5, 11), (14, 6), (15, 35), (22, 14), (5, 19), (20, 24), (27, 33), (18, 25), (20, 15), (26, 12), (2, 20), (8, 15), (10, 32), (22, 20), (10, 6), (18, 35), (22, 24), (26, 16), (4, 13), (25, 7), (28, 35), (3, 11), (22, 19), (28, 30), (17, 31), (8, 4), (3, 2), (28, 9), (21, 7), (29, 1), (32, 0), (5, 1), (9, 22), (24, 21), (15, 5), (8, 26), (5, 33), (20, 32), (13, 7), (11, 0), (15, 20), (9, 6), (9, 14), (19, 24), (6, 17), (18, 11), (30, 23), (16, 23), (3, 25), (13, 11), (1, 28), (31, 13), (11, 29), (1, 32), (18, 7), (1, 26), (16, 17), (6, 18), (28, 33), (32, 32), (25, 34), (26, 18), (5, 17), (17, 30), (19, 20), (26, 1), (26, 13), (11, 18), (15, 30), (5, 25), (29, 19), (18, 9), (31, 15), (13, 31), (11, 17), (21, 12), (10, 23), (0, 14), (1, 3), (9, 4), (13, 3), (25, 21), (20, 1), (9, 16), (26, 0), (30, 34), (11, 34), (29, 32), (24, 10), (2, 6), (20, 7), (19, 14), (26, 17), (20, 5), (17, 8), (3, 16), (0, 18), (26, 3), (5, 21), (1, 11), (12, 15), (27, 17), (1, 31), (28, 5), (20, 12), (20, 16), (6, 8), (23, 12), (24, 28), (12, 24), (6, 1), (11, 23), (16, 18), (19, 9), (6, 24), (24, 2), (17, 19), (27, 9), (12, 31), (3, 19), (24, 16), (30, 30), (21, 22), (1, 4), (32, 19), (23, 18), (22, 18), (22, 33), (4, 32), (16, 29), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715392", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 18), (19, 26), (8, 4), (30, 5), (5, 16), (1, 6), (16, 22), (8, 8), (3, 18), (25, 3), (25, 13), (17, 1), (7, 22), (12, 29), (27, 29), (17, 29), (2, 27), (28, 27), (11, 21), (7, 0), (16, 27), (14, 29), (33, 7), (27, 11), (24, 8), (24, 34), (31, 9), (28, 35), (0, 20), (23, 30), (11, 29), (20, 16), (18, 6), (25, 0), (31, 31), (30, 16), (12, 25), (12, 14), (29, 10), (31, 22), (12, 32), (8, 12), (28, 26), (18, 18), (1, 4), (33, 32), (28, 16), (10, 4), (12, 23), (20, 24), (7, 26), (25, 26), (33, 34), (28, 7), (20, 7), (21, 10), (21, 18), (26, 0), (10, 19), (4, 14), (18, 30), (14, 5), (5, 29), (23, 3), (30, 32), (31, 14), (29, 27), (32, 0), (22, 29), (33, 29), (16, 25), (33, 20), (32, 27), (28, 4), (33, 2), (23, 31), (7, 19), (22, 1), (13, 35), (13, 34), (26, 15), (16, 32), (17, 22), (27, 7), (29, 21), (3, 25), (3, 6), (11, 2), (17, 6), (31, 15), (16, 16), (27, 2), (4, 3), (2, 15), (14, 8), (24, 7), (8, 30), (29, 1), (26, 3), (27, 34), (2, 7), (22, 20), (28, 12), (0, 26), (31, 10), (24, 23), (9, 29), (27, 25), (10, 18), (32, 26), (29, 29), (13, 12), (33, 17), (27, 14), (19, 25), (27, 20), (2, 24), (5, 30), (19, 3), (15, 23), (23, 1), (30, 27), (27, 33), (1, 30), (27, 24), (2, 6), (1, 9), (18, 20), (1, 13), (29, 23), (32, 22), (10, 28), (29, 25), (1, 24), (8, 22), (12, 6), (10, 1), (21, 27), (33, 25), (15, 34), (20, 34), (19, 33), (33, 4), (32, 2), (29, 14), (25, 10), (14, 34), (20, 13), (10, 3), (29, 11), (19, 23), (10, 6), (27, 10), (30, 15), (24, 12), (24, 3), (32, 16), (3, 28), (25, 16), (31, 19), (8, 10), (3, 19), (24, 9), (14, 9), (26, 29), (26, 11), (22, 34), (12, 15), (17, 21), (3, 13), (12, 33), (30, 7), (6, 28), (28, 6), (20, 1), (13, 9), (33, 26), (5, 5), (26, 14), (11, 11), (7, 5), (22, 2), (13, 5), (0, 34), (1, 1), (27, 23), (18, 22), (4, 6), (24, 14), (6, 16), (21, 15), (16, 0), (2, 35), (25, 25), (31, 35), (3, 33), (20, 15), (8, 25), (11, 7), (11, 10), (26, 5), (11, 33), (7, 30), (32, 23), (13, 26), (0, 30), (1, 19), (19, 22), (6, 9), (5, 25), (30, 29), (23, 23), (11, 9), (30, 31), (1, 28), (3, 32), (18, 31), (23, 26), (21, 9), (1, 34), (9, 8), (7, 4), (29, 31), (20, 5), (27, 35), (22, 5), (13, 15), (5, 11), (10, 16), (11, 24), (8, 27), (29, 24), (24, 20), (16, 2), (5, 35), (28, 23), (13, 14), (4, 17), (27, 32), (5, 0), (4, 11), (16, 21), (2, 12), (5, 8), (2, 9), (6, 19), (13, 28), (19, 10), (23, 4), (23, 15), (16, 13), (22, 35), (23, 12), (23, 24), (6, 1), (28, 9), (3, 21), (15, 3), (3, 20), (8, 28), (30, 12), (28, 25), (30, 24), (31, 12), (4, 22), (1, 33), (30, 6), (11, 17), (19, 4), (0, 25), (7, 11), (33, 21), (33, 9), (2, 32), (26, 25), (6, 30), (29, 17), (25, 29), (22, 30), (19, 18), (18, 1), (4, 24), (7, 33), (33, 24), (4, 28), (16, 9), (14, 33), (10, 12), (9, 5), (30, 10), (14, 14), (10, 27), (1, 0), (21, 32), (29, 5), (27, 31), (6, 12), (22, 23), (5, 12), (19, 17), (9, 6), (13, 20), (20, 18), (10, 25), (33, 10), (4, 31), (7, 10), (18, 19), (14, 26), (3, 7), (3, 5), (22, 16), (11, 27), (26, 32), (33, 12), (7, 14), (6, 17), (15, 13), (12, 5), (10, 15), (18, 14), (20, 23), (24, 6), (14, 7), (7, 2), (16, 29), (33, 23), (23, 21), (29, 33), (23, 16), (13, 17), (4, 8), (11, 28), (5, 1), (32, 20), (19, 8), (25, 12), (28, 14), (6, 20), (4, 18), (12, 30), (12, 19), (1, 2), (17, 3), (9, 12), (2, 16), (10, 35), (13, 33), (17, 15), (23, 9), (27, 15), (26, 23), (32, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641880", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 4), (8, 10), (33, 18), (30, 0), (30, 16), (11, 14), (31, 29), (12, 2), (2, 16), (36, 29), (29, 32), (23, 5), (0, 6), (6, 21), (28, 3), (18, 11), (36, 22), (29, 15), (37, 9), (10, 4), (25, 35), (14, 20), (36, 11), (11, 30), (4, 12), (8, 18), (24, 34), (0, 17), (6, 9), (0, 32), (24, 2), (7, 28), (12, 31), (7, 8), (5, 21), (3, 27), (15, 35), (21, 5), (11, 9), (32, 32), (21, 24), (30, 22), (32, 30), (35, 20), (15, 12), (1, 31), (12, 36), (14, 2), (9, 1), (5, 18), (16, 25), (24, 13), (20, 24), (34, 15), (24, 30), (33, 12), (5, 25), (23, 7), (22, 22), (13, 35), (14, 34), (1, 4), (1, 20), (19, 1), (27, 22), (11, 8), (23, 25), (28, 15), (26, 32), (30, 21), (20, 18), (34, 17), (7, 1), (8, 8), (19, 30), (34, 11), (32, 24), (11, 19), (1, 1), (21, 4), (1, 15), (22, 19), (3, 30), (12, 10), (24, 4), (20, 19), (27, 33), (8, 32), (9, 22), (31, 2), (25, 14), (36, 1), (2, 31), (37, 0), (0, 30), (25, 29), (34, 20), (32, 23), (17, 10), (21, 31), (24, 6), (32, 8), (17, 32), (1, 14), (23, 3), (18, 36), (28, 4), (20, 23), (6, 18), (37, 8), (27, 4), (11, 2), (26, 5), (33, 19), (3, 17), (7, 32), (16, 16), (29, 26), (25, 2), (9, 31), (23, 10), (16, 28), (24, 1), (30, 32), (0, 24), (36, 32), (12, 19), (18, 2), (24, 15), (0, 4), (31, 23), (25, 16), (9, 33), (37, 10), (15, 2), (16, 26), (14, 36), (21, 8), (16, 20), (6, 3), (28, 25), (4, 2), (8, 0), (12, 33), (21, 11), (28, 28), (34, 31), (37, 22), (37, 31), (9, 7), (20, 27), (6, 24), (8, 12), (35, 31), (12, 30), (35, 2), (35, 9), (12, 27), (6, 29), (10, 28), (1, 19), (10, 21), (36, 19), (5, 12), (23, 29), (28, 6), (36, 15), (15, 32), (22, 32), (27, 21), (26, 0), (9, 13), (0, 14), (17, 36), (22, 1), (23, 36), (22, 36), (12, 25), (24, 8), (10, 15), (9, 4), (20, 5), (23, 24), (27, 25), (3, 18), (15, 13), (30, 33), (35, 18), (5, 24), (0, 19), (18, 3), (20, 28), (18, 16), (21, 35), (19, 4), (33, 15), (14, 17), (24, 32), (21, 15), (7, 16), (33, 33), (17, 29), (15, 17), (29, 13), (33, 31), (15, 5), (6, 34), (4, 34), (4, 17), (3, 4), (11, 28), (17, 11), (10, 24), (17, 14), (15, 30), (12, 23), (7, 19), (31, 20), (11, 27), (32, 7), (17, 16), (33, 8), (33, 36), (2, 33), (20, 16), (30, 3), (23, 31), (15, 16), (9, 36), (20, 32), (2, 19), (20, 17), (35, 16), (6, 13), (18, 27), (37, 11), (17, 33), (10, 31), (15, 24), (27, 19), (27, 30), (15, 6), (12, 17), (4, 28), (4, 22), (23, 0), (37, 35), (30, 5), (16, 3), (35, 33), (27, 14), (2, 11), (34, 29), (31, 0), (24, 23), (26, 17), (22, 24), (37, 28), (10, 33), (21, 9), (32, 1), (12, 35), (33, 16), (14, 28), (14, 27), (9, 15), (28, 5), (17, 28), (1, 26), (36, 31), (25, 10), (20, 6), (17, 12), (35, 3), (9, 35), (30, 4), (31, 17), (31, 1), (27, 11), (26, 16), (7, 26), (13, 36), (34, 7), (9, 17), (8, 16), (2, 6), (9, 9), (25, 12), (14, 33), (21, 19), (27, 29), (3, 6), (24, 31), (9, 3), (36, 17), (7, 23), (14, 18), (7, 0), (21, 25), (9, 27), (22, 15), (27, 5), (12, 16), (25, 0), (0, 27), (26, 29), (23, 22), (13, 7), (32, 28), (31, 6), (10, 25), (28, 8), (9, 30), (31, 15), (32, 29), (1, 9), (16, 18), (26, 27), (19, 34), (35, 35), (26, 23), (21, 20), (11, 17), (17, 35), (1, 33), (3, 35), (37, 27), (28, 9), (24, 26), (21, 34), (9, 16), (2, 24), (3, 23), (2, 10), (18, 20), (31, 34), (8, 17), (14, 29), (2, 28), (3, 15), (31, 10), (8, 9), (0, 7), (15, 19), (3, 29), (22, 0), (2, 7), (25, 6), (12, 32), (30, 13), (33, 23), (5, 7), (24, 22), (24, 18), (7, 4), (23, 11), (24, 35), (27, 9), (7, 7), (13, 17), (5, 30), (19, 11), (37, 26), (5, 27), (37, 7), (18, 24), (25, 7), (33, 14), (2, 12), (11, 22), (32, 18), (14, 25), (26, 6), (30, 12), (1, 18), (1, 10), (10, 30), (22, 3), (6, 10), (35, 22), (15, 21), (19, 9), (22, 12), (34, 22), (0, 33), (31, 22), (1, 7), (28, 16), (10, 2), (32, 2), (27, 32), (35, 8), (34, 35), (0, 1), (19, 16), (18, 7), (24, 3), (34, 27), (28, 12), (18, 28), (30, 30), (22, 2), (18, 19), (16, 7), (3, 7), (8, 29), (25, 28), (21, 21), (5, 1), (32, 13), (29, 9), (37, 20), (14, 9), (13, 24), (17, 1), (28, 18), (16, 8), (0, 36), (5, 26), (7, 31), (7, 10), (0, 34), (13, 30), (15, 31), (23, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "552072", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), 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), (3, 19), (18, 6), (12, 12), (7, 15), (8, 9), (28, 17), (33, 14), (21, 16), (14, 4), (32, 18), (4, 15), (5, 12), (0, 12), (17, 25), (10, 1), (14, 2), (29, 24), (32, 23), (21, 4), (30, 15), (7, 4), (8, 30), (14, 1), (29, 30), (15, 9), (33, 6), (23, 29), (16, 12), (29, 27), (1, 6), (21, 7), (5, 11), (16, 3), (35, 8), (2, 12), (3, 21), (27, 18), (4, 5), (26, 0), (34, 20), (12, 0), (19, 1), (1, 30), (33, 7), (35, 26), (27, 22), (2, 11), (33, 11), (2, 6), (29, 21), (9, 10), (16, 20), (16, 18), (22, 20), (25, 25), (28, 8), (26, 14), (35, 9), (29, 28), (31, 13), (11, 7), (19, 13), (23, 19), (13, 29), (6, 9), (8, 24), (30, 14), (18, 2), (21, 20), (28, 28), (21, 10), (15, 16), (35, 11), (21, 17), (33, 2), (3, 8), (3, 7), (11, 25), (18, 13), (33, 26), (10, 17), (19, 17), (21, 14), (28, 1), (5, 7), (20, 12), (32, 12), (19, 21), (29, 20), (35, 24), (11, 14), (13, 13), (6, 5), (7, 19), (1, 23), (5, 10), (25, 29), (17, 24), (10, 13), (4, 25), (24, 24), (11, 3), (11, 19), (9, 23), (25, 6), (8, 29), (0, 18), (20, 24), (29, 14), (3, 1), (7, 28), (29, 12), (12, 17), (13, 3), (4, 17), (4, 28), (4, 2), (0, 22), (21, 15), (10, 25), (23, 21), (29, 16), (19, 6), (10, 26), (10, 15), (10, 11), (9, 2), (19, 26), (8, 6), (2, 27), (19, 14), (11, 23), (5, 29), (34, 13), (0, 23), (16, 22), (11, 24), (10, 19), (32, 22), (12, 3), (4, 1), (7, 10), (14, 27), (34, 23), (26, 20), (18, 10), (25, 24), (0, 21), (15, 13), (11, 8), (9, 12), (26, 22), (17, 15), (29, 23), (13, 26), (15, 19), (34, 24), (3, 22), (1, 5), (18, 20), (0, 19), (28, 4), (35, 13), (9, 1), (19, 8), (6, 29), (7, 2), (12, 4), (5, 6), (34, 3), (23, 25), (17, 6), (17, 14), (7, 11), (28, 9), (7, 14), (7, 29), (14, 29), (18, 30), (35, 6), (6, 14), (20, 13), (2, 14), (22, 10), (22, 17), (19, 4), (8, 17), (29, 7), (0, 20), (9, 17), (3, 20), (34, 30), (25, 28), (18, 18), (24, 26), (9, 16), (14, 3), (33, 5), (18, 5), (23, 4), (27, 30), (23, 1), (34, 29), (8, 22), (27, 7), (31, 26), (12, 26), (26, 10), (32, 21), (23, 11), (0, 13), (25, 27), (27, 25), (3, 3), (10, 23), (11, 2), (10, 5), (8, 15), (28, 29), (4, 20), (6, 23), (12, 11), (27, 8), (19, 0), (25, 10), (33, 23), (17, 0), (6, 20), (33, 17), (8, 7), (32, 11), (5, 1), (7, 30), (27, 21), (19, 11), (2, 25), (18, 25), (8, 21), (12, 13), (34, 9), (25, 12), (33, 0), (26, 11), (26, 4), (34, 22), (7, 16), (8, 13), (18, 26), (23, 14), (0, 4), (27, 26), (9, 22), (8, 5), (19, 3), (15, 27), (27, 10), (27, 5), (14, 26), (26, 29), (6, 27), (7, 9), (6, 19), (0, 29), (24, 25), (29, 2), (2, 26), (32, 5), (28, 23), (31, 1), (34, 11), (16, 19), (8, 11), (6, 30), (20, 26), (24, 17), (18, 3), (26, 9), (2, 17), (16, 14), (3, 23), (3, 27), (33, 22), (12, 7), (27, 27), (18, 14), (26, 16), (0, 14), (22, 1), (26, 23), (8, 4), (16, 5), (13, 18), (19, 12), (10, 2), (16, 0), (18, 23), (3, 28), (16, 17), (5, 27), (24, 28), (2, 8), (21, 25), (35, 0), (33, 29), (26, 1), (13, 8), (1, 9), (24, 9), (16, 25), (32, 25), (5, 2), (24, 10), (29, 6), (12, 5), (18, 29), (3, 18), (7, 5), (6, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183456", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 11), (23, 1), (18, 7), (25, 21), (1, 3), (8, 13), (24, 14), (20, 18), (10, 15), (8, 34), (12, 36), (35, 2), (3, 28), (21, 27), (0, 20), (6, 32), (33, 33), (0, 17), (12, 2), (32, 36), (35, 28), (36, 23), (14, 17), (1, 2), (34, 17), (30, 13), (18, 8), (13, 9), (21, 22), (12, 23), (11, 26), (16, 13), (2, 32), (29, 24), (26, 15), (12, 13), (15, 12), (19, 4), (7, 11), (2, 12), (21, 33), (6, 16), (0, 25), (2, 14), (25, 24), (16, 28), (3, 26), (17, 12), (12, 19), (13, 11), (1, 18), (31, 6), (11, 38), (30, 28), (28, 5), (21, 24), (33, 20), (13, 30), (7, 17), (32, 8), (11, 0), (30, 29), (9, 5), (27, 13), (6, 14), (36, 0), (24, 28), (11, 28), (31, 20), (4, 8), (14, 9), (8, 15), (31, 33), (14, 24), (12, 24), (0, 26), (24, 18), (4, 14), 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(18, 4), (23, 32), (5, 14), (7, 15), (32, 32), (9, 21), (6, 34), (36, 8), (11, 1), (27, 3), (25, 9), (28, 9), (33, 21), (36, 11), (33, 1), (19, 15), (14, 6), (17, 7), (7, 26), (4, 12), (13, 7), (16, 11), (5, 24), (9, 32), (31, 34), (8, 28), (26, 32), (7, 9), (15, 19), (1, 11), (33, 5), (4, 22), (26, 35), (10, 12), (22, 14), (25, 13), (24, 35), (29, 8), (0, 37), (23, 18), (8, 8), (20, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "662949", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), 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), (29, 6), (13, 32), (12, 11), (7, 15), (4, 3), (29, 31), (9, 31), (22, 24), (29, 13), (16, 22), (15, 18), (0, 9), (6, 14), (3, 13), (17, 8), (4, 17), (10, 7), (15, 30), (5, 10), (21, 0), (15, 5), (31, 20), (14, 24), (15, 15), (8, 31), (32, 10), (30, 14), (16, 18), (6, 20), (26, 25), (21, 18), (0, 4), (28, 30), (7, 25), (24, 24), (0, 31), (11, 13), (19, 22), (17, 11), (29, 2), (27, 25), (10, 15), (32, 29), (32, 0), (12, 20), (33, 9), (19, 19), (29, 26), (23, 25), (18, 31), (16, 20), (18, 8), (25, 0), (33, 7), (21, 23), (22, 12), (25, 24), (10, 25), (9, 7), (27, 7), (25, 22), (18, 12), (13, 18), (30, 10), (13, 6), (14, 13), (11, 3), (20, 25), (13, 16), (1, 13), (22, 30), (25, 10), (21, 32), (17, 26), (0, 16), (4, 8), (23, 20), (6, 16), (23, 18), (15, 8), (11, 4), (6, 23), (8, 0), (13, 5), (32, 31), (2, 4), (22, 8), (9, 28), (10, 0), (17, 21), (2, 19), (16, 30), (10, 19), (6, 29), (10, 2), (29, 24), (26, 10), (30, 11), (28, 13), (6, 18), (2, 7), (22, 21), (20, 10), (6, 13), (23, 11), (13, 0), (30, 29), (16, 24), (9, 9), (32, 28), (24, 17), (7, 20), (19, 9), (28, 31), (32, 16), (0, 14), (28, 1), (10, 4), (13, 1), (7, 12), (30, 23), (31, 2), (21, 28), (31, 28), (27, 19), (14, 1), (20, 26), (3, 23), (25, 1), (31, 30), (4, 29), (1, 4), (22, 20), (10, 29), (8, 27), (32, 27), (18, 7), (33, 16), (9, 1), (9, 29), (14, 31), (2, 5), (31, 0), (22, 25), (5, 14), (22, 17), (18, 18), (2, 10), (8, 4), (33, 21), (17, 31), (3, 30), (8, 2), (33, 14), (5, 19), (3, 9), (1, 1), (7, 32), (22, 5), (6, 2), (21, 10), (3, 0), (23, 4), (26, 21), (1, 10), (1, 11), (2, 16), (12, 17), (32, 26), (9, 2), (7, 17), (22, 27), (28, 14), (5, 13), (11, 24), (14, 25), (12, 10), (16, 9), (19, 28), (11, 25), (19, 12), (8, 3), (16, 19), (11, 2), (24, 4), (8, 29), (0, 1), (19, 7), (15, 9), (22, 6), (30, 5), (19, 17), (2, 6), (12, 24), (33, 11), (16, 10), (14, 20), (18, 24), (2, 30), (25, 4), (4, 28), (30, 8), (8, 23), (2, 21), (30, 16), (15, 14), (27, 8), (32, 19), (14, 9), (16, 2), (27, 14), (1, 6), (25, 16), (15, 29), (14, 3), (31, 22), (4, 19), (21, 21), (7, 1), (21, 15), (4, 5), (26, 6), (10, 32), (2, 13), (28, 16), (10, 6), (6, 28), (24, 28), (32, 22), (1, 15), (14, 6), (24, 21), (12, 13), (24, 3), (14, 14), (13, 30), (6, 5), (31, 16), (0, 10), (1, 2), (11, 0), (24, 25), (3, 12), (25, 11), (24, 2), (25, 5), (28, 29), (27, 23), (14, 10), (32, 12), (20, 5), (31, 23), (15, 1), (28, 17), (26, 32), (12, 9), (4, 0), (23, 14), (15, 31), (8, 19), (29, 17), (8, 6), (23, 5), (20, 21), (9, 11), (15, 7), (19, 10), (20, 24), (26, 31), (13, 29), (17, 13), (12, 0), (24, 13), (20, 15), (33, 25), (3, 17), (24, 27), (24, 30), (24, 16), (27, 15), (9, 26), (29, 1), (5, 27), (14, 23), (6, 25), (20, 6), (29, 4), (16, 17), (21, 2), (25, 7), (23, 30), (30, 22), (21, 25), (21, 30), (31, 19), (27, 30), (33, 15), (11, 29), (8, 15), (3, 21), (29, 23), (9, 14), (16, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437400", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 12), (23, 7), (8, 24), (8, 14), (13, 19), (4, 32), (0, 19), (17, 35), (17, 4), (19, 24), (4, 3), (3, 7), (26, 9), (27, 22), (23, 15), (29, 37), (30, 16), (13, 29), (4, 29), (17, 9), (15, 19), (25, 9), (7, 12), (1, 13), (14, 24), (20, 3), (31, 5), (17, 38), (1, 30), (23, 0), (19, 33), (6, 22), (15, 14), (5, 37), (7, 21), (19, 14), (10, 16), (16, 13), (22, 32), (9, 36), (2, 12), (18, 2), (9, 2), (29, 8), (30, 0), (12, 22), (18, 18), (14, 18), (16, 18), (20, 4), (16, 9), (18, 5), (31, 1), (21, 14), (19, 30), (19, 32), (19, 6), (0, 2), (7, 32), (26, 8), (30, 6), (21, 15), (28, 8), (5, 1), (18, 34), (23, 32), (24, 30), (2, 8), (0, 23), (31, 36), (31, 30), (12, 11), (23, 24), (3, 24), (6, 16), (27, 32), (13, 7), (25, 19), (4, 6), (29, 20), (30, 29), (24, 19), (25, 32), (3, 26), (27, 20), (13, 13), (30, 27), (1, 6), (30, 11), (29, 23), (7, 22), (30, 24), (15, 2), (11, 26), (13, 6), (31, 27), (22, 34), (7, 1), (25, 0), (18, 30), (18, 28), (8, 3), (29, 0), (1, 8), (18, 36), (12, 12), (1, 0), (21, 5), (11, 4), (6, 2), (25, 13), (11, 32), (0, 8), (17, 29), (7, 0), (17, 27), (2, 11), (13, 15), (18, 27), (20, 33), (0, 10), (5, 8), (10, 33), (3, 14), (7, 5), (18, 15), (8, 34), (21, 1), (21, 18), (6, 25), (10, 27), (26, 16), (1, 12), (11, 23), (27, 16), (31, 13), (20, 2), (21, 38), (27, 2), (20, 29), (29, 29), (5, 38), (9, 30), (12, 0), (5, 25), (23, 34), (21, 29), (24, 17), (8, 19), (21, 4), (15, 23), (12, 35), (14, 37), (26, 12), (15, 6), (3, 34), (12, 34), (16, 30), (13, 23), (0, 33), (18, 9), (15, 29), (21, 10), (11, 31), (14, 11), (30, 36), (11, 29), (13, 14), (8, 11), (26, 10), (21, 31), (31, 35), (30, 35), (13, 12), (13, 5), (5, 26), (25, 1), (6, 4), (15, 30), (14, 34), (22, 11), (18, 11), (2, 5), (24, 21), (18, 35), (26, 37), (10, 34), (11, 17), (18, 20), (5, 29), (4, 28), (7, 26), (28, 19), (1, 38), (14, 10), (0, 11), (14, 23), (9, 23), (6, 0), (28, 29), (27, 7), (17, 13), (1, 25), (4, 1), (25, 17), (17, 37), (26, 3), (5, 15), (22, 23), (2, 6), (24, 5), (4, 22), (21, 28), (10, 18), (0, 15), (27, 4), (17, 2), (11, 16), (15, 18), (9, 11), (3, 27), (1, 14), (15, 11), (23, 11), (19, 20), (3, 9), (31, 18), (26, 36), (29, 36), (2, 7), (27, 21), (8, 10), (10, 25), (6, 15), (29, 7), (27, 9), (14, 29), (31, 29), (1, 33), (18, 4), (31, 33), (8, 4), (25, 18), (2, 29), (16, 36), (2, 2), (7, 33), (21, 11), (9, 19), (20, 24), (13, 28), (25, 5), (25, 14), (0, 29), (29, 24), (10, 19), (1, 20), (9, 8), (7, 37), (1, 7), (7, 8), (0, 27), (31, 7), (3, 20), (3, 15), (17, 18), (17, 16), (27, 10), (2, 14), (3, 36), (7, 24), (2, 33), (1, 9), (9, 34), (24, 37), (18, 17), (18, 22), (17, 6), (8, 17), (28, 2), (11, 24), (19, 29), (24, 24), (23, 19), (15, 33), (29, 21), (5, 27), (8, 5), (22, 29), (12, 1), (0, 28), (1, 32), (30, 34), (16, 6), (24, 33), (4, 17), (15, 12), (28, 18), (0, 9), (12, 23), (20, 37), (15, 25), (6, 35), (30, 10), (9, 24), (25, 25), (18, 10), (30, 31), (14, 27), (10, 20), (7, 28), (17, 31), (8, 37), (17, 17), (11, 2), (0, 17), (24, 0), (0, 31), (9, 4), (25, 11), (14, 19), (13, 18), (12, 9), (11, 14), (9, 14), (16, 29), (29, 17), (28, 15), (10, 17), (29, 22), (16, 1), (15, 36), (20, 27), (23, 2), (15, 28), (1, 28), (29, 5), (13, 36), (29, 4), (10, 36), (12, 37), (17, 7), (11, 19), (29, 18), (28, 3), (5, 28), (12, 4), (13, 3), (16, 26), (23, 4), (0, 6), (13, 38), (26, 31), (4, 12), (0, 36), (22, 18), (23, 9), (4, 33), (12, 2), (13, 35), (30, 14), (18, 3), (24, 9), (9, 1), (13, 16), (23, 1), (13, 2), (18, 16), (3, 22), (31, 0), (1, 15), (17, 36), (29, 34), (19, 31), (9, 25), (18, 25), (20, 17), (16, 27), (15, 31), (26, 14), (17, 0), (2, 4), (18, 1), (27, 15), (17, 19), (29, 3), (29, 16), (10, 0), (28, 30), (27, 14), (22, 36), (31, 9), (4, 18), (12, 31), (5, 34), (1, 36), (31, 11), (13, 27), (19, 17), (2, 28), (14, 13), (22, 26), (29, 13), (4, 24), (19, 21), (19, 16), (24, 38), (11, 36), (10, 6), (6, 32), (7, 31), (14, 38), (6, 7), (8, 13), (9, 22), (4, 27), (13, 33), (5, 4), (5, 18), (5, 6), (3, 16), (24, 6), (1, 26), (13, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931040", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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), (9, 27), (13, 1), (7, 15), (28, 1), (18, 27), (10, 3), (29, 6), (30, 8), (28, 16), (4, 16), (11, 28), (28, 26), (6, 12), (28, 3), (12, 14), (17, 22), (2, 12), (22, 8), (23, 8), (15, 8), (30, 21), (3, 33), (24, 16), (15, 7), (20, 33), (3, 0), (26, 17), (15, 14), (22, 17), (1, 36), (21, 26), (17, 28), (26, 3), (3, 7), (20, 1), (19, 30), (30, 33), (25, 22), (28, 11), (11, 16), (18, 24), (0, 12), (16, 0), (25, 0), (10, 34), (29, 8), (6, 1), (17, 16), (0, 7), (14, 4), (19, 7), (15, 21), (1, 33), (24, 1), (23, 24), (4, 14), (8, 21), (14, 0), (23, 3), (11, 34), (22, 2), (4, 18), (30, 6), (29, 21), (11, 15), (12, 12), (7, 5), (26, 9), (15, 1), (0, 32), (14, 1), (16, 16), (10, 19), (11, 2), (11, 23), (9, 6), (21, 28), (1, 20), (8, 8), (22, 6), (11, 25), (27, 36), (28, 29), (12, 19), (2, 5), (18, 8), (21, 29), (13, 21), (27, 23), (24, 28), (24, 18), (27, 13), (11, 29), (5, 27), (3, 31), (24, 7), (15, 32), (16, 26), (24, 19), (13, 2), (8, 35), (11, 0), (0, 23), (18, 16), (12, 31), (2, 20), (0, 30), (1, 14), (11, 27), (1, 22), (1, 35), (3, 21), (14, 23), (30, 15), (0, 21), (21, 36), (19, 29), (12, 27), (22, 10), (21, 9), (17, 8), (7, 29), (23, 11), (16, 6), (14, 3), (26, 10), (11, 19), (5, 5), (30, 4), (26, 30), (5, 14), (22, 28), (7, 36), (27, 20), (22, 12), (9, 14), (2, 10), (6, 10), (29, 0), (16, 11), (5, 24), (14, 6), (14, 14), (1, 18), (3, 28), (26, 20), (24, 15), (18, 32), (20, 22), (12, 7), (10, 15), (12, 17), (25, 12), (17, 31), (27, 18), (6, 8), (7, 3), (19, 28), (13, 22), (4, 30), (1, 21), (7, 28), (24, 34), (10, 31), (7, 13), (16, 34), (11, 5), (3, 12), (28, 25), (28, 28), (6, 9), (12, 18), (21, 0), (23, 26), (29, 36), (0, 14), (25, 16), (10, 6), (15, 11), (11, 3), (0, 8), (3, 6), (22, 27), (17, 32), (19, 11), (20, 16), (14, 24), (27, 7), (18, 7), (8, 25), (20, 27), (19, 5), (25, 11), (27, 6), (12, 24), (12, 10), (9, 32), (11, 11), (27, 4), (19, 9), (15, 25), (17, 10), (11, 26), (22, 3), (12, 33), (6, 7), (0, 34), (26, 18), (0, 25), (25, 6), (4, 13), (8, 29), (27, 2), (14, 2), (20, 28), (9, 21), (14, 18), (18, 18), (13, 5), (27, 27), (12, 6), (10, 10), (19, 0), (20, 5), (17, 3), (30, 27), (6, 24), (24, 10), (15, 16), (9, 25), (30, 24), (27, 1), (19, 34), (15, 35), (30, 29), (20, 17), (30, 17), (13, 27), (22, 14), (27, 3), (10, 23), (7, 7), (3, 20), (23, 28), (8, 5), (28, 31), (5, 35), (13, 9), (26, 12), (13, 13), (17, 19), (12, 3), (5, 31), (9, 28), (22, 31), (9, 33), (18, 36), (20, 18), (15, 28), (17, 12), (2, 11), (5, 23), (4, 8), (8, 0), (3, 25), (1, 15), (14, 34), (4, 26), (11, 20), (5, 3), (16, 9), (28, 10), (14, 20), (24, 22), (23, 2), (13, 16), (6, 17), (9, 7), (25, 23), (8, 28), (10, 9), (21, 12), (3, 36), (3, 13), (14, 16), (10, 30), (19, 31), (2, 0), (9, 30), (24, 30), (24, 3), (3, 4), (21, 5), (8, 1), (27, 12), (4, 28), (19, 15), (2, 30), (18, 10), (9, 34), (6, 32), (23, 19), (30, 26), (6, 21), (21, 25), (9, 24), (24, 21), (20, 11), (19, 33), (21, 1), (15, 27), (20, 7), (28, 8), (30, 13), (17, 4), (7, 32), (7, 16), (8, 27), (20, 26), (13, 11), (1, 29), (10, 4), (9, 10), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352296", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 16), (2, 16), (36, 17), (5, 15), (25, 14), (17, 24), (29, 10), (35, 7), (17, 7), (14, 9), (4, 19), (16, 6), (13, 21), (31, 4), (34, 4), (12, 11), (0, 16), (12, 20), (24, 16), (5, 24), (8, 22), (23, 18), (2, 15), (0, 9), (24, 4), (36, 11), (19, 27), (27, 22), (27, 2), (26, 21), (35, 30), (5, 3), (14, 11), (6, 16), (2, 9), (4, 25), (0, 1), (36, 12), (13, 1), (6, 24), (14, 23), (8, 2), (1, 29), (17, 11), (7, 0), (32, 5), (19, 19), (13, 4), (14, 26), (29, 25), (3, 4), (19, 25), (3, 19), (1, 5), (20, 24), (32, 15), (36, 24), (29, 17), (21, 26), (5, 5), (7, 2), (20, 17), (15, 27), (34, 1), (19, 7), (3, 28), (1, 7), (14, 0), (19, 15), (20, 30), (26, 20), (32, 20), (1, 4), (4, 14), (30, 20), (22, 16), (20, 6), (28, 15), (2, 3), (3, 13), (0, 13), (7, 24), (13, 13), (23, 19), (3, 7), (6, 29), (7, 25), (26, 6), (15, 17), (33, 10), (19, 23), (19, 6), (30, 9), (7, 17), (8, 30), (33, 9), (31, 3), (28, 23), (0, 26), (26, 23), (8, 16), (12, 3), (30, 8), (36, 18), (15, 7), (36, 27), (26, 17), (36, 25), (16, 26), (22, 14), (23, 9), (6, 21), (5, 12), (25, 19), (0, 3), (21, 10), (25, 23), (32, 19), (31, 0), (17, 8), (2, 17), (19, 22), (23, 22), (9, 8), (21, 23), (24, 11), (11, 12), (20, 29), (18, 14), (17, 5), (30, 24), (32, 0), (31, 21), (34, 23), (17, 6), (8, 29), (9, 26), (5, 7), (0, 8), (30, 14), (35, 21), (23, 3), (23, 23), (27, 9), (28, 1), (13, 14), (29, 8), (24, 19), (7, 23), (7, 29), (28, 29), (19, 3), (28, 18), (6, 25), (14, 12), (24, 20), (30, 22), (28, 3), (37, 10), (32, 8), (9, 7), (32, 25), (36, 15), (21, 30), (10, 25), (10, 1), (21, 11), (14, 30), (32, 1), (32, 21), (29, 21), (10, 2), (26, 22), (32, 7), (21, 13), (9, 9), (4, 0), (21, 19), (0, 5), (2, 10), (17, 27), (17, 23), (2, 12), (29, 22), (27, 29), (25, 11), (21, 2), (18, 23), (19, 10), (34, 3), (36, 3), (10, 29), (30, 27), (31, 14), (9, 17), (18, 1), (22, 25), (2, 29), (27, 27), (4, 12), (2, 20), (22, 10), (9, 21), (24, 9), (27, 21), (32, 28), (35, 16), (2, 21), (9, 24), (18, 2), (5, 27), (31, 11), (10, 3), (32, 14), (30, 19), (11, 23), (8, 8), (16, 3), (14, 17), (11, 21), (6, 12), (34, 15), (27, 17), (6, 23), (13, 25), (18, 29), (26, 0), (14, 8), (18, 8), (31, 20), (35, 4), (18, 4), (11, 26), (18, 28), (23, 8), (32, 30), (6, 10), (27, 12), (7, 19), (4, 22), (11, 5), (30, 26), (27, 23), (21, 14), (6, 15), (28, 27), (6, 28), (3, 8), (24, 3), (37, 15), (28, 11), (15, 25), (9, 29), (3, 14), (11, 1), (21, 16), (37, 23), (18, 22), (27, 1), (25, 27), (7, 28), (32, 16), (14, 20), (8, 7), (27, 15), (1, 6), (17, 25), (4, 13), (24, 15), (36, 2), (24, 12), (35, 13), (17, 17), (33, 4), (0, 22), (10, 9), (14, 22), (16, 20), (8, 21), (9, 27), (15, 12), (10, 6), (27, 13), (30, 29), (15, 23), (24, 24), (0, 2), (21, 25), (37, 3), (8, 27), (28, 0), (30, 18), (25, 21), (6, 0), (6, 20), (14, 6), (35, 20), (26, 11), (36, 19), (5, 28), (21, 24), (33, 17), (1, 14), (6, 7), (19, 26), (1, 2), (29, 12), (5, 20), (7, 26), (26, 24), (4, 3), (18, 16), (20, 10), (24, 17), (25, 3), (36, 30), (12, 27), (28, 21), (10, 12), (24, 23), (30, 11), (35, 9), (9, 6), (30, 16), (19, 18), (36, 22), (12, 14), (29, 30), (18, 20), (16, 1), (16, 21), (11, 18), (14, 13), (5, 8), (32, 23), (3, 30), (17, 4), (37, 18), (5, 11), (4, 4), (33, 28), (35, 12), (5, 17), (7, 12), (1, 12), (4, 17), (26, 3), (2, 13), (31, 1), (17, 13), (12, 30), (24, 29), (24, 18), (1, 30), (15, 22), (1, 9), (0, 19), (23, 5), (18, 18), (31, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "671040", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 18), (35, 16), (8, 20), (28, 13), (0, 12), (23, 5), (27, 14), (33, 19), (19, 19), (13, 5), (5, 28), (14, 30), (26, 6), (35, 10), (24, 33), (27, 13), (12, 1), (26, 30), (15, 34), (0, 35), (22, 15), (12, 14), (4, 33), (13, 27), (16, 4), (18, 33), (1, 9), (32, 29), (17, 1), (12, 16), (2, 31), (16, 14), (19, 9), (21, 6), (17, 34), (33, 31), (13, 8), (3, 31), (5, 22), (31, 15), (35, 6), (28, 17), (11, 15), (1, 28), (9, 1), (10, 18), (17, 16), (20, 4), (5, 27), (23, 20), (29, 8), (14, 14), (10, 23), (10, 20), (26, 15), (34, 4), (15, 29), (34, 35), (19, 34), (33, 15), (7, 18), (33, 32), (9, 17), (18, 19), (28, 29), (28, 26), (33, 27), (19, 30), (10, 8), (17, 9), (18, 17), (34, 22), (27, 18), (29, 20), (0, 16), (30, 3), (35, 24), (7, 20), (8, 16), (6, 21), (35, 5), (25, 25), (5, 21), (27, 30), (36, 5), (34, 13), (35, 15), (17, 3), (34, 9), (25, 18), (0, 11), (21, 14), (16, 21), (5, 19), (29, 11), (6, 35), (34, 16), (26, 20), (29, 15), (31, 12), (38, 26), (17, 7), (22, 1), (31, 33), (1, 23), (30, 31), (1, 21), (4, 11), (15, 35), (8, 34), (17, 14), (2, 12), (9, 13), (38, 33), (17, 4), (2, 17), (28, 32), (32, 20), (24, 28), (26, 26), (22, 9), (27, 5), (20, 20), (9, 15), (34, 12), (21, 10), (1, 35), (19, 31), (29, 0), (32, 25), (8, 14), (3, 27), (22, 25), (9, 21), (17, 29), (22, 20), (15, 11), (4, 7), (16, 11), (10, 21), (12, 3), (15, 18), (7, 5), (23, 28), (15, 8), (17, 15), (17, 12), (19, 3), (12, 9), (34, 19), (14, 22), (6, 23), (23, 15), (10, 15), (10, 9), (24, 26), (10, 12), (0, 5), (12, 22), (25, 28), (38, 16), (33, 28), (26, 25), (5, 23), (8, 28), (35, 20), (26, 32), (19, 15), (6, 16), (19, 24), (20, 17), (19, 32), (9, 29), (27, 12), (12, 26), (16, 9), (10, 33), (22, 29), (36, 21), (21, 21), (23, 3), (26, 11), (5, 2), (37, 3), (14, 31), (6, 0), (1, 22), (37, 9), (21, 4), (12, 32), (38, 20), (37, 16), (31, 22), (16, 29), (33, 24), (23, 12), (9, 3), (13, 7), (27, 31), (36, 24), (7, 26), (11, 4), (36, 33), (2, 24), (23, 27), (3, 18), (11, 19), (17, 17), (15, 15), (32, 4), (36, 14), (3, 33), (29, 3), (13, 28), (20, 11), (4, 32), (23, 24), (28, 3), (19, 5), (31, 26), (14, 21), (24, 4), (31, 21), (8, 17), (36, 19), (8, 6), (26, 23), (20, 26), (30, 5), (9, 7), (9, 26), (38, 24), (25, 4), (12, 21), (9, 23), (35, 13), (16, 5), (1, 11), (8, 26), (24, 29), (25, 32), (11, 9), (0, 4), (12, 33), (3, 7), (29, 1), (18, 18), (10, 25), (26, 19), (27, 9), (32, 23), (35, 22), (17, 11), (12, 8), (24, 30), (0, 28), (1, 27), (19, 4), (27, 27), (1, 33), (31, 5), (3, 15), (36, 17), (8, 35), (27, 1), (24, 11), (3, 17), (14, 10), (29, 26), (12, 24), (25, 19), (30, 32), (26, 8), (18, 20), (4, 17), (6, 4), (1, 2), (23, 22), (30, 11), (0, 8), (18, 5), (2, 9), (27, 8), (16, 10), (2, 18), (20, 30), (31, 23), (11, 14), (15, 16), (17, 8), (38, 14), (30, 0), (0, 32), (13, 11), (9, 16), (24, 0), (7, 23), (18, 10), (16, 8), (11, 8), (14, 3), (12, 15), (15, 13), (36, 8), (13, 9), (22, 22), (29, 5), (38, 10), (8, 9), (34, 15), (11, 23), (18, 23), (9, 19), (23, 21), (24, 20), (19, 22), (21, 13), (9, 28), (25, 34), (5, 8), (36, 30), (2, 28), (21, 34), (12, 5), (32, 18), (24, 23), (32, 3), (16, 35), (30, 27), (15, 28), (25, 14), (28, 27), (22, 14), (27, 19), (9, 35), (6, 7), (5, 11), (20, 1), (10, 1), (14, 28), (1, 17), (14, 11), (0, 22), (23, 25), (34, 34), (24, 15), (1, 31), (15, 2), (21, 19), (27, 15), (38, 32), (31, 8), (4, 2), (14, 23), (34, 18), (38, 27), (7, 33), (4, 10), (6, 20), (37, 15), (36, 31), (16, 28), (34, 11), (29, 14), (0, 17), (14, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "992628", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (25, 7), (18, 8), (0, 13), (13, 16), (26, 1), (11, 8), (19, 9), (19, 29), (5, 8), (13, 15), (18, 15), (16, 0), (14, 26), (7, 26), (11, 6), (28, 6), (0, 9), (5, 13), (22, 19), (33, 5), (1, 27), (1, 11), (5, 26), (23, 31), (10, 8), (2, 15), (15, 6), (19, 14), (4, 2), (27, 29), (19, 17), (23, 16), (22, 31), (12, 30), (9, 13), (2, 31), (9, 15), (13, 5), (16, 4), (4, 35), (0, 3), (3, 30), (21, 5), (13, 35), (14, 34), (5, 15), (4, 23), (10, 0), (1, 8), (29, 12), (31, 31), (23, 27), (3, 35), (18, 30), (0, 7), (23, 9), (1, 25), (21, 12), (1, 12), (16, 23), (16, 34), (28, 15), (30, 30), (25, 13), (29, 21), (17, 18), (28, 7), (3, 33), (2, 6), (13, 17), (15, 20), (16, 17), (30, 10), (11, 5), (22, 24), (15, 34), (31, 7), (13, 3), (19, 6), (27, 27), (23, 30), (3, 3), (22, 22), (14, 13), (21, 17), (12, 2), (9, 4), (14, 3), (16, 16), (26, 30), (18, 32), (6, 11), (26, 15), (0, 34), (19, 7), (11, 33), (8, 19), (2, 7), (8, 3), (30, 5), (0, 35), (21, 32), (10, 1), (15, 4), (9, 12), (28, 1), (25, 12), (1, 34), (24, 14), (8, 4), (29, 28), (7, 9), (22, 11), (17, 26), (22, 9), (0, 17), (29, 7), (30, 21), (6, 32), (5, 24), (6, 6), (9, 32), (18, 21), (10, 29), (28, 35), (19, 11), (23, 1), (5, 25), (31, 19), (7, 20), (13, 23), (13, 12), (5, 20), (1, 6), (6, 21), (4, 22), (19, 21), (11, 18), (32, 9), (13, 24), (2, 30), (2, 3), (7, 16), (10, 15), (29, 34), (12, 15), (30, 32), (18, 5), (32, 28), (19, 4), (5, 4), (1, 16), (30, 26), (20, 9), (30, 31), (27, 18), (0, 19), (2, 28), (4, 9), (4, 25), (15, 12), (28, 8), (28, 27), (5, 27), (12, 1), (27, 16), (20, 18), (7, 33), (28, 17), (6, 15), (30, 27), (14, 11), (32, 32), (19, 33), (29, 32), (0, 33), (2, 20), (16, 14), (10, 18), (33, 28), (14, 4), (24, 31), (0, 27), (28, 23), (29, 11), (12, 18), (20, 1), (25, 32), (19, 15), (24, 7), (23, 33), (9, 33), (22, 20), (4, 24), (6, 13), (4, 21), (17, 17), (15, 28), (30, 14), (11, 14), (9, 28), (28, 16), (6, 8), (32, 22), (6, 30), (21, 2), (4, 28), (12, 12), (28, 4), (28, 9), (3, 32), (2, 32), (27, 9), (8, 14), (26, 12), (15, 23), (31, 16), (19, 12), (29, 27), (19, 8), (7, 24), (5, 10), (15, 16), (31, 9), (19, 26), (2, 14), (20, 5), (12, 24), (13, 7), (17, 23), (0, 25), (2, 21), (14, 33), (29, 31), (33, 26), (25, 25), (18, 18), (15, 33), (10, 32), (30, 7), (29, 20), (11, 24), (9, 25), (24, 2), (25, 21), (28, 32), (8, 18), (17, 27), (28, 33), (7, 23), (15, 14), (29, 23), (22, 34), (19, 10), (16, 21), (25, 14), (22, 13), (22, 16), (33, 29), (17, 8), (29, 0), (25, 26), (12, 34), (11, 17), (20, 19), (26, 14), (6, 23), (1, 22), (10, 4), (20, 7), (6, 20), (24, 20), (15, 26), (21, 25), (30, 12), (19, 20), (3, 6), (27, 19), (31, 24), (23, 3), (11, 12), (32, 1), (23, 17), (9, 35), (18, 6), (14, 23), (9, 24), (8, 34), (30, 9), (2, 17), (6, 28), (25, 19), (15, 1), (22, 28), (9, 21), (32, 33), (30, 2), (11, 7), (26, 24), (1, 14), (23, 7), (7, 7), (2, 35), (16, 25), (9, 18), (17, 21), (4, 1), (32, 8), (15, 18), (27, 6), (32, 21), (13, 13), (12, 11), (10, 14), (11, 21), (29, 8), (14, 31), (6, 33), (15, 22), (27, 30), (21, 13), (8, 33), (19, 3), (9, 20), (1, 9), (16, 29), (6, 4), (27, 35), (10, 22), (22, 25), (27, 22), (2, 34), (10, 23), (26, 8), (16, 1), (21, 35), (32, 3), (7, 31), (2, 10), (24, 29), (1, 17), (20, 17), (30, 33), (5, 28), (24, 26), (17, 5), (10, 13), (1, 31), (31, 22), (3, 4), (28, 21), (5, 19), (16, 15), (33, 16), (19, 2), (25, 3), (2, 26), (2, 23), (17, 33), (17, 13), (14, 0), (22, 33), (15, 15), (4, 33), (25, 9), (15, 17), (3, 15), (11, 28), (29, 17), (2, 0), (9, 26), (5, 32), (0, 28), (21, 27), (9, 6), (31, 0), (23, 21), (15, 5), (20, 34), (18, 34), (32, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787968", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), 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), (27, 38), (8, 15), (6, 15), (11, 36), (24, 21), (18, 15), (14, 29), (14, 6), (25, 3), (21, 15), (24, 25), (28, 30), (13, 21), (10, 22), (11, 31), (28, 7), (20, 8), (27, 7), (8, 21), (26, 16), (5, 22), (11, 15), (5, 18), (5, 34), (10, 3), (27, 15), (8, 8), (0, 32), (23, 12), (13, 19), (23, 34), (19, 3), (5, 9), (2, 36), (19, 34), (26, 0), (6, 10), (8, 12), (5, 35), (26, 15), (0, 37), (7, 21), (22, 24), (27, 24), (2, 31), (7, 20), (6, 24), (12, 15), (27, 19), (2, 7), (11, 22), (14, 32), (15, 34), (20, 24), (21, 7), (23, 11), (19, 31), (24, 30), (9, 13), (13, 9), (14, 23), (21, 34), (17, 5), (27, 16), (3, 4), (24, 32), (28, 18), (19, 19), (8, 28), (1, 27), (27, 31), (24, 14), (18, 17), (1, 36), (7, 8), (23, 38), (22, 26), (0, 31), (2, 30), (13, 29), (6, 7), (18, 31), (3, 35), (21, 38), (23, 25), (28, 8), (4, 20), (28, 25), (18, 16), (22, 32), (26, 22), (4, 34), (10, 31), (19, 22), (18, 33), (3, 18), (8, 25), (26, 32), (19, 5), (3, 6), (20, 29), (29, 27), (2, 20), (22, 30), (13, 28), (23, 27), (2, 5), (4, 30), (4, 16), (0, 10), (26, 3), (7, 19), (25, 27), (10, 23), (26, 13), (12, 6), (5, 16), (1, 18), (11, 34), (25, 18), (16, 32), (8, 35), (15, 5), (21, 23), (23, 8), (19, 25), (26, 14), (6, 8), (16, 17), (5, 23), (24, 38), (15, 35), (23, 3), (23, 26), (10, 35), (16, 28), (6, 9), (17, 2), (3, 27), (13, 33), (20, 4), (7, 18), (25, 23), (12, 32), (16, 16), (16, 15), (6, 21), (6, 28), (0, 6), (19, 7), (0, 13), (15, 33), (0, 29), (27, 29), (13, 38), (3, 14), (10, 29), (7, 30), (16, 27), (3, 10), (18, 5), (23, 18), (2, 8), (4, 37), (16, 14), (25, 36), (10, 14), (11, 19), (0, 3), (5, 25), (7, 25), (3, 21), (6, 25), (20, 20), (6, 3), (15, 29), (4, 10), (8, 31), (24, 6), (6, 22), (5, 28), (17, 37), (3, 33), (26, 30), (17, 7), (24, 31), (11, 38), (23, 28), (14, 2), (23, 4), (2, 27), (17, 0), (3, 37), (8, 22), (24, 12), (22, 2), (9, 30), (3, 12), (9, 28), (6, 37), (18, 13), (6, 36), (22, 5), (3, 36), (17, 16), (20, 38), (19, 6), (1, 1), (4, 23), (15, 32), (22, 20), (23, 13), (2, 37), (16, 5), (18, 34), (3, 13), (27, 18), (4, 17), (8, 26), (1, 23), (24, 15), (14, 7), (22, 7), (26, 18), (14, 36), (1, 19), (22, 23), (15, 3), (5, 17), (1, 22), (24, 23), (14, 5), (12, 13), (29, 17), (16, 20), (2, 2), (17, 32), (10, 33), (28, 10), (21, 25), (11, 3), (21, 16), (13, 32), (7, 5), (25, 37), (2, 19), (3, 11), (22, 38), (8, 32), (20, 9), (20, 1), (11, 0), (11, 8), (24, 26), (14, 38), (14, 1), (6, 38), (2, 25), (7, 27), (26, 35), (17, 17), (7, 28), (27, 37), (28, 14), (22, 14), (25, 4), (5, 32), (8, 29), (17, 29), (10, 6), (5, 2), (11, 32), (29, 34), (12, 2), (10, 38), (5, 26), (14, 15), (27, 2), (29, 22), (28, 23), (12, 18), (7, 7), (15, 20), (2, 3), (3, 17), (27, 27), (13, 23), (16, 10), (1, 17), (0, 23), (19, 0), (12, 10), (11, 4), (27, 4), (9, 12), (18, 28), (7, 13), (3, 19), (28, 26), (21, 32), (7, 9), (6, 35), (23, 32), (18, 22), (4, 27), (16, 24), (5, 38), (3, 31), (12, 34), (9, 4), (28, 37), (22, 31), (24, 16), (10, 28), (20, 22), (8, 1), (1, 25), (27, 22), (26, 9), (13, 30), (13, 3), (12, 33), (10, 7), (27, 32), (10, 10), (19, 18), (19, 4), (2, 21), (10, 15), (26, 33), (21, 0), (0, 24), (27, 25), (5, 19), (7, 35), (6, 13), (13, 7), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "557655", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (0, 24), (1, 6), (20, 19), (13, 21), (23, 32), (20, 25), (15, 17), (18, 6), (18, 12), (13, 0), (16, 25), (19, 13), (14, 14), (26, 28), (20, 11), (25, 3), (3, 26), (6, 2), (33, 6), (28, 6), (6, 1), (15, 13), (10, 20), (29, 31), (5, 32), (29, 18), (8, 5), (4, 22), (10, 28), (31, 24), (25, 6), (9, 31), (12, 20), (1, 28), (1, 23), (1, 21), (28, 12), (24, 9), (24, 10), (6, 30), (9, 10), (7, 15), (27, 30), (18, 27), (2, 32), (18, 15), (33, 25), (0, 33), (32, 4), (29, 14), (24, 29), (10, 14), (2, 31), (21, 34), (15, 21), (12, 14), (13, 9), (7, 18), (16, 21), (7, 0), (22, 22), (18, 14), (8, 4), (31, 3), (24, 6), (16, 1), (21, 31), (2, 5), (31, 21), (28, 28), (10, 26), (9, 2), (17, 31), (2, 14), (32, 16), (1, 19), (17, 9), (32, 32), (21, 23), (14, 0), (8, 3), (9, 17), (23, 10), (18, 2), (31, 25), (12, 12), (8, 12), (29, 2), (23, 30), (14, 2), (11, 31), (11, 0), (15, 18), (33, 15), (6, 27), (0, 31), (1, 11), (19, 19), (6, 13), (14, 9), (10, 9), (9, 14), (11, 12), (19, 31), (17, 6), (21, 11), (11, 33), (14, 30), (18, 30), (12, 0), (8, 16), (11, 28), (19, 17), (10, 23), (15, 2), (27, 17), (32, 15), (5, 12), (25, 19), (27, 5), (6, 6), (0, 6), (24, 17), (24, 4), (2, 19), (33, 17), (26, 5), (17, 32), (30, 29), (4, 34), (15, 0), (30, 9), (16, 3), (8, 21), (30, 30), (15, 6), (13, 33), (13, 32), (23, 15), (23, 20), (19, 18), (14, 5), (32, 21), (24, 15), (1, 20), (4, 1), (8, 26), (15, 28), (21, 25), (29, 4), (26, 9), (9, 33), (14, 20), (8, 6), (3, 30), (18, 4), (26, 11), (4, 27), (16, 29), (16, 23), (26, 2), (12, 16), (26, 33), (7, 17), (30, 0), (12, 30), (10, 0), (26, 17), (13, 24), (16, 20), (31, 28), (6, 28), (31, 8), (27, 28), (7, 3), (1, 1), (15, 1), (2, 11), (1, 33), (32, 19), (22, 28), (20, 24), (22, 29), (31, 14), (20, 22), (1, 12), (29, 34), (27, 33), (23, 25), (8, 33), (13, 29), (2, 30), (9, 11), (13, 14), (18, 0), (12, 33), (26, 30), (11, 24), (18, 20), (28, 0), (1, 7), (17, 15), (27, 10), (9, 9), (28, 23), (13, 4), (18, 31), (12, 32), (0, 15), (26, 15), (25, 9), (25, 34), (9, 23), (5, 29), (23, 16), (26, 0), (24, 24), (14, 15), (2, 7), (26, 24), (0, 19), (1, 26), (13, 6), (18, 32), (0, 22), (10, 11), (22, 14), (12, 5), (20, 16), (33, 14), (17, 26), (23, 28), (9, 26), (0, 2), (0, 34), (6, 26), (5, 24), (16, 13), (22, 32), (27, 23), (27, 32), (25, 29), (9, 16), (32, 13), (25, 14), (27, 18), (17, 22), (14, 19), (13, 17), (7, 31), (12, 21), (10, 8), (14, 17), (32, 33), (15, 31), (19, 9), (8, 29), (16, 22), (32, 29), (29, 12), (11, 10), (17, 8), (16, 28), (13, 12), (1, 29), (24, 0), (1, 16), (15, 4), (3, 6), (3, 31), (26, 13), (29, 33), (25, 16), (30, 33), (9, 19), (0, 13), (32, 28), (11, 7), (11, 18), (8, 10), (28, 22), (24, 11), (3, 22), (11, 5), (0, 21), (13, 5), (29, 26), (6, 0), (8, 23), (5, 8), (8, 8), (14, 21), (25, 15), (27, 8), (17, 2), (3, 33), (33, 1), (16, 34), (8, 2), (14, 22), (25, 21), (7, 16), (21, 3), (19, 15), (21, 29), (17, 0), (5, 2), (22, 10), (26, 10), (23, 3), (20, 1), (18, 16), (15, 7), (24, 25), (5, 19), (0, 30), (8, 28), (12, 15), (14, 6), (26, 29), (7, 19), (5, 26), (26, 32), (4, 20), (5, 17), (10, 34), (23, 21), (12, 29), (6, 11), (28, 33), (21, 33), (31, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577800", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 9), (7, 28), (10, 7), (29, 24), (7, 19), (18, 10), (11, 26), (8, 5), (30, 19), (13, 2), (7, 5), (12, 9), (25, 2), (3, 5), (17, 3), (21, 12), (29, 11), (14, 8), (28, 6), (22, 6), (30, 9), (30, 24), (2, 5), (4, 23), (25, 1), (34, 8), (34, 6), (34, 0), (13, 7), (34, 3), (29, 2), (33, 25), (6, 14), (32, 19), (33, 29), (28, 27), (22, 22), (19, 3), (4, 10), (24, 21), (25, 24), (26, 9), (34, 4), (32, 16), (28, 19), (29, 9), (2, 23), (26, 20), (14, 11), (21, 19), (28, 0), (30, 15), (32, 1), (14, 25), (22, 7), (21, 3), (25, 3), (8, 4), (3, 9), (29, 6), (27, 26), (20, 13), (29, 29), (9, 5), (13, 9), (33, 6), (32, 13), (9, 29), (7, 16), (25, 13), (18, 0), (23, 18), (24, 19), (32, 3), (23, 17), (33, 27), (0, 6), (10, 1), (2, 20), (11, 13), (26, 17), (30, 26), (33, 16), (27, 18), (25, 4), (21, 24), (6, 10), (30, 27), (11, 2), (7, 26), (26, 28), (4, 2), (20, 18), (9, 27), (3, 12), (4, 27), (25, 20), (27, 6), (5, 22), (33, 10), (25, 29), (24, 4), (8, 6), (14, 13), (22, 0), (12, 14), (10, 13), (29, 28), (8, 1), (15, 17), (2, 6), (28, 23), (3, 2), (5, 5), (26, 2), (27, 24), (31, 8), (11, 21), (12, 19), (12, 0), (30, 13), (15, 10), (25, 9), (23, 6), (7, 3), (21, 20), (15, 23), (6, 29), (14, 21), (3, 17), (2, 7), (19, 15), (10, 5), (34, 17), (30, 10), (28, 10), (15, 20), (13, 27), (29, 0), (19, 7), (28, 26), (6, 18), (15, 12), (2, 19), (30, 17), (6, 27), (33, 13), (33, 20), (32, 5), (30, 21), (31, 17), (34, 27), (28, 22), (15, 7), (1, 8), (31, 1), (29, 22), (34, 10), (34, 2), (2, 18), (7, 11), (2, 14), (7, 12), (18, 9), (14, 7), (16, 22), (6, 20), (34, 24), (10, 6), (5, 29), (16, 14), (16, 26), (29, 15), (22, 13), (17, 21), (1, 19), (30, 16), (5, 27), (21, 23), (23, 25), (1, 15), (11, 1), (17, 8), (33, 17), (5, 2), (16, 2), (23, 23), (30, 23), (16, 8), (30, 3), (8, 0), (5, 13), (31, 19), (5, 24), (10, 28), (8, 9), (4, 18), (30, 2), (27, 4), (26, 13), (8, 16), (9, 11), (17, 1), (4, 6), (31, 4), (11, 17), (23, 12), (2, 17), (7, 22), (27, 20), (21, 1), (2, 3), (22, 26), (22, 25), (2, 24), (18, 6), (28, 14), (18, 24), (10, 17), (26, 29), (20, 27), (24, 15), (26, 0), (21, 16), (1, 6), (11, 15), (11, 24), (25, 27), (12, 16), (13, 24), (25, 25), (22, 4), (19, 25), (12, 24), (4, 13), (10, 0), (25, 6), (18, 11), (9, 1), (23, 8), (29, 4), (19, 29), (13, 11), (34, 5), (33, 4), (6, 7), (19, 1), (33, 22), (0, 8), (17, 29), (0, 17), (24, 18), (15, 4), (9, 17), (30, 11), (12, 2), (33, 12), (12, 3), (16, 16), (26, 11), (4, 28), (28, 21), (4, 4), (0, 18), (27, 19), (0, 1), (24, 27), (13, 23), (2, 0), (29, 8), (16, 11), (28, 12), (20, 22), (26, 3), (13, 15), (20, 20), (22, 8), (3, 8), (14, 5), (18, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541824", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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), (30, 25), (9, 14), (17, 23), (6, 23), (17, 10), (25, 4), (18, 22), (4, 28), (16, 13), (13, 19), (23, 6), (1, 38), (28, 13), (5, 6), (30, 23), (23, 8), (11, 25), (27, 31), (8, 25), (25, 6), (16, 10), (3, 28), (2, 28), (12, 10), (27, 21), (19, 19), (4, 7), (7, 11), (23, 10), (15, 22), (11, 15), (28, 36), (28, 29), (2, 18), (17, 18), (14, 23), (3, 19), (17, 25), (19, 1), (9, 32), (23, 14), (10, 31), (22, 10), (21, 21), (18, 15), (1, 14), (9, 10), (15, 24), (30, 28), (26, 37), (19, 33), (5, 9), (25, 7), (7, 26), (18, 37), (11, 31), (15, 38), (6, 24), (25, 22), (26, 5), (12, 34), (30, 11), (25, 10), (29, 13), (21, 26), (3, 29), (28, 16), (28, 25), (5, 22), (28, 38), (4, 2), (2, 27), (21, 22), (24, 34), (30, 14), (3, 4), (11, 38), (4, 36), (18, 31), (1, 33), (3, 1), (4, 18), (23, 30), (19, 2), (6, 33), (22, 31), (22, 14), (21, 17), (12, 2), (5, 15), (20, 24), (2, 8), (11, 7), (2, 11), (9, 24), (9, 15), (10, 26), (19, 21), (25, 24), (16, 28), (21, 13), (22, 7), (29, 3), (13, 24), (17, 2), (15, 12), (7, 20), (4, 9), (12, 20), (23, 12), (20, 33), (11, 10), (0, 2), (0, 37), (28, 17), (6, 25), (8, 33), (9, 6), (30, 4), (17, 32), (19, 11), (24, 38), (22, 5), (0, 18), (29, 7), (24, 6), (10, 9), (9, 38), (26, 22), (12, 3), (25, 12), (16, 15), (5, 27), (24, 19), (23, 4), (24, 1), (24, 13), (12, 28), (20, 22), (14, 17), (24, 31), (11, 2), (2, 6), (6, 31), (26, 34), (6, 28), (25, 38), (5, 18), (29, 36), (22, 35), (26, 33), (27, 34), (3, 26), (24, 0), (27, 30), (28, 12), (24, 35), (29, 35), (23, 13), (12, 33), (28, 18), (3, 38), (25, 30), (7, 2), (18, 25), (30, 9), (29, 18), (1, 31), (1, 19), (6, 26), (18, 23), (30, 34), (16, 33), (11, 3), (6, 5), (4, 1), (14, 29), (28, 30), (6, 13), (22, 8), (3, 31), (23, 25), (15, 18), (23, 9), (4, 5), (10, 35), (13, 22), (28, 21), (18, 26), (22, 4), (30, 18), (20, 18), (12, 30), (14, 12), (27, 4), (4, 26), (26, 10), (27, 33), (22, 23), (7, 14), (11, 32), (16, 23), (28, 3), (0, 16), (16, 11), (8, 37), (7, 6), (6, 29), (8, 21), (29, 4), (6, 36), (26, 25), (10, 19), (8, 35), (2, 10), (17, 14), (21, 0), (1, 27), (0, 11), (4, 0), (13, 38), (10, 23), (30, 16), (7, 12), (26, 7), (6, 8), (0, 33), (30, 15), (11, 37), (4, 37), (3, 32), (8, 23), (1, 32), (22, 0), (13, 8), (18, 8), (28, 24), (14, 19), (18, 6), (7, 22), (28, 0), (0, 31), (8, 20), (16, 8), (14, 37), (28, 2), (2, 12), (19, 14), (1, 4), (20, 13), (10, 22), (16, 3), (9, 17), (4, 27), (15, 7), (17, 12), (28, 26), (26, 11), (15, 9), (22, 34), (27, 13), (18, 27), (17, 30), (26, 9), (5, 19), (19, 5), (9, 34), (0, 10), (13, 7), (5, 30), (10, 4), (20, 10), (4, 15), (29, 31), (16, 24), (19, 7), (5, 11), (2, 22), (23, 11), (19, 37), (9, 30), (9, 37), (13, 28), (5, 8), (14, 30), (15, 30), (11, 9), (7, 1), (20, 4), (1, 0), (12, 37), (1, 11), (11, 17), (27, 16), (28, 10), (0, 4), (21, 38), (18, 38), (9, 31), (25, 25), (30, 1), (4, 22), (9, 2), (5, 34), (13, 18), (9, 35), (10, 20), (8, 27), (3, 27), (24, 26), (3, 5), (29, 17), (29, 32), (28, 6), (22, 29), (12, 4), (0, 27), (1, 37), (20, 11), (24, 36), (0, 21), (23, 20), (16, 6), (21, 16), (26, 28), (5, 31), (6, 2), (11, 1), (8, 18), (23, 22), (1, 24), (15, 21), (7, 23), (15, 23), (4, 20), (18, 0), (6, 38), (13, 5), (14, 21), (16, 27), (20, 20), (24, 4), (27, 7), (25, 26), (30, 13), (9, 19), (1, 7), (29, 6), (25, 18), (27, 29), (23, 32), (4, 8), (27, 11), (29, 15), (14, 35), (28, 27), (5, 0), (13, 14), (23, 5), (10, 30), (3, 37), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742392", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (28, 6), (13, 15), (6, 7), (7, 8), (22, 6), (3, 0), (3, 19), (4, 16), (3, 26), (7, 7), (12, 5), (23, 13), (27, 8), (11, 1), (23, 7), (19, 2), (23, 5), (29, 20), (19, 20), (21, 18), (24, 18), (4, 5), (22, 21), (0, 4), (17, 1), (23, 21), (23, 23), (20, 12), (28, 11), (22, 10), (16, 21), (20, 19), (29, 18), (24, 19), (23, 1), (26, 2), (10, 6), (23, 27), (20, 27), (9, 9), (21, 6), (13, 20), (10, 17), (25, 18), (1, 26), (3, 24), (24, 15), (5, 22), (4, 21), (19, 22), (18, 17), (25, 12), (1, 16), (26, 27), (2, 23), (11, 5), (9, 17), (2, 20), (17, 13), (17, 25), (16, 14), (5, 23), (3, 22), (4, 23), (20, 4), (11, 28), (8, 29), (16, 1), (27, 12), (14, 22), (13, 1), (13, 13), (27, 17), (0, 28), (30, 23), (6, 26), (23, 2), (27, 0), (21, 4), (8, 5), (26, 6), (12, 20), (8, 3), (30, 24), (18, 21), (3, 25), (9, 19), (19, 12), (27, 11), (24, 14), (26, 8), (23, 10), (7, 29), (8, 11), (5, 19), (11, 2), (10, 11), (16, 2), (27, 13), (12, 12), (17, 23), (6, 19), (23, 29), (29, 0), (1, 27), (0, 7), (17, 7), (6, 15), (13, 11), (12, 27), (7, 13), (2, 16), (14, 15), (27, 23), (18, 14), (30, 14), (13, 2), (19, 16), (24, 8), (2, 24), (18, 5), (7, 0), (2, 27), (15, 28), (5, 10), (4, 27), (8, 6), (17, 5), (13, 8), (12, 2), (2, 2), (13, 14), (25, 5), (27, 28), (9, 4), (28, 19), (21, 11), (22, 18), (11, 9), (25, 19), (27, 26), (18, 13), (3, 6), (20, 16), (9, 29), (17, 27), (18, 25), (13, 19), (21, 29), (12, 1), (10, 10), (2, 1), (26, 0), (30, 4), (5, 1), (17, 10), (18, 16), (23, 6), (10, 1), (13, 29), (20, 28), (26, 15), (0, 10), (13, 28), (11, 8), (20, 0), (16, 11), (10, 4), (6, 28), (3, 12), (25, 21), (5, 28), (13, 17), (27, 10), (11, 23), (12, 28), (7, 27), (11, 21), (6, 16), (29, 4), (5, 21), (6, 6), (16, 25), (30, 1), (19, 7), (26, 14), (20, 13), (23, 14), (17, 22), (4, 14), (7, 23), (29, 13), (19, 8), (24, 5), (2, 4), (30, 16), (29, 9), (2, 14), (9, 5), (25, 22), (14, 20), (10, 21), (0, 24), (24, 10), (1, 5), (21, 2), (28, 21), (4, 9), (12, 9), (9, 24), (24, 29), (9, 6), (24, 6), (19, 25), (16, 8), (0, 26), (19, 11), (7, 2), (11, 26), (7, 11), (14, 25), (29, 26), (24, 17), (30, 27), (21, 14), (0, 25), (6, 14), (1, 7), (22, 26), (0, 21), (4, 4), (4, 8), (29, 24), (5, 0), (29, 16), (10, 2), (27, 3), (19, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46144", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), 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, 29), (21, 7), (10, 9), (18, 14), (4, 20), (18, 13), (29, 23), (29, 30), (7, 23), (1, 24), (6, 3), (6, 21), (15, 3), (7, 4), (29, 13), (5, 17), (23, 21), (13, 21), (14, 0), (17, 14), (3, 15), (13, 8), (20, 5), (8, 22), (22, 21), (12, 26), (16, 25), (11, 9), (10, 18), (17, 12), (32, 5), (19, 30), (26, 19), (13, 4), (4, 12), (28, 28), (19, 2), (6, 20), (6, 9), (11, 26), (28, 29), (0, 30), (27, 10), (28, 20), (16, 13), (12, 16), (13, 13), (9, 1), (8, 17), (3, 24), (1, 5), (9, 27), (30, 13), (28, 18), (32, 27), (31, 15), (4, 4), (28, 0), (18, 16), (2, 31), (7, 0), (26, 17), (7, 14), (11, 14), (11, 28), (21, 19), (25, 1), (13, 25), (18, 5), (20, 23), (27, 16), (24, 10), (25, 16), (31, 29), (23, 14), (29, 14), (25, 25), (24, 28), (13, 15), (14, 24), (7, 10), (8, 11), (21, 2), (17, 10), (4, 25), (22, 11), (15, 15), (3, 30), (14, 22), (12, 17), (3, 10), (19, 24), (28, 14), (12, 14), (24, 22), (18, 7), (16, 12), (18, 12), (22, 29), (24, 20), (30, 6), (0, 17), (20, 28), (12, 21), (0, 18), (12, 23), (27, 6), (23, 10), (11, 4), (31, 10), (30, 19), (3, 17), (2, 3), (4, 13), (22, 2), (23, 24), (21, 23), (12, 7), (23, 13), (23, 1), (3, 12), (13, 18), (2, 9), (30, 21), (0, 13), (1, 20), (18, 20), (6, 5), (21, 24), (3, 14), (23, 0), (30, 20), (2, 22), (4, 30), (3, 28), (28, 10), (30, 5), (14, 14), (23, 30), (32, 26), (18, 1), (15, 7), (22, 12), (20, 2), (29, 18), (30, 30), (21, 14), (14, 17), (31, 27), (10, 0), (15, 10), (1, 12), (18, 27), (9, 10), (6, 27), (31, 5), (24, 29), (20, 19), (28, 5), (7, 12), (4, 22), (9, 7), (5, 15), (9, 2), (8, 24), (27, 30), (4, 24), (4, 28), (22, 26), (18, 28), (17, 25), (2, 2), (13, 2), (14, 30), (18, 17), (11, 21), (30, 25), (3, 29), (14, 12), (5, 27), (6, 30), (15, 18), (3, 21), (30, 8), (28, 25), (8, 15), (11, 25), (11, 22), (7, 25), (15, 6), (7, 31), (12, 4), (32, 20), (14, 20), (2, 28), (8, 25), (0, 1), (32, 17), (32, 6), (12, 20), (12, 27), (30, 14), (15, 12), (32, 22), (26, 25), (22, 27), (0, 19), (9, 22), (3, 26), (22, 5), (10, 5), (1, 26), (19, 18), (7, 26), (21, 5), (6, 1), (8, 31), (0, 2), (31, 19), (0, 22), (29, 1), (29, 12), (15, 4), (10, 27), (5, 16), (16, 14), (31, 8), (13, 17), (21, 20), (29, 27), (0, 16), (31, 17), (26, 1), (25, 20), (25, 8), (4, 26), (11, 23), (20, 9), (22, 20), (23, 23), (25, 17), (15, 26), (2, 24), (9, 0), (9, 26), (24, 1), (3, 22), (20, 0), (4, 21), (11, 31), (25, 23), (22, 14), (30, 9), (7, 19), (10, 16), (13, 12), (2, 1), (4, 5), (1, 27), (16, 27), (4, 10), (2, 19), (9, 23), (23, 4), (0, 7), (26, 29), (14, 29), (18, 2), (27, 4), (9, 3), (17, 28), (14, 8), (2, 16), (4, 0), (8, 10), (21, 26), (10, 6), (25, 26), (32, 30), (22, 24), (7, 7), (6, 0), (25, 5), (17, 13), (25, 13), (7, 30), (24, 12), (3, 5), (13, 1), (12, 9), (17, 31), (12, 30), (14, 1), (1, 16), (11, 18), (31, 16), (16, 30), (4, 9), (30, 16), (26, 11), (17, 2), (15, 24), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "769080", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 7), (8, 3), (12, 3), (31, 33), (26, 34), (27, 17), (22, 4), (23, 17), (32, 16), (2, 3), (27, 27), (5, 21), (32, 33), (21, 6), (21, 15), (1, 27), (19, 15), (26, 8), (33, 0), (18, 17), (2, 18), (25, 20), (20, 19), (24, 3), (24, 18), (13, 15), (17, 1), (16, 25), (30, 16), (25, 31), (31, 13), (20, 18), (16, 28), (11, 13), (31, 28), (1, 24), (33, 4), (7, 24), (15, 16), (16, 22), (31, 14), (3, 34), (28, 16), (7, 13), (26, 6), (8, 18), (14, 22), (10, 2), (10, 5), (13, 19), (30, 18), (31, 15), (27, 28), (22, 24), (16, 19), (6, 17), (14, 0), (32, 35), (14, 33), (2, 19), (15, 7), (10, 7), (24, 34), (17, 7), (31, 10), (18, 4), (5, 4), (21, 35), (19, 9), (27, 12), (24, 30), (30, 32), (10, 15), (32, 5), (16, 8), (25, 22), (24, 22), (6, 10), (21, 11), (11, 29), (10, 28), (11, 1), (31, 22), (4, 15), (21, 1), (9, 32), (11, 11), (13, 17), (30, 1), (26, 22), (2, 31), (21, 16), (9, 29), (27, 30), (3, 22), (9, 26), (16, 33), (22, 30), (29, 31), (8, 2), (24, 19), (12, 9), (0, 7), (7, 4), (33, 9), (29, 8), (32, 34), (15, 26), (11, 35), (20, 7), (16, 11), (0, 11), (26, 14), (21, 17), (14, 7), (25, 6), (14, 8), (18, 7), (3, 15), (15, 34), (24, 23), (12, 1), (16, 17), (14, 24), (10, 14), (32, 12), (7, 30), (25, 4), (14, 12), (30, 35), (3, 2), (30, 22), (1, 6), (12, 18), (29, 1), (10, 8), (23, 29), (14, 27), (2, 25), (22, 11), (21, 28), (17, 19), (31, 26), (16, 31), (21, 24), (6, 33), (7, 23), (21, 33), (25, 30), (32, 9), (31, 8), (23, 22), (10, 12), (19, 14), (2, 20), (17, 17), (8, 7), (21, 13), (32, 25), (27, 19), (33, 26), (9, 13), (7, 20), (24, 8), (12, 23), (20, 1), (26, 27), (10, 19), (25, 25), (20, 26), (4, 27), (29, 11), (9, 23), (19, 21), (21, 4), (11, 33), (3, 26), (22, 9), (5, 13), (16, 1), (4, 5), (32, 0), (32, 21), (33, 13), (26, 16), (23, 13), (22, 5), (2, 33), (6, 8), (29, 13), (18, 5), (23, 8), (17, 23), (3, 23), (10, 20), (30, 8), (27, 9), (28, 8), (11, 24), (29, 21), (28, 28), (27, 34), (8, 9), (11, 2), (3, 10), (8, 14), (25, 15), (23, 31), (25, 12), (23, 19), (21, 3), (18, 35), (28, 23), (18, 23), (22, 22), (17, 3), (24, 15), (8, 8), (16, 20), (0, 5), (0, 22), (6, 7), (28, 30), (12, 32), (30, 11), (0, 1), (30, 19), (14, 34), (24, 31), (29, 3), (4, 34), (13, 18), (14, 9), (11, 27), (13, 26), (25, 26), (31, 0), (16, 16), (19, 11), (27, 22), (2, 14), (30, 2), (28, 12), (7, 2), (32, 13), (12, 14), (16, 12), (21, 30), (13, 14), (31, 6), (6, 6), (10, 13), (7, 8), (24, 12), (18, 10), (33, 22), (19, 4), (19, 0), (16, 24), (5, 1), (30, 31), (24, 0), (28, 14), (29, 24), (26, 30), (17, 0), (15, 12), (20, 12), (10, 4), (21, 18), (33, 27), (26, 15), (8, 30), (4, 17), (26, 35), (2, 21), (22, 34), (5, 10), (18, 22), (29, 32), (17, 24), (2, 15), (26, 26), (23, 11), (29, 20), (4, 3), (20, 10), (33, 31), (24, 1), (31, 31), (28, 2), (3, 11), (20, 21), (11, 17), (13, 21), (22, 12), (30, 14), (12, 35), (7, 0), (10, 26), (24, 2), (26, 25), (25, 28), (19, 27), (22, 8), (31, 3), (7, 1), (13, 27), (28, 35), (9, 22), (21, 27), (12, 33), (17, 21), (11, 32), (27, 14), (13, 10), (33, 20), (22, 10), (25, 24), (2, 32), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "549360", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 19), (26, 19), (19, 10), (23, 29), (1, 16), (11, 23), (19, 12), (18, 28), (18, 1), (3, 13), (1, 8), (5, 27), (7, 6), (6, 17), (10, 23), (25, 26), (18, 14), (1, 30), (28, 29), (15, 30), (9, 14), (24, 14), (20, 21), (22, 8), (26, 13), (21, 24), (3, 1), (2, 17), (26, 23), (0, 10), (12, 9), (31, 14), (29, 24), (19, 28), (31, 20), (15, 4), (10, 13), (29, 21), (14, 17), (14, 26), (2, 25), (22, 26), (3, 6), (11, 6), (28, 18), (10, 22), (14, 16), (4, 6), (9, 13), (11, 14), (4, 24), (21, 8), (14, 23), (11, 21), (27, 11), (8, 21), (31, 29), (15, 21), (9, 6), (21, 10), (7, 10), (15, 23), (18, 21), (7, 27), (4, 15), (23, 13), (7, 19), (27, 22), (0, 4), (22, 11), (31, 9), (19, 27), (23, 21), (4, 4), (11, 10), (6, 19), (8, 13), (6, 1), (19, 4), (25, 17), (9, 28), (3, 29), (0, 21), (20, 2), (0, 26), (22, 10), (10, 21), (19, 5), (25, 3), (11, 18), (11, 2), (13, 18), (18, 26), (26, 8), (20, 28), (9, 22), (12, 16), (6, 2), (28, 26), (13, 17), (23, 24), (5, 17), (12, 20), (26, 5), (23, 16), (7, 29), (29, 15), (27, 16), (19, 18), (18, 0), (8, 29), (6, 16), (3, 17), (27, 10), (16, 8), (27, 27), (6, 24), (2, 10), (23, 8), (18, 20), (26, 16), (25, 14), (4, 21), (13, 30), (14, 21), (0, 28), (15, 27), (25, 15), (5, 26), (17, 16), (3, 19), (26, 22), (17, 0), (27, 26), (24, 18), (7, 30), (25, 29), (13, 20), (15, 7), (0, 27), (7, 24), (26, 28), (16, 2), (12, 28), (12, 6), (19, 1), (15, 5), (27, 7), (9, 4), (20, 27), (21, 3), (22, 12), (8, 24), (16, 4), (19, 8), (0, 11), (25, 30), (10, 28), (31, 16), (20, 26), (13, 21), (2, 22), (14, 2), (1, 18), (9, 30), (11, 22), (23, 17), (9, 1), (16, 9), (2, 11), (16, 29), (12, 13), (5, 7), (17, 30), (3, 30), (21, 23), (21, 0), (15, 20), (13, 29), (3, 10), (12, 7), (5, 5), (5, 21), (1, 15), (7, 26), (15, 19), (21, 9), (4, 5), (24, 11), (19, 25), (25, 12), (1, 5), (26, 12), (12, 11), (15, 12), (11, 0), (12, 30), (20, 4), (16, 26), (18, 8), (22, 0), (8, 9), (6, 23), (9, 17), (31, 7), (17, 2), (20, 0), (1, 26), (30, 1), (4, 10), (12, 15), (11, 9), (7, 2), (3, 21), (20, 1), (2, 8), (10, 18), (26, 24), (24, 28), (3, 16), (29, 1), (10, 20), (2, 18), (0, 7), (21, 11), (23, 18), (30, 7), (4, 0), (5, 0), (1, 9), (31, 5), (24, 4), (19, 24), (24, 19), (10, 15), (15, 22), (16, 20), (17, 1), (6, 6), (11, 17), (28, 25), (10, 7), (0, 3), (31, 4), (29, 27), (6, 3), (5, 13), (11, 4), (28, 14), (26, 18), (2, 13), (2, 19), (17, 29), (27, 24), (29, 9), (31, 27), (5, 29), (9, 15), (9, 5), (16, 21), (5, 25), (29, 3), (8, 12), (13, 14), (3, 4), (13, 27), (10, 29), (14, 1), (19, 13), (7, 23), (30, 15), (22, 23), (20, 5), (28, 12), (29, 6), (7, 16), (6, 22), (20, 25), (20, 13), (20, 8), (3, 14), (22, 25), (2, 20), (26, 30), (26, 29), (12, 18), (23, 10), (20, 23), (22, 27), (22, 13), (26, 4), (5, 28), (12, 2), (17, 10), (4, 26), (1, 10), (25, 18), (0, 23), (13, 2), (8, 4), (17, 25), (9, 19), (29, 0), (20, 10), (15, 13), (19, 19), (7, 5), (8, 20), (26, 20), (7, 18), (22, 17), (3, 25), (3, 0), (20, 3), (15, 9), (12, 24), (28, 27), (24, 12), (18, 15), (14, 19), (28, 0), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "542880", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 9), (20, 5), (31, 31), (24, 4), (13, 32), (13, 31), (15, 4), (8, 22), (10, 15), (35, 13), (16, 30), (28, 26), (16, 19), (28, 31), (38, 6), (18, 4), (35, 34), (36, 14), (10, 28), (30, 0), (30, 26), (37, 23), (27, 15), (17, 4), (4, 24), (10, 23), (11, 20), (25, 27), (5, 9), (31, 7), (9, 15), (0, 29), (10, 33), (7, 9), (16, 18), (18, 12), (1, 32), (21, 14), (13, 3), (13, 11), (17, 0), (27, 13), (13, 26), (0, 6), (8, 34), (1, 21), (20, 14), (11, 8), (15, 18), (33, 22), (12, 25), (16, 7), (28, 4), (27, 6), (0, 34), (18, 33), (2, 17), (24, 13), (37, 13), (13, 6), (18, 2), (32, 2), (10, 34), (24, 9), (25, 31), (37, 32), (19, 16), (35, 28), (21, 32), (1, 13), (34, 25), (22, 16), (22, 18), (37, 0), (15, 16), (11, 4), (29, 24), (31, 5), (19, 0), (31, 22), (22, 14), (23, 1), (14, 6), (13, 33), (36, 30), (8, 30), (6, 14), (15, 9), (5, 7), (24, 34), (3, 3), (31, 15), (11, 3), (6, 1), (23, 31), (16, 23), (38, 24), (25, 25), (17, 31), (11, 31), (7, 4), (24, 8), (36, 4), (30, 4), (16, 31), (38, 22), (38, 4), (23, 28), (25, 6), (26, 8), (27, 17), (15, 21), (38, 15), (12, 9), (4, 33), (8, 25), (7, 7), (22, 29), (3, 10), (17, 2), (13, 13), (28, 5), (11, 2), (3, 34), (9, 11), (9, 34), (3, 19), (35, 21), (1, 24), (10, 3), (23, 32), (28, 27), (30, 19), (9, 17), (10, 31), (31, 21), (29, 0), (11, 34), (28, 18), (35, 17), (18, 23), (16, 6), (30, 14), (4, 5), (13, 20), (1, 4), (27, 0), (8, 17), (12, 22), (27, 7), (0, 8), (33, 34), (22, 3), (9, 8), (3, 17), (0, 25), (7, 31), (35, 14), (9, 1), (21, 16), (5, 17), (31, 4), (22, 10), (11, 6), (2, 34), (9, 16), (21, 17), (15, 12), (32, 24), (20, 29), (10, 1), (12, 11), (33, 3), (26, 14), (33, 33), (6, 7), (29, 29), (18, 29), (15, 6), (12, 14), (10, 26), (20, 32), (38, 20), (32, 33), (32, 32), (4, 29), (16, 0), (36, 6), (14, 25), (26, 5), (19, 9), (21, 13), (10, 27), (16, 27), (13, 25), (3, 14), (36, 7), (21, 3), (10, 4), (29, 5), (9, 21), (12, 30), (14, 22), (7, 23), (35, 6), (8, 28), (22, 23), (35, 12), (6, 19), (10, 8), (18, 3), (29, 25), (1, 18), (37, 19), (6, 32), (0, 22), (19, 13), (11, 14), (3, 6), (34, 27), (23, 18), (32, 8), (36, 23), (11, 11), (31, 1), (16, 15), (16, 33), (16, 26), (6, 8), (30, 7), (8, 21), (26, 25), (30, 16), (8, 24), (32, 34), (9, 24), (25, 23), (36, 25), (15, 24), (26, 0), (34, 23), (14, 29), (13, 8), (28, 21), (24, 10), (20, 27), (11, 0), (32, 18), (24, 24), (26, 18), (19, 11), (31, 27), (31, 30), (36, 27), (11, 18), (28, 2), (37, 27), (25, 14), (27, 18), (10, 16), (12, 13), (2, 3), (22, 19), (20, 0), (4, 12), (22, 22), (1, 6), (23, 17), (2, 31), (23, 26), (4, 28), (32, 27), (26, 24), (29, 21), (1, 8), (19, 19), (36, 13), (2, 14), (19, 24), (2, 19), (19, 29), (27, 1), (37, 1), (18, 34), (3, 25), (38, 0), (5, 32), (14, 0), (26, 23), (31, 19), (7, 0), (23, 23), (37, 22), (26, 30), (30, 33), (5, 23), (9, 32), (29, 7), (24, 3), (26, 33), (33, 6), (1, 17), (8, 7), (21, 19), (27, 28), (30, 2), (18, 20), (8, 0), (9, 20), (37, 12), (5, 12), (25, 10), (6, 30), (14, 34), (30, 8), (26, 20), (19, 15), (27, 25), (7, 3), (17, 3), (25, 12), (14, 14), (24, 5), (33, 2), (27, 27), (26, 13), (3, 21), (19, 34), (23, 11), (33, 20), (38, 13), (7, 30), (7, 15), (4, 25), (32, 16), (15, 17), (30, 20), (20, 1), (36, 20), (4, 34), (29, 26), (12, 7), (22, 5), (18, 28), (31, 24), (21, 21), (15, 13), (19, 33), (27, 2), (31, 25), (1, 7), (35, 3), (19, 28), (25, 17), (3, 11), (30, 9), (16, 8), (28, 15), (22, 8), (5, 18), (12, 20), (6, 21), (38, 14), (19, 26), (15, 14), (28, 33), (25, 29), (20, 9), (20, 2), (22, 20), (19, 6), (33, 30), (4, 7), (17, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798300", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), 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), (29, 31), (30, 2), (18, 17), (5, 3), (16, 7), (20, 13), (1, 1), (3, 2), (29, 18), (21, 36), (21, 4), (23, 19), (7, 35), (2, 28), (8, 31), (8, 17), (16, 6), (15, 22), (27, 35), (31, 16), (29, 23), (30, 29), (29, 13), (26, 25), (20, 12), (3, 0), (15, 26), (32, 35), (25, 34), (32, 3), (25, 29), (0, 15), (19, 26), (14, 34), (30, 31), (16, 27), (15, 27), (0, 22), (10, 31), (26, 7), (23, 27), (30, 16), (14, 33), (1, 33), (26, 29), (20, 32), (2, 15), (33, 31), (21, 7), (6, 10), (30, 33), (29, 34), (18, 29), (22, 6), (21, 23), (6, 12), (6, 14), (2, 32), (32, 13), (32, 1), (27, 4), (19, 21), (9, 35), (33, 26), (25, 11), (12, 2), (15, 37), (0, 16), (13, 29), (33, 35), (17, 24), (25, 15), (32, 20), (7, 31), (31, 27), (12, 30), (23, 24), (30, 18), (5, 11), (11, 28), (21, 30), (3, 8), (12, 27), (34, 8), (25, 12), (19, 13), (28, 35), (24, 5), (22, 36), (19, 11), (4, 31), (9, 7), (35, 15), (9, 26), (2, 37), (27, 29), (23, 33), (24, 10), (27, 7), (3, 15), (18, 16), (20, 33), (34, 20), (2, 2), (4, 14), (29, 30), (10, 18), (3, 16), (10, 15), (16, 35), (12, 14), (31, 32), (29, 14), (29, 37), (20, 0), (5, 15), (4, 29), (23, 30), (22, 8), (3, 9), (9, 0), (1, 3), (1, 4), (12, 20), (21, 16), (14, 9), (0, 25), (21, 11), (2, 4), (2, 24), (14, 15), (3, 35), (29, 25), (22, 5), (13, 7), (27, 1), (1, 16), (10, 32), (20, 19), (33, 12), (8, 4), (20, 20), (20, 28), (27, 0), (7, 2), (28, 16), (18, 24), (34, 19), (30, 6), (35, 17), (30, 7), (9, 10), (9, 17), (18, 23), (7, 13), (34, 4), (5, 21), (14, 14), (5, 9), (35, 14), (1, 5), (12, 28), (0, 31), (3, 12), (28, 37), (12, 17), (33, 27), (6, 28), (33, 20), (23, 11), (23, 32), (4, 9), (18, 26), (0, 14), (15, 25), (19, 30), (28, 1), (24, 29), (17, 16), (21, 29), (2, 19), (10, 13), (14, 18), (33, 11), (13, 13), (24, 32), (1, 11), (17, 6), (10, 22), (9, 24), (0, 18), (30, 13), (24, 35), (25, 8), (21, 22), (1, 19), (16, 17), (29, 12), (4, 11), (16, 16), (34, 36), (22, 16), (11, 4), (35, 7), (19, 22), (32, 22), (26, 5), (16, 36), (7, 28), (7, 4), (16, 14), (11, 0), (4, 25), (22, 11), (0, 34), (27, 20), (12, 7), (12, 25), (34, 25), (25, 3), (23, 26), (12, 8), (24, 36), (24, 21), (16, 15), (35, 18), (24, 19), (19, 15), (13, 23), (20, 18), (23, 16), (28, 6), (30, 26), (10, 21), (5, 13), (27, 2), (5, 7), (22, 28), (13, 27), (18, 37), (30, 11), (5, 1), (4, 22), (19, 35), (8, 28), (27, 31), (6, 30), (12, 21), (26, 8), (7, 16), (2, 22), (8, 10), (16, 24), (34, 21), (20, 25), (30, 19), (32, 9), (28, 33), (22, 29), (31, 21), (24, 15), (26, 10), (18, 14), (6, 27), (8, 5), (0, 32), (12, 3), (6, 6), (14, 27), (0, 8), (0, 7), (2, 21), (18, 34), (15, 3), (2, 18), (21, 17), (11, 14), (11, 36), (17, 5), (28, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "477351", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 33), (30, 4), (4, 21), (30, 19), (29, 30), (8, 25), (21, 7), (27, 7), (13, 20), (0, 20), (27, 4), (4, 27), (8, 18), (36, 4), (2, 24), (36, 18), (11, 11), (31, 17), (21, 22), (1, 15), (30, 36), (11, 38), (30, 0), (28, 33), (0, 23), (35, 34), (0, 10), (23, 1), (19, 16), (14, 6), (14, 2), (35, 24), (29, 24), (24, 27), (2, 35), (20, 20), (7, 24), (20, 28), (8, 12), (1, 24), (25, 15), (17, 12), (3, 36), (37, 24), (22, 0), (11, 9), (19, 19), (16, 25), (32, 4), (30, 8), (26, 28), (29, 5), (17, 37), (38, 16), (12, 38), (25, 27), (21, 8), (1, 18), (16, 31), (24, 25), (16, 13), (33, 18), (25, 1), (26, 6), (9, 18), (25, 25), (38, 13), (38, 2), (12, 6), (33, 5), (7, 4), (35, 9), (33, 6), (1, 21), (8, 16), (3, 11), (20, 19), (14, 12), (22, 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(18, 30), (34, 5), (38, 8), (17, 9), (20, 3), (16, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "506880", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), 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), (19, 35), (9, 27), (10, 31), (22, 17), (13, 0), (23, 25), (4, 33), (12, 34), (20, 34), (2, 26), (23, 11), (19, 25), (7, 20), (3, 32), (4, 13), (2, 4), (12, 15), (8, 12), (17, 34), (2, 35), (20, 25), (12, 12), (27, 4), (20, 4), (22, 7), (0, 31), (17, 12), (22, 29), (9, 31), (29, 16), (11, 24), (5, 15), (15, 2), (5, 2), (18, 33), (21, 7), (28, 19), (17, 29), (8, 23), (28, 28), (29, 34), (24, 33), (10, 23), (18, 15), (27, 32), (13, 10), (10, 30), (12, 9), (5, 32), (2, 6), (22, 18), (23, 4), (16, 0), (15, 35), (27, 5), (15, 26), (1, 33), (10, 9), (17, 33), (5, 33), (18, 14), (18, 6), (0, 11), (15, 5), (23, 30), (1, 32), (23, 10), (9, 13), (18, 34), (10, 32), (3, 3), (14, 8), (24, 34), (1, 22), (29, 3), (20, 28), (9, 8), (23, 7), (8, 5), (15, 29), (26, 20), (3, 33), (27, 12), (13, 32), (4, 29), (29, 24), (28, 8), (2, 33), (24, 27), (11, 4), (27, 8), (27, 18), (25, 33), (25, 8), (5, 13), (26, 16), (12, 10), (8, 24), (23, 16), (9, 28), (2, 11), (7, 21), (17, 10), (29, 6), (6, 11), (20, 23), (5, 9), (8, 30), (14, 2), (29, 25), (26, 17), (15, 33), (21, 29), (17, 31), (1, 6), (25, 6), (5, 1), (24, 26), (3, 28), (11, 31), (7, 33), (9, 15), (5, 23), (18, 17), (1, 34), (21, 5), (22, 33), (14, 24), (21, 28), (7, 13), (24, 13), (6, 31), (15, 30), (4, 18), (21, 15), (15, 27), (1, 7), (14, 21), (3, 23), (24, 15), (22, 27), (23, 19), (14, 15), (18, 1), (21, 25), (24, 14), (13, 18), (21, 24), (25, 26), (4, 20), (5, 27), (13, 34), (2, 1), (14, 22), (3, 14), (15, 20), (5, 4), (14, 34), (19, 19), (12, 16), (7, 5), (2, 15), (16, 14), (18, 3), (23, 29), (16, 11), (10, 20), (26, 6), (25, 24), (4, 5), (16, 35), (19, 2), (26, 11), (9, 17), (23, 35), (10, 15), (17, 15), (9, 14), (15, 10), (18, 31), (29, 4), (25, 1), (4, 23), (7, 30), (29, 29), (26, 4), (19, 29), (5, 16), (25, 28), (26, 9), (14, 26), (9, 20), (26, 13), (20, 26), (5, 17), (8, 13), (28, 4), (0, 27), (15, 28), (29, 18), (25, 19), (1, 28), (18, 2), (27, 21), (10, 0), (13, 7), (28, 0), (2, 31), (10, 34), (14, 17), (12, 25), (13, 33), (0, 17), (24, 20), (9, 21), (6, 24), (3, 34), (12, 0), (6, 19), (16, 26), (1, 8), (1, 18), (8, 7), (16, 16), (17, 32), (21, 23), (8, 32), (21, 20), (6, 26), (12, 5), (16, 19), (0, 6), (0, 9), (9, 7), (17, 19), (20, 16), (17, 23), (12, 18), (24, 18), (14, 32), (0, 19), (0, 5), (24, 12), (1, 31), (25, 0), (26, 15), (15, 24), (4, 7), (1, 30), (26, 22), (27, 33), (0, 16), (15, 19), (7, 14), (5, 29), (16, 25), (1, 15), (5, 26), (8, 33), (17, 4), (29, 0), (13, 29), (25, 2), (19, 26), (6, 21), (19, 30), (13, 15), (15, 8), (11, 26), (20, 6), (10, 11), (14, 18), (24, 29), (3, 9), (9, 4), (23, 9), (20, 22), (22, 9), (7, 12), (18, 11), (27, 17), (1, 35), (26, 12), (18, 8), (7, 10), (25, 22), (25, 3), (7, 16), (29, 2), (16, 12), (7, 17), (12, 30), (7, 29), (9, 24), (20, 32), (28, 20), (10, 6), (11, 0), (0, 23), (28, 22), (10, 5), (28, 5), (9, 33), (26, 29), (25, 25), (26, 1), (16, 3), (9, 30), (22, 1), (29, 13), (4, 14), (3, 35), (24, 24), (4, 34), (15, 11), (28, 16), (7, 25), (24, 32), (16, 28), (22, 13), (29, 22), (3, 31), (0, 12), (22, 25), (0, 30), (11, 2), (12, 1), (9, 22), (10, 1), (27, 13), (21, 18), (17, 21), (16, 24), (0, 18), (29, 12), (17, 26), (28, 24), (17, 6), (16, 33), (1, 14), (5, 18), (8, 19), (6, 32), (21, 16), (27, 26), (7, 26), (4, 10), (6, 23), (10, 12), (9, 10), (11, 12), (12, 26), (19, 22), (16, 17), (20, 5), (27, 9), (4, 25), (9, 26), (0, 7), (25, 13), (19, 4), (20, 10), (16, 23), (15, 32), (15, 3), (19, 33), (16, 5), (23, 6), (21, 10), (18, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "163296", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 32), (17, 22), (12, 33), (29, 32), (32, 16), (5, 29), (28, 35), (0, 5), (36, 1), (27, 20), (10, 29), (25, 33), (18, 29), (22, 6), (32, 7), (7, 19), (37, 2), (9, 0), (4, 26), (22, 30), (3, 36), (14, 28), (25, 17), (30, 20), (3, 31), (12, 10), (5, 10), (31, 20), (22, 32), (36, 21), (36, 28), (8, 25), (26, 4), (32, 14), (37, 6), (4, 25), (33, 37), (34, 11), (8, 15), (12, 17), (5, 5), (10, 8), (35, 25), (27, 31), (29, 13), (5, 26), (26, 32), (32, 21), (37, 17), (9, 20), (31, 34), (26, 8), (8, 36), (20, 24), (25, 4), (33, 24), (21, 29), (6, 28), (10, 17), (17, 29), (11, 9), (7, 30), (1, 3), (31, 28), (36, 14), (25, 19), (23, 28), (26, 28), (25, 11), (21, 25), (28, 11), (5, 1), (18, 3), (24, 37), (3, 21), (26, 10), (22, 31), (28, 22), (11, 26), (1, 32), (22, 16), (35, 29), (15, 5), (34, 23), (31, 11), (12, 25), (11, 2), (9, 11), (5, 15), (25, 25), (27, 16), (36, 17), (16, 12), (32, 26), (26, 2), (15, 35), (22, 10), (23, 1), (33, 28), (11, 27), (16, 24), (27, 26), (15, 31), (16, 29), (2, 10), (11, 12), (35, 6), (25, 29), (26, 27), (24, 10), (31, 33), (20, 32), (27, 25), (23, 9), (37, 25), (33, 35), (34, 2), (11, 25), (6, 1), (20, 4), (13, 29), (30, 13), (36, 34), (3, 29), (29, 28), (12, 27), (12, 20), (15, 18), (3, 10), (29, 3), (24, 23), (35, 19), (8, 31), (1, 0), (19, 22), (6, 9), (13, 7), (16, 3), (22, 15), (6, 37), (26, 29), (21, 21), (37, 33), (29, 24), (29, 7), (30, 14), (21, 33), (0, 10), (36, 26), (22, 3), (25, 8), (3, 14), (24, 32), (9, 5), (12, 19), (36, 25), (13, 35), (31, 12), (35, 13), (0, 6), (32, 33), (9, 12), (24, 27), (24, 22), (11, 21), (14, 3), (24, 25), (8, 29), (27, 30), (1, 13), (31, 14), (32, 0), (4, 5), (18, 15), (27, 33), (10, 25), (16, 7), (21, 17), (3, 20), (6, 31), (15, 11), (13, 14), (35, 16), (16, 20), (30, 3), (22, 8), (19, 11), (33, 15), (24, 16), (18, 8), (17, 16), (3, 22), (16, 4), (16, 30), (9, 34), (32, 5), (22, 14), (21, 11), (30, 33), (33, 30), (10, 31), (13, 25), (14, 12), (20, 25), (21, 5), (35, 11), (7, 20), (12, 32), (25, 30), (7, 3), (3, 18), (25, 26), (17, 28), (7, 8), (37, 11), (17, 12), (9, 14), (14, 5), (20, 20), (11, 17), (21, 16), (15, 14), (34, 16), (37, 29), (14, 32), (8, 0), (9, 15), (18, 4), (7, 35), (28, 8), (1, 23), (6, 5), (15, 16), (11, 14), (26, 22), (37, 34), (18, 24), (14, 14), (28, 5), (21, 12), (12, 37), (29, 36), (14, 8), (28, 10), (35, 18), (1, 7), (31, 22), (20, 31), (17, 2), (2, 17), (23, 29), (33, 9), (7, 25), (31, 19), (30, 30), (13, 16), (37, 28), (20, 5), (7, 4), (15, 10), (25, 15), (17, 35), (4, 1), (8, 8), (8, 32), (30, 21), (36, 29), (20, 6), (17, 26), (7, 37), (23, 23), (27, 35), (9, 24), (31, 17), (5, 19), (2, 27), (17, 24), (33, 3), (13, 30), (0, 9), (28, 34), (28, 28), (20, 10), (32, 4), (24, 24), (30, 11), (17, 1), (32, 24), (4, 35), (34, 12), (8, 34), (2, 24), (13, 1), (24, 14), (2, 13), (23, 25), (8, 11), (18, 19), (8, 6), (15, 27), (15, 8), (31, 37), (19, 0), (29, 14), (2, 9), (34, 24), (36, 36), (10, 37), (7, 7), (24, 35), (9, 37), (34, 36), (24, 0), (7, 26), (28, 29), (23, 0), (5, 31), (7, 13), (36, 24), (1, 8), (28, 25), (7, 16), (30, 32), (18, 10), (4, 28), (20, 33), (25, 22), (19, 15), (10, 11), (32, 19), (14, 11), (30, 15), (28, 3), (29, 18), (20, 19), (0, 19), (15, 21), (33, 14), (28, 14), (28, 1), (34, 1), (33, 20), (8, 20), (17, 17), (33, 16), (19, 3), (16, 2), (17, 5), (15, 25), (9, 27), (22, 37), (12, 2), (12, 26), (16, 10), (27, 28), (18, 5), (27, 11), (8, 9), (18, 33), (28, 7), (6, 3), (35, 36), (30, 10), (13, 19), (23, 20), (36, 18), (22, 36), (34, 32), (36, 13), (21, 20), (34, 20), (17, 18), (21, 32), (17, 23), (27, 32), (0, 17), (31, 27), (7, 11), (0, 29), (21, 23), (2, 22), (26, 24), (5, 17), (14, 1), (31, 30), (0, 21), (0, 36), (6, 15), (4, 0), (10, 36), (20, 27), (17, 7), (5, 6), (12, 30), (6, 7), (15, 4), (10, 23), (32, 22), (36, 7), (28, 33), (2, 0), (22, 29), (14, 29), (19, 35), (30, 4), (3, 25), (4, 9), (11, 6), (7, 10), (25, 31), (30, 18), (23, 22), (5, 35), (22, 12), (21, 14), (14, 23), (36, 23), (25, 37), (18, 21), (17, 9), (34, 8), (12, 35), (27, 37), (11, 28), (3, 17), (21, 27), (16, 1), (0, 37), (22, 7), (10, 33), (21, 36), (35, 9), (33, 17), (7, 28), (36, 4), (26, 9), (17, 31), (8, 21), (32, 28), (17, 8), (29, 2), (11, 32), (37, 9), (0, 24), (33, 25), (4, 15), (10, 10), (25, 2), (14, 15), (7, 27), (27, 18), (16, 35), (25, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900432", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 25), (13, 20), (23, 25), (8, 13), (16, 8), (20, 8), (33, 13), (22, 2), (20, 30), (21, 27), (31, 30), (17, 27), (10, 18), (35, 1), (20, 21), (33, 27), (10, 8), (33, 25), (33, 19), (13, 27), (15, 9), (21, 29), (15, 0), (25, 16), (7, 23), (1, 2), (23, 7), (22, 1), (0, 20), (4, 3), (12, 8), (19, 20), (7, 30), (25, 4), (30, 10), (0, 25), (32, 2), (10, 4), (35, 21), (10, 10), (11, 10), (11, 25), (23, 14), (7, 17), (20, 7), (1, 7), (10, 28), (16, 13), (26, 10), (31, 27), (29, 13), (35, 0), (19, 21), (33, 2), (21, 16), (5, 15), (17, 26), (28, 5), (4, 25), (17, 16), (24, 23), (8, 29), (16, 22), (7, 19), (25, 12), (34, 10), (18, 19), (23, 19), (13, 13), (24, 18), (4, 22), (14, 8), (5, 28), (0, 27), (6, 10), (24, 10), (36, 13), (6, 6), (27, 10), (33, 29), (28, 0), (23, 8), (28, 3), (26, 25), (31, 17), (24, 6), (13, 17), (23, 3), (37, 22), (29, 2), (10, 13), (21, 6), (12, 18), (3, 10), (31, 10), (7, 8), (21, 24), (0, 26), (28, 29), (18, 0), (15, 11), (21, 2), (11, 0), (32, 9), (34, 4), (23, 23), (16, 16), (29, 3), (36, 1), (28, 12), (19, 23), (20, 5), (19, 8), (3, 9), (5, 18), (36, 3), (35, 18), (27, 3), (26, 3), (24, 0), (11, 18), (29, 27), (34, 6), (15, 1), (32, 11), (19, 28), (5, 30), (24, 17), (27, 25), (17, 22), (35, 14), (4, 12), (28, 8), (28, 7), (28, 21), (10, 3), (18, 29), (4, 11), (23, 15), (20, 12), (8, 27), (11, 28), (33, 14), (23, 1), (32, 15), (21, 4), (14, 14), (22, 27), (25, 26), (24, 28), (10, 20), (20, 25), (26, 5), (9, 5), (35, 30), (13, 6), (2, 24), (19, 19), (4, 24), (17, 28), (27, 29), (21, 20), (13, 16), (20, 2), (14, 5), (6, 3), (12, 14), (12, 22), (1, 12), (17, 6), (12, 17), (17, 7), (0, 18), (17, 12), (26, 0), (31, 14), (35, 12), (5, 23), (8, 25), (15, 15), (37, 18), (11, 1), (24, 3), (29, 9), (26, 30), (8, 12), (35, 16), (32, 0), (19, 14), (24, 13), (35, 24), (17, 5), (19, 15), (10, 15), (0, 6), (33, 3), (31, 1), (21, 1), (6, 26), (9, 16), (35, 15), (8, 21), (25, 20), (8, 24), (6, 27), (18, 1), (6, 12), (35, 29), (21, 21), (27, 21), (29, 26), (13, 23), (24, 24), (33, 23), (2, 3), (23, 24), (7, 20), (7, 14), (20, 26), (9, 15), (26, 27), (29, 20), (27, 12), (28, 23), (10, 22), (32, 19), (34, 30), (3, 19), (3, 17), (7, 9), (15, 25), (12, 30), (21, 26), (11, 12), (17, 20), (16, 26), (36, 16), (29, 29), (15, 5), (2, 18), (4, 9), (32, 3), (37, 26), (17, 29), (6, 8), (11, 21), (21, 7), (17, 17), (11, 11), (0, 30), (6, 18), (7, 22), (9, 21), (7, 26), (29, 28), (37, 17), (31, 0), (14, 24), (31, 15), (25, 28), (21, 23), (8, 17), (33, 0), (28, 1), (37, 2), (3, 0), (24, 21), (37, 12), (0, 28), (0, 10), (21, 15), (12, 12), (34, 12), (2, 13), (13, 15), (5, 25), (26, 21), (24, 7), (30, 19), (17, 30), (0, 13), (5, 20), (28, 6), (19, 13), (33, 26), (33, 18), (3, 6), (37, 20), (25, 24), (31, 5), (0, 2), (0, 9), (8, 14), (35, 10), (24, 5), (33, 15), (3, 22), (5, 16), (1, 27), (1, 17), (29, 25), (26, 23), (30, 29), (15, 20), (28, 17), (9, 29), (6, 4), (28, 25), (24, 1), (33, 30), (33, 6), (9, 8), (6, 22), (18, 11), (5, 19), (2, 28), (26, 6), (10, 21), (24, 8), (23, 28), (9, 10), (21, 28), (25, 17), (0, 5), (3, 23), (26, 9), (9, 13), (15, 16), (21, 9), (11, 14), (12, 16), (2, 22), (27, 7), (16, 18), (30, 18), (37, 15), (34, 22), (27, 11), (14, 21), (32, 16), (37, 23), (4, 14), (26, 16), (19, 2), (7, 15), (27, 26), (30, 20), (21, 19), (9, 30), (13, 30), (9, 4), (14, 15), (14, 17), (23, 9), (7, 16), (16, 11), (11, 2), (37, 1), (26, 8), (36, 15), (29, 10), (16, 3), (9, 17), (5, 7), (4, 23), (6, 2), (8, 8), (9, 27), (25, 10), (26, 1), (15, 23), (13, 19), (34, 26), (37, 13), (23, 16), (33, 20), (14, 18), (28, 16), (27, 13), (20, 19), (0, 19), (37, 4), (15, 21), (16, 14), (10, 11), (34, 1), (27, 14), (21, 10), (26, 2), (17, 2), (25, 27), (37, 5), (30, 14), (4, 29), (18, 20), (30, 13), (17, 23), (23, 27), (20, 23), (31, 12), (36, 5), (17, 9), (22, 11), (3, 30), (35, 2), (8, 4), (14, 2), (30, 21), (33, 12), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "762048", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 16), (28, 25), (24, 8), (27, 31), (21, 30), (9, 21), (4, 12), (32, 9), (19, 20), (3, 28), (31, 14), (12, 21), (13, 13), (9, 16), (30, 17), (14, 18), (24, 32), (27, 13), (27, 6), (31, 7), (15, 27), (6, 26), (18, 18), (23, 25), (16, 33), (16, 25), (17, 26), (24, 17), (8, 2), (15, 19), (31, 11), (20, 6), (13, 8), (29, 6), (30, 29), (10, 24), (22, 8), (27, 22), (2, 24), (0, 18), (14, 15), (0, 23), (9, 15), (6, 29), (28, 0), (11, 28), (17, 13), (0, 17), (13, 5), (1, 2), (5, 2), (21, 1), (8, 0), (27, 32), (23, 1), (25, 9), (18, 23), (8, 18), (20, 12), (17, 5), (20, 5), (5, 17), (10, 31), (11, 20), (4, 30), (17, 14), (14, 3), (17, 18), (30, 9), (8, 29), (17, 23), (13, 12), (8, 24), (29, 11), (15, 10), (31, 27), (28, 19), (22, 3), (11, 16), (4, 26), (30, 32), (18, 17), (14, 27), (29, 17), (2, 22), (10, 7), (17, 32), (4, 32), (30, 4), (4, 13), (23, 11), (32, 6), (19, 5), (28, 3), (32, 22), (5, 11), (17, 7), (26, 28), (10, 28), (18, 4), (30, 11), (24, 13), (23, 29), (30, 28), (29, 18), (15, 30), (2, 10), (28, 1), (18, 2), (5, 3), (25, 17), (31, 12), (6, 15), (31, 3), (27, 17), (6, 4), (1, 28), (27, 16), (5, 30), (6, 32), (20, 10), (23, 7), (20, 21), (4, 27), (28, 26), (15, 22), (13, 11), (9, 2), (22, 31), (9, 26), (10, 20), (14, 23), (0, 30), (23, 16), (18, 30), (11, 1), (15, 26), (28, 7), (15, 17), (13, 3), (8, 12), (32, 1), (0, 12), (17, 29), (21, 33), (14, 2), (31, 31), (20, 25), (7, 11), (26, 10), (13, 29), (6, 25), (32, 18), (4, 28), (24, 12), (21, 11), (2, 7), (16, 5), (15, 23), (4, 9), (25, 13), (8, 22), (2, 1), (12, 25), (24, 27), (5, 15), (17, 0), (12, 6), (2, 29), (8, 11), (30, 6), (15, 12), (9, 1), (6, 17), (31, 21), (26, 0), (23, 27), (12, 16), (20, 17), (31, 24), (27, 1), (15, 2), (32, 29), (15, 20), (29, 5), (28, 14), (25, 15), (22, 5), (27, 27), (11, 32), (12, 20), (5, 20), (24, 31), (9, 12), (21, 3), (2, 2), (19, 0), (23, 0), (0, 26), (0, 20), (17, 19), (6, 2), (14, 5), (31, 20), (2, 11), (1, 22), (3, 30), (32, 0), (26, 7), (17, 6), (18, 6), (0, 24), (23, 9), (27, 19), (20, 14), (20, 16), (12, 3), (24, 20), (17, 25), (5, 1), (10, 0), (19, 19), (10, 5), (7, 20), (0, 19), (11, 5), (19, 32), (27, 7), (23, 21), (2, 30), (26, 9), (2, 17), (22, 15), (5, 24), (9, 20), (14, 8), (27, 29), (3, 22), (6, 9), (1, 26), (1, 10), (6, 20), (29, 27), (16, 24), (3, 24), (21, 26), (21, 6), (6, 7), (30, 18), (8, 1), (17, 20), (31, 19), (11, 8), (10, 12), (14, 31), (14, 30), (0, 8), (11, 17), (18, 15), (29, 15), (25, 2), (2, 12), (6, 12), (3, 19), (32, 13), (20, 7), (6, 6), (8, 17), (19, 18), (7, 33), (22, 16), (7, 23), (28, 10), (30, 15), (17, 27), (23, 18), (17, 9), (28, 16), (31, 23), (5, 19), (20, 4), (16, 9), (6, 18), (3, 25), (22, 32), (23, 32), (25, 29), (12, 11), (19, 33), (24, 26), (14, 0), (3, 10), (32, 8), (27, 10), (26, 30), (10, 19), (12, 31), (2, 27), (17, 10), (21, 32), (25, 10), (28, 29), (23, 19), (20, 31), (20, 22), (1, 18), (4, 7), (23, 10), (30, 12), (17, 4), (8, 7), (28, 30), (3, 32), (7, 22), (22, 11), (25, 7), (23, 3), (1, 11), (26, 6), (28, 22), (4, 17), (29, 8), (1, 13), (22, 29), (14, 14), (26, 25), (28, 32), (16, 17), (11, 25), (25, 22), (30, 25), (7, 5), (30, 23), (19, 6), (20, 26), (11, 7), (4, 23), (4, 4), (31, 30), (6, 13), (5, 13), (8, 16), (13, 32), (32, 10), (28, 15), (10, 3), (7, 32), (19, 17), (14, 4), (3, 13), (29, 24), (24, 33), (18, 3), (19, 30), (28, 5), (12, 19), (32, 12), (1, 33), (20, 1), (19, 16), (20, 23), (19, 4), (15, 33), (22, 27), (23, 2), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944055", "dataset": "MATH"}
{"messages": [{"content": "In a 35x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 33), 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), (28, 20), (14, 1), (20, 5), (26, 5), (11, 6), (5, 5), (24, 7), (14, 31), (23, 10), (2, 11), (4, 12), (4, 4), (33, 28), (1, 17), (7, 9), (14, 19), (6, 1), (15, 3), (16, 13), (31, 27), (8, 20), (17, 14), (18, 4), (26, 26), (5, 25), (19, 18), (10, 1), (26, 31), (16, 23), (4, 6), (11, 9), (32, 5), (10, 11), (23, 32), (30, 29), (0, 12), (20, 23), (11, 0), (28, 27), (28, 4), (16, 26), (27, 19), (21, 9), (31, 1), (10, 27), (2, 29), (11, 8), (20, 13), (10, 19), (22, 12), (1, 21), (28, 1), (10, 2), (32, 27), (11, 23), (11, 18), (32, 10), (9, 16), (12, 12), (17, 29), (6, 3), (19, 17), (22, 16), (29, 18), (13, 15), (8, 23), (28, 10), (3, 14), (15, 4), (26, 29), (0, 33), (0, 28), (5, 33), (8, 28), (29, 26), (33, 33), (16, 4), (10, 13), (30, 22), (8, 12), (19, 7), (30, 3), (1, 28), (2, 26), (1, 27), (11, 19), (7, 4), (34, 17), (10, 5), (27, 9), (10, 24), (1, 2), (24, 21), (27, 33), (16, 16), (32, 15), (0, 10), (1, 7), (17, 3), (23, 4), (11, 15), (10, 12), (33, 30), (27, 23), (2, 14), (24, 23), (6, 13), (25, 19), (21, 11), (3, 9), (18, 11), (28, 5), (20, 2), (9, 17), (24, 14), (17, 22), (8, 8), (5, 14), (34, 27), (33, 21), (29, 4), (25, 21), (33, 13), (1, 24), (24, 6), (34, 10), (32, 23), (8, 14), (17, 26), (11, 31), (16, 9), (25, 33), (18, 8), (6, 9), (25, 8), (13, 32), (8, 1), (30, 30), (31, 25), (22, 13), (28, 15), (0, 22), (4, 31), (28, 8), (20, 20), (9, 2), (28, 7), (2, 15), (15, 1), (9, 5), (13, 9), (6, 0), (4, 5), (32, 17), (0, 23), (2, 22), (32, 0), (2, 5), (30, 0), (22, 15), (22, 5), (6, 14), (25, 11), (10, 30), (34, 20), (14, 20), (15, 9), (19, 32), (33, 24), (23, 3), (31, 22), (29, 11), (33, 1), (30, 18), (22, 24), (33, 29), (6, 21), (12, 29), (24, 20), (22, 25), (7, 26), (12, 8), (11, 13), (23, 2), (25, 1), (27, 26), (32, 8), (9, 27), (20, 30), (10, 15), (18, 10), (22, 33), (14, 21), (6, 30), (26, 28), (17, 2), (28, 25), (34, 26), (34, 2), (17, 1), (19, 31), (22, 2), (13, 17), (12, 26), (17, 19), (5, 23), (7, 0), (34, 0), (15, 18), (0, 11), (0, 15), (15, 11), (0, 16), (7, 20), (4, 23), (18, 32), (5, 30), (17, 23), (16, 15), (11, 7), (21, 10), (8, 18), (24, 30), (18, 24), (9, 29), (16, 5), (10, 7), (15, 12), (3, 23), (12, 22), (4, 16), (27, 18), (34, 4), (17, 31), (4, 10), (26, 30), (9, 24), (6, 4), (29, 25), (31, 9), (11, 5), (24, 10), (4, 32), (5, 11), (7, 1), (32, 19), (24, 29), (5, 24), (26, 20), (32, 32), (3, 11), (22, 8), (6, 8), (27, 3), (18, 1), (3, 28), (22, 32), (17, 6), (30, 14), (26, 18), (11, 14), (15, 2), (8, 0), (20, 3), (20, 27), (1, 15), (31, 12), (9, 8), (16, 27), (12, 16), (28, 13), (4, 9), (12, 33), (30, 4), (29, 3), (21, 8), (9, 32), (26, 16), (23, 8), (21, 19), (1, 5), (19, 29), (1, 1), (33, 17), (25, 30), (15, 24), (14, 11), (8, 17), (8, 30), (22, 28), (27, 27), (12, 6), (21, 31), (25, 0), (5, 17), (7, 15), (15, 8), (0, 19), (8, 31), (25, 26), (13, 26), (31, 5), (7, 13), (21, 14), (24, 1), (32, 25), (24, 22), (3, 7), (30, 10), (25, 28), (25, 32), (19, 14), (14, 28), (29, 0), (29, 27), (30, 21), (13, 10), (14, 14), (18, 12), (15, 23), (9, 20), (7, 8), (16, 18), (18, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4992", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 34), (17, 33), (21, 21), (18, 6), (6, 7), (5, 6), (8, 19), (2, 2), (27, 16), (7, 16), (8, 3), (22, 24), (10, 6), (18, 15), (16, 35), (28, 2), (19, 18), (6, 21), (30, 30), (28, 30), (5, 33), (3, 1), (21, 11), (25, 4), (24, 5), (24, 0), (19, 29), (24, 15), (13, 13), (24, 12), (15, 19), (16, 31), (24, 32), (33, 15), (32, 20), (29, 23), (4, 14), (18, 11), (23, 5), (28, 7), (2, 20), (26, 13), (20, 26), (18, 8), (25, 20), (1, 28), (1, 26), (19, 11), (19, 13), (6, 22), (19, 30), (32, 28), (12, 0), (26, 29), (5, 12), (25, 27), (17, 14), (19, 9), (2, 7), (20, 15), (11, 20), (13, 21), (23, 36), (1, 32), (31, 10), (19, 0), (9, 10), (12, 22), (11, 8), (31, 15), (25, 10), (26, 3), (2, 22), (27, 6), (20, 1), (18, 21), (33, 26), (22, 6), (12, 12), (3, 21), (14, 24), (0, 16), (12, 28), (19, 1), (4, 31), (17, 18), (4, 32), (16, 15), (21, 25), (25, 7), (27, 12), (24, 8), (26, 31), (32, 19), (5, 2), (15, 14), (26, 18), (11, 7), (26, 2), (27, 20), (13, 24), (33, 19), (23, 21), (14, 27), (8, 34), (8, 33), (31, 2), (15, 6), (9, 23), (20, 25), (24, 2), (31, 30), (24, 35), (16, 27), (22, 3), (28, 4), (15, 18), (14, 5), (16, 17), (32, 13), (9, 2), (33, 13), (9, 24), (11, 29), (13, 34), (27, 24), (13, 1), (26, 22), (17, 25), (2, 4), (7, 28), (21, 30), (32, 17), (15, 2), (31, 36), (12, 15), (21, 23), (31, 25), (22, 14), (28, 6), (16, 5), (32, 34), (9, 5), (6, 35), (20, 6), (9, 8), (11, 10), (32, 11), (3, 18), (29, 22), (12, 13), (8, 8), (24, 23), (28, 19), (27, 14), (19, 22), (8, 4), (5, 24), (26, 14), (15, 1), (9, 14), (22, 1), (20, 10), (25, 24), (2, 5), (27, 18), (30, 19), (25, 25), (31, 16), (20, 21), (0, 14), (21, 9), (17, 32), (6, 0), (13, 28), (12, 9), (1, 30), (24, 7), (7, 18), (32, 29), (30, 5), (13, 30), (30, 11), (33, 21), (19, 25), (33, 0), (0, 4), (10, 33), (32, 9), (31, 23), (22, 33), (14, 0), (9, 12), (22, 23), (25, 30), (26, 7), (24, 30), (1, 12), (24, 36), (16, 4), (27, 26), (5, 30), (4, 30), (15, 16), (25, 9), (29, 26), (5, 1), (7, 5), (11, 2), (27, 35), (17, 3), (16, 20), (20, 35), (28, 17), (25, 31), (19, 28), (4, 23), (25, 28), (1, 7), (27, 31), (8, 32), (4, 36), (10, 5), (24, 9), (12, 19), (11, 19), (2, 24), (25, 1), (3, 14), (0, 10), (4, 29), (6, 15), (32, 12), (20, 30), (16, 16), (10, 25), (31, 29), (28, 35), (10, 23), (18, 24), (7, 27), (13, 32), (11, 1), (7, 21), (16, 24), (13, 0), (9, 33), (1, 17), (13, 22), (12, 11), (15, 5), (11, 27), (10, 35), (33, 7), (16, 25), (4, 5), (9, 35), (29, 13), (0, 23), (15, 35), (7, 11), (2, 3), (10, 18), (24, 17), (1, 21), (2, 16), (15, 28), (28, 34), (28, 1), (3, 31), (2, 13), (2, 31), (21, 4), (16, 32), (31, 7), (0, 36), (3, 4), (29, 14), (22, 27), (14, 23), (24, 29), (14, 33), (7, 8), (3, 32), (18, 30), (11, 35), (33, 34), (20, 33), (17, 9), (33, 30), (6, 8), (23, 12), (4, 24), (26, 36), (12, 6), (22, 26), (0, 31), (25, 5), (21, 6), (28, 21), (3, 36), (33, 35), (33, 31), (18, 12), (5, 3), (10, 15), (3, 28), (32, 2), (27, 21), (17, 17), (9, 9), (11, 22), (18, 26), (3, 17), (1, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "350784", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 24), (12, 5), (8, 25), (21, 23), (8, 5), (8, 23), (31, 13), (11, 4), (17, 21), (24, 5), (17, 19), (11, 19), (12, 25), (9, 7), (15, 2), (23, 15), (28, 1), (11, 26), (10, 19), (14, 23), (20, 21), (29, 2), (9, 18), (14, 21), (26, 2), (29, 13), (17, 27), (24, 12), (8, 14), (19, 28), (17, 4), (32, 24), (19, 2), (2, 17), (22, 25), (30, 15), (27, 21), (23, 10), (16, 22), (24, 19), (12, 22), (2, 16), (14, 1), (16, 21), (6, 21), (30, 3), (19, 15), (33, 26), (15, 26), (8, 21), (14, 24), (29, 24), (23, 11), (15, 28), (5, 12), (28, 6), (24, 22), (19, 24), (8, 29), (15, 6), (16, 23), (3, 2), (23, 5), (5, 13), (23, 28), (23, 27), (27, 13), (23, 1), (10, 22), (1, 16), (3, 8), (15, 22), (18, 25), (9, 1), (20, 16), (12, 14), (13, 8), (7, 29), (11, 27), (21, 6), (16, 20), (23, 26), (25, 6), (9, 0), (15, 1), (7, 11), (20, 2), (2, 30), (21, 30), (1, 18), (0, 29), (9, 30), (24, 8), (25, 23), (2, 7), (21, 27), (14, 12), (18, 19), (18, 14), (14, 7), (16, 14), (13, 17), (25, 19), (4, 21), (18, 20), (8, 1), (5, 0), (7, 23), (28, 26), (29, 5), (26, 14), (18, 26), (8, 2), (5, 15), (24, 3), (27, 8), (15, 11), (31, 18), (10, 4), (18, 28), (23, 0), (20, 1), (14, 17), (8, 7), (12, 11), (2, 15), (8, 13), (32, 29), (30, 21), (31, 29), (30, 1), (27, 4), (3, 11), (6, 3), (3, 0), (24, 27), (5, 2), (16, 0), (12, 26), (22, 20), (20, 19), (32, 26), (20, 6), (3, 18), (28, 23), (27, 25), (19, 10), (25, 27), (5, 6), (16, 26), (8, 19), (13, 10), (16, 28), (0, 12), (19, 14), (31, 8), (23, 8), (14, 5), (27, 1), (6, 26), (27, 26), (2, 26), (1, 24), (12, 19), (19, 25), (33, 1), (13, 13), (25, 14), (30, 6), (29, 25), (13, 0), (18, 5), (5, 21), (15, 16), (24, 28), (10, 18), (29, 22), (33, 11), (1, 12), (30, 2), (29, 19), (25, 0), (7, 27), (26, 8), (4, 26), (24, 7), (8, 8), (8, 16), (7, 20), (19, 9), (1, 5), (5, 1), (16, 5), (27, 27), (28, 12), (26, 15), (4, 6), (14, 26), (29, 29), (10, 26), (24, 18), (12, 23), (6, 0), (24, 29), (32, 28), (25, 9), (2, 1), (6, 16), (6, 11), (11, 28), (21, 16), (30, 28), (5, 28), (11, 16), (16, 11), (13, 11), (29, 26), (11, 20), (17, 16), (22, 0), (12, 12), (7, 10), (18, 16), (32, 22), (17, 15), (14, 27), (1, 14), (32, 17), (11, 22), (4, 10), (7, 12), (11, 7), (31, 17), (32, 7), (12, 0), (21, 8), (15, 18), (31, 28), (20, 15), (22, 30), (4, 13), (4, 0), (28, 16), (4, 7), (22, 15), (23, 9), (23, 17), (5, 20), (8, 30), (22, 28), (27, 2), (13, 9), (9, 2), (3, 17), (32, 9), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185680", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 36), (5, 5), (1, 26), (25, 35), (27, 18), (21, 24), (23, 10), (33, 30), (25, 10), (27, 23), (19, 21), (15, 22), (18, 22), (21, 13), (19, 23), (8, 13), (2, 17), (21, 11), (35, 11), (17, 31), (18, 32), (0, 13), (16, 28), (29, 27), (3, 34), (24, 34), (23, 33), (22, 5), (12, 34), (3, 36), (9, 32), (1, 13), (3, 26), (19, 5), (25, 9), (14, 31), (16, 12), (34, 28), (13, 11), (9, 18), (8, 1), (19, 11), (5, 21), (21, 25), (8, 6), (24, 3), (3, 32), (33, 0), (26, 14), (16, 6), (33, 24), (14, 23), (36, 35), (17, 3), (1, 12), (35, 25), (37, 1), (1, 28), (26, 18), (4, 14), (9, 27), (20, 0), (19, 4), (22, 25), (0, 3), (5, 24), (16, 5), (7, 21), (21, 31), (9, 33), (3, 30), (33, 8), (19, 6), (10, 22), (10, 4), (16, 29), (26, 0), (4, 11), (16, 13), (28, 14), (13, 3), (6, 33), (5, 1), (28, 20), (36, 28), (37, 23), (28, 6), (27, 6), (31, 18), (29, 17), (16, 31), (21, 4), (15, 35), (31, 3), (16, 4), (22, 9), (35, 35), (0, 25), (37, 13), (15, 28), (34, 30), (16, 3), (33, 17), (3, 35), (37, 28), (32, 19), (19, 35), (32, 23), (15, 11), (9, 16), (28, 34), (28, 33), (6, 3), (22, 29), (19, 12), (31, 17), (12, 4), (8, 27), (12, 27), (30, 3), (23, 15), (34, 26), (6, 8), (10, 2), (19, 26), (33, 31), (15, 0), (12, 7), (0, 9), (10, 13), (26, 27), (7, 34), (6, 30), (27, 17), (12, 18), (9, 1), (36, 23), (12, 10), (14, 25), (4, 3), (20, 16), (33, 26), (11, 6), (15, 4), (15, 30), (4, 31), (11, 34), (37, 19), (33, 35), (33, 29), (36, 18), (18, 12), (13, 17), (32, 4), (4, 22), (2, 23), (6, 36), (18, 8), (24, 28), (8, 25), (17, 8), (27, 12), (31, 16), (13, 35), (17, 9), (35, 15), (7, 17), (24, 15), (13, 25), (11, 24), (13, 34), (8, 3), (10, 25), (10, 29), (30, 20), (33, 6), (9, 21), (9, 28), (19, 17), (26, 19), (30, 17), (32, 36), (10, 24), (2, 6), (0, 4), (11, 0), (5, 33), (16, 36), (28, 32), (26, 11), (20, 32), (37, 2), (16, 10), (18, 26), (17, 33), (19, 32), (25, 13), (14, 3), (15, 34), (11, 23), (29, 18), (7, 30), (34, 0), (31, 9), (6, 17), (15, 20), (22, 4), (3, 14), (14, 34), (27, 16), (36, 26), (20, 10), (1, 21), (8, 21), (36, 4), (6, 18), (24, 0), (0, 24), (25, 23), (20, 36), (22, 32), (36, 30), (10, 32), (22, 36), (32, 31), (35, 7), (36, 31), (23, 17), (34, 23), (36, 0), (11, 27), (10, 26), (0, 16), (3, 25), (2, 27), (20, 18), (3, 5), (24, 32), (3, 18), (9, 17), (36, 33), (0, 17), (1, 16), (17, 7), (7, 9), (2, 10), (29, 22), (17, 15), (11, 17), (16, 15), (32, 10), (15, 10), (4, 2), (30, 8), (9, 4), (3, 22), (2, 36), (11, 35), (34, 4), (9, 23), (27, 11), (11, 29), (37, 6), (20, 31), (31, 13), (27, 1), (13, 12), (30, 2), (0, 20), (37, 21), (28, 27), (13, 8), (37, 14), (10, 30), (32, 0), (2, 9), (2, 8), (32, 9), (33, 27), (5, 4), (29, 15), (31, 27), (34, 24), (25, 2), (23, 25), (7, 3), (25, 30), (27, 3), (30, 16), (32, 25), (18, 11), (29, 11), (32, 27), (14, 16), (1, 17), (11, 18), (28, 5), (32, 2), (33, 3), (5, 15), (8, 23), (23, 31), (16, 27), (21, 15), (12, 30), (26, 5), (31, 20), (22, 35), (24, 19), (33, 36), (35, 26), (19, 0), (27, 13), (23, 13), (14, 24), (30, 15), (4, 32), (6, 24), (14, 19), (11, 7), (11, 26), (24, 26), (20, 12), (14, 0), (18, 34), (21, 27), (19, 8), (0, 26), (17, 14), (35, 22), (23, 0), (36, 7), (34, 10), (21, 22), (3, 21), (30, 4), (10, 19), (7, 12), (6, 29), (14, 27), (25, 0), (37, 12), (12, 35), (18, 17), (13, 27), (14, 6), (18, 2), (36, 20), (33, 20), (6, 20), (0, 6), (0, 35), (20, 8), (25, 7), (18, 4), (12, 21), (15, 29), (10, 28), (35, 4), (12, 1), (31, 10), (9, 25), (21, 23), (33, 28), (36, 11), (18, 5), (37, 29), (11, 1), (13, 29), (15, 15), (25, 29), (15, 12), (31, 6), (29, 36), (23, 19), (35, 10), (2, 20), (7, 33), (19, 25), (2, 29), (4, 19), (32, 17), (18, 6), (24, 4), (20, 28), (7, 4), (29, 16), (0, 7), (12, 6), (13, 0), (34, 5), (36, 36), (3, 12), (35, 6), (16, 17), (2, 1), (20, 34), (10, 35), (3, 23), (2, 14), (5, 29), (31, 14), (12, 19), (9, 26), (32, 16), (18, 20), (1, 15), (31, 30), (26, 13), (5, 9), (15, 36), (9, 7), (36, 2), (32, 28), (15, 19), (16, 11), (34, 2), (30, 32), (11, 4), (20, 17), (5, 34), (12, 17), (12, 3), (26, 8), (4, 4), (35, 19), (19, 3), (23, 11), (35, 20), (33, 21), (21, 14), (16, 23), (18, 36), (36, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "812520", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), 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), (23, 11), (2, 10), (32, 8), (25, 17), (16, 22), (12, 15), (34, 28), (36, 3), (33, 19), (17, 11), (1, 2), (1, 28), (20, 20), (30, 20), (16, 29), (0, 28), (15, 30), (1, 3), (36, 15), (9, 24), (3, 20), (15, 2), (24, 4), (28, 12), (33, 8), (19, 29), (7, 27), (29, 21), (12, 19), (27, 28), (18, 22), (29, 13), (6, 12), (32, 3), (13, 12), (18, 7), (7, 26), (12, 0), (9, 27), (14, 9), (14, 28), (6, 3), (27, 18), (25, 2), (8, 3), (37, 24), (34, 21), (19, 4), (12, 25), (8, 8), (1, 0), (33, 20), (19, 11), (9, 23), (20, 21), (11, 4), (31, 18), (1, 29), (13, 21), (12, 20), (7, 0), (37, 28), (15, 6), (11, 24), (1, 18), (12, 16), (32, 22), (8, 23), (20, 2), (23, 12), (8, 26), (30, 18), (27, 6), (31, 10), (1, 26), (16, 20), (9, 13), (29, 25), (4, 14), (37, 8), (29, 28), (34, 5), (14, 27), (36, 26), (26, 28), (10, 13), (11, 21), (36, 29), (14, 17), (27, 16), (25, 24), (5, 18), (22, 12), (29, 11), (13, 4), (15, 20), (35, 1), (17, 23), (17, 26), (36, 17), (5, 4), (8, 0), (31, 29), (31, 17), (26, 4), (6, 23), (24, 14), (38, 9), (22, 16), (23, 4), (23, 8), (13, 20), (11, 0), (38, 7), (22, 5), (15, 11), (30, 6), (15, 13), (24, 20), (35, 29), (36, 13), (2, 22), (13, 2), (31, 27), (1, 9), (14, 6), (26, 25), (4, 11), (37, 2), (32, 23), (37, 1), (31, 22), (0, 26), (16, 4), (31, 16), (22, 25), (4, 27), (15, 0), (33, 1), (4, 7), (13, 17), (17, 27), (34, 30), (11, 27), (21, 19), (2, 7), (10, 24), (7, 23), (19, 14), (16, 0), (24, 30), (33, 7), (13, 25), (33, 2), (6, 1), (1, 17), (30, 15), (11, 19), (34, 29), (26, 10), (1, 19), (9, 6), (12, 30), (10, 25), (35, 3), (3, 19), (29, 6), (4, 9), (25, 0), (8, 17), (37, 11), (26, 22), (9, 28), (18, 27), (0, 17), (4, 2), (3, 26), (28, 17), (7, 18), (24, 12), (36, 0), (7, 8), (1, 13), (14, 11), (36, 14), (10, 20), (10, 5), (29, 14), (26, 29), (8, 4), (1, 14), (37, 21), (16, 13), (23, 21), (28, 26), (35, 15), (21, 23), (30, 28), (25, 18), (32, 16), (19, 21), (19, 18), (8, 14), (36, 27), (25, 22), (23, 18), (32, 9), (15, 24), (16, 21), (6, 14), (7, 14), (13, 5), (11, 30), (37, 15), (27, 2), (38, 11), (37, 16), (12, 14), (19, 17), (35, 4), (2, 8), (18, 30), (2, 5), (25, 11), (21, 24), (13, 30), (35, 16), (16, 26), (17, 19), (14, 3), (8, 30), (9, 22), (36, 28), (10, 6), (4, 18), (6, 22), (3, 27), (29, 9), (19, 3), (35, 13), (38, 26), (13, 8), (7, 25), (24, 26), (32, 4), (2, 1), (38, 16), (27, 22), (18, 16), (4, 10), (13, 23), (18, 14), (31, 8), (8, 29), (9, 14), (22, 22), (2, 14), (18, 12), (6, 17), (34, 16), (20, 4), (17, 29), (34, 22), (33, 22), (16, 3), (32, 24), (1, 22), (3, 28), (3, 17), (24, 7), (37, 22), (27, 26), (14, 30), (26, 12), (11, 22), (17, 8), (1, 25), (8, 16), (6, 0), (10, 7), (25, 19), (25, 12), (23, 14), (5, 27), (1, 1), (22, 18), (18, 18), (17, 16), (11, 3), (32, 15), (13, 26), (23, 9), (5, 26), (1, 6), (5, 24), (9, 4), (35, 27), (11, 7), (1, 15), (9, 11), (27, 29), (8, 27), (14, 25), (6, 6), (13, 16), (13, 19), (16, 25), (21, 12), (34, 11), (2, 20), (14, 12), (2, 28), (32, 14), (20, 26), (28, 25), (11, 26), (14, 4), (35, 19), (6, 8), (13, 13), (10, 23), (25, 7), (32, 11), (23, 2), (5, 23), (15, 18), (24, 23), (36, 10), (32, 19), (5, 11), (17, 18), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631800", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (2, 28), (26, 4), (11, 21), (2, 30), (27, 14), (2, 23), (3, 10), (32, 14), (16, 4), (29, 22), (15, 13), (32, 27), (6, 13), (10, 2), (0, 3), (31, 3), (18, 26), (25, 3), (3, 4), (29, 5), (27, 20), (21, 6), (2, 11), (30, 27), (6, 22), (6, 14), (14, 14), (12, 20), (25, 23), (18, 21), (14, 9), (8, 4), (22, 30), (2, 22), (2, 29), (11, 2), (10, 28), (8, 10), (0, 26), (22, 14), (11, 10), (16, 1), (28, 9), (25, 7), (23, 2), (7, 12), (0, 16), (19, 27), (21, 25), (5, 21), (32, 8), (10, 22), (9, 11), (6, 20), (3, 22), (3, 23), (20, 10), (28, 15), (0, 30), (21, 14), (14, 29), (17, 2), (9, 21), (28, 29), (13, 19), (13, 13), (30, 2), (20, 15), (20, 12), (9, 24), (23, 28), (18, 20), (6, 25), (15, 17), (2, 19), (15, 8), (5, 0), (12, 21), (5, 15), (19, 26), (17, 21), (12, 2), (11, 4), (7, 3), (30, 28), (3, 15), (16, 5), (25, 6), (16, 17), (32, 2), (26, 7), (10, 16), (32, 0), (16, 12), (21, 12), (17, 4), (1, 10), (5, 30), (20, 1), (28, 4), (29, 10), (32, 21), (1, 3), (13, 25), (24, 21), (12, 15), (27, 28), (25, 5), (11, 17), (23, 16), (18, 0), (27, 27), (2, 1), (27, 3), (9, 4), (9, 9), (1, 4), (31, 7), (21, 2), (7, 2), (18, 19), (2, 14), (7, 29), (0, 10), (9, 1), (23, 22), (28, 28), (30, 21), (27, 7), (30, 12), (15, 2), (1, 5), (3, 27), (21, 4), (0, 15), (18, 27), (6, 15), (5, 2), (8, 17), (13, 28), (3, 14), (24, 8), (3, 1), (7, 1), (4, 26), (2, 8), (5, 16), (22, 18), (19, 8), (18, 22), (26, 25), (19, 6), (2, 20), (5, 23), (25, 26), (8, 30), (31, 9), (0, 6), (12, 14), (0, 1), (13, 26), (29, 12), (2, 18), (25, 0), (27, 22), (3, 8), (13, 20), (8, 14), (27, 21), (18, 9), (4, 30), (28, 8), (6, 16), (15, 21), (8, 18), (2, 6), (8, 12), (9, 18), (1, 29), (3, 7), (0, 21), (11, 9), (0, 13), (14, 1), (23, 13), (29, 14), (28, 19), (27, 13), (24, 0), (21, 29), (21, 21), (31, 0), (8, 9), (9, 0), (28, 21), (25, 16), (24, 6), (21, 1), (20, 18), (25, 11), (20, 5), (6, 27), (27, 16), (26, 17), (10, 9), (0, 8), (18, 10), (24, 13), (9, 14), (11, 20), (7, 9), (6, 5), (10, 29), (11, 12), (30, 26), (4, 3), (10, 20), (23, 7), (28, 23), (16, 22), (3, 21), (6, 29), (10, 15), (24, 3), (26, 9), (12, 25), (4, 21), (27, 24), (0, 11), (12, 9), (25, 18), (21, 11), (16, 16), (29, 1), (29, 15), (16, 7), (30, 14), (30, 11), (25, 1), (6, 7), (7, 30), (4, 2), (20, 14), (15, 15), (6, 28), (7, 20), (1, 12), (15, 10), (0, 24), (27, 4), (14, 8), (12, 28), (3, 29), (3, 18), (16, 8), (25, 12), (31, 19), (27, 26), (6, 3), (21, 20), (5, 6), (9, 19), (17, 0), (3, 16), (12, 29), (17, 17), (23, 6), (6, 10), (9, 7), (30, 13), (2, 27), (20, 26), (22, 20), (8, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141000", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 10), (25, 3), (11, 5), (15, 10), (27, 17), (5, 11), (18, 6), (13, 34), (15, 20), (26, 27), (10, 21), (17, 30), (16, 33), (21, 30), (21, 7), (2, 16), (14, 8), (21, 31), (28, 16), (9, 0), (19, 2), (15, 3), (7, 14), (12, 11), (5, 30), (6, 27), (6, 34), (21, 11), (26, 21), (6, 5), (7, 20), (6, 32), (27, 31), (23, 19), (18, 3), (5, 21), (13, 1), (10, 1), (29, 10), (5, 6), (1, 28), (6, 14), (17, 19), (5, 0), (21, 21), (13, 24), (4, 17), (24, 26), (4, 2), (25, 22), (27, 11), (12, 12), (12, 1), (27, 24), (5, 5), (6, 30), (2, 5), (19, 4), (24, 22), (11, 1), (27, 2), (25, 25), (22, 23), (23, 20), (19, 33), (23, 22), (18, 14), (22, 27), (14, 21), (5, 15), (7, 33), (0, 18), (23, 30), (7, 25), (21, 9), (9, 3), (4, 13), (23, 31), (28, 6), (10, 23), (25, 14), (29, 1), (22, 9), (4, 20), (22, 21), (3, 4), (21, 14), (1, 20), (13, 2), (15, 29), (10, 27), (18, 28), (8, 21), (16, 4), (10, 26), (13, 25), (13, 14), (5, 28), (15, 8), (28, 33), (26, 13), (26, 20), (26, 1), (16, 2), (16, 20), (25, 8), (7, 6), (21, 6), (9, 26), (24, 9), (11, 2), (14, 32), (15, 19), (10, 24), (0, 12), (28, 15), (24, 17), (3, 29), (25, 4), (6, 17), (23, 14), (14, 23), (5, 26), (13, 11), (15, 25), (4, 16), (28, 20), (23, 23), (15, 1), (0, 10), (26, 12), (14, 5), (0, 16), (0, 3), (12, 4), (13, 6), (16, 27), (9, 10), (11, 31), (25, 16), (11, 13), (24, 6), (0, 14), (28, 26), (27, 16), (8, 20), (6, 2), (2, 13), (20, 3), (23, 15), (26, 22), (17, 7), (0, 32), (1, 15), (2, 34), (29, 23), (12, 33), (25, 1), (10, 5), (8, 10), (29, 5), (18, 8), (0, 23), (4, 1), (9, 23), (6, 19), (29, 22), (11, 34), (5, 32), (28, 31), (2, 4), (24, 30), (14, 1), (3, 23), (16, 1), (26, 0), (5, 24), (14, 10), (17, 21), (23, 5), (20, 29), (18, 25), (5, 3), (4, 14), (26, 25), (19, 0), (11, 29), (5, 16), (5, 17), (23, 32), (0, 28), (22, 28), (19, 26), (7, 23), (9, 16), (22, 16), (11, 24), (19, 7), (13, 31), (14, 14), (15, 12), (18, 11), (27, 26), (28, 0), (3, 18), (2, 10), (7, 7), (7, 17), (2, 2), (27, 1), (4, 5), (4, 10), (14, 0), (8, 0), (17, 5), (21, 2), (18, 18), (11, 11), (4, 29), (23, 17), (24, 25), (27, 19), (4, 19), (25, 15), (4, 28), (22, 2), (5, 22), (28, 10), (3, 27), (11, 25), (9, 34), (15, 31), (16, 23), (3, 7), (20, 8), (6, 28), (25, 7), (23, 10), (17, 8), (5, 1), (18, 33), (26, 23), (0, 30), (15, 16), (8, 6), (27, 5), (18, 32), (6, 7), (0, 19), (17, 15), (8, 13), (13, 28), (26, 33), (25, 20), (23, 9), (26, 7), (5, 12), (15, 18), (13, 17), (19, 3), (19, 32), (25, 31), (14, 13), (24, 12), (10, 8), (25, 12), (2, 14), (18, 2), (10, 19), (12, 34), (10, 17), (1, 9), (13, 29), (7, 10), (28, 21), (28, 12), (22, 25), (0, 29), (21, 25), (11, 16), (13, 30), (27, 9), (10, 16), (29, 17), (14, 12), (1, 31), (10, 3), (28, 17), (11, 19), (26, 4), (24, 31), (13, 8), (23, 27), (16, 7), (23, 29), (12, 32), (26, 5), (24, 8), (9, 25), (14, 20), (3, 17), (12, 27), (21, 20), (17, 27), (19, 8), (0, 17), (19, 5), (3, 9), (12, 13), (14, 29), (10, 29), (17, 10), (17, 23), (17, 26), (20, 1), (13, 15), (11, 26), (28, 9), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315900", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), 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), (4, 26), (27, 21), (26, 0), (12, 12), (6, 6), (14, 21), (27, 5), (33, 14), (32, 13), (17, 16), (12, 2), (29, 30), (11, 32), (11, 3), (11, 21), (13, 24), (30, 32), (11, 26), (3, 19), (17, 14), (31, 2), (4, 0), (17, 1), (22, 6), (12, 19), (3, 8), (16, 25), (8, 20), (16, 32), (10, 29), (11, 9), (23, 15), (13, 5), (33, 24), (26, 23), (4, 31), (21, 5), (20, 10), (19, 3), (31, 14), (6, 17), (23, 21), (12, 7), (17, 6), (15, 11), (15, 4), (7, 30), (19, 2), (18, 4), (5, 25), (18, 15), (14, 15), (9, 7), (12, 9), (11, 28), (15, 28), (24, 14), (13, 9), (13, 14), (22, 31), (6, 25), (30, 2), (29, 26), (29, 28), (20, 15), (6, 0), (33, 18), (10, 7), (20, 13), (29, 5), (29, 32), (15, 13), (12, 5), (26, 7), (7, 14), (10, 22), (27, 18), (15, 3), (13, 12), (18, 13), (25, 26), (17, 13), (12, 15), (23, 32), (10, 17), (30, 6), (21, 29), (1, 12), (11, 25), (29, 0), (16, 3), (30, 21), (11, 12), (3, 0), (16, 31), (27, 2), (18, 12), (5, 2), (28, 0), (25, 0), (29, 1), (7, 7), (22, 20), (13, 3), (27, 8), (15, 24), (33, 1), (4, 5), (2, 3), (27, 31), (25, 31), (8, 9), (7, 5), (6, 28), (26, 2), (16, 9), (13, 30), (19, 27), (16, 15), (12, 13), (6, 21), (14, 26), (3, 11), (6, 22), (2, 17), (17, 4), (33, 20), (6, 16), (14, 5), (31, 19), (30, 30), (1, 16), (7, 29), (3, 26), (28, 16), (0, 9), (20, 8), (8, 2), (29, 3), (15, 29), (14, 28), (30, 18), (2, 20), (20, 30), (18, 26), (11, 0), (14, 7), (11, 27), (14, 4), (25, 2), (4, 27), (20, 28), (26, 26), (23, 11), (0, 19), (21, 12), (31, 22), (31, 7), (21, 25), (10, 14), (23, 18), (30, 15), (11, 6), (6, 4), (26, 3), (0, 28), (3, 31), (21, 21), (14, 10), (22, 9), (5, 17), (8, 18), (5, 27), (19, 0), (18, 9), (32, 18), (0, 31), (17, 8), (0, 11), (28, 32), (31, 27), (31, 30), (0, 8), (4, 29), (7, 23), (24, 5), (27, 6), (33, 19), (32, 1), (28, 1), (4, 16), (26, 9), (31, 21), (6, 5), (5, 32), (7, 20), (30, 22), (32, 17), (31, 15), (10, 21), (26, 18), (14, 25), (3, 2), (32, 0), (32, 3), (5, 24), (21, 4), (12, 6), (13, 6), (16, 28), (20, 32), (10, 24), (8, 13), (10, 2), (33, 0), (25, 6), (29, 23), (28, 9), (31, 31), (24, 1), (30, 25), (21, 7), (13, 28), (8, 27), (24, 22), (26, 13), (2, 18), (25, 5), (0, 24), (20, 19), (1, 1), (6, 14), (9, 26), (12, 20), (9, 21), (23, 19), (31, 29), (28, 20), (27, 14), (17, 25), (33, 2), (22, 24), (9, 24), (7, 25), (4, 13), (14, 27), (4, 15), (25, 32), (22, 25), (27, 10), (31, 32), (20, 20), (3, 28), (28, 23), (32, 28), (29, 7), (18, 14), (3, 18), (0, 1), (27, 15), (14, 31), (32, 26), (8, 3), (5, 3), (3, 24), (0, 29), (19, 28), (15, 5), (24, 23), (11, 8), (28, 2), (5, 30), (19, 5), (11, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "471988", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 34), (25, 28), (0, 20), (27, 22), (19, 23), (24, 22), (29, 30), (25, 10), (15, 18), (18, 1), (0, 35), (27, 36), (37, 13), (14, 22), (22, 16), (8, 16), (15, 25), (21, 13), (1, 27), (23, 22), (27, 4), (38, 7), (23, 16), (12, 14), (24, 37), (16, 12), (12, 36), (7, 34), (27, 20), (20, 2), (26, 9), (13, 9), (6, 24), (29, 27), (26, 17), (14, 25), (6, 6), (19, 22), (20, 18), (35, 9), (36, 34), (29, 0), (6, 27), (14, 16), (28, 0), (6, 5), (7, 1), (14, 20), (23, 11), (15, 5), (10, 5), (29, 28), (9, 9), (4, 32), (21, 30), (16, 19), (4, 23), (17, 11), (36, 36), (28, 36), (6, 9), (30, 17), (6, 38), (9, 27), (14, 29), (5, 4), (31, 36), (26, 2), (10, 12), (23, 28), (17, 4), (6, 21), (36, 28), (23, 4), (16, 15), (5, 17), (37, 7), (10, 7), (38, 36), (24, 18), (36, 35), (20, 28), (9, 30), (20, 23), (26, 38), (22, 19), (24, 33), (24, 19), (37, 9), (34, 12), (5, 38), (23, 33), (29, 20), (9, 10), (15, 27), (6, 11), (29, 35), (0, 22), (29, 25), (13, 4), (5, 26), (12, 24), (35, 29), (29, 7), (28, 32), (30, 15), (37, 8), (36, 33), (38, 9), (6, 14), (17, 21), (4, 3), (0, 27), (3, 25), (12, 2), (19, 30), (38, 2), (32, 34), (15, 34), (10, 17), (18, 23), (5, 31), (35, 0), (12, 3), (33, 31), (26, 19), (33, 8), (27, 28), (16, 37), (6, 7), (27, 10), (13, 8), (28, 30), (22, 13), (23, 18), (13, 35), (33, 7), (1, 25), (26, 28), (12, 0), (25, 11), (31, 1), (22, 7), (38, 19), (31, 4), (4, 18), (33, 17), (26, 29), (7, 23), (0, 10), (6, 30), (33, 4), (13, 18), (9, 4), (33, 34), (16, 9), (11, 15), (13, 34), (6, 1), (19, 12), (4, 37), (10, 6), (19, 27), (4, 8), (12, 35), (21, 25), (35, 13), (14, 33), (6, 8), (25, 5), (31, 26), (0, 12), (22, 29), (8, 28), (7, 11), (4, 34), (4, 20), (35, 6), (18, 0), (1, 4), (2, 14), (0, 5), (10, 4), (4, 30), (37, 34), (2, 9), (20, 5), (35, 8), (6, 28), (13, 36), (19, 36), (10, 24), (27, 11), (34, 13), (25, 4), (17, 36), (16, 21), (10, 14), (1, 19), (30, 38), (38, 16), (5, 16), (28, 13), (30, 33), (28, 27), (12, 38), (24, 29), (17, 9), (14, 6), (27, 7), (8, 12), (32, 13), (27, 1), (33, 16), (9, 22), (21, 32), (16, 4), (37, 20), (20, 8), (20, 33), (3, 31), (14, 1), (0, 19), (23, 36), (28, 8), (3, 11), (23, 9), (17, 28), (15, 19), (37, 6), (1, 3), (32, 25), (4, 19), (18, 34), (8, 26), (22, 14), (28, 34), (10, 37), (28, 16), (14, 11), (30, 37), (36, 7), (10, 34), (8, 18), (5, 35), (24, 15), (33, 23), (4, 9), (20, 27), (6, 13), (30, 27), (33, 11), (33, 27), (37, 4), (33, 14), (32, 10), (9, 36), (10, 19), (8, 9), (7, 22), (21, 15), (19, 17), (21, 17), (17, 3), (6, 36), (30, 2), (37, 3), (25, 3), (34, 6), (38, 4), (23, 1), (2, 11), (26, 11), (15, 24), (13, 23), (0, 21), (25, 9), (6, 32), (19, 11), (28, 11), (36, 25), (35, 27), (18, 2), (17, 33), (36, 3), (24, 2), (4, 31), (35, 34), (3, 9), (11, 6), (34, 14), (2, 26), (9, 14), (24, 17), (19, 9), (2, 3), (25, 8), (23, 17), (14, 23), (37, 30), (8, 38), (26, 8), (4, 28), (18, 30), (2, 2), (12, 11), (25, 13), (24, 38), (14, 19), (16, 20), (12, 8), (38, 20), (38, 6), (11, 18), (4, 35), (14, 32), (36, 6), (19, 13), (6, 10), (21, 3), (32, 16), (7, 14), (29, 5), (36, 22), (9, 35), (34, 27), (7, 26), (23, 23), (24, 4), (25, 17), (16, 36), (20, 12), (31, 33), (25, 15), (38, 22), (24, 16), (21, 28), (12, 13), (0, 26), (30, 13), (1, 26), (26, 21), (14, 35), (17, 12), (13, 2), (18, 3), (30, 23), (6, 31), (4, 2), (12, 7), (4, 15), (0, 23), (27, 16), (37, 22), (21, 24), (14, 0), (23, 5), (22, 17), (30, 6), (26, 12), (7, 21), (20, 7), (31, 10), (35, 26), (11, 38), (2, 19), (35, 37), (36, 11), (12, 23), (3, 36), (16, 5), (28, 35), (29, 26), (31, 35), (19, 31), (29, 13), (4, 25), (6, 0), (26, 15), (33, 13), (18, 6), (34, 18), (11, 31), (36, 5), (34, 1), (12, 5), (38, 33), (19, 26), (26, 33), (33, 2), (1, 14), (32, 3), (24, 27), (19, 33), (9, 37), (11, 27), (10, 38), (6, 4), (24, 14), (33, 25), (37, 17), (37, 28), (24, 1), (15, 10), (24, 35), (38, 31), (23, 35), (33, 9), (11, 1), (26, 5), (5, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638928", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (29, 13), (22, 30), (27, 26), (4, 28), (17, 30), (29, 15), (6, 3), (28, 7), (28, 17), (23, 15), (8, 7), (14, 30), (12, 21), (4, 23), (9, 8), (28, 9), (31, 31), (8, 8), (33, 3), (4, 16), (21, 25), (16, 10), (5, 30), (31, 9), (24, 26), (16, 8), (29, 24), (11, 16), (4, 4), (12, 0), (9, 31), (6, 31), (15, 10), (16, 24), (15, 0), (10, 3), (7, 7), (3, 11), (12, 25), (32, 31), (11, 12), (18, 31), (23, 10), (26, 23), (28, 10), (8, 11), (21, 11), (4, 12), (8, 20), (22, 32), (17, 4), (19, 19), (31, 26), (11, 0), (1, 25), (6, 10), (5, 25), (15, 21), (14, 1), (14, 2), (4, 27), (34, 0), (14, 27), (11, 13), (5, 23), (0, 11), (27, 1), (6, 7), (0, 2), (13, 17), (4, 6), (13, 15), (2, 15), (26, 31), (0, 9), (22, 18), (18, 32), (32, 30), (34, 20), (9, 23), (32, 9), (16, 32), (7, 22), (0, 32), (22, 24), (11, 18), (18, 19), (22, 15), (22, 10), (19, 4), (20, 22), (32, 20), (31, 6), (32, 16), (15, 19), (10, 30), (26, 29), (18, 6), (21, 31), (17, 14), (11, 2), (23, 23), (5, 9), (31, 11), (6, 5), (29, 2), (33, 16), (12, 15), (30, 4), (1, 32), (7, 2), (24, 23), (5, 15), (7, 0), (6, 32), (34, 12), (12, 1), (24, 19), (0, 24), (27, 4), (30, 24), (6, 18), (18, 9), (16, 15), (13, 20), (8, 19), (26, 3), (19, 3), (21, 19), (6, 30), (8, 4), (30, 32), (20, 6), (14, 31), (28, 14), (28, 27), (14, 4), (16, 17), (15, 16), (24, 18), (2, 26), (0, 14), (1, 26), (27, 30), (32, 10), (4, 31), (25, 11), (10, 20), (23, 17), (31, 20), (21, 6), (30, 26), (0, 21), (20, 23), (18, 13), (25, 21), (3, 19), (12, 32), (29, 21), (29, 6), (33, 26), (34, 16), (5, 18), (6, 11), (34, 9), (8, 16), (10, 27), (34, 21), (14, 20), (22, 23), (23, 11), (22, 9), (11, 14), (8, 25), (6, 0), (34, 1), (24, 6), (26, 11), (25, 12), (30, 15), (4, 29), (29, 1), (20, 27), (20, 30), (27, 23), (3, 30), (21, 32), (33, 22), (26, 6), (16, 7), (3, 18), (13, 10), (3, 31), (6, 17), (21, 14), (21, 29), (18, 4), (29, 14), (10, 10), (2, 7), (15, 11), (14, 11), (31, 24), (14, 8), (20, 14), (26, 27), (23, 8), (22, 19), (29, 18), (8, 1), (17, 21), (18, 24), (21, 30), (14, 9), (9, 25), (2, 28), (27, 31), (0, 30), (3, 17), (28, 22), (15, 14), (23, 19), (34, 30), (24, 21), (27, 5), (23, 30), (7, 14), (7, 17), (19, 7), (19, 6), (3, 6), (31, 10), (9, 6), (0, 26), (10, 29), (9, 28), (28, 12), (27, 24), (2, 29), (8, 30), (26, 20), (1, 13), (7, 19), (17, 10), (10, 16), (12, 11), (12, 28), (2, 23), (13, 32), (5, 6), (4, 15), (7, 6), (2, 17), (10, 19), (31, 5), (29, 10), (34, 25), (4, 1), (14, 0), (28, 24), (15, 15), (12, 27), (2, 20), (9, 3), (11, 10), (2, 19), (15, 32), (10, 6), (19, 2), (20, 7), (0, 19), (7, 23), (2, 2), (3, 12), (28, 32), (31, 4), (16, 19), (1, 2), (20, 9), (17, 28), (20, 10), (22, 16), (6, 15), (34, 10), (28, 25), (29, 29), (11, 30), (9, 0), (6, 14), (33, 6), (5, 11), (1, 20), (24, 11), (4, 19), (21, 12), (28, 19), (3, 22), (4, 0), (13, 4), (3, 0), (27, 21), (14, 17), (27, 8), (7, 21), (21, 8), (25, 2), (14, 18), (26, 12), (11, 9), (21, 2), (2, 27), (24, 4), (17, 5), (9, 11), (26, 8), (1, 30), (20, 11), (14, 32), (6, 12), (30, 31), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787968", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 32), (31, 20), (19, 5), (22, 4), (5, 13), (11, 32), (21, 12), (15, 29), (0, 10), (2, 17), (28, 13), (14, 16), (29, 12), (25, 1), (20, 31), (16, 10), (4, 1), (34, 8), (1, 0), (6, 26), (32, 13), (27, 11), (16, 31), (24, 29), (22, 22), (18, 20), (29, 11), (10, 6), (31, 1), (26, 8), (22, 3), (5, 3), (31, 10), (0, 28), (18, 22), (1, 22), (27, 5), (20, 10), (2, 22), (24, 26), (33, 1), (1, 15), (13, 3), (1, 1), (18, 15), (23, 1), (3, 15), (10, 27), (18, 27), (15, 23), (20, 16), (6, 14), (4, 3), (28, 31), (12, 30), (32, 17), (8, 24), (34, 21), (4, 5), (33, 16), (26, 28), (33, 21), (18, 14), (30, 24), (1, 2), (20, 4), (23, 10), (1, 17), (3, 18), (8, 27), (24, 24), (16, 28), (19, 9), (28, 1), (5, 14), (25, 0), (16, 12), (34, 1), (29, 10), (27, 22), (27, 27), (34, 20), (11, 6), (23, 14), (14, 10), (15, 19), (27, 25), (18, 10), (22, 21), (26, 26), (0, 30), (26, 24), (30, 7), (32, 22), (26, 17), (0, 29), (27, 8), (7, 25), (6, 32), (9, 27), (12, 31), (35, 25), (29, 13), (35, 8), (5, 6), (22, 7), (23, 32), (15, 15), (15, 1), (21, 28), (23, 29), (33, 2), (30, 26), (17, 16), (30, 25), (16, 21), (34, 27), (21, 15), (35, 15), (20, 5), (14, 19), (25, 18), (34, 31), (20, 30), (19, 10), (17, 20), (32, 2), (1, 21), (21, 6), (11, 31), (6, 20), (32, 14), (23, 30), (14, 9), (34, 12), (29, 30), (18, 7), (10, 21), (22, 23), (13, 23), (28, 17), (23, 11), (5, 12), (9, 6), (25, 23), (8, 25), (4, 20), (14, 22), (17, 26), (6, 27), (12, 7), (28, 11), (25, 12), (19, 21), (20, 9), (31, 12), (26, 20), (8, 12), (8, 16), (3, 2), (5, 18), (29, 20), (15, 14), (4, 8), (34, 6), (8, 17), (14, 8), (33, 0), (3, 12), (5, 29), (2, 20), (26, 22), (26, 21), (35, 23), (22, 2), (6, 18), (15, 3), (12, 27), (12, 5), (35, 7), (17, 24), (3, 25), (6, 0), (3, 8), (14, 32), (35, 14), (7, 22), (19, 29), (31, 24), (21, 16), (17, 30), (22, 12), (17, 31), (29, 23), (27, 17), (34, 17), (31, 27), (34, 29), (12, 15), (5, 1), (24, 4), (19, 14), (9, 13), (9, 11), (12, 20), (0, 15), (8, 13), (2, 24), (33, 17), (35, 9), (24, 28), (2, 28), (19, 2), (10, 14), (31, 7), (21, 17), (9, 9), (2, 27), (11, 17), (32, 25), (14, 20), (6, 31), (10, 25), (29, 27), (8, 3), (16, 3), (13, 26), (20, 12), (30, 31), (13, 0), (12, 23), (24, 16), (9, 32), (25, 24), (30, 32), (14, 18), (27, 32), (4, 27), (27, 24), (33, 23), (29, 0), (20, 26), (3, 0), (11, 21), (35, 18), (22, 32), (29, 2), (16, 20), (12, 1), (4, 24), (17, 18), (18, 17), (30, 3), (16, 32), (27, 10), (5, 17), (23, 6), (13, 2), (9, 0), (5, 11), (33, 18), (22, 13), (10, 9), (17, 15), (22, 31), (26, 27), (8, 8), (15, 32), (32, 15), (10, 16), (32, 3), (11, 22), (5, 26), (29, 29), (7, 13), (28, 15), (28, 14), (6, 16), (3, 11), (25, 26), (35, 4), (7, 4), (34, 16), (2, 8), (6, 22), (35, 29), (17, 19), (6, 1), (35, 20), (32, 29), (15, 12), (3, 5), (6, 15), (15, 18), (24, 3), (16, 13), (25, 25), (28, 30), (28, 10), (34, 30), (33, 7), (13, 13), (31, 8), (5, 10), (12, 28), (12, 21), (21, 13), (18, 2), (30, 30), (11, 13), (32, 21), (17, 1), (24, 0), (13, 27), (29, 15), (7, 7), (10, 13), (2, 16), (2, 32), (14, 13), (15, 27), (31, 2), (32, 5), (7, 9), (24, 22), (13, 31), (8, 7), (31, 17), (4, 9), (20, 25), (0, 5), (11, 5), (24, 32), (29, 16), (30, 16), (2, 25), (30, 11), (16, 7), (13, 6), (28, 29), (2, 26), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349272", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), 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), (2, 35), (26, 10), (35, 26), (17, 25), (19, 30), (21, 1), (26, 27), (14, 30), (24, 11), (32, 20), (21, 4), (3, 20), (29, 27), (7, 22), (16, 28), (5, 5), (28, 16), (23, 20), (17, 18), (26, 6), (24, 29), (10, 27), (7, 25), (11, 18), (26, 24), (30, 15), (22, 1), (5, 26), (15, 21), (8, 10), (3, 3), (33, 30), (10, 25), (26, 9), (15, 8), (11, 21), (8, 26), (0, 28), (25, 11), (19, 32), (1, 9), (7, 32), (4, 20), (6, 17), (24, 16), (33, 16), (11, 14), (26, 0), (18, 24), (28, 35), (23, 2), (4, 6), (9, 16), (32, 12), (11, 10), (4, 22), (3, 17), (9, 30), (22, 12), (5, 11), (16, 6), (27, 28), (19, 28), (32, 26), (14, 16), (21, 32), (31, 15), (8, 16), (26, 22), (15, 7), (19, 16), (31, 25), (18, 35), (24, 18), (0, 32), (2, 23), (25, 26), (0, 33), (6, 11), (22, 33), (14, 9), (11, 12), (7, 15), (35, 4), (19, 25), (18, 23), (2, 26), (5, 34), (32, 30), (29, 4), (23, 13), (27, 31), (29, 8), (35, 18), (26, 18), (19, 29), (22, 14), (11, 13), (32, 11), (0, 17), (20, 11), (15, 34), (35, 29), (9, 29), (33, 27), (33, 22), (15, 2), (21, 27), (21, 30), (11, 27), (17, 32), (1, 17), (13, 12), (14, 35), (8, 25), (0, 23), (25, 9), (10, 5), (20, 23), (35, 30), (13, 35), (35, 19), (20, 27), (6, 22), (9, 5), (9, 6), (19, 27), (1, 3), (26, 21), (21, 9), (18, 11), (20, 34), (2, 12), (22, 18), (27, 11), (13, 1), (7, 8), (17, 4), (25, 15), (15, 26), (30, 5), (30, 33), (1, 28), (18, 25), (7, 11), (23, 31), (21, 8), (25, 32), (10, 1), (26, 16), (4, 18), (35, 16), (11, 34), (34, 21), (6, 2), (10, 8), (10, 11), (30, 16), (7, 19), (6, 6), (7, 30), (32, 10), (29, 6), (1, 35), (2, 30), (27, 8), (17, 24), (25, 2), (2, 19), (6, 34), (15, 10), (0, 12), (32, 21), (14, 6), (12, 16), (4, 28), (22, 5), (25, 34), (27, 32), (10, 21), (2, 28), (13, 4), (25, 29), (17, 16), (14, 32), (17, 7), (16, 20), (29, 5), (3, 28), (35, 15), (28, 22), (3, 27), (18, 12), (17, 13), (30, 1), (13, 30), (33, 28), (26, 34), (20, 26), (1, 29), (11, 17), (22, 21), (12, 15), (14, 24), (24, 1), (14, 3), (12, 18), (35, 32), (14, 20), (25, 4), (31, 1), (3, 2), (29, 22), (11, 2), (17, 5), (0, 3), (23, 19), (6, 27), (22, 8), (17, 12), (18, 16), (30, 13), (34, 14), (5, 1), (1, 15), (6, 28), (15, 14), (25, 14), (28, 7), (21, 10), (13, 16), (12, 5), (3, 33), (28, 18), (11, 6), (16, 3), (3, 9), (15, 28), (24, 25), (30, 28), (27, 26), (24, 7), (8, 34), (5, 9), (35, 23), (20, 10), (19, 21), (5, 4), (23, 16), (16, 35), (0, 22), (21, 29), (29, 29), (3, 5), (10, 2), (5, 12), (2, 7), (20, 14), (21, 22), (20, 19), (1, 27), (8, 33), (4, 9), (11, 9), (19, 33), (28, 23), (32, 23), (35, 12), (29, 0), (13, 6), (25, 19), (11, 19), (21, 25), (1, 10), (30, 19), (22, 20), (34, 15), (24, 35), (16, 17), (27, 6), (30, 12), (9, 28), (17, 22), (2, 1), (15, 23), (23, 6), (13, 5), (22, 17), (26, 28), (3, 7), (3, 18), (25, 16), (1, 7), (20, 1), (14, 11), (22, 26), (19, 22), (5, 0), (5, 20), (21, 28), (14, 18), (29, 14), (33, 32), (31, 19), (35, 28), (14, 7), (4, 32), (9, 19), (0, 9), (10, 30), (20, 5), (5, 15), (18, 13), (25, 31), (16, 16), (3, 10), (25, 35), (11, 29), (32, 29), (14, 14), (15, 3), (12, 11), (35, 7), (19, 18), (1, 33), (11, 28), (29, 17), (22, 23), (5, 22), (17, 27), (35, 9), (13, 9), (12, 3), (34, 33), (10, 9), (20, 17), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "830592", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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), (24, 13), (9, 24), (14, 5), (19, 9), (15, 6), (33, 23), (16, 5), (27, 4), (18, 7), (29, 11), (20, 29), (4, 25), (2, 1), (26, 7), (15, 31), (20, 27), (31, 12), (10, 14), (3, 18), (27, 14), (30, 5), (10, 0), (25, 16), (8, 13), (23, 4), (11, 3), (14, 29), (27, 21), (30, 25), (30, 15), (26, 25), (34, 19), (25, 0), (26, 9), (6, 4), (17, 26), (22, 23), (2, 3), (15, 21), (3, 3), (21, 17), (12, 12), (22, 28), (19, 8), (13, 19), (34, 16), (31, 17), (18, 19), (1, 19), (29, 23), (20, 7), (30, 6), (2, 5), (31, 5), (27, 16), (9, 15), (27, 7), (30, 18), (15, 18), (1, 12), (22, 20), (28, 12), (34, 5), (1, 5), (28, 23), (29, 22), (24, 10), (2, 28), (8, 27), (15, 5), (9, 11), (21, 10), (31, 28), (26, 18), (8, 31), (17, 13), (4, 3), (33, 25), (17, 18), (11, 20), (4, 10), (10, 4), (3, 31), (17, 30), (14, 22), (31, 27), (6, 11), (2, 18), (30, 20), (10, 1), (30, 23), (15, 29), (31, 29), (5, 10), (29, 27), (34, 13), (6, 29), (34, 7), (22, 11), (13, 3), (0, 1), (0, 20), (7, 16), (13, 26), (33, 1), (12, 5), (30, 11), (31, 14), (22, 31), (20, 9), (28, 20), (3, 12), (31, 0), (6, 17), (12, 27), (12, 11), (20, 20), (16, 6), (15, 25), (30, 29), (25, 22), (1, 28), (3, 20), (11, 17), (29, 0), (2, 16), (0, 17), (0, 19), (6, 30), (24, 29), (3, 25), (27, 28), (19, 31), (13, 15), (32, 13), (21, 5), (31, 25), (27, 24), (17, 27), (26, 22), (6, 23), (11, 10), (19, 4), (21, 19), (6, 8), (31, 22), (6, 1), (19, 2), (34, 9), (10, 15), (30, 21), (10, 18), (26, 31), (5, 14), (34, 21), (26, 10), (0, 26), (30, 0), (0, 3), (7, 25), (19, 12), (13, 16), (10, 3), (13, 31), (21, 30), (29, 1), (28, 31), (32, 25), (12, 8), (14, 30), (16, 3), (5, 16), (21, 9), (33, 15), (20, 5), (16, 7), (5, 30), (33, 14), (14, 28), (28, 6), (16, 25), (19, 1), (12, 29), (19, 20), (23, 22), (7, 17), (6, 18), (25, 23), (22, 5), (16, 1), (12, 13), (18, 0), (23, 13), (1, 30), (30, 4), (29, 21), (4, 0), (23, 12), (11, 22), (3, 16), (9, 10), (8, 30), (0, 8), (6, 20), (25, 31), (17, 28), (0, 11), (29, 28), (18, 3), (4, 26), (3, 24), (20, 13), (11, 16), (0, 12), (27, 19), (15, 12), (4, 17), (23, 16), (3, 5), (27, 18), (1, 29), (4, 8), (10, 21), (33, 26), (7, 31), (18, 22), (27, 22), (30, 1), (28, 19), (1, 16), (9, 16), (1, 9), (6, 10), (24, 23), (4, 21), (24, 22), (15, 22), (13, 1), (7, 26), (3, 8), (0, 31), (11, 7), (18, 31), (1, 8), (30, 28), (33, 12), (27, 20), (7, 21), (24, 15), (22, 8), (28, 7), (9, 13), (4, 2), (10, 12), (23, 14), (28, 5), (0, 16), (30, 17), (6, 22), (23, 25), (14, 11), (4, 19), (4, 15), (31, 15), (34, 24), (5, 31), (28, 1), (8, 25), (7, 3), (17, 1), (14, 25), (22, 27), (18, 28), (16, 21), (7, 23), (33, 19), (29, 12), (0, 21), (33, 30), (9, 21), (22, 1), (16, 30), (23, 1), (31, 9), (1, 17), (17, 12), (26, 24), (31, 24), (25, 15), (19, 15), (5, 11), (26, 30), (11, 19), (9, 18), (32, 2), (31, 7), (11, 5), (32, 15), (32, 26), (13, 12), (27, 25), (1, 25), (8, 8), (28, 18), (1, 10), (28, 4), (1, 13), (24, 31), (17, 14), (11, 14), (6, 16), (25, 2), (25, 5), (20, 31), (22, 25), (7, 22), (32, 14), (28, 24), (10, 29), (20, 15), (21, 31), (28, 27), (15, 28), (19, 18), (22, 21), (34, 29), (9, 19), (3, 4), (0, 10), (24, 30), (6, 13), (22, 19), (15, 8), (13, 30), (25, 29), (10, 8), (28, 0), (34, 8), (26, 26), (31, 6), (18, 24), (28, 25), (4, 22), (33, 16), (28, 13), (0, 2), (2, 22), (24, 1), (19, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127008", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 23), (6, 0), (7, 22), (29, 17), (6, 12), (8, 31), (0, 18), (28, 23), (1, 31), (26, 7), (17, 8), (11, 10), (15, 0), (9, 26), (10, 6), (28, 34), (8, 8), (14, 18), (10, 28), (4, 34), (18, 3), (15, 13), (2, 14), (16, 3), (2, 2), (26, 21), (25, 26), (15, 1), (21, 0), (1, 14), (12, 18), (13, 14), (26, 30), (23, 5), (14, 6), (22, 17), (25, 21), (5, 6), (0, 26), (19, 34), (14, 20), (17, 33), (14, 1), (30, 30), (12, 11), (5, 19), (22, 12), (14, 32), (4, 5), (22, 30), (28, 6), (16, 19), (9, 13), (24, 7), (23, 23), (1, 0), (5, 16), (0, 32), (20, 7), (15, 3), (2, 34), (9, 20), (20, 11), (17, 20), (6, 33), (4, 0), (15, 30), (1, 13), (17, 22), (12, 24), (7, 12), (9, 6), (11, 1), (12, 9), (15, 18), (25, 32), (2, 18), (3, 18), (23, 7), (17, 0), (21, 13), (25, 18), (26, 5), (25, 13), (11, 11), (8, 20), (14, 33), (27, 6), (12, 15), (29, 13), (25, 27), (12, 31), (18, 19), (2, 31), (28, 21), (10, 18), (20, 16), (24, 12), (3, 26), (27, 17), (8, 16), (4, 6), (2, 20), (26, 18), (23, 33), (1, 32), (27, 22), (25, 25), (2, 9), (20, 29), (10, 4), (7, 18), (19, 23), (14, 8), (21, 10), (25, 17), (15, 25), (3, 20), (13, 34), (6, 26), (22, 27), (26, 20), (17, 31), (11, 7), (22, 22), (21, 6), (1, 23), (29, 10), (11, 24), (23, 6), (22, 6), (29, 20), (22, 18), (8, 7), (7, 15), (14, 34), (27, 31), (11, 5), (1, 27), (1, 24), (14, 17), (9, 19), (20, 18), (17, 5), (27, 2), (5, 27), (3, 7), (27, 25), (2, 21), (2, 19), (10, 21), (29, 29), (7, 3), (23, 11), (23, 17), (15, 31), (9, 28), (16, 26), (19, 25), (13, 23), (28, 18), (4, 9), (6, 15), (3, 30), (24, 23), (5, 10), (11, 32), (5, 5), (24, 3), (7, 6), (5, 33), (19, 20), (19, 10), (14, 15), (12, 20), (24, 13), (21, 31), (6, 22), (8, 2), (0, 6), (11, 19), (26, 26), (5, 20), (1, 5), (11, 2), (19, 11), (1, 18), (1, 29), (21, 3), (7, 21), (27, 7), (30, 0), (9, 27), (29, 8), (13, 26), (5, 29), (26, 10), (30, 29), (1, 25), (4, 1), (12, 34), (13, 13), (11, 33), (29, 3), (29, 12), (10, 2), (2, 10), (16, 32), (30, 26), (27, 14), (4, 11), (30, 19), (13, 20), (22, 14), (28, 4), (24, 18), (28, 32), (26, 15), (20, 26), (30, 10), (0, 30), (4, 18), (25, 28), (19, 9), (6, 21), (15, 28), (10, 9), (27, 26), (6, 11), (19, 16), (0, 23), (2, 13), (19, 5), (25, 5), (22, 13), (13, 10), (28, 20), (18, 25), (16, 13), (26, 34), (8, 14), (7, 26), (29, 21), (16, 24), (30, 11), (0, 15), (25, 12), (16, 29), (24, 19), (28, 1), (25, 14), (29, 1), (0, 28), (15, 22), (7, 34), (7, 14), (23, 18), (1, 2), (18, 20), (13, 29), (3, 24), (17, 7), (19, 3), (4, 24), (0, 33), (2, 1), (13, 6), (23, 10), (14, 10), (6, 27), (23, 34), (16, 0), (25, 9), (27, 23), (29, 33), (13, 16), (24, 34), (17, 10), (4, 2), (29, 16), (8, 32), (28, 29), (10, 29), (11, 31), (14, 28), (24, 28), (10, 7), (1, 6), (28, 25), (25, 11), (12, 1), (14, 16), (30, 4), (8, 12), (11, 13), (16, 15), (4, 17), (25, 2), (20, 25), (30, 6), (14, 21), (15, 5), (23, 8), (30, 27), (3, 31), (18, 17), (30, 9), (11, 9), (4, 20), (1, 10), (28, 11), (3, 5), (10, 27), (25, 10), (20, 22), (26, 31), (21, 28), (24, 25), (15, 7), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818496", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 18), (11, 26), (7, 5), (36, 25), (20, 22), (8, 0), (1, 7), (22, 32), (30, 27), (7, 3), (0, 20), (33, 4), (21, 17), (12, 8), (32, 25), (34, 34), (38, 14), (34, 7), (10, 12), (5, 30), (7, 18), (5, 22), (27, 24), (37, 28), (27, 20), (21, 1), (37, 9), (28, 28), (16, 20), (34, 17), (7, 12), (25, 1), (14, 17), (5, 9), (24, 27), (33, 27), (4, 21), (6, 27), (25, 24), (13, 26), (3, 30), (2, 13), (29, 28), (16, 32), (24, 33), (3, 8), (11, 9), (28, 4), (14, 18), (35, 7), (26, 27), (5, 25), (38, 20), (8, 28), (20, 6), (28, 11), (36, 24), (7, 13), (28, 18), (31, 27), (9, 1), (16, 18), (34, 19), (5, 4), (6, 33), (16, 2), (35, 12), (17, 14), (20, 32), (38, 2), (27, 27), (26, 33), (20, 30), (38, 10), (30, 8), (18, 27), (13, 20), (17, 20), (3, 3), (12, 34), (10, 26), (25, 16), (32, 23), (1, 28), (12, 4), (0, 2), (33, 20), (33, 10), (5, 12), (8, 19), (12, 29), (16, 22), (19, 5), (1, 29), (18, 30), (10, 0), (19, 18), (16, 21), (22, 21), (30, 7), (22, 8), (1, 13), (28, 30), (25, 18), (0, 32), (11, 6), (5, 10), (33, 33), (36, 20), (33, 1), (34, 3), (22, 16), (5, 21), (21, 6), (8, 8), (18, 31), (13, 22), (16, 30), (22, 3), (23, 23), (27, 4), (21, 27), (0, 17), (21, 33), (1, 10), (19, 1), (16, 23), (14, 16), (15, 14), (18, 12), (25, 19), (27, 26), (27, 29), (13, 14), (5, 5), (14, 29), (33, 17), (0, 28), (0, 10), (24, 25), (37, 15), (23, 24), (22, 15), (18, 10), (8, 25), (21, 8), (22, 0), (33, 8), (36, 0), (10, 5), (16, 8), (9, 18), (0, 12), (7, 22), (36, 13), (31, 33), (3, 25), (2, 30), (0, 4), (11, 24), (0, 11), (5, 26), (13, 11), (35, 20), (19, 20), (18, 22), (25, 15), (8, 12), (22, 26), (29, 30), (3, 23), (1, 22), (38, 17), (26, 21), (12, 7), (10, 27), (38, 33), (4, 7), (19, 3), (5, 32), (1, 23), (30, 20), (21, 26), (23, 11), (29, 27), (7, 2), (12, 24), (34, 4), (5, 31), (8, 7), (13, 1), (29, 18), (36, 32), (25, 0), (16, 16), (20, 10), (2, 4), (34, 30), (0, 21), (29, 4), (6, 35), (33, 28), (30, 34), (15, 4), (28, 31), (18, 19), (1, 19), (20, 20), (18, 0), (37, 22), (17, 8), (1, 25), (26, 29), (29, 33), (14, 28), (38, 27), (30, 6), (2, 34), (36, 7), (30, 31), (32, 16), (32, 17), (19, 10), (25, 4), (35, 9), (2, 28), (5, 7), (19, 24), (13, 32), (25, 22), (6, 16), (21, 0), (3, 28), (8, 3), (16, 15), (30, 21), (15, 11), (0, 34), (24, 17), (13, 4), (12, 19), (1, 35), (29, 0), (0, 22), (30, 30), (30, 25), (20, 27), (10, 16), (15, 26), (15, 0), (29, 15), (0, 6), (30, 33), (27, 23), (30, 29), (37, 10), (28, 3), (19, 7), (31, 6), (26, 0), (24, 28), (2, 22), (1, 24), (30, 11), (4, 19), (8, 34), (25, 13), (24, 9), (24, 35), (26, 15), (27, 1), (6, 20), (27, 31), (20, 3), (24, 18), (1, 8), (37, 31), (1, 0), (30, 28), (33, 16), (10, 15), (20, 1), (31, 10), (6, 24), (6, 15), (11, 11), (26, 19), (7, 0), (18, 5), (2, 14), (38, 34), (28, 15), (23, 8), (12, 5), (3, 7), (17, 5), (21, 13), (6, 3), (3, 29), (1, 26), (16, 1), (13, 33), (17, 6), (27, 32), (21, 18), (1, 18), (33, 25), (13, 9), (33, 5), (25, 33), (23, 25), (25, 31), (26, 34), (16, 7), (36, 16), (12, 28), (32, 14), (8, 33), (8, 20), (0, 14), (36, 35), (8, 9), (32, 21), (1, 11), (17, 32), (2, 20), (15, 24), (2, 5), (17, 15), (5, 33), (29, 32), (17, 16), (22, 12), (2, 24), (28, 26), (20, 33), (10, 28), (14, 22), (21, 19), (25, 11), (5, 18), (10, 8), (11, 4), (15, 5), (18, 17), (2, 12), (23, 6), (32, 28), (31, 15), (8, 17), (14, 26), (7, 9), (21, 16), (33, 11), (38, 13), (23, 35), (7, 14), (17, 11), (35, 35), (19, 16), (6, 19), (37, 7), (27, 6), (2, 16), (5, 0), (6, 1), (8, 35), (24, 29), (29, 31), (20, 23), (3, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "765072", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (35, 13), (15, 25), (14, 26), (25, 20), (30, 35), (29, 15), (8, 6), (16, 2), (10, 3), (30, 37), (12, 13), (36, 31), (20, 7), (0, 13), (23, 6), (32, 20), (22, 20), (14, 8), (27, 31), (6, 23), (24, 14), (28, 14), (19, 8), (6, 7), (23, 31), (30, 30), (2, 28), (27, 34), (31, 27), (9, 1), (12, 20), (33, 11), (15, 17), (0, 3), (29, 8), (7, 23), (3, 32), (7, 10), (6, 8), (20, 8), (26, 18), (35, 10), (9, 26), (24, 10), (5, 35), (16, 37), (36, 11), (10, 18), (34, 26), (3, 3), (0, 31), (16, 20), (24, 21), (19, 32), (21, 22), (8, 25), (35, 11), (32, 34), (32, 27), (12, 18), (30, 2), (2, 32), (22, 2), (24, 2), (19, 22), (21, 3), (8, 37), (7, 30), (7, 24), (10, 12), (28, 1), (17, 28), (26, 12), (8, 21), (16, 21), (4, 18), (36, 36), (29, 25), (6, 19), (36, 23), (16, 4), (18, 21), (2, 22), (9, 13), (33, 14), (25, 12), (7, 16), (18, 35), (32, 35), (27, 33), (33, 30), (10, 28), (18, 13), (32, 4), (3, 7), (24, 15), (4, 30), (30, 19), (14, 11), (28, 10), (32, 33), (26, 15), (31, 36), (33, 15), (31, 37), (3, 27), (34, 18), (27, 29), (26, 20), (31, 30), (10, 30), (19, 9), (26, 28), (2, 1), (36, 20), (4, 11), (23, 12), (9, 24), (31, 12), (20, 23), (6, 15), (6, 4), (36, 4), (0, 22), (19, 23), (6, 35), (14, 30), (0, 2), (25, 30), (2, 15), (16, 25), (26, 11), (18, 5), (19, 11), (6, 36), (22, 3), (18, 24), (6, 21), (11, 34), (17, 33), (19, 26), (11, 18), (18, 14), (26, 17), (33, 37), (22, 35), (11, 16), (30, 4), (20, 26), (12, 12), (1, 13), (19, 10), (11, 27), (11, 32), (36, 9), (36, 6), (0, 21), (32, 18), (8, 9), (0, 27), (33, 13), (20, 22), (9, 9), (1, 8), (2, 21), (8, 29), (30, 34), (15, 14), (5, 21), (32, 12), (19, 36), (23, 23), (13, 3), (18, 12), (22, 16), (7, 19), (1, 28), (28, 9), (28, 18), (5, 29), (12, 8), (23, 35), (21, 8), (23, 13), (24, 24), (23, 19), (15, 12), (25, 11), (22, 18), (9, 16), (17, 7), (32, 28), (5, 5), (17, 35), (20, 20), (20, 6), (36, 0), (0, 30), (18, 23), (30, 31), (9, 5), (11, 1), (13, 20), (4, 26), (2, 18), (17, 1), (32, 25), (13, 22), (21, 27), (35, 35), (16, 35), (21, 36), (0, 20), (4, 34), (0, 10), (10, 13), (9, 6), (20, 24), (13, 1), (35, 18), (0, 5), (14, 32), (30, 32), (14, 29), (11, 6), (19, 5), (6, 25), (18, 29), (0, 32), (6, 34), (5, 17), (8, 31), (6, 18), (2, 12), (8, 32), (8, 13), (1, 26), (8, 22), (33, 32), (6, 5), (0, 8), (8, 3), (12, 10), (2, 14), (34, 30), (19, 17), (19, 21), (23, 14), (17, 14), (4, 13), (35, 32), (2, 4), (6, 1), (9, 15), (20, 17), (14, 19), (33, 8), (18, 6), (36, 3), (6, 33), (0, 11), (16, 7), (22, 28), (23, 20), (35, 17), (16, 33), (11, 24), (0, 26), (34, 14), (27, 6), (21, 11), (34, 21), (1, 36), (6, 10), (18, 10), (23, 26), (11, 31), (1, 32), (25, 4), (10, 4), (20, 12), (28, 37), (0, 17), (21, 5), (29, 9), (24, 18), (26, 24), (2, 20), (4, 9), (7, 28), (18, 37), (2, 37), (5, 6), (21, 33), (4, 29), (27, 32), (20, 10), (13, 28), (31, 21), (29, 5), (3, 35), (1, 0), (22, 25), (7, 14), (28, 3), (33, 27), (3, 37), (10, 2), (1, 35), (22, 37), (1, 24), (22, 27), (31, 28), (12, 28), (6, 20), (1, 9), (16, 23), (9, 19), (5, 28), (34, 29), (7, 7), (28, 8), (12, 36), (19, 30), (35, 26), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "708720", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 30), (2, 25), (22, 3), (5, 14), (28, 0), (10, 17), (16, 22), (6, 13), (3, 26), (15, 26), (5, 19), (16, 17), (15, 20), (26, 31), (12, 14), (17, 9), (22, 28), (2, 12), (23, 22), (28, 7), (7, 21), (26, 13), (26, 7), (23, 14), (25, 27), (6, 4), (16, 29), (6, 20), (5, 30), (11, 0), (14, 24), (17, 14), (25, 31), (21, 19), (5, 3), (20, 3), (1, 2), (3, 21), (13, 13), (17, 28), (16, 1), (9, 2), (21, 15), (15, 9), (12, 3), (7, 23), (28, 16), (2, 30), (5, 6), (18, 14), (7, 7), (3, 23), (19, 2), (3, 31), (3, 8), (25, 14), (6, 2), (10, 12), (5, 2), (4, 23), (22, 30), (11, 29), (15, 31), (28, 19), (4, 20), (1, 19), (16, 31), (4, 9), (23, 8), (21, 29), (26, 2), (24, 31), (11, 2), (6, 30), (3, 6), (6, 25), (12, 15), (14, 29), (28, 22), (26, 29), (15, 0), (22, 25), (13, 28), (7, 29), (21, 26), (0, 16), (0, 26), (17, 16), (15, 30), (26, 14), (2, 18), (28, 31), (24, 14), (5, 9), (14, 15), (21, 14), (16, 3), (6, 7), (9, 21), (9, 6), (5, 5), (22, 6), (16, 0), (4, 18), (2, 23), (22, 5), (24, 3), (16, 23), (26, 30), (1, 16), (29, 13), (13, 27), (11, 18), (25, 0), (8, 18), (16, 20), (24, 4), (29, 18), (16, 8), (20, 18), (29, 21), (17, 22), (24, 23), (1, 30), (3, 28), (9, 8), (7, 15), (25, 24), (26, 12), (4, 2), (19, 24), (0, 22), (0, 11), (27, 20), (18, 0), (1, 20), (21, 16), (20, 29), (29, 2), (2, 27), (20, 30), (23, 1), (6, 0), (29, 7), (24, 15), (2, 29), (20, 2), (9, 28), (9, 22), (22, 19), (25, 8), (3, 29), (3, 12), (2, 19), (23, 28), (14, 4), (2, 15), (9, 12), (3, 20), (16, 16), (3, 14), (26, 1), (16, 6), (22, 24), (25, 9), (12, 19), (27, 28), (4, 21), (13, 10), (25, 23), (2, 5), (19, 13), (20, 5), (1, 15), (2, 3), (9, 31), (29, 22), (27, 15), (27, 9), (24, 16), (4, 24), (14, 18), (25, 1), (22, 23), (21, 10), (4, 29), (2, 20), (16, 21), (10, 28), (18, 24), (15, 2), (14, 22), (13, 1), (1, 23), (25, 7), (26, 23), (4, 14), (28, 23), (29, 17), (24, 9), (3, 11), (26, 19), (2, 9), (17, 15), (10, 2), (5, 25), (3, 19), (29, 11), (9, 18), (7, 8), (15, 27), (10, 0), (29, 3), (1, 0), (26, 27), (21, 12), (18, 1), (15, 1), (12, 4), (17, 13), (8, 30), (21, 27), (23, 31), (23, 26), (0, 14), (3, 10), (12, 31), (25, 11), (0, 2), (11, 27), (9, 5), (12, 21), (21, 0), (29, 0), (7, 6), (23, 18), (13, 21), (14, 8), (14, 2), (5, 18), (20, 31), (26, 20), (0, 21), (21, 6), (9, 30), (23, 21), (9, 26), (16, 12), (2, 6), (15, 5), (13, 11), (21, 9), (17, 25), (18, 16), (8, 28), (15, 4), (0, 3), (12, 16), (10, 9), (6, 3), (12, 29), (18, 10), (23, 17), (2, 31), (14, 21), (22, 15), (20, 24), (22, 18), (18, 17), (15, 14), (13, 14), (29, 26), (8, 5), (15, 7), (0, 29), (2, 4), (10, 16), (28, 14), (11, 7), (13, 4), (9, 9), (9, 11), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28000", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 26), (2, 4), (37, 29), (36, 33), (2, 2), (20, 3), (7, 17), (20, 31), (21, 10), (19, 3), (12, 12), (9, 21), (35, 16), (37, 3), (3, 18), (37, 1), (30, 30), (35, 5), (14, 0), (17, 31), (28, 16), (27, 9), (15, 6), (27, 31), (24, 10), (11, 2), (19, 2), (13, 28), (29, 21), (20, 30), (14, 7), (16, 2), (29, 6), (12, 9), (6, 20), (16, 11), (30, 25), (8, 10), (17, 6), (8, 8), (21, 19), (31, 3), (3, 2), (31, 34), (21, 27), (3, 14), (14, 17), (3, 17), (33, 23), (28, 6), (10, 0), (18, 1), (0, 28), (16, 33), (8, 17), (7, 4), (6, 25), (27, 29), (26, 29), (11, 23), (4, 27), (27, 18), (8, 29), (4, 19), (19, 8), (2, 10), (16, 1), (1, 28), (15, 10), (19, 27), (8, 25), (31, 20), (13, 8), (17, 7), (9, 27), (34, 6), (5, 17), (15, 25), (7, 30), (16, 32), (5, 5), (24, 11), (35, 14), (2, 23), (25, 23), (36, 23), (7, 3), (17, 14), (23, 31), (24, 23), (14, 34), (12, 19), (24, 5), (14, 15), (27, 1), (29, 11), (3, 24), (9, 12), (11, 25), (34, 17), (11, 11), (26, 32), (22, 17), (4, 5), (6, 4), (15, 9), (4, 0), (15, 8), (33, 31), (32, 0), (4, 20), (10, 25), (29, 3), (10, 15), (10, 6), (15, 26), (11, 6), (0, 27), (26, 2), (13, 4), (8, 5), (9, 14), (12, 3), (31, 33), (12, 21), (19, 30), (36, 8), (33, 32), (25, 32), (11, 14), (21, 24), (30, 20), (8, 7), (9, 4), (1, 20), (5, 28), (12, 23), (5, 24), (0, 32), (7, 1), (25, 33), (17, 30), (34, 2), (1, 25), (37, 6), (19, 12), (23, 6), (26, 21), (34, 34), (17, 29), (23, 21), (0, 6), (33, 30), (37, 2), (35, 13), (37, 5), (30, 16), (13, 11), (19, 9), (23, 17), (33, 6), (28, 34), (4, 6), (34, 18), (21, 8), (32, 18), (16, 8), (22, 3), (27, 10), (33, 28), (15, 24), (35, 32), (7, 5), (3, 25), (22, 32), (24, 18), (11, 4), (13, 16), (22, 12), (2, 9), (22, 5), (15, 30), (25, 25), (30, 0), (26, 14), (16, 0), (20, 17), (16, 25), (29, 2), (13, 12), (3, 20), (23, 7), (11, 9), (27, 17), (6, 31), (32, 29), (3, 8), (27, 25), (23, 27), (16, 22), (21, 7), (0, 2), (33, 34), (14, 2), (32, 26), (7, 2), (11, 0), (34, 4), (25, 8), (32, 21), (15, 22), (22, 28), (8, 31), (10, 16), (37, 4), (18, 3), (8, 30), (0, 29), (36, 34), (31, 13), (24, 6), (4, 3), (16, 12), (19, 4), (21, 1), (17, 19), (0, 17), (21, 33), (1, 0), (18, 20), (16, 6), (6, 29), (28, 15), (35, 4), (12, 29), (0, 23), (2, 3), (19, 17), (10, 17), (24, 16), (14, 16), (13, 5), (8, 13), (30, 12), (10, 12), (15, 13), (11, 20), (3, 27), (21, 23), (7, 28), (18, 23), (11, 26), (11, 13), (14, 6), (8, 16), (4, 10), (28, 8), (3, 12), (33, 33), (15, 7), (23, 28), (22, 8), (21, 18), (11, 28), (15, 17), (0, 31), (31, 21), (9, 11), (14, 21), (37, 23), (3, 33), (10, 27), (5, 12), (0, 24), (21, 12), (12, 1), (28, 14), (31, 29), (12, 32), (34, 8), (29, 25), (27, 3), (36, 22), (5, 33), (6, 33), (6, 34), (3, 13), (16, 13), (4, 15), (18, 29), (14, 26), (28, 28), (18, 18), (30, 5), (4, 29), (24, 32), (34, 3), (36, 28), (4, 30), (9, 28), (26, 34), (37, 27), (36, 18), (10, 24), (7, 11), (32, 14), (27, 13), (28, 1), (34, 26), (23, 2), (6, 30), (11, 15), (2, 6), (29, 19), (18, 26), (31, 26), (26, 20), (7, 27), (15, 16), (12, 18), (25, 13), (11, 30), (14, 29), (29, 9), (32, 17), (14, 8), (3, 28), (34, 29), (35, 21), (26, 30), (29, 5), (19, 24), (23, 18), (14, 33), (23, 34), (11, 21), (35, 25), (21, 32), (24, 33), (16, 3), (29, 30), (15, 32), (24, 21), (2, 34), (28, 13), (25, 10), (12, 24), (20, 15), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), 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), (20, 9), (26, 32), (27, 29), (24, 21), (0, 32), (32, 8), (13, 2), (25, 12), (10, 30), (31, 4), (0, 29), (23, 31), (4, 31), (31, 26), (24, 15), (25, 0), (0, 33), (3, 33), (26, 22), (24, 27), (3, 18), (26, 16), (23, 8), (26, 5), (15, 5), (20, 20), (11, 15), (12, 28), (17, 24), (6, 21), (3, 10), (5, 17), (14, 0), (2, 29), (17, 25), (33, 17), (4, 21), (9, 14), (31, 6), (22, 6), (8, 23), (28, 16), (28, 11), (19, 22), (7, 6), (26, 8), (32, 0), (21, 12), (13, 32), (34, 11), (13, 13), (26, 6), (31, 2), (33, 25), (2, 28), (27, 10), (23, 12), (16, 10), (18, 34), (17, 1), (0, 9), (24, 13), (18, 16), (7, 25), (28, 2), (10, 7), (1, 23), (3, 2), (14, 32), (7, 1), (21, 29), (5, 1), (13, 34), (16, 26), (16, 3), (19, 26), (14, 13), (13, 33), (24, 19), (2, 16), (12, 22), (24, 17), (24, 28), (4, 1), (23, 6), (33, 0), (24, 2), (31, 28), (11, 26), (6, 31), (31, 33), (27, 3), (9, 32), (11, 25), (18, 31), (33, 31), (16, 27), (25, 22), (6, 26), (29, 7), (16, 1), (30, 24), (34, 18), (20, 3), (14, 9), (21, 16), (19, 32), (25, 24), (19, 3), (16, 20), (17, 19), (1, 26), (30, 33), (28, 0), (20, 28), (14, 15), (11, 11), (24, 29), (4, 25), (30, 7), (22, 14), (19, 10), (8, 2), (30, 30), (1, 13), (28, 30), (26, 13), (12, 16), (28, 32), (16, 19), (12, 23), (28, 22), (20, 5), (13, 31), (26, 11), (0, 5), (21, 5), (7, 13), (9, 26), (34, 26), (25, 10), (10, 33), (10, 26), (34, 22), (28, 24), (15, 33), (6, 6), (15, 12), (27, 27), (16, 15), (14, 31), (33, 28), (4, 11), (15, 22), (16, 17), (28, 31), (29, 18), (9, 29), (11, 29), (28, 21), (34, 2), (4, 16), (0, 14), (7, 10), (25, 7), (3, 19), (18, 25), (21, 19), (18, 12), (3, 29), (30, 28), (9, 19), (34, 29), (34, 5), (4, 17), (13, 24), (13, 26), (27, 22), (34, 17), (27, 26), (1, 12), (21, 32), (5, 11), (4, 19), (4, 32), (34, 8), (14, 27), (14, 23), (16, 24), (7, 8), (27, 4), (33, 15), (30, 12), (8, 25), (15, 26), (18, 33), (0, 24), (34, 25), (19, 15), (12, 24), (2, 31), (0, 4), (11, 28), (4, 23), (10, 25), (31, 27), (30, 17), (0, 11), (18, 15), (11, 19), (17, 33), (3, 0), (29, 22), (26, 30), (34, 3), (4, 14), (24, 26), (3, 1), (12, 30), (32, 15), (9, 31), (10, 19), (15, 1), (8, 17), (34, 32), (32, 4), (23, 25), (22, 0), (13, 29), (15, 3), (26, 34), (14, 19), (9, 3), (8, 26), (22, 10), (8, 7), (18, 3), (1, 24), (24, 12), (22, 26), (7, 29), (2, 0), (20, 34), (2, 13), (32, 24), (29, 32), (18, 6), (22, 8), (30, 23), (21, 9), (14, 1), (16, 9), (32, 2), (5, 10), (20, 8), (5, 21), (27, 17), (21, 27), (23, 13), (6, 29), (20, 21), (28, 4), (26, 7), (22, 4), (27, 34), (26, 33), (29, 13), (4, 4), (29, 17), (30, 0), (18, 24), (21, 21), (15, 20), (8, 19), (27, 0), (11, 16), (1, 18), (9, 20), (25, 4), (6, 12), (0, 20), (25, 15), (16, 8), (22, 9), (26, 25), (8, 14), (15, 13), (6, 0), (31, 29), (17, 12), (6, 33), (7, 31), (1, 7), (5, 29), (25, 28), (16, 12), (19, 7), (15, 32), (33, 11), (11, 1), (32, 5), (10, 20), (2, 1), (6, 5), (4, 28), (29, 10), (23, 26), (22, 5), (19, 18), (24, 10), (7, 26), (6, 4), (3, 9), (5, 5), (32, 29), (7, 19), (32, 10), (6, 8), (9, 25), (2, 17), (20, 2), (22, 3), (29, 23), (34, 7), (8, 15), (33, 13), (6, 2), (23, 10), (1, 8), (14, 26), (14, 14), (31, 25), (27, 20), (1, 14), (28, 34), (13, 22), (34, 33), (1, 16), (11, 24), (2, 25), (22, 12), (25, 33), (22, 23), (16, 4), (18, 7), (30, 27), (16, 31), (13, 14), (30, 20), (29, 21), (12, 15), (31, 32), (4, 8), (18, 13), (20, 13), (30, 11), (15, 7), (2, 3), (25, 18), (26, 14), (9, 7), (11, 13), (17, 2), (24, 30), (30, 6), (13, 0), (22, 32), (30, 22), (32, 33), (10, 23), (18, 9), (17, 15), (17, 4), (4, 12), (10, 18), (7, 22), (12, 34), (10, 32), (15, 24), (24, 7), (29, 5), (9, 27), (0, 15), (33, 8), (23, 27), (22, 20), (26, 10), (31, 22), (5, 20), (19, 13), (27, 11), (2, 6), (5, 0), (22, 2), (2, 21), (34, 15), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "581760", "dataset": "MATH"}
{"messages": [{"content": "In a 31x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 32), 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), (15, 32), (22, 8), (9, 0), (5, 3), (26, 2), (14, 20), (27, 30), (25, 3), (7, 16), (18, 6), (15, 6), (16, 0), (22, 32), (16, 5), (25, 19), (0, 2), (4, 17), (16, 26), (6, 29), (7, 25), (2, 30), (0, 6), (24, 32), (30, 25), (20, 2), (9, 15), (8, 21), (19, 3), (19, 15), (2, 27), (30, 15), (12, 20), (20, 9), (16, 16), (27, 29), (13, 22), (19, 32), (1, 9), (29, 13), (5, 12), (14, 18), (26, 29), (3, 4), (9, 10), (29, 18), (2, 16), (7, 5), (11, 5), (18, 4), (12, 8), (25, 11), (18, 31), (12, 0), (12, 4), (21, 2), (17, 25), (13, 8), (23, 1), (5, 10), (11, 28), (1, 8), (20, 15), (13, 12), (27, 31), (24, 28), (3, 23), (2, 28), (20, 30), (21, 23), (7, 2), (18, 5), (26, 27), (7, 23), (23, 3), (12, 6), (18, 29), (20, 13), (5, 0), (7, 10), (10, 12), (3, 18), (27, 8), (0, 23), (11, 11), (13, 32), (30, 1), (8, 13), (16, 3), (20, 12), (10, 30), (14, 10), (23, 27), (19, 4), (29, 3), (28, 28), (3, 26), (4, 27), (1, 5), (16, 17), (1, 6), (18, 21), (18, 24), (27, 28), (11, 18), (22, 31), (15, 21), (12, 19), (21, 18), (0, 24), (4, 8), (19, 2), (21, 20), (16, 15), (20, 24), (0, 15), (20, 0), (17, 9), (13, 26), (22, 16), (22, 11), (12, 12), (7, 26), (10, 16), (27, 12), (11, 29), (21, 24), (9, 12), (7, 32), (7, 11), (27, 16), (7, 3), (10, 0), (7, 14), (19, 24), (19, 10), (23, 14), (23, 24), (5, 20), (9, 4), (5, 24), (30, 23), (12, 32), (1, 20), (27, 26), (1, 28), (10, 29), (2, 4), (19, 6), (7, 21), (24, 26), (0, 21), (26, 15), (22, 3), (19, 13), (0, 18), (24, 24), (16, 8), (28, 24), (13, 4), (4, 6), (2, 12), (12, 26), (3, 17), (7, 22), (17, 28), (21, 1), (2, 13), (21, 26), (5, 17), (5, 5), (27, 21), (13, 15), (9, 24), (29, 16), (19, 26), (9, 21), (4, 23), (25, 24), (14, 13), (20, 17), (14, 21), (23, 0), (4, 29), (13, 13), (22, 13), (6, 20), (2, 21), (10, 28), (4, 19), (4, 32), (6, 28), (21, 12), (2, 20), (26, 24), (9, 18), (25, 1), (22, 29), (14, 4), (13, 29), (6, 1), (0, 13), (16, 10), (30, 18), (17, 6), (11, 21), (1, 17), (1, 22), (15, 9), (20, 20), (11, 9), (16, 32), (16, 4), (4, 3), (17, 5), (0, 12), (8, 12), (17, 18), (8, 6), (5, 11), (12, 24), (19, 21), (2, 22), (18, 0), (24, 17), (1, 29), (17, 11), (14, 15), (7, 7), (29, 7), (29, 31), (29, 15), (9, 14), (0, 26), (14, 16), (22, 0), (27, 32), (16, 20), (11, 7), (2, 1), (26, 6), (4, 20), (11, 14), (18, 7), (16, 29), (22, 19), (23, 18), (1, 14), (13, 14), (28, 18), (10, 15), (6, 30), (5, 25), (28, 8), (9, 1), (18, 32), (15, 2), (23, 16), (8, 32), (11, 17), (28, 10), (20, 32), (20, 1), (17, 4), (13, 0), (6, 25), (25, 26), (29, 23), (8, 3), (3, 5), (0, 10), (27, 7), (7, 1), (16, 19), (7, 28), (19, 31), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "733824", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (17, 18), (29, 12), (29, 28), (9, 27), (12, 1), (20, 30), (24, 19), (1, 3), (8, 23), (23, 7), (6, 0), (29, 23), (2, 3), (17, 29), (12, 2), (9, 1), (16, 18), (7, 26), (8, 4), (20, 17), (25, 0), (16, 14), (16, 24), (24, 27), (1, 7), (9, 24), (12, 31), (25, 5), (4, 3), (17, 28), (15, 18), (14, 3), (12, 23), (7, 16), (12, 9), (23, 26), (15, 19), (22, 30), (2, 16), (15, 4), (8, 28), (15, 9), (5, 29), (17, 25), (21, 1), (30, 6), (9, 29), (30, 5), (30, 3), (20, 22), (19, 25), (18, 2), (20, 1), (6, 22), (25, 6), (1, 27), (29, 26), (21, 22), (6, 1), (28, 5), (24, 11), (28, 11), (1, 24), (17, 19), (26, 11), (3, 17), (2, 19), (24, 28), (30, 11), (27, 25), (29, 3), (28, 10), (5, 2), (6, 28), (29, 18), (11, 3), (5, 18), (8, 26), (8, 21), (18, 17), (22, 7), (25, 27), (3, 6), (27, 7), (5, 5), (1, 29), (27, 0), (11, 22), (4, 9), (17, 4), (3, 25), (13, 2), (11, 9), (26, 9), (17, 13), (12, 14), (27, 1), (19, 28), (15, 29), (14, 4), (16, 16), (16, 7), (13, 16), (20, 7), (13, 29), (11, 20), (0, 14), (27, 8), (27, 13), (1, 16), (23, 10), (7, 8), (9, 25), (26, 17), (16, 13), (2, 24), (15, 1), (17, 30), (2, 11), (4, 15), (21, 20), (10, 13), (18, 6), (11, 7), (21, 5), (28, 31), (12, 22), (13, 0), (18, 26), (14, 10), (23, 4), (18, 7), (4, 18), (18, 11), (7, 13), (23, 29), (28, 30), (3, 18), (9, 9), (6, 12), (10, 21), (12, 26), (0, 19), (30, 8), (21, 7), (20, 20), (1, 1), (4, 26), (8, 17), (12, 3), (5, 13), (15, 20), (23, 24), (29, 10), (24, 14), (2, 27), (5, 4), (22, 25), (21, 31), (20, 16), (26, 31), (2, 8), (7, 19), (23, 14), (30, 12), (28, 3), (25, 21), (26, 18), (8, 3), (17, 9), (12, 13), (28, 12), (17, 16), (13, 28), (30, 21), (26, 16), (28, 1), (7, 10), (3, 31), (9, 11), (5, 30), (23, 6), (21, 9), (23, 5), (30, 23), (9, 4), (7, 6), (8, 20), (14, 8), (21, 13), (13, 24), (4, 6), (4, 10), (20, 3), (22, 29), (22, 15), (11, 11), (16, 30), (21, 19), (8, 13), (0, 28), (24, 9), (10, 3), (25, 17), (23, 0), (10, 20), (9, 12), (27, 4), (1, 28), (17, 11), (25, 29), (13, 30), (5, 15), (20, 8), (4, 16), (16, 22), (1, 9), (22, 14), (11, 18), (26, 24), (3, 29), (1, 20), (3, 24), (21, 2), (18, 30), (26, 19), (4, 19), (4, 28), (29, 29), (3, 8), (21, 11), (30, 2), (19, 31), (30, 19), (3, 23), (23, 23), (16, 6), (15, 8), (7, 29), (0, 31), (0, 12), (21, 17), (18, 0), (18, 12), (19, 6), (0, 25), (7, 5), (11, 13), (12, 10), (2, 25), (8, 16), (16, 8), (12, 19), (30, 25), (6, 15), (8, 5), (2, 14), (8, 0), (16, 12), (11, 15), (16, 31), (2, 23), (7, 0), (3, 14), (14, 24), (16, 26), (26, 30), (14, 30), (15, 0), (28, 13), (4, 30), (10, 17), (15, 24), (5, 3), (23, 22), (19, 27), (29, 20), (25, 10), (22, 10), (3, 27), (18, 31), (1, 11), (24, 30), (5, 26), (26, 10), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351108", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 29), (16, 34), (21, 1), (2, 16), (21, 32), (29, 9), (11, 19), (24, 31), (34, 26), (12, 6), (14, 25), (7, 22), (1, 29), (2, 2), (23, 21), (24, 6), (29, 5), (30, 24), (18, 10), (8, 0), (33, 25), (23, 29), (34, 10), (20, 21), (28, 2), (11, 20), (0, 15), (3, 33), (29, 0), (3, 15), (9, 12), (31, 6), (17, 32), (26, 31), (1, 3), (27, 2), (31, 12), (8, 23), (32, 15), (22, 28), (34, 21), (32, 30), (8, 4), (26, 22), (13, 9), (1, 8), (14, 27), (20, 11), (26, 8), (21, 10), (5, 18), (4, 1), (25, 33), (22, 24), (13, 8), (7, 21), (5, 7), (26, 28), (13, 34), (1, 28), (28, 34), (29, 15), (7, 34), (11, 21), (28, 35), (28, 30), (19, 22), (18, 29), (27, 26), (13, 28), (24, 13), (22, 1), (25, 30), (4, 14), (33, 0), (4, 2), (9, 15), (14, 5), (19, 27), (24, 15), (26, 3), (13, 16), (26, 35), (20, 2), (33, 34), (1, 24), (9, 26), (4, 28), (34, 13), (18, 1), (18, 32), (10, 23), (33, 10), (19, 28), (26, 5), (31, 9), (32, 23), (14, 26), (12, 29), (3, 26), (23, 3), (12, 27), (22, 10), (19, 2), (2, 4), (5, 21), (19, 8), (2, 27), (3, 10), (24, 11), (8, 7), (32, 34), (18, 31), (15, 16), (0, 12), (4, 10), (18, 5), (25, 5), (33, 27), (32, 22), (27, 12), (24, 32), (16, 19), (16, 12), (30, 6), (19, 21), (32, 29), (27, 22), (12, 16), (20, 29), (10, 14), (11, 4), (8, 15), (17, 22), (14, 9), (28, 6), (5, 5), (13, 22), (2, 32), (23, 6), (20, 35), (10, 19), (18, 24), (13, 25), (22, 7), (0, 7), (31, 11), (9, 11), (19, 9), (14, 17), (0, 34), (2, 29), (33, 18), (10, 25), (24, 20), (10, 34), (28, 20), (1, 5), (32, 21), (18, 16), (22, 31), (5, 22), (6, 17), (16, 4), (0, 4), (31, 24), (29, 16), (16, 27), (0, 29), (16, 28), (7, 15), (23, 30), (24, 4), (1, 20), (17, 24), (23, 11), (13, 32), (6, 6), (26, 23), (23, 31), (15, 11), (31, 0), (23, 23), (26, 15), (6, 7), (22, 6), (31, 2), (7, 2), (23, 4), (17, 6), (34, 24), (5, 20), (33, 19), (16, 33), (16, 31), (15, 23), (27, 34), (22, 15), (7, 14), (29, 21), (33, 26), (15, 24), (32, 10), (12, 11), (11, 27), (31, 35), (10, 21), (31, 28), (23, 7), (11, 33), (16, 35), (19, 25), (4, 30), (9, 34), (21, 33), (16, 6), (25, 27), (11, 23), (20, 23), (2, 1), (33, 6), (9, 2), (8, 34), (16, 0), (32, 35), (12, 33), (17, 13), (27, 3), (29, 32), (24, 0), (18, 17), (24, 33), (22, 17), (10, 4), (21, 5), (0, 13), (20, 30), (22, 2), (30, 28), (28, 9), (28, 8), (32, 20), (30, 20), (33, 1), (32, 26), (27, 18), (15, 14), (1, 2), (30, 31), (11, 12), (33, 5), (21, 17), (12, 20), (34, 9), (25, 13), (11, 14), (34, 22), (17, 15), (16, 17), (6, 26), (15, 28), (23, 15), (9, 0), (17, 11), (32, 6), (3, 29), (12, 22), (0, 2), (20, 17), (27, 17), (34, 31), (1, 31), (17, 18), (11, 17), (34, 2), (32, 18), (10, 27), (8, 30), (17, 3), (7, 20), (30, 34), (14, 2), (33, 28), (8, 8), (23, 13), (19, 10), (16, 2), (14, 1), (30, 14), (1, 32), (1, 10), (22, 0), (26, 0), (1, 33), (3, 8), (4, 9), (9, 24), (2, 20), (20, 4), (18, 4), (23, 25), (15, 8), (4, 15), (29, 22), (26, 7), (24, 17), (6, 27), (25, 15), (24, 12), (19, 29), (15, 3), (18, 8), (8, 32), (10, 32), (6, 29), (0, 35), (10, 9), (34, 14), (11, 22), (23, 26), (9, 35), (20, 10), (20, 20), (18, 27), (10, 20), (14, 4), (30, 13), (3, 28), (33, 3), (12, 35), (26, 19), (30, 35), (16, 32), (27, 24), (21, 14), (17, 26), (32, 1), (27, 7), (15, 34), (28, 23), (25, 23), (18, 30), (25, 1), (29, 12), (7, 18), (32, 11), (27, 28), (34, 19), (14, 15), (34, 5), (5, 26), (15, 25), (4, 35), (18, 35), (10, 11), (13, 1), (16, 11), (18, 21), (2, 13), (22, 16), (14, 19), (16, 25), (26, 25), (24, 18), (7, 27), (18, 25), (28, 32), (26, 10), (3, 4), (18, 15), (13, 18), (5, 27), (9, 27), (9, 14), (2, 7), (26, 11), (2, 15), (13, 3), (30, 4), (11, 18), (15, 19), (2, 19), (14, 33), (2, 5), (28, 4), (17, 17), (29, 4), (32, 0), (1, 13), (30, 22), (28, 27), (20, 34), (28, 28), (20, 22), (33, 12), (6, 5), (7, 5), (2, 14), (15, 32), (23, 35), (32, 13), (22, 20), (27, 30), (1, 19), (0, 20), (18, 33), (25, 4), (11, 31), (15, 15), (25, 2), (5, 9), (17, 35), (10, 6), (21, 11), (12, 31), (31, 26), (8, 28), (13, 19), (23, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "736290", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 30), (12, 19), (10, 25), (5, 9), (3, 21), (23, 6), (24, 7), (5, 6), (23, 16), (29, 22), (31, 6), (25, 19), (28, 10), (18, 5), (8, 2), (9, 28), (0, 29), (1, 21), (30, 20), (14, 14), (24, 30), (24, 23), (1, 9), (32, 3), (13, 17), (26, 13), (30, 26), (32, 8), (24, 16), (0, 3), (6, 29), (14, 1), (2, 11), (0, 19), (14, 30), (25, 4), (14, 4), (31, 13), (20, 26), (11, 28), (28, 26), (25, 25), (31, 3), (17, 11), (4, 26), (12, 13), (14, 28), (11, 30), (28, 30), (25, 10), (10, 9), (21, 10), (9, 0), (4, 25), (31, 28), (2, 18), (14, 6), (7, 4), (8, 14), (10, 3), (6, 11), (6, 12), (18, 24), (10, 18), (14, 22), (15, 18), (15, 20), (12, 2), (12, 24), (1, 4), (4, 30), (29, 23), (14, 27), (15, 26), (7, 24), (27, 25), (31, 14), (0, 20), (19, 21), (21, 22), (1, 17), (8, 6), (16, 27), (8, 25), (16, 18), (2, 14), (9, 17), (19, 7), (20, 27), (3, 4), (27, 21), (13, 20), (11, 17), (28, 29), (1, 28), (29, 20), (28, 28), (27, 4), (31, 18), (1, 23), (12, 21), (9, 19), (16, 16), (23, 30), (0, 12), (23, 1), (30, 8), (0, 1), (12, 4), (5, 25), (9, 15), (7, 26), (20, 11), (3, 29), (11, 21), (22, 25), (20, 2), (26, 7), (4, 28), (24, 27), (2, 21), (31, 19), (16, 6), (1, 24), (26, 26), (31, 1), (31, 20), (10, 4), (29, 2), (16, 23), (17, 15), (23, 17), (10, 6), (7, 25), (20, 10), (17, 28), (8, 8), (21, 4), (30, 21), (26, 4), (24, 22), (11, 11), (7, 23), (12, 1), (18, 12), (9, 1), (6, 14), (1, 27), (15, 24), (23, 4), (23, 10), (11, 6), (29, 29), (14, 10), (2, 3), (20, 15), (10, 5), (26, 11), (4, 22), (12, 11), (32, 9), (1, 15), (25, 29), (5, 11), (22, 6), (17, 26), (5, 0), (27, 19), (26, 24), (0, 10), (22, 23), (24, 5), (27, 1), (10, 0), (11, 0), (16, 5), (5, 15), (26, 9), (13, 0), (2, 4), (11, 13), (21, 11), (19, 6), (4, 24), (9, 20), (6, 8), (32, 19), (13, 3), (13, 25), (28, 13), (11, 10), (0, 23), (7, 17), (9, 30), (11, 27), (7, 14), (28, 16), (5, 5), (30, 19), (28, 14), (20, 7), (12, 25), (25, 18), (27, 13), (29, 26), (18, 4), (5, 7), (5, 3), (19, 17), (12, 0), (13, 11), (11, 8), (11, 26), (28, 11), (20, 28), (20, 9), (26, 20), (32, 24), (26, 1), (16, 3), (24, 2), (5, 29), (23, 21), (25, 16), (18, 9), (1, 8), (30, 14), (23, 15), (17, 30), (22, 18), (26, 3), (17, 1), (29, 9), (12, 26), (25, 13), (24, 3), (9, 29), (10, 12), (24, 1), (27, 29), (4, 16), (6, 4), (10, 11), (23, 24), (22, 29), (0, 7), (22, 30), (26, 19), (1, 3), (2, 29), (16, 21), (3, 30), (1, 2), (8, 10), (18, 8), (9, 25), (25, 12), (7, 28), (7, 15), (3, 7), (27, 0), (0, 14), (5, 18), (11, 5), (5, 8), (11, 29), (28, 18), (22, 0), (19, 26), (11, 7), (15, 0), (2, 30), (4, 7), (28, 9), (15, 12), (30, 25), (22, 2), (13, 7), (32, 17), (31, 5), (17, 0), (21, 9), (9, 4), (13, 19), (30, 10), (19, 20), (27, 26), (29, 8), (19, 11), (24, 20), (1, 13), (15, 19), (30, 18), (21, 30), (17, 8), (6, 10), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "649264", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (4, 17), (33, 6), (17, 33), (32, 15), (1, 7), (21, 10), (11, 27), (13, 28), (17, 7), (15, 21), (22, 18), (1, 16), (8, 24), (36, 1), (8, 8), (16, 25), (18, 31), (37, 20), (10, 3), (25, 28), (24, 23), (15, 22), (32, 19), (18, 15), (26, 0), (33, 23), (5, 5), (33, 1), (15, 18), (13, 23), (13, 33), (22, 0), (0, 3), (10, 33), (34, 29), (5, 31), (29, 25), (10, 23), (14, 29), (23, 32), (19, 16), (1, 31), (17, 3), (22, 11), (30, 21), (0, 33), (20, 11), (15, 29), (30, 9), (1, 1), (30, 12), (10, 11), (35, 19), (7, 24), (7, 0), (23, 34), (36, 5), (2, 27), (16, 33), (5, 21), (31, 33), (5, 32), (36, 13), (8, 26), (28, 23), (27, 14), (35, 12), (29, 33), (9, 5), (29, 18), (36, 22), (35, 10), (25, 19), (34, 10), (12, 25), (26, 28), (3, 9), 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0), (19, 6), (13, 29), (37, 4), (31, 19), (14, 32), (7, 19), (24, 29), (6, 5), (18, 23), (22, 6), (16, 32), (1, 34), (28, 11), (1, 33), (34, 32), (13, 16), (22, 4), (24, 10), (29, 3), (17, 30), (10, 13), (13, 27), (27, 13), (28, 0), (32, 22), (17, 17), (2, 22), (11, 0), (15, 24), (7, 20), (9, 25), (13, 30), (7, 14), (14, 21), (8, 23), (13, 32), (31, 5), (30, 31), (28, 30), (23, 24), (13, 26), (6, 28), (21, 16), (33, 24), (7, 10), (37, 33), (10, 32), (20, 4), (17, 23), (35, 31), (34, 22), (17, 34), (4, 1), (2, 25), (13, 5), (18, 4), (34, 31), (13, 10), (16, 8), (26, 3), (37, 30), (18, 7), (11, 29), (10, 2), (18, 14), (25, 30), (28, 14), (9, 14), (1, 9), (29, 31), (1, 8), (4, 28), (7, 4), (12, 10), (33, 11), (6, 26), (10, 27), (4, 4), (38, 24), (30, 6), (7, 16), (4, 27), (23, 27), (22, 21), (30, 20), (7, 17), (23, 29), (22, 29), (15, 9), (28, 16), (5, 9), (14, 1), (7, 11), (21, 27), (11, 1), (11, 25), (8, 19), (38, 1), (29, 17), (37, 6), (27, 7), (27, 4), (36, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "786600", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), 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), (31, 30), (25, 19), (9, 33), (5, 18), (26, 0), (23, 31), (7, 36), (13, 11), (6, 8), (1, 34), (32, 17), (17, 6), (18, 22), (12, 11), (3, 32), (14, 24), (9, 7), (24, 31), (2, 1), (3, 9), (19, 33), (25, 22), (9, 11), (0, 18), (5, 19), (28, 20), (12, 3), (15, 8), (32, 15), (29, 13), (24, 16), (11, 3), (32, 9), (8, 25), (21, 11), (31, 28), (9, 16), (31, 23), (9, 30), (32, 3), (14, 14), (25, 36), (32, 25), (16, 16), (12, 9), (14, 9), (28, 21), (9, 35), (4, 3), (32, 32), (13, 27), (27, 33), (29, 0), (1, 4), (25, 11), (6, 34), (24, 12), (0, 24), (17, 31), (14, 23), (5, 20), (4, 21), (9, 23), (20, 26), (3, 8), (30, 36), (10, 9), (27, 18), (29, 8), (17, 7), (21, 13), (19, 21), (30, 1), (22, 10), (12, 19), (19, 24), (18, 36), (6, 14), (8, 27), (17, 27), (31, 29), (1, 22), (7, 26), (4, 32), (7, 27), (24, 27), (22, 32), (23, 2), (29, 19), (17, 22), (25, 6), (10, 3), (0, 11), (17, 34), (0, 36), (17, 26), (21, 21), (13, 17), (1, 25), (24, 28), (4, 7), (27, 6), (2, 17), (20, 1), (7, 2), (20, 10), (0, 30), (14, 12), (0, 19), (10, 30), (22, 21), (6, 23), (19, 15), (3, 31), (2, 14), (13, 5), (22, 15), (10, 24), (1, 8), (1, 3), (4, 30), (16, 5), (20, 6), (7, 16), (19, 1), (2, 23), (27, 32), (15, 5), (16, 8), (17, 20), (15, 36), (22, 28), (8, 6), (28, 24), (30, 30), (2, 19), (7, 33), (2, 10), (23, 17), (26, 34), (30, 26), (5, 0), (24, 35), (16, 11), (15, 13), (9, 13), (5, 29), (4, 36), (6, 17), (15, 32), (29, 33), (25, 13), (17, 28), (1, 20), (30, 11), (27, 1), (11, 7), (29, 21), (3, 18), (15, 2), (26, 30), (2, 16), (11, 25), (25, 5), (18, 8), (9, 14), (4, 2), (19, 12), (16, 25), (4, 13), (17, 14), (29, 30), (28, 18), (28, 13), (14, 11), (11, 16), (16, 7), (5, 11), (32, 28), (19, 11), (28, 10), (14, 33), (3, 29), (3, 17), (21, 17), (17, 25), (8, 8), (1, 6), (4, 22), (13, 24), (32, 33), (14, 1), (24, 34), (7, 31), (5, 3), (21, 0), (15, 29), (32, 35), (9, 29), (32, 5), (1, 28), (6, 29), (16, 6), (8, 17), (21, 30), (19, 34), (16, 34), (3, 16), (15, 33), (15, 18), (18, 0), (32, 10), (15, 31), (12, 30), (0, 12), (18, 13), (10, 14), (5, 12), (11, 33), (30, 34), (4, 33), (22, 13), (8, 29), (14, 3), (23, 5), (7, 35), (18, 1), (15, 6), (12, 18), (10, 31), (27, 36), (9, 0), (19, 9), (20, 29), (2, 18), (14, 13), (5, 13), (28, 8), (26, 20), (13, 22), (31, 9), (24, 3), (15, 22), (13, 7), (27, 31), (27, 34), (6, 35), (28, 4), (24, 26), (26, 27), (30, 2), (32, 31), (26, 5), (21, 26), (0, 28), (10, 28), (10, 12), (12, 28), (30, 13), (6, 24), (9, 10), (16, 24), (0, 2), (22, 17), (26, 16), (21, 24), (9, 32), (17, 5), (24, 7), (7, 19), (28, 35), (9, 12), (16, 14), (20, 13), (8, 2), (1, 12), (13, 0), (26, 1), (4, 11), (21, 3), (24, 9), (32, 27), (6, 1), (4, 10), (24, 8), (14, 7), (3, 34), (26, 10), (28, 22), (20, 32), (6, 4), (24, 11), (10, 32), (11, 4), (27, 28), (24, 36), (31, 1), (31, 19), (14, 30), (14, 0), (26, 35), (5, 7), (23, 7), (15, 14), (3, 21), (10, 34), (19, 19), (6, 22), (17, 29), (15, 34), (20, 35), (6, 6), (5, 36), (16, 3), (21, 2), (9, 31), (6, 18), (11, 13), (4, 8), (18, 2), (2, 33), (5, 26), (31, 11), (14, 31), (27, 8), (27, 13), (18, 31), (12, 14), (2, 26), (4, 14), (17, 16), (7, 7), (2, 22), (27, 20), (9, 18), (32, 11), (14, 10), (3, 0), (4, 19), (25, 27), (31, 5), (18, 5), (19, 14), (5, 25), (21, 23), (6, 30), (31, 21), (12, 6), (14, 15), (21, 19), (20, 17), (15, 25), (30, 32), (27, 0), (9, 6), (22, 30), (14, 34), (27, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "638080", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (36, 1), (26, 31), (23, 31), (24, 12), (13, 5), (23, 22), (22, 17), (37, 8), (20, 0), (12, 4), (30, 12), (23, 24), (15, 30), (10, 7), (28, 11), (28, 10), (31, 9), (29, 5), (36, 3), (6, 1), (24, 30), (6, 4), (9, 14), (1, 29), (13, 8), (20, 11), (28, 23), (12, 22), (24, 23), (9, 30), (36, 18), (29, 24), (17, 29), (20, 2), (0, 32), (7, 23), (28, 28), (8, 23), (26, 10), (27, 4), (35, 32), (7, 17), (35, 6), (19, 17), (7, 27), (20, 18), (19, 1), (19, 14), (28, 29), (30, 18), (8, 13), (10, 12), (5, 2), (22, 22), (5, 6), (16, 10), (27, 1), (20, 32), (10, 22), (20, 19), (3, 4), (33, 28), (27, 31), (14, 20), (24, 18), (9, 32), (23, 9), (37, 5), (16, 18), (30, 17), (9, 17), (22, 30), (24, 32), (30, 21), (6, 12), (33, 24), (29, 3), (26, 26), (0, 19), (37, 15), (30, 15), (6, 26), (27, 32), (8, 15), (35, 22), (6, 5), (2, 22), (16, 2), (14, 5), (26, 6), (22, 25), (21, 4), (4, 31), (13, 11), (19, 13), (14, 14), (31, 4), (11, 14), (0, 30), (19, 26), (19, 28), (2, 27), (1, 18), (27, 24), (4, 26), (13, 32), (2, 9), (10, 24), (18, 13), (34, 28), (32, 28), (2, 3), (28, 12), (2, 7), (9, 12), (26, 29), (10, 18), (6, 9), (7, 19), (22, 9), (14, 15), (32, 25), (17, 11), (33, 8), (33, 26), (13, 25), (22, 26), (15, 23), (22, 21), (28, 24), (22, 11), (7, 9), (12, 25), (36, 9), (17, 8), (18, 30), (3, 2), (13, 30), (36, 24), (3, 11), (23, 12), (3, 18), (32, 16), (27, 18), (15, 15), (37, 18), (3, 28), (27, 30), (15, 12), (21, 24), (8, 20), (8, 29), (13, 14), (0, 13), (6, 23), (31, 10), (11, 26), (30, 30), (37, 31), (23, 20), (20, 10), (34, 16), (16, 31), (35, 21), (19, 22), (35, 16), (27, 9), (2, 28), (11, 29), (34, 17), (11, 28), (7, 28), (15, 18), (9, 0), (31, 24), (9, 2), (5, 21), (5, 0), (33, 3), (19, 0), (30, 9), (1, 11), (27, 16), (17, 24), (36, 12), (5, 14), (34, 11), (21, 16), (7, 12), (12, 15), (33, 20), (13, 21), (13, 18), (29, 20), (31, 12), (11, 25), (37, 24), (29, 17), (14, 22), (10, 2), (19, 25), (2, 25), (15, 20), (35, 8), (7, 29), (12, 18), (29, 22), (5, 1), (29, 30), (2, 0), (27, 2), (14, 3), (0, 11), (3, 6), (28, 0), (5, 3), (6, 25), (1, 14), (22, 1), (10, 20), (26, 8), (37, 7), (0, 12), (31, 6), (35, 24), (16, 9), (20, 8), (4, 27), (9, 29), (11, 24), (4, 22), (33, 17), (15, 2), (18, 17), (4, 20), (29, 1), (31, 5), (3, 12), (12, 9), (36, 23), (7, 15), (5, 8), (17, 19), (20, 22), (7, 32), (16, 3), (19, 8), (10, 30), (29, 11), (17, 14), (35, 13), (4, 2), (6, 21), (17, 0), (26, 25), (22, 4), (12, 12), (0, 24), (4, 17), (12, 21), (17, 27), (18, 15), (27, 20), (12, 6), (34, 31), (28, 4), (1, 20), (11, 5), (32, 23), (21, 32), (8, 26), (13, 28), (1, 28), (22, 14), (26, 30), (31, 19), (4, 9), (7, 1), (4, 25), (33, 6), (28, 26), (3, 31), (23, 28), (15, 6), (26, 14), (6, 8), (21, 20), (20, 26), (29, 0), (2, 16), (7, 20), (24, 6), (28, 32), (28, 2), (22, 31), (35, 15), (19, 30), (8, 0), (8, 6), (30, 3), (25, 20), (1, 23), (37, 29), (10, 21), (32, 1), (5, 20), (25, 17), (10, 8), (32, 19), (1, 12), (26, 23), (4, 28), (11, 1), (28, 1), (2, 14), (33, 16), (25, 5), (29, 2), (28, 30), (26, 4), (28, 5), (34, 19), (9, 7), (29, 21), (19, 16), (14, 21), (16, 6), (7, 31), (30, 23), (28, 7), (8, 16), (30, 11), (31, 28), (32, 11), (2, 26), (6, 29), (14, 28), (2, 6), (20, 7), (18, 10), (23, 25), (14, 24), (1, 8), (19, 21), (35, 10), (17, 26), (15, 22), (3, 14), (1, 2), (25, 29), (18, 28), (5, 11), (12, 1), (35, 14), (6, 10), (34, 1), (36, 7), (26, 7), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188024", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 31), (31, 9), (14, 14), (37, 16), (9, 18), (0, 10), (28, 17), (24, 4), (34, 6), (8, 21), (25, 8), (35, 5), (33, 20), (14, 4), (16, 31), (38, 17), (11, 29), (20, 26), (35, 11), (0, 21), (3, 25), (21, 14), (16, 2), (24, 12), (27, 30), (0, 18), (20, 5), (2, 4), (19, 11), (15, 3), (27, 19), (26, 23), (19, 3), (18, 5), (5, 1), (11, 0), (36, 5), (6, 3), (3, 27), (21, 24), (29, 14), (4, 32), (32, 28), (36, 14), (2, 26), (5, 6), (35, 34), (22, 19), (22, 10), (15, 16), (29, 9), (0, 33), (20, 6), (15, 14), (35, 29), (2, 25), (7, 1), (21, 6), (5, 9), (34, 29), (36, 4), (31, 18), (3, 6), (7, 14), (28, 24), (25, 22), (7, 17), (6, 1), (31, 34), (33, 13), (15, 30), (10, 1), (1, 28), (15, 22), (12, 0), (38, 12), (25, 21), (0, 4), (16, 0), (16, 22), (2, 34), (4, 11), (16, 30), (12, 2), (18, 0), (10, 16), (29, 15), (19, 17), (14, 19), (17, 16), (19, 23), (10, 0), (27, 6), (36, 9), (21, 5), (30, 34), (24, 21), (35, 28), (18, 32), (27, 24), (1, 5), (9, 33), (3, 1), (10, 23), (13, 26), (11, 18), (21, 28), (19, 32), (12, 16), (19, 12), (29, 13), (36, 25), (35, 12), (7, 8), (4, 5), (17, 8), (2, 9), (19, 15), (30, 5), (20, 14), (23, 17), (7, 2), (26, 26), (15, 8), (25, 15), (29, 16), (31, 15), (15, 1), (19, 5), (36, 11), (0, 12), (17, 15), (21, 30), (11, 33), (30, 31), (19, 6), (20, 9), (11, 34), (12, 7), (35, 17), (9, 5), (23, 2), (29, 10), (13, 0), (18, 22), (14, 16), (18, 2), (3, 9), (34, 17), (34, 26), (13, 8), (5, 21), (9, 23), (35, 31), (23, 32), (32, 16), (27, 17), (27, 7), (23, 18), (2, 28), (17, 17), (36, 33), (20, 3), (25, 24), (27, 15), (29, 6), (33, 14), (8, 5), (12, 27), (15, 29), (2, 11), (21, 32), (23, 12), (25, 26), (17, 19), (20, 34), (31, 20), (6, 10), (5, 14), (30, 22), (0, 9), (26, 12), (20, 2), (18, 6), (32, 18), (24, 34), (38, 22), (16, 24), (33, 23), (37, 9), (10, 18), (12, 4), (19, 7), (5, 25), (32, 5), (27, 22), (20, 1), (28, 1), (11, 11), (37, 30), (37, 11), (31, 3), (16, 15), (32, 21), (21, 22), (31, 31), (36, 31), (13, 30), (10, 13), (17, 11), (16, 18), (23, 10), (11, 27), (24, 20), (5, 2), (37, 31), (16, 9), (10, 17), (30, 25), (8, 8), (4, 6), (28, 12), (9, 19), (37, 18), (6, 24), (15, 20), (2, 30), (38, 0), (34, 0), (12, 23), (34, 24), (31, 29), (30, 9), (32, 8), (23, 22), (33, 17), (11, 23), (34, 19), (32, 24), (38, 15), (17, 13), (34, 18), (26, 17), (10, 8), (19, 34), (35, 3), (30, 8), (7, 13), (38, 28), (4, 1), (37, 10), (27, 33), (13, 25), (13, 29), (12, 1), (2, 5), (32, 19), (17, 27), (15, 7), (18, 8), (21, 9), (26, 1), (0, 13), (17, 32), (9, 31), (16, 5), (4, 2), (19, 31), (14, 12), (9, 32), (4, 12), (27, 5), (0, 15), (16, 3), (23, 29), (24, 6), (0, 30), (27, 0), (4, 9), (21, 25), (11, 1), (11, 5), (13, 3), (1, 33), (9, 22), (3, 17), (1, 2), (21, 29), (17, 24), (20, 32), (11, 31), (31, 13), (13, 34), (5, 27), (8, 4), (13, 32), (0, 5), (22, 31), (33, 19), (3, 7), (1, 15), (29, 7), (10, 28), (18, 4), (36, 0), (2, 14), (22, 27), (5, 33), (32, 33), (34, 25), (7, 12), (22, 3), (20, 18), (18, 19), (5, 11), (29, 17), (26, 18), (4, 27), (33, 34), (30, 6), (15, 25), (18, 24), (13, 11), (18, 33), (16, 20), (27, 10), (28, 19), (14, 2), (37, 7), (21, 10), (14, 32), (2, 33), (32, 4), (27, 11), (31, 32), (0, 23), (17, 12), (37, 15), (14, 5), (12, 24), (11, 6), (28, 30), (23, 16), (11, 25), (2, 6), (33, 2), (26, 15), (33, 4), (2, 27), (23, 11), (3, 34), (1, 10), (1, 31), (22, 23), (34, 32), (25, 11), (4, 26), (6, 2), (9, 26), (15, 21), (21, 0), (0, 31), (30, 1), (6, 6), (34, 2), (1, 30), (29, 26), (19, 30), (36, 6), (30, 32), (26, 22), (9, 16), (32, 0), (11, 22), (17, 26), (5, 10), (34, 11), (5, 24), (34, 15), (22, 21), (12, 22), (27, 25), (8, 13), (18, 29), (9, 30), (1, 20), (15, 19), (20, 11), (23, 24), (13, 19), (15, 9), (17, 33), (33, 30), (7, 6), (2, 31), (9, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750960", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), 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), (4, 20), (31, 29), (5, 7), (12, 22), (19, 0), (28, 28), (31, 8), (27, 12), (13, 2), (18, 31), (23, 12), (31, 14), (7, 25), (9, 29), (24, 4), (24, 28), (17, 2), (25, 31), (11, 0), (2, 17), (2, 1), (12, 5), (19, 28), (6, 4), (26, 18), (18, 21), (1, 5), (28, 26), (4, 0), (16, 8), (30, 31), (18, 7), (13, 5), (10, 19), (20, 29), (8, 26), (31, 16), (7, 7), (29, 4), (22, 27), (8, 4), (7, 1), (23, 26), (24, 25), (3, 1), (22, 19), (25, 11), (27, 9), (24, 8), (20, 34), (11, 33), (22, 20), (10, 3), (23, 22), (26, 31), (21, 28), (6, 27), (2, 23), (24, 11), (7, 28), (11, 9), (5, 20), (31, 4), (13, 9), (0, 25), (26, 10), (16, 24), (21, 12), (5, 29), (6, 21), (27, 31), (30, 5), (2, 18), (3, 3), (10, 31), (10, 11), (26, 8), (19, 3), (7, 21), (8, 5), (20, 33), (26, 27), (27, 24), (22, 6), (8, 12), (24, 7), (1, 7), (16, 10), (2, 10), (31, 1), (3, 15), (24, 16), (16, 20), (27, 15), (1, 6), (2, 0), (3, 17), (14, 9), (18, 13), (5, 1), (10, 25), (3, 4), (2, 31), (30, 9), (1, 17), (25, 20), (21, 1), (31, 2), (0, 1), (15, 21), (29, 26), (5, 34), (17, 15), (6, 6), (2, 7), (0, 13), (2, 32), (12, 25), (8, 7), (7, 23), (15, 13), (17, 9), (23, 17), (25, 32), (2, 28), (16, 17), (26, 16), (16, 14), (7, 2), (16, 0), (6, 22), (8, 19), (15, 0), (6, 28), (13, 14), (29, 22), (23, 8), (10, 7), (31, 3), (26, 28), (25, 33), (27, 8), (19, 4), (9, 6), (24, 27), (14, 14), (4, 29), (12, 8), (12, 33), (23, 30), (29, 29), (17, 22), (29, 9), (6, 17), (27, 16), (29, 18), (22, 0), (8, 11), (5, 28), (23, 28), (0, 5), (8, 13), (16, 27), (30, 34), (4, 27), (23, 21), (9, 24), (15, 32), (3, 19), (27, 25), (10, 20), (20, 15), (28, 23), (20, 10), (21, 0), (18, 34), (11, 14), (10, 4), (9, 5), (6, 18), (2, 13), (0, 26), (20, 16), (28, 19), (12, 23), (8, 1), (18, 2), (13, 8), (0, 30), (19, 20), (23, 33), (11, 24), (1, 22), (15, 3), (27, 4), (21, 29), (16, 29), (13, 21), (16, 25), (4, 19), (26, 11), (4, 21), (22, 32), (20, 12), (17, 17), (11, 5), (18, 30), (1, 19), (18, 10), (2, 19), (12, 9), (27, 29), (5, 19), (17, 7), (1, 34), (6, 1), (26, 25), (20, 3), (23, 27), (2, 2), (6, 33), (4, 1), (14, 20), (20, 21), (17, 14), (28, 32), (1, 31), (20, 32), (13, 1), (18, 22), (15, 30), (7, 24), (19, 18), (14, 5), (6, 29), (12, 11), (29, 12), (27, 28), (27, 14), (17, 10), (17, 26), (25, 16), (2, 25), (6, 2), (23, 5), (3, 13), (4, 4), (3, 10), (11, 29), (12, 13), (28, 6), (0, 7), (0, 33), (9, 7), (24, 15), (3, 22), (13, 26), (31, 6), (7, 9), (9, 3), (8, 18), (13, 25), (0, 8), (29, 3), (29, 25), (13, 34), (3, 6), (0, 6), (4, 23), (1, 24), (13, 29), (30, 21), (1, 12), (0, 15), (15, 29), (0, 14), (22, 10), (22, 17), (2, 29), (17, 4), (11, 32), (23, 18), (0, 27), (15, 28), (19, 6), (22, 30), (12, 21), (22, 9), (22, 5), (22, 24), (25, 1), (15, 17), (10, 15), (30, 4), (10, 32), (4, 14), (24, 20), (21, 13), (31, 0), (14, 28), (8, 28), (7, 17), (14, 25), (16, 18), (13, 10), (3, 28), (11, 28), (17, 6), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739584", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 12), (22, 0), (14, 29), (27, 9), (12, 10), (2, 5), (1, 1), (37, 2), (0, 28), (15, 11), (15, 15), (21, 13), (19, 4), (36, 7), (3, 28), (35, 2), (38, 0), (17, 7), (32, 6), (24, 10), (15, 16), (25, 24), (28, 23), (37, 15), (15, 9), (6, 25), (14, 2), (4, 15), (18, 15), (21, 18), (36, 25), (4, 20), (8, 19), (23, 24), (29, 0), (33, 10), (24, 26), (0, 10), (35, 9), (15, 30), (11, 20), (5, 17), (11, 25), (13, 19), (29, 2), (26, 4), (10, 1), (33, 16), (15, 24), (25, 3), (25, 15), (7, 3), (8, 14), (37, 11), (18, 2), (1, 18), (38, 7), (7, 11), (32, 5), (31, 24), (16, 26), (35, 25), (3, 20), (6, 26), (20, 0), (33, 8), (0, 23), (8, 2), (20, 26), (3, 11), (2, 6), (34, 16), (1, 25), (35, 19), (33, 5), (14, 16), (25, 1), (26, 15), (34, 1), (18, 4), (33, 25), (19, 23), (0, 13), (21, 20), (31, 21), (36, 5), (30, 10), (6, 31), (0, 27), (38, 5), (7, 28), (3, 30), (34, 11), (9, 17), (10, 19), (9, 22), (25, 23), (36, 14), (30, 5), (11, 8), (4, 3), (34, 17), (35, 31), (23, 2), (14, 18), (10, 20), (37, 13), (30, 19), (31, 25), (14, 24), (28, 11), (8, 23), (4, 22), (3, 13), (10, 25), (29, 12), (17, 0), (35, 17), (17, 10), (9, 15), (31, 28), (34, 23), (17, 12), (38, 10), (23, 19), (4, 19), (23, 10), (4, 7), (21, 17), (10, 12), (16, 27), (15, 0), (7, 24), (6, 18), (23, 9), (6, 15), (16, 16), (20, 23), (38, 28), (23, 17), (4, 26), (23, 4), (14, 13), (27, 23), (7, 25), (17, 26), (27, 16), (35, 16), (14, 9), (26, 28), (18, 16), (9, 28), (35, 1), (25, 5), (25, 11), (16, 4), (11, 9), (13, 12), (13, 18), (1, 13), (18, 17), (17, 31), (20, 24), (17, 5), (17, 24), (6, 27), (6, 24), (30, 22), (15, 5), (33, 26), (8, 5), (32, 22), (35, 21), (27, 13), (36, 3), (15, 14), (19, 30), (7, 20), (11, 5), (21, 25), (24, 20), (13, 8), (14, 11), (5, 25), (27, 27), (3, 24), (15, 2), (31, 0), (8, 25), (35, 26), (21, 22), (3, 7), (19, 8), (27, 1), (6, 9), (19, 29), (20, 14), (31, 29), (9, 20), (11, 19), (30, 6), (24, 1), (36, 1), (25, 28), (37, 28), (23, 14), (3, 0), (18, 14), (16, 28), (23, 1), (10, 22), (26, 1), (9, 1), (33, 23), (8, 15), (5, 23), (22, 2), (28, 7), (20, 17), (23, 31), (30, 26), (8, 18), (35, 10), (20, 18), (25, 25), (35, 0), (19, 15), (24, 30), (12, 24), (34, 30), (29, 6), (30, 12), (38, 19), (12, 14), (22, 7), (22, 15), (5, 28), (35, 18), (30, 29), (28, 22), (11, 29), (3, 16), (37, 22), (29, 28), (1, 19), (12, 11), (4, 14), (29, 4), (32, 9), (34, 19), (23, 15), (33, 29), (24, 27), (29, 23), (18, 27), (23, 21), (38, 11), (32, 8), (13, 14), (4, 30), (34, 18), (9, 12), (4, 23), (27, 29), (1, 3), (32, 7), (5, 13), (10, 16), (24, 16), (25, 10), (23, 3), (1, 29), (1, 6), (31, 26), (3, 12), (9, 8), (6, 6), (22, 26), (26, 14), (13, 2), (33, 21), (35, 11), (8, 3), (0, 21), (2, 4), (27, 0), (30, 3), (30, 20), (7, 22), (2, 24), (18, 12), (5, 19), (26, 8), (10, 29), (9, 6), (28, 25), (10, 23), (29, 18), (24, 18), (33, 30), (9, 16), (12, 31), (10, 27), (27, 30), (19, 18), (7, 2), (21, 2), (27, 25), (24, 17), (26, 2), (38, 22), (36, 18), (16, 7), (7, 1), (0, 19), (37, 23), (28, 5), (17, 30), (6, 30), (18, 22), (32, 26), (13, 29), (24, 8), (3, 23), (33, 2), (22, 16), (23, 7), (10, 5), (3, 21), (22, 20), (0, 31), (2, 26), (38, 25), (13, 30), (4, 4), (0, 1), (22, 24), (30, 4), (16, 31), (30, 18), (18, 21), (13, 20), (10, 0), (21, 14), (1, 27), (32, 24), (25, 17), (18, 7), (31, 9), (7, 31), (19, 10), (17, 21), (34, 6), (6, 3), (0, 20), (32, 1), (27, 28), (11, 26), (25, 2), (1, 30), (7, 23), (20, 1), (4, 10), (18, 20), (16, 0), (30, 31), (16, 8), (22, 29), (37, 29), (17, 19), (30, 23), (19, 21), (22, 17), (35, 20), (34, 25), (32, 4), (36, 0), (13, 7), (38, 29), (30, 21), (21, 23), (9, 10), (34, 10), (1, 22), (9, 13), (5, 4), (3, 29), (7, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926478", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 1), (17, 8), (27, 18), (30, 23), (32, 13), (14, 25), (3, 27), (17, 10), (14, 8), (1, 9), (22, 6), (6, 25), (22, 28), (25, 4), (3, 22), (12, 2), (7, 25), (5, 18), (28, 0), (10, 18), (16, 10), (31, 11), (8, 11), (6, 26), (4, 28), (18, 13), (15, 4), (31, 14), (11, 8), (30, 19), (16, 7), (3, 16), (19, 23), (3, 9), (2, 1), (20, 18), (2, 31), (16, 28), (23, 4), (12, 1), (3, 21), (24, 29), (2, 5), (25, 31), (2, 0), (22, 1), (25, 20), (8, 29), (12, 8), (20, 15), (0, 20), (2, 20), (24, 28), (3, 26), (1, 26), (6, 31), (21, 30), (18, 21), (20, 19), (22, 4), (22, 23), (1, 11), (5, 10), (18, 17), (0, 10), (29, 10), (21, 22), (6, 14), (7, 29), (32, 21), (29, 25), (13, 12), (8, 31), (2, 11), (23, 2), (19, 2), (6, 15), (26, 29), (21, 16), (28, 18), (8, 8), (1, 24), (20, 20), (16, 3), (30, 8), (14, 16), (11, 16), (25, 13), (21, 3), (20, 6), (5, 26), (30, 2), (16, 2), (25, 21), (24, 4), (7, 5), (0, 25), (7, 6), (0, 24), (30, 27), (20, 2), (0, 21), (4, 27), (18, 27), (12, 25), (18, 23), (26, 31), (25, 2), (32, 26), (6, 16), (26, 24), (21, 1), (11, 17), (20, 22), (7, 18), (17, 4), (27, 6), (30, 30), (8, 0), (24, 15), (31, 25), (0, 22), (18, 26), (31, 28), (29, 26), (28, 20), (25, 15), (19, 0), (8, 13), (0, 27), (15, 14), (11, 19), (32, 4), (17, 2), (4, 12), (25, 3), (9, 5), (31, 4), (28, 12), (23, 26), (6, 28), (28, 5), (5, 1), (5, 24), (9, 11), (0, 28), (24, 17), (2, 2), (3, 8), (4, 22), (18, 3), (26, 16), (12, 15), (20, 25), (7, 9), (1, 18), (4, 1), (8, 28), (7, 26), (20, 11), (13, 9), (9, 25), (9, 17), (30, 7), (22, 16), (12, 31), (26, 12), (21, 12), (26, 8), (22, 21), (10, 29), (26, 5), (28, 7), (5, 13), (1, 16), (31, 2), (9, 19), (5, 14), (14, 2), (14, 12), (29, 29), (18, 20), (17, 3), (11, 11), (19, 1), (17, 6), (5, 11), (9, 30), (31, 27), (3, 14), (21, 0), (1, 0), (23, 30), (17, 20), (20, 9), (2, 29), (7, 24), (1, 1), (13, 13), (10, 25), (17, 9), (23, 11), (21, 6), (17, 13), (6, 11), (5, 7), (1, 6), (28, 13), (4, 9), (18, 14), (18, 19), (27, 30), (10, 31), (19, 19), (9, 7), (27, 8), (14, 11), (4, 25), (3, 12), (15, 6), (31, 23), (10, 28), (26, 14), (9, 2), (13, 14), (6, 27), (10, 13), (21, 25), (5, 15), (14, 29), (32, 18), (25, 5), (24, 6), (24, 21), (21, 21), (9, 10), (18, 18), (20, 17), (0, 18), (32, 10), (18, 8), (6, 0), (29, 14), (2, 28), (2, 22), (16, 24), (30, 15), (13, 26), (4, 13), (20, 26), (19, 16), (17, 22), (30, 22), (29, 6), (10, 11), (22, 30), (4, 4), (20, 13), (12, 17), (15, 25), (11, 14), (9, 27), (12, 21), (28, 3), (8, 25), (5, 4), (28, 21), (4, 7), (8, 23), (5, 3), (6, 23), (10, 21), (30, 14), (3, 13), (12, 24), (10, 27), (5, 16), (22, 3), (12, 9), (6, 22), (23, 25), (20, 23), (23, 29), (11, 5), (8, 15), (21, 5), (22, 5), (9, 13), (8, 1), (9, 9), (9, 8), (2, 13), (21, 11), (10, 16), (13, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "871920", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (15, 25), (27, 31), (4, 14), (5, 7), (1, 8), (37, 12), (22, 17), (18, 34), (4, 23), (5, 8), (28, 0), (22, 0), (28, 6), (13, 18), (32, 18), (17, 16), (0, 5), (10, 28), (37, 28), (3, 24), (32, 11), (23, 19), (30, 15), (31, 30), (22, 1), (3, 5), (35, 3), (16, 0), (29, 29), (29, 24), (16, 10), (0, 8), (17, 33), (6, 18), (7, 33), (26, 20), (17, 15), (30, 7), (28, 3), (37, 19), (9, 6), (37, 22), (7, 17), (16, 27), (16, 28), (21, 3), (31, 32), (20, 15), (7, 31), (31, 20), (35, 23), (0, 2), (3, 8), (21, 22), (22, 11), (3, 27), (6, 17), (8, 34), (15, 2), (2, 21), (12, 17), (32, 24), (7, 27), (14, 20), (33, 25), (12, 27), (9, 17), (32, 33), (32, 32), (28, 12), (13, 22), (27, 1), (20, 25), (20, 35), (27, 11), (11, 32), (18, 27), (34, 23), (35, 15), (35, 30), (7, 23), (20, 12), (11, 31), (36, 34), (34, 18), (0, 20), (31, 22), (7, 7), (33, 32), (20, 13), (20, 29), (30, 5), (23, 36), (1, 34), (9, 14), (0, 30), (25, 25), (20, 6), (1, 15), (37, 25), (24, 28), (15, 23), (14, 16), (20, 22), (35, 31), (29, 5), (18, 31), (20, 19), (24, 21), (12, 28), (26, 14), (9, 2), (22, 8), (29, 0), (3, 32), (7, 5), (3, 10), (16, 7), (33, 6), (23, 1), (21, 10), (21, 28), (1, 17), (5, 0), (18, 13), (21, 29), (33, 17), (32, 35), (9, 21), (33, 36), (27, 17), (6, 34), (3, 13), (10, 36), (2, 35), (26, 12), (15, 12), (3, 16), (14, 28), (30, 35), (34, 28), (21, 13), (17, 18), (30, 0), (31, 8), (33, 5), (29, 3), (37, 31), (3, 11), (19, 26), (9, 26), (2, 26), (10, 34), (26, 18), (2, 1), (0, 3), (0, 31), (37, 2), (25, 1), (17, 21), (33, 10), (30, 8), (22, 4), (9, 4), (28, 29), (0, 1), (8, 16), (31, 23), (25, 31), (27, 21), (20, 5), (17, 25), (3, 21), (13, 0), (2, 16), (34, 30), (22, 2), (19, 21), (9, 1), (18, 19), (21, 14), (8, 26), (11, 26), (10, 18), (8, 5), (27, 3), (9, 18), (6, 8), (24, 13), (36, 2), (17, 1), (23, 27), (28, 34), (4, 1), (8, 0), (37, 6), (16, 3), (13, 19), (7, 30), (20, 8), (7, 34), (20, 4), (25, 28), (17, 31), (3, 33), (33, 35), (21, 20), (32, 22), (21, 18), (12, 23), (21, 1), (0, 33), (35, 8), (17, 4), (8, 24), (19, 13), (0, 24), (18, 17), (27, 12), (4, 9), (36, 10), (0, 13), (15, 10), (19, 36), (36, 23), (30, 25), (3, 9), (29, 20), (16, 1), (7, 18), (34, 15), (34, 24), (26, 4), (20, 16), (24, 7), (23, 25), (32, 27), (5, 4), (7, 4), (8, 36), (31, 14), (3, 30), (36, 26), (28, 1), (22, 23), (2, 25), (13, 24), (14, 32), (9, 11), (27, 23), (22, 6), (36, 8), (19, 16), (16, 13), (9, 27), (6, 23), (4, 17), (32, 29), (23, 33), (10, 12), (31, 2), (19, 25), (14, 8), (32, 0), (17, 22), (16, 33), (12, 7), (16, 31), (7, 20), (28, 10), (8, 27), (11, 34), (17, 30), (8, 18), (25, 33), (17, 9), (29, 16), (35, 35), (5, 33), (35, 28), (0, 12), (36, 20), (24, 18), (18, 20), (10, 6), (30, 13), (5, 30), (9, 36), (30, 17), (1, 7), (10, 20), (29, 28), (0, 25), (11, 21), (27, 19), (22, 3), (9, 24), (6, 26), (37, 11), (7, 26), (20, 31), (35, 24), (3, 3), (18, 16), (22, 21), (5, 31), (28, 30), (15, 8), (12, 1), (30, 27), (35, 13), (13, 25), (36, 21), (17, 7), (17, 5), (28, 17), (13, 13), (27, 7), (19, 17), (33, 0), (1, 29), (27, 4), (0, 10), (16, 16), (9, 23), (23, 14), (3, 18), (27, 30), (8, 6), (35, 7), (30, 10), (1, 11), (6, 22), (14, 12), (11, 12), (7, 11), (7, 0), (13, 23), (23, 9), (21, 16), (28, 23), (15, 32), (23, 11), (35, 4), (17, 28), (6, 35), (26, 15), (6, 31), (9, 8), (32, 21), (12, 15), (37, 9), (10, 1), (19, 14), (3, 23), (6, 0), (13, 16), (33, 23), (7, 21), (18, 0), (25, 27), (37, 27), (8, 21), (23, 6), (13, 34), (17, 0), (3, 22), (23, 17), (18, 3), (31, 12), (36, 1), (37, 33), (12, 25), (8, 33), (11, 19), (12, 18), (8, 4), (16, 26), (5, 27), (0, 7), (12, 12), (25, 19), (21, 17), (37, 7), (1, 18), (20, 36), (9, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30240", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 31), (11, 23), (24, 20), (24, 30), (0, 5), (12, 16), (2, 21), (26, 31), (31, 21), (0, 21), (28, 2), (25, 12), (22, 26), (25, 3), (26, 28), (14, 26), (9, 20), (11, 6), (15, 7), (21, 2), (18, 3), (11, 4), (7, 8), (17, 20), (12, 7), (20, 2), (19, 18), (7, 14), (11, 2), (24, 6), (4, 27), (4, 26), (26, 26), (3, 30), (33, 12), (24, 2), (34, 27), (28, 23), (10, 25), (14, 7), (27, 30), (16, 6), (34, 13), (21, 11), (3, 3), (15, 21), (30, 21), (22, 6), (14, 28), (30, 4), (15, 13), (4, 28), (8, 14), (0, 26), (28, 10), (32, 8), (9, 9), (0, 20), (23, 2), (30, 31), (17, 23), (3, 22), (20, 1), (3, 29), (17, 9), (30, 0), (34, 10), (30, 19), (33, 7), (14, 9), (21, 21), (0, 6), (2, 15), (33, 14), (22, 23), (34, 15), (26, 7), (20, 24), (24, 0), (19, 4), (25, 5), (9, 10), (0, 12), (27, 17), (0, 14), (10, 24), (29, 23), (0, 27), (1, 6), (16, 18), (1, 13), (21, 25), (1, 26), (24, 13), (10, 17), (34, 17), (14, 0), (9, 15), (13, 27), (4, 6), (13, 20), (16, 21), (34, 29), (5, 26), (7, 13), (26, 22), (9, 12), (35, 20), (12, 3), (28, 30), (6, 1), (25, 22), (6, 25), (27, 12), (10, 28), (3, 9), (29, 7), (19, 17), (34, 23), (1, 31), (12, 9), (22, 11), (18, 25), (25, 26), (16, 2), (15, 12), (27, 10), (26, 23), (19, 0), (23, 19), (7, 5), (28, 7), (15, 23), (8, 30), (25, 27), (31, 24), (23, 7), (29, 13), (9, 6), (32, 23), (1, 7), (4, 3), (30, 7), (32, 0), (32, 20), (2, 1), (5, 6), (4, 0), (10, 11), (8, 21), (19, 5), (11, 15), (19, 3), (34, 18), (22, 18), (33, 31), (29, 28), (27, 15), (18, 11), (23, 20), (21, 13), (33, 15), (27, 1), (28, 14), (1, 11), (32, 26), (24, 15), (19, 13), (10, 18), (23, 6), (31, 26), (18, 31), (12, 6), (8, 23), (20, 10), (6, 3), (4, 22), (14, 15), (22, 13), (4, 29), (22, 5), (19, 22), (4, 20), (1, 19), (35, 8), (24, 23), (9, 21), (10, 29), (35, 13), (25, 28), (13, 21), (32, 1), (19, 23), (8, 2), (26, 8), (13, 4), (5, 9), (18, 30), (9, 26), (34, 4), (2, 7), (15, 4), (8, 25), (17, 6), (28, 29), (23, 12), (23, 23), (30, 10), (2, 19), (2, 30), (7, 3), (16, 11), (1, 1), (6, 5), (30, 15), (16, 16), (25, 10), (9, 13), (20, 28), (15, 0), (28, 19), (12, 21), (23, 4), (33, 17), (14, 6), (21, 14), (2, 28), (20, 14), (0, 11), (23, 24), (5, 5), (9, 25), (20, 23), (30, 6), (5, 2), (34, 30), (9, 22), (33, 29), (18, 18), (15, 18), (3, 7), (9, 5), (4, 23), (22, 21), (29, 17), (21, 31), (28, 11), (4, 24), (35, 19), (2, 24), (16, 13), (6, 23), (18, 1), (20, 8), (8, 28), (27, 22), (26, 16), (5, 11), (32, 30), (1, 9), (11, 10), (25, 19), (8, 20), (15, 6), (16, 26), (3, 31), (22, 7), (25, 23), (25, 9), (32, 7), (6, 12), (6, 21), (24, 17), (34, 12), (35, 2), (26, 11), (35, 16), (12, 27), (20, 29), (15, 10), (28, 8), (3, 24), (10, 20), (24, 3), (19, 19), (14, 18), (15, 28), (29, 24), (16, 31), (4, 10), (29, 18), (16, 24), (6, 28), (22, 14), (5, 10), (7, 26), (23, 14), (1, 22), (20, 9), (26, 17), (11, 0), (31, 9), (33, 3), (4, 17), (27, 21), (10, 21), (21, 3), (23, 30), (11, 31), (23, 25), (9, 0), (1, 21), (19, 16), (12, 26), (34, 16), (31, 27), (18, 28), (13, 6), (15, 5), (31, 10), (25, 8), (5, 0), (20, 30), (33, 2), (18, 6), (15, 2), (8, 18), (32, 25), (13, 30), (16, 28), (1, 30), (32, 14), (27, 7), (17, 4), (31, 12), (35, 23), (15, 31), (10, 23), (17, 8), (26, 14), (15, 30), (7, 7), (13, 23), (3, 8), (18, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399168", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 34), (31, 23), (31, 18), (7, 30), (15, 6), (30, 33), (12, 14), (16, 0), (23, 9), (25, 2), (27, 14), (6, 23), (16, 4), (1, 2), (1, 10), (25, 31), (7, 34), (6, 29), (12, 3), (24, 29), (7, 23), (13, 19), (25, 4), (29, 33), (6, 20), (4, 24), (25, 8), (16, 31), (5, 25), (18, 14), (16, 19), (30, 4), (11, 31), (16, 7), (12, 20), (13, 25), (6, 19), (21, 20), (4, 20), (27, 35), (13, 20), (15, 16), (12, 23), (24, 6), (2, 1), (27, 19), (19, 25), (22, 25), (18, 30), (10, 11), (0, 12), (30, 32), (19, 8), (16, 26), (28, 16), (26, 20), (32, 22), (25, 24), (29, 35), (1, 32), (22, 24), (27, 36), (23, 17), (4, 17), (16, 15), (30, 6), (30, 3), (25, 32), (30, 8), (8, 2), (31, 15), (2, 23), (12, 7), (22, 14), (11, 33), (1, 27), (0, 2), (24, 12), (15, 15), (32, 31), (8, 11), (7, 4), (0, 11), (12, 15), (3, 3), (14, 25), (19, 13), (18, 21), (11, 29), (21, 24), (21, 10), (17, 7), (16, 34), (28, 26), (16, 25), (4, 21), (23, 23), (27, 15), (16, 32), (9, 6), (5, 20), (32, 15), (32, 10), (10, 6), (9, 17), (17, 10), (13, 6), (8, 6), (12, 5), (23, 3), (29, 0), (11, 12), (24, 18), (24, 20), (14, 30), (20, 34), (11, 28), (5, 24), (18, 0), (27, 4), (28, 36), (31, 32), (6, 25), (27, 33), (17, 6), (4, 10), (17, 35), (2, 12), (32, 23), (13, 13), (4, 3), (0, 6), (6, 0), (14, 2), (31, 22), (28, 18), (3, 31), (23, 20), (6, 14), (28, 28), (0, 26), (25, 7), (20, 16), (27, 18), (27, 3), (26, 25), (29, 2), (11, 15), (13, 10), (21, 2), (17, 36), (7, 11), (18, 22), (10, 23), (29, 1), (2, 17), (29, 9), (14, 4), (1, 3), (18, 13), (26, 13), (17, 34), (5, 8), (21, 27), (12, 13), (25, 12), (23, 1), (28, 0), (32, 34), (9, 30), (15, 23), (9, 10), (0, 14), (19, 14), (22, 4), (13, 34), (7, 13), (8, 24), (14, 16), (22, 12), (23, 6), (4, 4), (18, 1), (11, 6), (9, 3), (31, 21), (18, 35), (32, 0), (9, 28), (16, 5), (5, 22), (24, 22), (30, 20), (18, 19), (14, 11), (19, 17), (25, 25), (10, 1), (29, 23), (13, 30), (20, 24), (25, 15), (6, 21), (21, 1), (3, 32), (11, 25), (1, 26), (13, 12), (28, 5), (3, 28), (0, 32), (10, 2), (32, 11), (16, 22), (17, 29), (26, 6), (13, 11), (10, 20), (18, 15), (13, 27), (28, 21), (4, 26), (19, 31), (14, 24), (18, 29), (5, 35), (11, 1), (23, 13), (24, 26), (2, 26), (17, 2), (27, 5), (24, 1), (11, 21), (21, 25), (8, 26), (26, 35), (18, 24), (10, 16), (17, 22), (31, 2), (19, 7), (31, 9), (13, 22), (2, 13), (17, 13), (17, 26), (21, 5), (19, 30), (31, 31), (27, 17), (22, 1), (15, 13), (1, 13), (17, 1), (31, 17), (18, 27), (5, 34), (1, 31), (19, 23), (9, 5), (8, 9), (30, 25), (2, 21), (3, 8), (19, 26), (27, 1), (0, 20), (12, 35), (2, 28), (11, 34), (32, 14), (5, 29), (3, 23), (13, 1), (22, 27), (1, 12), (3, 35), (20, 21), (23, 30), (31, 0), (31, 36), (13, 9), (9, 0), (18, 36), (25, 21), (31, 26), (3, 33), (19, 20), (22, 6), (1, 14), (13, 32), (10, 8), (18, 28), (21, 6), (25, 5), (31, 12), (8, 31), (19, 22), (25, 13), (15, 8), (30, 7), (0, 27), (19, 4), (4, 28), (10, 19), (29, 11), (13, 16), (7, 20), (9, 31), (2, 36), (21, 30), (14, 36), (12, 30), (2, 18), (8, 21), (16, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112320", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 2), (14, 15), (0, 17), (23, 17), (24, 6), (35, 17), (3, 14), (10, 16), (16, 21), (9, 2), (17, 14), (26, 21), (5, 27), (14, 22), (14, 5), (1, 11), (19, 1), (33, 17), (29, 11), (25, 18), (28, 21), (11, 19), (22, 24), (19, 7), (4, 26), (2, 26), (7, 5), (17, 29), (25, 5), (3, 11), (32, 11), (1, 13), (29, 14), (16, 20), (15, 23), (5, 18), (12, 26), (3, 12), (31, 21), (35, 6), (20, 24), (8, 0), (13, 14), (13, 30), (11, 15), (32, 0), (15, 2), (1, 30), (5, 6), (31, 16), (4, 18), (7, 19), (33, 22), (6, 19), (30, 24), (6, 26), (15, 5), (2, 1), (29, 2), (11, 9), (27, 1), (22, 19), (32, 5), (13, 10), (10, 19), (13, 6), (0, 3), (29, 19), (3, 20), (6, 17), (15, 11), (32, 19), (16, 26), (0, 7), (22, 14), (34, 2), (4, 17), (4, 12), (28, 10), (24, 11), (1, 19), (13, 5), (5, 8), (16, 16), (11, 25), (25, 4), (5, 4), (18, 18), (9, 26), (21, 28), (8, 15), (25, 6), (32, 9), (9, 16), (22, 22), (30, 0), (15, 20), (4, 0), (17, 1), (14, 26), (6, 8), (18, 6), (19, 12), (25, 8), (10, 6), (26, 8), (29, 18), (10, 24), (26, 7), (0, 11), (34, 1), (23, 24), (35, 0), (30, 15), (21, 21), (34, 10), (22, 1), (16, 2), (33, 5), (3, 18), (30, 17), (31, 13), (20, 11), (10, 1), (9, 8), (24, 29), (15, 13), (22, 13), (33, 24), (24, 18), (30, 20), (34, 27), (13, 26), (0, 6), (29, 23), (20, 12), (16, 28), (2, 14), (8, 24), (27, 2), (21, 3), (19, 13), (27, 8), (29, 6), (4, 10), (29, 13), (24, 7), (3, 24), (13, 20), (9, 12), (13, 3), (23, 30), (35, 16), (25, 11), (17, 22), (28, 16), (21, 12), (14, 23), (20, 19), (21, 27), (12, 1), (23, 16), (20, 25), (0, 22), (15, 1), (16, 10), (1, 28), (3, 15), (34, 7), (24, 10), (29, 26), (4, 30), (12, 5), (17, 30), (12, 14), (14, 18), (0, 14), (21, 5), (6, 16), (19, 0), (13, 24), (21, 13), (1, 6), (9, 27), (34, 18), (19, 10), (28, 12), (7, 7), (33, 8), (16, 5), (23, 21), (23, 0), (1, 8), (19, 3), (25, 24), (25, 30), (33, 3), (13, 9), (3, 21), (34, 28), (34, 19), (27, 10), (0, 12), (15, 26), (10, 7), (9, 23), (10, 18), (8, 6), (33, 13), (10, 8), (22, 15), (2, 15), (0, 29), (7, 6), (6, 21), (11, 4), (30, 11), (20, 5), (15, 9), (23, 22), (17, 6), (19, 4), (10, 23), (25, 19), (19, 8), (17, 16), (11, 3), (19, 20), (35, 19), (18, 21), (34, 5), (30, 28), (16, 30), (15, 14), (35, 22), (19, 14), (9, 14), (25, 3), (15, 30), (13, 8), (21, 17), (34, 13), (8, 19), (1, 2), (17, 20), (12, 2), (7, 10), (25, 1), (33, 2), (6, 24), (10, 9), (7, 9), (2, 12), (32, 16), (28, 28), (24, 8), (17, 26), (4, 1), (32, 1), (21, 8), (32, 30), (24, 22), (23, 23), (17, 0), (8, 18), (4, 19), (0, 9), (6, 14), (23, 13), (24, 19), (7, 1), (5, 22), (17, 12), (21, 20), (5, 3), (5, 25), (24, 4), (8, 26), (19, 21), (34, 8), (26, 1), (23, 2), (17, 21), (15, 10), (19, 5), (32, 15), (23, 15), (16, 22), (12, 25), (1, 4), (26, 16), (7, 11), (12, 16), (27, 4), (20, 15), (14, 24), (7, 18), (27, 20), (16, 27), (34, 23), (2, 5), (20, 6), (12, 3), (29, 16), (25, 10), (0, 20), (34, 12), (29, 9), (31, 3), (35, 5), (15, 6), (34, 22), (30, 23), (17, 19), (13, 2), (30, 2), (32, 29), (34, 3), (28, 8), (22, 23), (13, 19), (13, 0), (25, 25), (29, 22), (4, 5), (26, 6), (22, 8), (27, 3), (11, 30), (35, 26), (34, 29), (3, 17), (1, 20), (19, 6), (12, 18), (5, 7), (1, 24), (35, 8), (21, 14), (0, 23), (29, 1), (35, 11), (24, 25), (13, 4), (33, 7), (35, 7), (11, 27), (8, 22), (29, 27), (6, 11), (34, 15), (31, 25), (2, 29), (10, 4), (14, 3), (15, 22), (19, 28), (15, 8), (34, 9), (20, 27), (2, 9), (32, 24), (6, 12), (7, 0), (1, 29), (8, 1), (2, 4), (15, 3), (9, 7), (11, 18), (17, 27), (25, 29), (33, 25), (31, 6), (32, 23), (32, 3), (16, 29), (13, 29), (15, 7), (8, 25), (13, 1), (17, 10), (19, 19), (10, 10), (24, 16), (19, 22), (14, 16), (7, 14), (7, 21), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "502200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 29), (21, 9), (28, 19), (18, 31), (26, 13), (10, 0), (0, 30), (17, 4), (6, 6), (17, 11), (10, 5), (10, 6), (26, 15), (5, 30), (21, 14), (1, 3), (18, 20), (26, 18), (22, 31), (28, 6), (6, 19), (25, 17), (17, 24), (24, 20), (3, 20), (16, 2), (13, 31), (28, 26), (11, 5), (11, 10), (2, 11), (9, 24), (13, 32), (29, 10), (4, 32), (22, 15), (23, 20), (3, 1), (9, 14), (2, 25), (3, 18), (9, 15), (17, 25), (15, 1), (22, 19), (1, 19), (25, 5), (15, 14), (22, 8), (21, 25), (16, 22), (7, 26), (8, 29), (20, 15), (22, 27), (22, 26), (21, 15), (8, 3), (15, 17), (10, 26), (9, 23), (9, 22), (6, 15), (25, 26), (27, 31), (17, 30), (8, 7), (18, 1), (14, 17), (19, 19), (26, 16), (22, 1), (12, 11), (24, 25), (21, 18), (11, 17), (5, 26), (6, 12), (22, 14), (29, 1), (12, 32), (18, 13), (29, 26), (17, 1), (27, 10), (21, 5), (11, 25), (20, 19), (2, 26), (20, 28), (11, 12), (24, 15), (17, 28), (4, 15), (17, 10), (3, 15), (6, 28), (19, 17), (0, 29), (15, 18), (7, 12), (26, 23), (19, 8), (12, 22), (19, 0), (19, 3), (26, 8), (6, 10), (23, 21), (28, 13), (7, 9), (22, 16), (29, 13), (19, 27), (17, 31), (27, 8), (20, 17), (23, 5), (16, 14), (27, 0), (14, 28), (29, 22), (8, 20), (8, 27), (22, 6), (23, 6), (14, 20), (0, 8), (5, 1), (24, 21), (12, 18), (24, 6), (29, 29), (27, 9), (16, 9), (6, 14), (29, 8), (9, 29), (17, 5), (11, 24), (14, 31), (27, 15), (26, 14), (25, 27), (19, 14), (4, 12), (19, 21), (17, 7), (26, 1), (26, 9), (23, 32), (9, 30), (26, 26), (21, 12), (16, 3), (24, 23), (13, 16), (29, 18), (14, 3), (24, 2), (9, 13), (4, 20), (25, 19), (22, 13), (1, 25), (26, 22), (26, 30), (20, 5), (29, 24), (6, 29), (1, 22), (6, 26), (28, 8), (15, 28), (12, 5), (15, 21), (16, 25), (0, 4), (1, 24), (28, 20), (15, 32), (17, 26), (17, 8), (29, 21), (1, 8), (11, 13), (1, 13), (12, 27), (3, 6), (2, 28), (3, 25), (15, 9), (5, 15), (12, 26), (9, 7), (24, 12), (10, 4), (7, 13), (29, 16), (11, 4), (20, 24), (2, 7), (21, 16), (0, 25), (18, 8), (28, 5), (10, 23), (24, 9), (7, 10), (6, 21), (7, 23), (25, 29), (2, 31), (29, 2), (3, 5), (5, 31), (14, 27), (5, 4), (24, 0), (28, 28), (11, 0), (24, 19), (27, 12), (18, 22), (8, 9), (14, 7), (10, 14), (22, 0), (8, 17), (3, 11), (5, 20), (2, 12), (6, 13), (21, 19), (24, 18), (25, 10), (15, 4), (28, 29), (21, 28), (28, 9), (27, 7), (21, 6), (28, 16), (11, 22), (23, 3), (5, 25), (4, 1), (21, 29), (4, 11), (19, 18), (12, 29), (1, 6), (1, 14), (13, 0), (11, 29), (14, 9), (3, 10), (1, 10), (4, 8), (20, 20), (29, 5), (1, 31), (7, 20), (10, 10), (14, 6), (16, 24), (29, 7), (11, 6), (10, 18), (6, 18), (17, 29), (22, 2), (5, 27), (19, 20), (27, 6), (1, 23), (24, 28), (14, 14), (19, 31), (1, 18), (1, 30), (4, 30), (27, 32), (11, 27), (24, 22), (25, 21), (13, 22), (9, 12), (28, 31), (26, 6), (24, 14), (12, 28), (5, 22), (18, 6), (1, 32), (27, 17), (10, 21), (26, 31), (20, 12), (5, 19), (22, 25), (12, 30), (19, 5), (15, 13), (28, 10), (6, 3), (13, 5), (22, 10), (23, 18), (28, 27), (17, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "607743", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), 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), (35, 13), (28, 16), (22, 24), (33, 27), (6, 18), (8, 25), (21, 25), (2, 24), (30, 14), (11, 26), (36, 26), (37, 3), (13, 14), (11, 23), (35, 23), (3, 22), (25, 22), (9, 21), (3, 26), (18, 5), (27, 27), (0, 7), (28, 22), (28, 3), (34, 19), (36, 18), (16, 14), (16, 2), (5, 19), (27, 12), (31, 5), (0, 2), (11, 1), (17, 21), (24, 18), (33, 1), (24, 23), (25, 13), (0, 1), (7, 29), (32, 11), (27, 8), (30, 27), (5, 11), (21, 28), (12, 11), (26, 7), (27, 5), (30, 1), (23, 19), (13, 5), (28, 13), (19, 19), (8, 19), (12, 1), (5, 1), (22, 2), (16, 24), (36, 8), (38, 23), (33, 18), (25, 25), (14, 21), (38, 16), (31, 29), (22, 25), (37, 19), (33, 17), (33, 28), (38, 3), (19, 2), (25, 18), (31, 28), (18, 24), (34, 20), (37, 11), (31, 15), (10, 13), (15, 17), (11, 5), (7, 27), (33, 15), (12, 13), (27, 20), (20, 25), (10, 29), (0, 20), (1, 12), (35, 0), (27, 28), (34, 3), (12, 26), (0, 18), (14, 13), (9, 12), (34, 7), (4, 25), (9, 15), (24, 6), (18, 28), (13, 15), (19, 18), (9, 11), (19, 7), (0, 24), (31, 6), (30, 10), (36, 21), (7, 14), (9, 10), (28, 8), (37, 14), (26, 27), (28, 11), (12, 3), (24, 10), (11, 27), (20, 22), (26, 20), (6, 19), (13, 16), (32, 2), (1, 17), (1, 16), (36, 28), (8, 21), (25, 23), (14, 9), (7, 17), (33, 23), (36, 12), (16, 18), (6, 13), (26, 21), (27, 14), (3, 12), (33, 24), (31, 22), (9, 4), (1, 15), (9, 0), (9, 22), (22, 29), (36, 3), (34, 22), (31, 11), (20, 20), (21, 8), (25, 5), (10, 15), (37, 24), (12, 12), (8, 24), (4, 7), (25, 10), (27, 18), (18, 27), (19, 17), (5, 9), (6, 11), (17, 13), (17, 25), (35, 3), (8, 11), (10, 4), (6, 15), (30, 22), (22, 9), (32, 13), (30, 28), (35, 2), (11, 18), (16, 19), (23, 18), (33, 19), (36, 15), (26, 22), (26, 18), (32, 27), (31, 1), (7, 15), (15, 19), (27, 26), (26, 26), (15, 9), (33, 8), (3, 7), (17, 2), (25, 9), (20, 1), (32, 25), (18, 29), (28, 2), (1, 3), (8, 3), (33, 10), (21, 4), (29, 16), (23, 5), (18, 6), (5, 10), (3, 23), (31, 18), (22, 15), (11, 21), (35, 26), (33, 21), (24, 12), (38, 27), (9, 9), (30, 16), (17, 27), (10, 25), (14, 14), (33, 11), (9, 14), (25, 27), (21, 7), (19, 14), (26, 29), (37, 6), (28, 1), (28, 17), (32, 15), (7, 9), (32, 21), (8, 10), (20, 16), (12, 23), (23, 22), (38, 9), (25, 24), (33, 25), (38, 10), (29, 22), (27, 2), (3, 28), (25, 3), (32, 6), (25, 7), (17, 28), (0, 4), (2, 2), (7, 16), (16, 23), (0, 16), (36, 6), (21, 15), (20, 28), (26, 23), (18, 14), (28, 21), (26, 1), (34, 26), (21, 27), (26, 19), (29, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341520", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 24), (14, 21), (9, 5), (9, 31), (24, 13), (7, 3), (6, 21), (16, 16), (32, 1), (3, 30), (32, 28), (20, 26), (11, 12), (20, 24), (9, 22), (7, 28), (25, 24), (8, 1), (30, 4), (5, 22), (19, 24), (30, 13), (16, 31), (0, 27), (28, 12), (25, 17), (20, 18), (32, 13), (11, 4), (26, 11), (11, 33), (24, 18), (5, 17), (13, 23), (12, 26), (30, 1), (15, 11), (11, 17), (32, 27), (9, 25), (32, 34), (12, 17), (10, 6), (27, 8), (8, 20), (7, 29), (7, 17), (8, 30), (1, 20), (3, 4), (28, 29), (24, 24), (18, 15), (3, 23), (12, 1), (5, 0), (22, 25), (17, 15), (29, 32), (7, 31), (24, 2), (9, 18), (18, 16), (4, 25), (23, 5), (10, 34), (27, 1), (5, 11), (27, 30), (29, 14), (10, 31), (5, 13), (6, 28), (3, 32), (29, 31), (23, 16), (11, 20), (0, 26), (26, 3), (24, 19), (29, 13), (17, 32), (2, 0), (33, 24), (3, 14), (22, 9), (19, 4), (30, 34), (4, 11), (10, 30), (29, 33), (30, 32), (33, 21), (31, 0), (32, 29), (23, 12), (9, 20), (12, 30), (23, 28), (6, 1), (22, 24), (28, 2), (13, 34), (4, 3), (17, 19), (16, 27), (5, 9), (21, 18), (29, 19), (2, 20), (16, 20), (23, 27), (29, 1), (17, 34), (8, 14), (16, 25), (8, 15), (14, 6), (32, 19), (25, 32), (16, 7), (9, 30), (15, 15), (15, 22), (30, 33), (18, 26), (24, 21), (14, 3), (7, 6), (31, 3), (15, 8), (1, 8), (10, 5), (14, 1), (34, 7), (8, 25), (25, 31), (29, 12), (22, 32), (10, 10), (30, 6), (26, 21), (16, 21), (27, 11), (0, 30), (5, 15), (31, 19), (19, 1), (28, 4), (34, 14), (30, 16), (29, 15), (27, 5), (21, 26), (21, 29), (25, 18), (28, 18), (23, 14), (25, 0), (4, 32), (30, 23), (24, 6), (1, 25), (32, 31), (0, 20), (13, 16), (26, 2), (4, 28), (15, 6), (4, 24), (25, 16), (8, 18), (2, 32), (15, 27), (3, 19), (1, 29), (13, 9), (4, 30), (29, 25), (4, 13), (11, 25), (26, 30), (9, 19), (19, 25), (18, 31), (10, 4), (21, 15), (20, 4), (32, 26), (15, 4), (1, 31), (30, 5), (8, 29), (23, 20), (13, 7), (6, 0), (5, 1), (10, 28), (0, 33), (12, 28), (2, 17), (31, 25), (22, 21), (29, 28), (7, 7), (27, 23), (12, 3), (2, 12), (17, 5), (27, 26), (26, 18), (7, 18), (9, 26), (22, 11), (25, 14), (12, 14), (10, 21), (12, 8), (28, 6), (9, 4), (11, 14), (31, 32), (26, 16), (29, 20), (22, 29), (29, 4), (0, 17), (8, 8), (13, 30), (24, 34), (32, 8), (31, 18), (0, 13), (17, 10), (4, 18), (29, 3), (6, 13), (25, 34), (18, 10), (32, 23), (1, 9), (28, 27), (30, 9), (20, 11), (31, 31), (15, 5), (1, 5), (33, 29), (7, 14), (16, 34), (19, 23), (17, 6), (27, 6), (12, 27), (2, 10), (30, 14), (32, 22), (19, 13), (4, 33), (8, 0), (13, 6), (26, 8), (15, 17), (8, 21), (17, 18), (6, 2), (16, 13), (12, 34), (23, 4), (29, 16), (6, 25), (11, 23), (9, 12), (8, 2), (6, 12), (7, 34), (30, 2), (9, 10), (28, 10), (32, 4), (13, 10), (34, 31), (21, 6), (13, 21), (30, 28), (9, 24), (3, 27), (10, 11), (16, 11), (33, 34), (0, 4), (9, 29), (26, 12), (29, 10), (2, 27), (10, 14), (22, 7), (13, 18), (33, 12), (31, 22), (22, 23), (13, 25), (0, 10), (33, 11), (16, 2), (34, 5), (0, 5), (15, 29), (11, 8), (17, 22), (4, 20), (18, 28), (24, 7), (18, 2), (25, 26), (28, 7), (17, 9), (28, 14), (17, 2), (20, 25), (0, 2), (15, 30), (3, 11), (20, 30), (13, 22), (34, 27), (6, 29), (5, 24), (29, 24), (34, 21), (25, 25), (10, 32), (16, 4), (13, 0), (6, 5), (31, 7), (22, 16), (16, 30), (20, 7), (7, 0), (12, 18), (11, 10), (18, 13), (31, 2), (16, 24), (16, 5), (32, 6), (15, 33), (1, 33), (22, 19), (21, 11), (15, 0), (30, 30), (26, 20), (18, 30), (2, 4), (0, 29), (18, 20), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682560", "dataset": "MATH"}
{"messages": [{"content": "In a 35x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 2), (24, 6), (27, 34), (11, 6), (4, 0), (23, 17), (13, 2), (19, 11), (2, 14), (22, 15), (11, 9), (6, 23), (17, 15), (22, 32), (7, 36), (19, 1), (32, 1), (29, 13), (2, 8), (30, 0), (34, 13), (25, 30), (12, 38), (8, 13), (32, 25), (12, 13), (17, 10), (31, 14), (6, 32), (28, 27), (24, 5), (0, 30), (0, 22), (23, 11), (34, 24), (9, 2), (2, 18), (3, 35), (6, 38), (21, 32), (12, 2), (8, 23), (8, 21), (27, 21), (5, 17), (21, 23), (15, 15), (26, 28), (32, 15), (4, 22), (3, 19), (30, 25), (24, 36), (28, 18), (14, 36), (3, 21), (11, 17), (20, 0), (8, 28), (12, 27), (34, 6), (12, 21), (28, 29), (18, 27), (17, 13), (11, 1), (7, 14), (4, 32), (22, 24), (17, 27), (30, 17), (1, 9), (4, 28), (10, 33), (16, 32), (12, 16), (19, 8), (14, 18), (34, 34), (2, 26), (11, 36), (33, 8), (10, 7), (14, 21), (13, 28), (25, 23), (13, 23), (20, 15), (24, 12), (6, 9), (23, 32), (12, 30), (5, 22), (25, 19), (31, 21), (30, 7), (18, 34), (18, 16), (14, 13), (27, 23), (20, 31), (18, 7), (30, 32), (15, 4), (3, 12), (30, 34), (9, 4), (20, 24), (28, 1), (17, 16), (24, 21), (0, 8), (28, 36), (9, 15), (34, 3), (22, 8), (27, 38), (11, 15), (4, 34), (13, 29), (29, 23), (34, 7), (32, 29), (14, 15), (28, 32), (22, 10), (32, 24), (34, 8), (13, 27), (25, 35), (19, 6), (16, 2), (29, 11), (32, 3), (32, 16), (22, 0), (14, 5), (5, 11), (6, 3), (30, 38), (21, 7), (26, 32), (24, 7), (23, 14), (25, 1), (27, 32), (9, 38), (18, 28), (32, 12), (15, 17), (10, 1), (17, 36), (28, 16), (21, 34), (22, 16), (0, 23), (6, 0), (18, 10), (18, 35), (5, 35), (15, 27), (27, 4), (26, 35), (27, 36), (12, 6), (0, 9), (20, 8), (25, 33), (4, 19), (4, 1), (28, 15), (4, 38), (21, 28), (11, 32), (22, 36), (31, 18), (4, 8), (15, 21), (25, 14), (9, 26), (10, 37), (11, 35), (17, 20), (11, 18), (30, 15), (11, 11), (33, 35), (25, 11), (0, 35), (4, 17), (6, 15), (6, 4), (0, 18), (4, 6), (23, 15), (5, 9), (7, 7), (11, 19), (25, 26), (0, 19), (7, 32), (3, 6), (12, 24), (1, 3), (22, 7), (30, 31), (18, 30), (32, 4), (6, 14), (5, 12), (9, 19), (0, 5), (15, 18), (30, 23), (9, 27), (16, 9), (10, 4), (34, 37), (14, 37), (21, 17), (0, 7), (16, 31), (7, 2), (15, 2), (22, 14), (9, 30), (23, 9), (31, 34), (1, 10), (19, 21), (32, 17), (21, 31), (32, 8), (16, 30), (20, 5), (17, 2), (10, 35), (3, 3), (31, 36), (22, 37), (13, 6), (8, 37), (4, 16), (16, 15), (9, 6), (1, 32), (14, 17), (19, 12), (12, 29), (34, 15), (1, 25), (22, 17), (7, 16), (20, 13), (24, 25), (30, 4), (17, 25), (24, 15), (1, 20), (18, 22), (12, 22), (12, 11), (25, 2), (34, 17), (15, 24), (14, 10), (20, 22), (30, 5), (28, 17), (16, 27), (11, 27), (5, 3), (1, 29), (14, 14), (7, 23), (32, 6), (13, 31), (13, 35), (32, 18), (33, 19), (13, 21), (7, 34), (0, 15), (5, 38), (11, 3), (14, 8), (23, 0), (34, 12), (9, 25), (13, 1), (34, 1), (5, 13), (13, 0), (8, 25), (21, 11), (19, 19), (2, 11), (22, 25), (27, 20), (34, 27), (14, 33), (17, 24), (13, 24), (20, 20), (30, 24), (23, 3), (31, 25), (22, 35), (4, 21), (24, 34), (2, 23), (23, 13), (30, 33), (9, 11), (27, 30), (11, 14), (13, 18), (11, 16), (10, 0), (28, 3), (4, 7), (23, 20), (10, 17), (25, 17), (22, 6), (2, 16), (31, 16), (19, 14), (21, 37), (34, 35), (8, 7), (32, 28), (20, 30), (27, 7), (32, 37), (27, 8), (10, 34), (22, 13), (30, 6), (2, 33), (31, 1), (3, 23), (8, 8), (22, 12), (2, 34), (1, 21), (18, 36), (24, 23), (1, 37), (0, 21), (0, 33), (21, 0), (18, 1), (7, 19), (20, 6), (24, 13), (10, 26), (21, 9), (25, 0), (33, 6), (13, 25), (1, 28), (19, 29), (5, 4), (7, 25), (11, 21), (26, 29), (6, 25), (10, 5), (25, 37), (23, 25), (33, 9), (30, 21), (32, 21), (29, 0), (2, 5), (31, 23), (34, 29), (5, 10), (24, 24), (27, 5), (13, 4), (26, 20), (0, 32), (23, 12), (21, 36), (18, 0), (3, 13), (28, 21), (16, 28), (11, 12), (34, 14), (8, 30), (33, 7), (19, 3), (23, 38), (31, 11), (29, 37), (33, 26), (30, 12), (1, 12), (3, 38), (32, 19), (31, 12), (27, 15), (13, 38), (7, 8), (31, 38), (13, 11), (3, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "409320", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (17, 13), (12, 0), (8, 11), (20, 10), (22, 19), (19, 11), (30, 18), (6, 31), (5, 10), (2, 16), (9, 20), (6, 20), (6, 3), (13, 31), (12, 26), (30, 22), (35, 15), (7, 8), (15, 22), (14, 6), (29, 7), (27, 13), (26, 10), (33, 25), (18, 6), (20, 13), (20, 8), (29, 2), (26, 19), (9, 13), (33, 29), (6, 21), (17, 30), (27, 30), (10, 30), (30, 7), (24, 23), (1, 30), (10, 2), (10, 1), (16, 4), (23, 31), (12, 5), (20, 0), (13, 2), (14, 13), (31, 25), (34, 26), (10, 18), (5, 31), (30, 20), (28, 25), (16, 8), (1, 28), (29, 19), (2, 15), (24, 27), (20, 14), (21, 22), (26, 4), (21, 5), (9, 3), (29, 14), (7, 31), (13, 19), (25, 24), (17, 14), (19, 31), (22, 5), (30, 14), (19, 9), (8, 25), (12, 8), (17, 19), (8, 3), (27, 27), (21, 11), (34, 16), (18, 24), (34, 27), (15, 18), (5, 19), (26, 0), (13, 23), (3, 26), (29, 15), (0, 27), (18, 3), (30, 29), (19, 23), (4, 14), (25, 2), (31, 20), (22, 6), (12, 2), (3, 4), (32, 19), (7, 20), (11, 30), (2, 27), (2, 10), (7, 2), (33, 17), (11, 18), (7, 23), (18, 14), (1, 22), (25, 15), (32, 18), (15, 19), (17, 31), (25, 11), (18, 12), (21, 4), (1, 16), (13, 24), (16, 20), (24, 28), (24, 3), (28, 30), (20, 25), (4, 27), (9, 0), (25, 28), (18, 9), (35, 4), (23, 4), (20, 9), (8, 10), (35, 9), (14, 4), (0, 10), (3, 28), (22, 26), (30, 6), (21, 10), (6, 30), (21, 26), (27, 25), (0, 20), (11, 14), (18, 1), (19, 25), (16, 12), (1, 20), (12, 17), (19, 6), (19, 14), (31, 3), (4, 2), (27, 0), (12, 22), (4, 13), (2, 0), (19, 26), (4, 12), (5, 21), (4, 9), (10, 15), (8, 29), (1, 31), (16, 29), (16, 31), (19, 4), (11, 15), (0, 28), (4, 28), (8, 21), (14, 31), (11, 9), (29, 5), (24, 2), (28, 28), (32, 25), (11, 21), (32, 4), (27, 1), (27, 16), (3, 16), (33, 20), (30, 24), (17, 25), (34, 21), (17, 16), (13, 20), (1, 26), (12, 3), (25, 20), (28, 19), (28, 5), (33, 24), (0, 26), (1, 23), (6, 6), (33, 5), (23, 6), (35, 21), (2, 21), (33, 7), (1, 0), (15, 12), (11, 16), (14, 12), (32, 14), (29, 28), (8, 26), (18, 29), (15, 26), (10, 9), (26, 31), (4, 23), (11, 0), (17, 9), (24, 14), (25, 23), (22, 21), (25, 27), (29, 11), (32, 7), (1, 8), (0, 25), (30, 4), (11, 24), (17, 11), (20, 21), (10, 14), (29, 18), (20, 17), (27, 22), (34, 15), (14, 25), (27, 26), (22, 20), (30, 9), (17, 3), (26, 30), (33, 2), (4, 5), (32, 27), (24, 25), (24, 19), (28, 7), (29, 31), (32, 0), (31, 10), (13, 16), (10, 25), (32, 26), (7, 1), (32, 31), (28, 9), (14, 10), (5, 4), (26, 7), (23, 1), (28, 0), (1, 29), (14, 18), (26, 28), (4, 31), (22, 29), (16, 30), (6, 7), (1, 3), (30, 31), (34, 3), (26, 6), (26, 16), (18, 7), (3, 0), (28, 21), (26, 23), (17, 26), (21, 16), (11, 11), (5, 20), (29, 21), (32, 5), (17, 22), (28, 27), (18, 10), (27, 4), (17, 24), (1, 7), (0, 30), (31, 27), (23, 5), (12, 7), (15, 14), (9, 21), (23, 23), (30, 8), (21, 19), (27, 7), (19, 2), (13, 13), (16, 2), (15, 4), (13, 11), (22, 7), (6, 5), (26, 17), (11, 6), (15, 25), (10, 21), (20, 7), (10, 16), (15, 24), (7, 17), (35, 12), (9, 27), (20, 30), (5, 0), (27, 3), (6, 24), (11, 22), (15, 31), (8, 15), (13, 27), (18, 8), (13, 5), (20, 4), (20, 19), (2, 22), (34, 17), (26, 9), (17, 27), (0, 11), (34, 28), (3, 31), (23, 18), (27, 6), (21, 3), (6, 0), (34, 0), (20, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "750615", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 24), (2, 12), (26, 12), (4, 17), (3, 28), (5, 13), (9, 4), (27, 1), (31, 21), (11, 3), (27, 2), (33, 14), (22, 11), (6, 23), (31, 24), (7, 14), (10, 16), (21, 22), (20, 24), (9, 7), (0, 17), (18, 18), (32, 28), (32, 5), (4, 6), (16, 11), (9, 11), (2, 24), (19, 24), (5, 30), (21, 23), (29, 5), (23, 30), (10, 3), (25, 13), (11, 23), (26, 24), (20, 29), (11, 0), (12, 2), (9, 30), (3, 25), (15, 3), (27, 28), (7, 28), (20, 10), (25, 17), (31, 16), (12, 6), (29, 8), (25, 28), (17, 13), (10, 15), (10, 14), (5, 19), (1, 8), (17, 25), (10, 29), (29, 17), (20, 14), (22, 17), (27, 14), (20, 19), (2, 20), (30, 20), (29, 4), (15, 31), (0, 31), (23, 12), (12, 21), (14, 31), (28, 14), (4, 29), (33, 20), (12, 15), (3, 12), (14, 1), (16, 13), (0, 5), (24, 15), (18, 17), (10, 17), (12, 30), (8, 0), (33, 23), (16, 7), (14, 0), (4, 19), (24, 8), (25, 14), (24, 7), (3, 0), (26, 10), (17, 31), (32, 10), (30, 29), (1, 2), (8, 20), (5, 16), (19, 31), (4, 10), (11, 13), (17, 22), (19, 19), (23, 16), (27, 12), (12, 26), (30, 24), (19, 15), (1, 26), (29, 13), (15, 6), (20, 31), (6, 13), (17, 11), (13, 30), (8, 6), (18, 13), (16, 28), (18, 3), (16, 22), (21, 4), (8, 7), (17, 6), (32, 17), (30, 26), (29, 11), (18, 5), (9, 28), (21, 17), (30, 13), (27, 13), (23, 15), (8, 26), (1, 5), (13, 19), (28, 8), (11, 26), (5, 0), (26, 7), (16, 12), (12, 10), (25, 9), (33, 29), (14, 21), (2, 5), (32, 15), (6, 15), (3, 5), (25, 11), (4, 30), (33, 19), (20, 21), (33, 28), (33, 21), (1, 6), (21, 27), (10, 6), (1, 20), (26, 28), (33, 1), (0, 30), (0, 29), (32, 1), (23, 9), (11, 16), (27, 16), (26, 25), (33, 17), (25, 23), (28, 20), (20, 5), (23, 18), (18, 19), (33, 18), (6, 30), (22, 14), (14, 10), (18, 4), (30, 5), (5, 23), (26, 3), (12, 28), (11, 29), (18, 1), (4, 26), (10, 25), (26, 29), (23, 2), (30, 11), (24, 2), (27, 23), (9, 12), (25, 7), (6, 21), (5, 25), (18, 21), (14, 29), (11, 31), (26, 20), (31, 20), (9, 24), (4, 21), (12, 7), (18, 29), (13, 23), (16, 21), (14, 15), (26, 23), (20, 23), (21, 16), (21, 11), (22, 22), (8, 31), (3, 16), (4, 2), (17, 16), (22, 7), (28, 10), (29, 0), (1, 1), (26, 27), (32, 20), (9, 15), (21, 25), (7, 2), (19, 25), (16, 19), (1, 21), (19, 13), (1, 13), (14, 13), (32, 6), (4, 27), (21, 15), (24, 21), (28, 7), (4, 20), (17, 4), (1, 22), (7, 4), (30, 1), (31, 0), (12, 27), (6, 12), (9, 23), (1, 27), (10, 4), (8, 11), (28, 27), (27, 30), (6, 3), (26, 15), (26, 4), (6, 10), (29, 9), (9, 8), (12, 22), (21, 7), (11, 11), (31, 9), (28, 26), (9, 5), (12, 5), (10, 28), (25, 16), (33, 30), (8, 21), (28, 1), (22, 30), (23, 4), (22, 3), (21, 8), (4, 14), (4, 31), (9, 21), (21, 29), (28, 22), (8, 30), (24, 28), (23, 8), (31, 27), (19, 6), (18, 15), (4, 4), (22, 29), (29, 1), (8, 9), (32, 16), (3, 23), (14, 17), (26, 5), (25, 30), (23, 23), (28, 5), (17, 19), (25, 1), (22, 15), (5, 5), (10, 11), (10, 24), (14, 6), (31, 5), (9, 26), (10, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946484", "dataset": "MATH"}
{"messages": [{"content": "In a 38x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 29), 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), (37, 9), (0, 22), (1, 19), (25, 23), (20, 4), (19, 17), (34, 4), (15, 12), (13, 14), (23, 24), (11, 0), (20, 9), (16, 19), (1, 28), (17, 14), (14, 2), (10, 25), (20, 22), (33, 21), (2, 2), (21, 12), (23, 16), (30, 0), (29, 19), (20, 17), (15, 15), (5, 19), (15, 1), (3, 8), (5, 14), (27, 1), (6, 29), (24, 6), (36, 14), (4, 27), (10, 1), (33, 19), (5, 21), (17, 29), (30, 23), (1, 0), (25, 13), (28, 3), (5, 8), (21, 3), (33, 7), (25, 17), (19, 6), (19, 22), (15, 14), (37, 8), (11, 7), (22, 18), (5, 0), (21, 25), (21, 18), (21, 4), (21, 17), (32, 24), (9, 11), (25, 11), (8, 6), (32, 21), (33, 3), (27, 11), (30, 13), (11, 14), (3, 12), (11, 20), (15, 24), (29, 9), (17, 1), (15, 27), (9, 3), (21, 8), (34, 18), (0, 23), (11, 18), (17, 5), (32, 0), (23, 0), (2, 23), (21, 14), (22, 20), (37, 12), (19, 0), (25, 14), (35, 2), (0, 21), (30, 4), (0, 19), (27, 5), (4, 0), (19, 1), (15, 7), (15, 0), (6, 8), (1, 7), (1, 10), (26, 4), (1, 15), (15, 20), (1, 23), (28, 15), (0, 9), (26, 7), (2, 22), (22, 22), (35, 7), (29, 21), (0, 5), (18, 10), (22, 27), (25, 26), (1, 4), (37, 23), (11, 11), (5, 29), (3, 14), (34, 9), (12, 27), (35, 10), (7, 28), (4, 5), (18, 22), (32, 18), (27, 7), (30, 24), (18, 6), (16, 13), (6, 16), (8, 0), (35, 8), (33, 20), (9, 22), (2, 12), (27, 23), (28, 16), (0, 25), (2, 25), (2, 9), (9, 21), (22, 26), (20, 13), (3, 3), (13, 0), (33, 13), (3, 27), (14, 1), (29, 25), (5, 20), (27, 0), (26, 28), (25, 9), (10, 24), (23, 12), (8, 4), (18, 14), (24, 23), (7, 0), (4, 4), (24, 13), (35, 6), (0, 12), (24, 10), (21, 7), (13, 2), (21, 26), (33, 14), (33, 1), (2, 26), (7, 5), (7, 6), (4, 14), (8, 28), (32, 25), (32, 4), (22, 15), (15, 10), (11, 28), (16, 18), (32, 10), (36, 28), (33, 2), (23, 21), (35, 12), (27, 25), (13, 28), (32, 2), (31, 0), (33, 15), (37, 18), (27, 14), (27, 29), (36, 16), (0, 15), (30, 3), (34, 25), (5, 26), (29, 26), (23, 20), (10, 13), (34, 21), (23, 25), (22, 13), (1, 16), (12, 2), (30, 29), (8, 20), (5, 17), (36, 13), (20, 12), (30, 1), (20, 2), (15, 19), (26, 27), (22, 17), (37, 21), (36, 23), (24, 1), (27, 9), (18, 11), (16, 12), (3, 23), (23, 6), (4, 21), (28, 29), (28, 7), (18, 21), (13, 26), (21, 24), (17, 27), (33, 6), (25, 3), (27, 17), (20, 8), (29, 28), (16, 9), (9, 16), (35, 13), (36, 24), (17, 25), (5, 15), (0, 17), (18, 19), (14, 11), (6, 1), (31, 22), (4, 11), (0, 28), (17, 13), (9, 8), (11, 22), (36, 7), (9, 13), (12, 25), (33, 9), (9, 15), (33, 17), (25, 19), (13, 27), (19, 9), (19, 25), (10, 27), (12, 13), (8, 3), (32, 17), (1, 25), (1, 18), (15, 13), (3, 13), (34, 2), (9, 5), (27, 20), (11, 17), (7, 29), (3, 18), (30, 26), (29, 20), (12, 21), (31, 13), (21, 2), (25, 5), (4, 3), (25, 16), (36, 19), (2, 14), (37, 0), (18, 2), (7, 9), (27, 22), (2, 10), (36, 0), (12, 4), (35, 25), (10, 8), (1, 29), (5, 5), (11, 9), (2, 16), (13, 19), (30, 20), (8, 22), (9, 7), (16, 20), (30, 22), (36, 10), (4, 12), (31, 7), (16, 2), (18, 20), (24, 11), (32, 3), (1, 8), (27, 28), (6, 14), (12, 18), (1, 13), (18, 26), (11, 12), (31, 18), (2, 3), (6, 4), (27, 19), (22, 25), (26, 8), (10, 23), (30, 16), (24, 2), (17, 7), (27, 8), (5, 16), (9, 10), (11, 29), (12, 28), (16, 23), (36, 17), (23, 2), (9, 26), (30, 17), (22, 5), (32, 1), (32, 14), (11, 21), (24, 4), (24, 29), (30, 10), (19, 4), (5, 11), (11, 6), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "476280", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), 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), (26, 36), (16, 24), (8, 12), (14, 14), (21, 4), (16, 5), (15, 26), (17, 12), (17, 14), (35, 5), (5, 29), (28, 33), (7, 37), (28, 9), (7, 19), (12, 33), (18, 32), (5, 28), (36, 5), (33, 17), (33, 35), (29, 19), (20, 9), (9, 25), (4, 22), (32, 8), (14, 5), (17, 32), (22, 16), (4, 8), (19, 4), (24, 29), (20, 10), (34, 19), (15, 21), (0, 22), (14, 28), (23, 20), (8, 7), (36, 6), (6, 31), (26, 38), (6, 27), (16, 32), (30, 28), (4, 28), (4, 15), (33, 29), (21, 17), (0, 36), (23, 23), (24, 34), (5, 37), (14, 10), (20, 26), (27, 10), (11, 11), (10, 38), (32, 3), (1, 21), (4, 35), (7, 18), (21, 25), (23, 18), (23, 1), (27, 7), (30, 14), (4, 24), (15, 4), (15, 9), (30, 22), (20, 12), (12, 23), (11, 25), (36, 4), (24, 15), (3, 36), 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31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "698880", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), 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), (1, 24), (26, 19), (23, 30), (30, 11), (17, 33), (6, 16), (13, 12), (27, 27), (20, 14), (11, 16), (7, 13), (3, 30), (10, 27), (5, 10), (15, 16), (7, 3), (29, 31), (27, 12), (6, 3), (4, 32), (21, 7), (29, 9), (22, 33), (7, 6), (29, 0), (13, 15), (26, 24), (20, 26), (19, 5), (8, 16), (26, 32), (21, 28), (27, 0), (2, 15), (0, 14), (10, 33), (20, 32), (27, 33), (23, 24), (12, 4), (21, 4), (14, 16), (8, 7), (8, 21), (8, 5), (30, 7), (10, 7), (20, 2), (19, 20), (8, 8), (27, 1), (14, 2), (8, 12), (24, 20), (0, 2), (28, 23), (27, 21), (25, 3), (25, 10), (26, 33), (14, 5), (12, 25), (2, 0), (15, 12), (31, 12), (24, 5), (27, 14), (0, 9), (27, 26), (28, 28), (2, 29), (28, 9), (27, 24), (5, 29), (25, 28), (0, 33), (26, 5), (10, 10), (7, 1), (1, 17), (11, 11), (31, 1), (10, 19), (2, 10), (18, 17), (4, 25), (9, 27), (9, 16), (15, 25), (26, 31), (4, 23), (17, 19), (25, 25), (22, 17), (6, 20), (29, 20), (6, 18), (3, 1), (29, 3), (22, 15), (28, 20), (30, 3), (30, 14), (24, 17), (24, 31), (31, 27), (13, 20), (29, 12), (23, 21), (26, 26), (14, 6), (26, 8), (26, 2), (10, 20), (23, 23), (17, 21), (10, 3), (22, 32), (0, 21), (6, 33), (13, 33), (31, 20), (29, 14), (15, 2), (13, 27), (13, 8), (18, 33), (10, 17), (27, 32), (22, 0), (0, 3), (11, 17), (10, 26), (2, 16), (25, 26), (24, 29), (9, 17), (18, 24), (1, 15), (16, 8), (20, 5), (28, 18), (3, 16), (28, 24), (20, 9), (31, 5), (12, 13), (27, 6), (31, 11), (8, 24), (12, 31), (13, 21), (21, 17), (8, 25), (23, 10), (16, 10), (18, 26), (12, 14), (22, 14), (1, 3), (25, 21), (9, 8), (17, 28), (3, 21), (4, 24), (29, 4), (27, 31), (16, 22), (3, 11), (17, 31), (21, 24), (2, 5), (9, 30), (11, 27), (18, 9), (2, 11), (6, 22), (27, 19), (2, 28), (15, 11), (28, 10), (20, 30), (13, 31), (16, 18), (17, 20), (22, 26), (3, 8), (1, 7), (27, 8), (23, 11), (31, 29), (10, 1), (2, 12), (3, 12), (23, 28), (4, 14), (31, 6), (19, 17), (15, 24), (6, 17), (15, 4), (31, 9), (18, 2), (12, 30), (20, 24), (26, 4), (7, 14), (12, 6), (24, 14), (14, 20), (2, 23), (8, 13), (24, 16), (29, 8), (22, 7), (23, 33), (19, 29), (15, 13), (5, 13), (28, 25), (28, 0), (20, 29), (28, 3), (15, 28), (28, 11), (0, 22), (4, 28), (19, 2), (30, 4), (10, 22), (2, 24), (17, 27), (30, 18), (5, 17), (16, 0), (1, 12), (18, 22), (14, 14), (6, 26), (5, 24), (29, 1), (22, 25), (29, 19), (18, 12), (7, 16), (5, 8), (26, 17), (13, 24), (23, 26), (29, 22), (22, 30), (6, 13), (0, 32), (15, 3), (8, 10), (22, 19), (31, 22), (13, 2), (3, 14), (30, 13), (27, 20), (0, 8), (24, 4), (20, 12), (25, 15), (14, 4), (23, 7), (3, 33), (28, 22), (5, 7), (4, 8), (19, 0), (14, 24), (22, 8), (23, 20), (20, 11), (5, 16), (25, 32), (12, 33), (3, 17), (20, 17), (24, 1), (19, 12), (21, 14), (21, 30), (13, 6), (1, 8), (11, 4), (19, 31), (22, 13), (6, 29), (14, 32), (10, 31), (11, 10), (23, 31), (7, 10), (14, 28), (12, 27), (28, 30), (9, 29), (5, 23), (28, 13), (16, 3), (16, 12), (20, 16), (30, 21), (15, 8), (21, 13), (27, 17), (20, 33), (0, 13), (19, 15), (24, 11), (9, 20), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "748800", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 30), (3, 13), (24, 17), (23, 19), (19, 32), (15, 7), (22, 31), (32, 8), (14, 0), (5, 15), (1, 10), (30, 13), (32, 5), (9, 5), (28, 26), (27, 21), (20, 28), (8, 25), (19, 28), (27, 27), (8, 6), (19, 4), (28, 13), (17, 10), (12, 30), (18, 22), (14, 3), (31, 9), (5, 24), (29, 26), (23, 28), (2, 19), (15, 23), (2, 20), (32, 4), (0, 9), (5, 3), (28, 16), (31, 16), (21, 24), (10, 14), (1, 33), (20, 2), (2, 5), (20, 17), (5, 1), (11, 3), (5, 30), (8, 4), (28, 14), (4, 24), (18, 5), (29, 2), (8, 19), (9, 31), (22, 28), (14, 25), (1, 6), (11, 2), (32, 27), (24, 10), (23, 13), (15, 26), (3, 15), (4, 0), (4, 13), (2, 16), (12, 19), (23, 25), (0, 33), (21, 19), (27, 25), (13, 30), (9, 12), (25, 10), (24, 14), (6, 29), (27, 11), (0, 8), (12, 11), (17, 27), (10, 24), (9, 27), (15, 32), (18, 8), (8, 23), (29, 21), (17, 8), (9, 18), (31, 28), (10, 22), (2, 4), (20, 21), (15, 2), (25, 29), (26, 22), (13, 29), (20, 10), (17, 18), (19, 6), (31, 4), (19, 19), (29, 19), (3, 0), (9, 6), (14, 7), (11, 28), (24, 8), (7, 17), (12, 3), (20, 15), (22, 20), (2, 15), (7, 10), (10, 7), (17, 9), (13, 26), (18, 16), (23, 14), (4, 28), (31, 23), (24, 22), (8, 7), (7, 33), (6, 0), (15, 10), (27, 4), (7, 27), (5, 27), (6, 15), (3, 9), (10, 28), (15, 5), (30, 26), (10, 17), (6, 30), (14, 27), (29, 24), (11, 20), (25, 13), (29, 1), (8, 14), (23, 30), (17, 12), (27, 22), (7, 2), (26, 6), (18, 7), (19, 5), (6, 6), (13, 4), (17, 26), (7, 31), (7, 14), (22, 30), (9, 32), (11, 9), (1, 27), (28, 20), (27, 7), (2, 21), (4, 17), (18, 32), (30, 3), (4, 2), (21, 29), (26, 31), (11, 14), (2, 14), (9, 17), (4, 14), (11, 7), (30, 27), (6, 25), (19, 17), (23, 7), (12, 12), (0, 10), (13, 17), (28, 33), (30, 12), (10, 18), (8, 0), (25, 23), (11, 4), (11, 5), (22, 8), (16, 27), (5, 16), (8, 22), (9, 3), (27, 0), (10, 10), (1, 30), (2, 32), (16, 9), (13, 1), (25, 17), (18, 9), (27, 9), (7, 30), (19, 3), (1, 18), (4, 15), (21, 4), (32, 6), (1, 0), (14, 8), (4, 11), (22, 3), (14, 15), (9, 0), (7, 18), (20, 3), (17, 32), (6, 27), (15, 25), (30, 8), (7, 21), (23, 11), (12, 22), (12, 18), (15, 15), (13, 23), (30, 15), (27, 5), (8, 5), (7, 13), (29, 30), (0, 11), (16, 10), (32, 22), (29, 29), (25, 11), (12, 8), (0, 22), (15, 31), (13, 12), (15, 12), (16, 14), (25, 9), (24, 27), (3, 5), (8, 28), (24, 6), (31, 1), (11, 22), (31, 10), (4, 22), (26, 33), (21, 0), (13, 24), (9, 19), (19, 20), (4, 7), (0, 30), (17, 1), (5, 6), (20, 1), (15, 6), (29, 33), (13, 21), (22, 26), (18, 13), (12, 4), (27, 15), (4, 5), (31, 30), (10, 2), (20, 5), (10, 25), (26, 25), (11, 31), (13, 15), (21, 10), (10, 3), (24, 11), (22, 14), (2, 26), (27, 30), (25, 19), (32, 16), (2, 8), (24, 25), (22, 15), (11, 16), (4, 8), (9, 29), (11, 17), (13, 14), (13, 32), (16, 24), (2, 25), (19, 11), (31, 33), (30, 19), (18, 23), (29, 28), (3, 25), (17, 0), (3, 32), (6, 32), (10, 0), (1, 19), (7, 24), (14, 20), (30, 11), (26, 26), (27, 18), (20, 7), (15, 27), (28, 15), (10, 19), (7, 16), (32, 28), (14, 2), (30, 31), (15, 33), (21, 6), (4, 32), (22, 9), (7, 1), (9, 20), (11, 0), (25, 2), (24, 20), (25, 20), (6, 18), (24, 13), (23, 4), (29, 15), (12, 24), (6, 22), (29, 8), (27, 17), (32, 15), (24, 21), (18, 4), (25, 4), (2, 22), (4, 3), (31, 22), (21, 25), (10, 30), (27, 10), (11, 10), (27, 28), (10, 12), (28, 17), (26, 18), (0, 13), (4, 29), (29, 11), (19, 13), (22, 29), (22, 5), (26, 1), (20, 33), (4, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "161992", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 31), (34, 1), (22, 5), (3, 17), (33, 36), (18, 6), (17, 19), (14, 35), (29, 34), (14, 22), (7, 24), (1, 33), (10, 12), (27, 32), (29, 6), (18, 36), (19, 24), (20, 17), (27, 2), (26, 4), (0, 13), (2, 21), (27, 19), (3, 35), (31, 21), (6, 3), (30, 23), (9, 30), (7, 0), (17, 31), (26, 6), (7, 36), (10, 34), (30, 11), (34, 11), (27, 36), (6, 11), (26, 17), (28, 31), (19, 31), (24, 18), (9, 18), (29, 0), (15, 34), (33, 6), (26, 5), (31, 0), (18, 1), (11, 35), (18, 8), (23, 10), (22, 15), (6, 22), (32, 19), (22, 18), (26, 21), (2, 7), (8, 18), (27, 25), (25, 33), (2, 11), (1, 26), (22, 21), (23, 0), (10, 0), (29, 27), (8, 11), (12, 1), (3, 1), (30, 28), (34, 33), (19, 36), (22, 11), (12, 7), (22, 35), (4, 14), (1, 28), (20, 7), (17, 13), (31, 23), (10, 29), (14, 18), (9, 6), (4, 33), (6, 13), (34, 10), (19, 33), (3, 15), (20, 12), (9, 8), (13, 31), (1, 16), (6, 8), (17, 22), (31, 17), (28, 36), (20, 5), (5, 5), (4, 13), (27, 28), (5, 27), (27, 0), (0, 8), (28, 8), (24, 26), (25, 0), (30, 33), (21, 19), (1, 8), (34, 0), (31, 13), (12, 32), (24, 28), (22, 17), (25, 22), (12, 19), (15, 24), (15, 25), (27, 34), (2, 30), (2, 23), (24, 2), (25, 1), (8, 23), (22, 7), (26, 2), (16, 14), (32, 13), (15, 3), (13, 12), (22, 28), (33, 12), (15, 32), (31, 9), (5, 23), (0, 26), (4, 6), (13, 20), (8, 21), (25, 20), (31, 35), (22, 10), (32, 14), (30, 17), (24, 22), (5, 28), (21, 20), (20, 35), (1, 35), (10, 31), (3, 2), (34, 29), (6, 21), (13, 19), (17, 34), (11, 28), (4, 0), (12, 30), (16, 18), (8, 14), (33, 11), (26, 11), (26, 28), (23, 13), (11, 34), (28, 30), (1, 9), (8, 17), (0, 10), (10, 11), (15, 23), (6, 31), (9, 15), (16, 28), (10, 18), (19, 20), (4, 27), (33, 21), (10, 33), (29, 9), (11, 27), (30, 15), (27, 29), (16, 24), (8, 28), (25, 7), (33, 3), (17, 17), (10, 22), (0, 16), (13, 29), (17, 11), (24, 12), (3, 25), (33, 1), (13, 1), (12, 24), (34, 24), (28, 11), (30, 30), (19, 6), (19, 15), (16, 21), (15, 29), (4, 12), (0, 33), (10, 32), (32, 0), (19, 4), (20, 36), (29, 5), (14, 33), (1, 23), (21, 18), (24, 33), (15, 28), (8, 4), (32, 23), (28, 1), (28, 3), (7, 30), (17, 27), (5, 0), (34, 15), (23, 5), (19, 28), (12, 21), (3, 16), (31, 5), (11, 2), (17, 23), (23, 20), (9, 9), (14, 15), (5, 6), (12, 0), (11, 36), (7, 2), (31, 14), (27, 3), (0, 27), (17, 28), (19, 17), (6, 5), (9, 33), (14, 8), (23, 24), (9, 12), (19, 0), (4, 4), (11, 26), (29, 28), (30, 24), (3, 20), (28, 26), (19, 11), (32, 3), (27, 11), (12, 3), (2, 25), (31, 24), (3, 30), (13, 21), (5, 25), (16, 32), (15, 14), (8, 1), (29, 14), (6, 12), (25, 13), (6, 28), (24, 16), (28, 24), (7, 5), (7, 31), (19, 21), (29, 22), (16, 27), (11, 1), (14, 20), (31, 6), (11, 30), (14, 2), (7, 26), (26, 1), (24, 25), (13, 33), (28, 20), (22, 25), (3, 4), (31, 36), (17, 4), (8, 12), (22, 32), (7, 20), (34, 3), (28, 13), (2, 5), (2, 27), (12, 22), (25, 21), (12, 29), (3, 28), (18, 21), (5, 8), (10, 20), (31, 3), (15, 8), (30, 4), (29, 26), (1, 0), (13, 6), (19, 18), (34, 31), (34, 27), (32, 30), (29, 13), (28, 35), (19, 25), (3, 29), (32, 6), (22, 14), (0, 12), (1, 18), (18, 13), (15, 18), (33, 34), (8, 5), (24, 32), (17, 5), (31, 32), (7, 15), (26, 20), (16, 19), (2, 16), (7, 6), (23, 8), (7, 25), (33, 29), (26, 13), (14, 16), (17, 2), (7, 1), (4, 20), (34, 21), (28, 34), (2, 36), (22, 8), (15, 31), (2, 29), (20, 33), (18, 22), (9, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456624", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 26), (8, 28), (24, 21), (24, 20), (23, 10), (17, 9), (1, 27), (25, 27), (3, 17), (29, 32), (22, 19), (22, 21), (28, 32), (18, 5), (0, 20), (25, 32), (9, 11), (2, 20), (11, 19), (0, 28), (1, 12), (22, 20), (10, 18), (35, 10), (34, 13), (16, 8), (28, 10), (9, 21), (0, 1), (32, 19), (8, 20), (33, 13), (3, 20), (32, 8), (30, 15), (13, 8), (19, 3), (20, 2), (17, 27), (11, 31), (8, 5), (11, 25), (2, 27), (13, 10), (24, 1), (14, 23), (4, 31), (27, 10), (24, 6), (27, 23), (33, 4), (6, 27), (32, 23), (26, 1), (33, 25), (5, 0), (19, 17), (11, 6), (34, 26), (12, 2), (20, 20), (8, 21), (18, 15), (6, 31), (36, 8), (8, 3), (32, 33), (9, 13), (2, 14), (12, 11), (35, 31), (11, 7), (1, 26), (20, 13), (4, 29), (4, 30), (31, 0), (7, 31), (25, 5), (24, 9), (27, 15), (5, 28), (28, 0), (25, 17), (32, 15), (12, 24), (36, 16), (29, 22), (30, 28), (3, 22), (9, 33), (24, 7), (0, 8), (21, 11), (31, 8), (20, 21), (16, 21), (6, 21), (0, 31), (18, 8), (26, 31), (9, 17), (5, 8), (13, 4), (17, 3), (26, 14), (22, 4), (0, 7), (0, 5), (22, 28), (28, 23), (0, 4), (2, 26), (29, 14), (34, 27), (16, 28), (33, 1), (35, 15), (17, 33), (13, 7), (34, 5), (36, 27), (5, 12), (17, 23), (35, 32), (27, 28), (11, 4), (21, 16), (30, 33), (24, 27), (10, 23), (4, 25), (21, 26), (22, 6), (27, 27), (16, 14), (12, 16), (25, 12), (9, 3), (24, 12), (33, 5), (35, 5), (3, 4), (22, 29), (25, 10), (32, 22), (7, 8), (12, 10), (29, 18), (1, 9), (33, 10), (5, 16), (30, 13), (32, 4), (34, 23), (31, 20), (1, 4), (31, 12), (36, 24), (10, 3), (21, 2), (34, 32), (8, 26), (13, 30), (8, 4), (27, 33), (5, 17), (35, 3), (23, 29), (27, 13), (16, 5), (14, 28), (30, 10), (19, 19), (21, 5), (35, 13), (32, 12), (26, 21), (27, 30), (33, 2), (2, 21), (21, 14), (23, 21), (0, 16), (10, 5), (29, 2), (17, 4), (5, 11), (1, 3), (30, 11), (1, 6), (8, 22), (12, 7), (14, 26), (13, 1), (3, 6), (18, 20), (25, 19), (11, 29), (5, 24), (17, 11), (16, 25), (22, 1), (33, 29), (28, 20), (23, 3), (27, 8), (24, 28), (2, 4), (12, 17), (27, 14), (23, 23), (1, 22), (7, 5), (1, 16), (33, 12), (34, 18), (4, 21), (11, 27), (15, 28), (9, 23), (5, 9), (1, 30), (16, 22), (7, 0), (24, 17), (1, 13), (27, 31), (23, 25), (26, 30), (20, 29), (33, 28), (7, 15), (1, 20), (2, 6), (0, 30), (32, 1), (23, 4), (34, 4), (31, 27), (24, 0), (10, 10), (1, 31), (21, 12), (4, 27), (35, 18), (25, 20), (36, 11), (32, 30), (18, 13), (3, 26), (19, 28), (10, 17), (9, 26), (19, 26), (16, 16), (12, 15), (15, 24), (4, 17), (9, 8), (36, 23), (25, 24), (33, 31), (21, 28), (29, 7), (2, 10), (16, 20), (31, 22), (27, 19), (2, 5), (32, 24), (6, 1), (19, 2), (17, 16), (3, 15), (31, 9), (29, 27), (14, 24), (0, 10), (20, 27), (8, 25), (15, 7), (20, 26), (5, 2), (36, 29), (16, 29), (32, 5), (8, 23), (33, 0), (1, 33), (17, 28), (3, 21), (29, 21), (18, 30), (18, 12), (2, 19), (5, 25), (6, 7), (34, 33), (11, 3), (11, 2), (27, 22), (29, 8), (34, 19), (1, 18), (2, 23), (35, 23), (7, 9), (32, 14), (24, 25), (8, 31), (2, 30), (15, 6), (28, 29), (32, 29), (17, 7), (15, 16), (2, 11), (14, 15), (26, 23), (33, 9), (20, 30), (36, 1), (5, 26), (20, 9), (14, 20), (6, 23), (18, 27), (30, 32), (25, 28), (28, 3), (8, 15), (10, 21), (16, 19), (34, 1), (4, 13), (34, 25), (18, 33), (18, 11), (11, 22), (35, 6), (21, 29), (6, 22), (36, 26), (10, 28), (7, 7), (1, 25), (25, 9), (16, 15), (15, 19), (14, 33), (18, 29), (33, 8), (22, 8), (12, 30), (5, 23), (19, 11), (33, 3), (33, 16), (11, 1), (21, 1), (17, 14), (9, 16), (24, 23), (17, 15), (10, 20), (17, 0), (35, 9), (21, 7), (15, 29), (30, 1), (27, 6), (24, 2), (16, 26), (3, 3), (2, 29), (16, 2), (8, 24), (29, 20), (0, 25), (2, 32), (27, 7), (3, 5), (24, 22), (31, 14), (8, 2), (13, 17), (10, 12), (20, 8), (12, 8), (13, 28), (21, 15), (21, 19), (20, 1), (4, 5), (20, 11), (11, 10), (16, 17), (21, 0), (14, 29), (23, 16), (35, 16), (17, 25), (32, 17), (17, 29), (16, 33), (29, 23), (1, 24), (31, 25), (1, 28), (20, 24), (6, 32), (17, 18), (13, 13), (12, 21), (0, 27), (32, 20), (32, 2), (27, 29), (30, 7), (29, 10), (26, 7), (24, 8), (16, 12), (14, 18), (25, 30), (2, 28), (0, 22), (1, 19), (10, 16), (26, 11), (28, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "826140", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (28, 10), (28, 20), (11, 8), (1, 17), (3, 28), (18, 22), (5, 31), (22, 28), (26, 4), (5, 2), (31, 5), (11, 2), (32, 14), (28, 17), (11, 4), (25, 8), (12, 19), (14, 15), (11, 14), (5, 5), (20, 9), (9, 26), (20, 5), (19, 18), (19, 17), (23, 35), (28, 6), (3, 24), (3, 1), (14, 28), (17, 32), (31, 21), (19, 4), (10, 9), (16, 7), (18, 30), (14, 29), (19, 11), (28, 1), (24, 19), (27, 13), (22, 13), (24, 9), (0, 25), (24, 10), (5, 29), (13, 13), (22, 3), (6, 31), (11, 1), (30, 5), (16, 0), (32, 17), (14, 8), (7, 5), (20, 25), (17, 3), (18, 23), (8, 24), (29, 26), (6, 27), (31, 2), (6, 28), (12, 23), (24, 32), (6, 16), (6, 2), (28, 4), (4, 2), (30, 19), (0, 14), (17, 4), (29, 25), (17, 18), (31, 4), (23, 13), (24, 17), (26, 15), (33, 13), (13, 21), (16, 24), (26, 26), (30, 2), (13, 17), (18, 35), (32, 27), (27, 16), (33, 34), (32, 24), (21, 27), (25, 14), (25, 26), (20, 0), (8, 15), (26, 27), (28, 13), (11, 28), (24, 1), (10, 31), (1, 22), (6, 12), (27, 4), (6, 24), (1, 8), (31, 9), (21, 29), (7, 3), (7, 19), (10, 13), (28, 31), (14, 5), (4, 4), (15, 22), (8, 35), (2, 9), (12, 17), (22, 17), (2, 15), (7, 29), (28, 33), (24, 26), (26, 24), (6, 7), (5, 14), (28, 25), (6, 0), (18, 10), (16, 21), (14, 22), (13, 22), (13, 24), (14, 32), (26, 16), (26, 18), (27, 9), (3, 2), (22, 9), (13, 27), (20, 30), (29, 23), (11, 7), (18, 20), (7, 7), (12, 30), (12, 10), (21, 23), (20, 21), (11, 21), (12, 7), (29, 30), (19, 24), (22, 23), (10, 18), (20, 13), (18, 28), (31, 29), (25, 1), (20, 28), (4, 10), (33, 6), (32, 30), (22, 25), (2, 0), (30, 30), (14, 23), (8, 5), (15, 19), (30, 32), (32, 16), (23, 22), (10, 5), (13, 35), (5, 16), (0, 1), (15, 23), (8, 17), (27, 14), (2, 34), (14, 20), (8, 26), (16, 35), (31, 15), (14, 33), (31, 13), (2, 29), (30, 17), (0, 9), (1, 6), (11, 25), (31, 33), (32, 3), (11, 22), (31, 17), (2, 7), (31, 10), (25, 27), (21, 20), (21, 24), (32, 26), (8, 8), (12, 34), (3, 5), (0, 10), (8, 4), (15, 4), (21, 32), (24, 7), (5, 4), (25, 34), (30, 21), (24, 8), (16, 29), (2, 16), (6, 11), (32, 9), (22, 4), (20, 11), (30, 23), (8, 1), (11, 20), (12, 18), (22, 31), (22, 21), (27, 15), (21, 28), (26, 6), (28, 24), (20, 12), (21, 11), (13, 15), (4, 33), (9, 15), (1, 7), (25, 32), (31, 34), (4, 22), (10, 4), (9, 21), (24, 24), (31, 19), (32, 10), (16, 18), (10, 20), (17, 26), (13, 26), (28, 34), (30, 16), (29, 16), (26, 12), (21, 3), (25, 23), (30, 6), (25, 16), (17, 20), (21, 26), (4, 26), (14, 19), (17, 25), (11, 10), (27, 21), (23, 10), (8, 25), (32, 1), (21, 18), (6, 19), (24, 21), (11, 35), (7, 13), (11, 32), (21, 13), (10, 19), (12, 9), (31, 12), (19, 2), (4, 29), (11, 9), (1, 2), (8, 29), (26, 11), (14, 6), (22, 10), (2, 31), (10, 21), (27, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332864", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), 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), (18, 1), (16, 16), (7, 19), (30, 18), (30, 2), (11, 11), (3, 27), (5, 19), (6, 4), (25, 28), (8, 10), (28, 23), (17, 16), (6, 18), (17, 26), (22, 8), (19, 9), (14, 14), (20, 18), (21, 25), (29, 10), (25, 6), (30, 7), (7, 12), (26, 2), (4, 17), (26, 20), (29, 27), (17, 12), (22, 9), (22, 17), (17, 10), (5, 3), (29, 14), (27, 18), (5, 27), (7, 2), (2, 2), (22, 6), (0, 8), (15, 1), (21, 12), (13, 5), (15, 17), (17, 24), (25, 18), (25, 15), (26, 25), (25, 27), (28, 5), (3, 4), (5, 9), (4, 2), (28, 27), (12, 1), (10, 23), (23, 9), (26, 14), (29, 22), (2, 6), (19, 24), (19, 20), (2, 5), (3, 6), (1, 4), (9, 19), (26, 5), (11, 23), (19, 25), (10, 2), (18, 0), (14, 9), (14, 22), (19, 26), (25, 7), (14, 24), (30, 22), (30, 21), (28, 28), (5, 4), (23, 22), (20, 7), (6, 17), (13, 20), (22, 23), (11, 13), (16, 11), (19, 10), (12, 29), (21, 29), (21, 13), (30, 12), (12, 14), (28, 22), (3, 16), (30, 14), (18, 20), (11, 19), (6, 7), (16, 29), (23, 6), (12, 23), (0, 14), (3, 15), (24, 0), (28, 13), (21, 14), (4, 20), (12, 7), (8, 28), (5, 24), (17, 21), (17, 6), (18, 8), (17, 29), (23, 23), (16, 1), (19, 5), (29, 3), (18, 10), (7, 8), (12, 18), (9, 26), (16, 24), (12, 20), (29, 1), (26, 11), (27, 4), (10, 22), (23, 19), (4, 26), (21, 7), (26, 17), (23, 4), (9, 5), (10, 9), (2, 28), (14, 19), (2, 23), (2, 7), (19, 19), (20, 2), (2, 8), (2, 29), (7, 4), (4, 4), (9, 21), (21, 1), (16, 5), (3, 23), (25, 11), (5, 18), (28, 9), (8, 12), (30, 10), (7, 27), (25, 13), (12, 26), (21, 16), (21, 3), (3, 10), (10, 0), (26, 19), (29, 28), (5, 2), (13, 6), (24, 16), (0, 24), (29, 7), (21, 9), (16, 13), (19, 1), (15, 20), (29, 0), (10, 28), (6, 26), (29, 2), (7, 14), (8, 9), (29, 16), (23, 2), (18, 21), (9, 6), (0, 2), (22, 1), (24, 6), (20, 5), (27, 5), (10, 1), (27, 21), (26, 27), (23, 3), (5, 0), (11, 10), (7, 21), (8, 5), (0, 11), (7, 6), (7, 22), (10, 6), (24, 24), (1, 2), (21, 6), (24, 5), (10, 19), (8, 27), (0, 18), (8, 15), (1, 28), (17, 27), (4, 14), (10, 18), (13, 11), (0, 19), (30, 20), (29, 12), (4, 6), (11, 29), (6, 8), (24, 28), (4, 19), (26, 24), (13, 1), (0, 6), (18, 23), (30, 11), (12, 13), (22, 5), (6, 5), (2, 14), (6, 28), (30, 25), (7, 11), (26, 1), (9, 27), (8, 23), (2, 18), (2, 9), (28, 8), (27, 25), (9, 10), (2, 10), (30, 5), (4, 24), (30, 28), (1, 22), (15, 2), (17, 17), (29, 20), (28, 17), (20, 3), (28, 6), (0, 29), (26, 8), (15, 8), (11, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "373230", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (24, 29), (29, 27), (3, 27), (29, 20), (10, 1), (8, 9), (2, 0), (19, 25), (17, 22), (15, 28), (15, 22), (18, 24), (4, 4), (10, 11), (6, 10), (17, 26), (20, 16), (16, 29), (20, 31), (20, 22), (23, 17), (13, 15), (2, 29), (27, 17), (8, 26), (15, 27), (29, 22), (21, 15), (1, 4), (11, 24), (8, 31), (26, 0), (9, 29), (19, 29), (5, 5), (17, 3), (1, 30), (25, 2), (22, 12), (18, 6), (19, 5), (1, 28), (29, 15), (27, 21), (18, 0), (27, 1), (8, 22), (8, 13), (13, 2), (17, 30), (17, 6), (20, 19), (25, 7), (9, 2), (26, 8), (5, 25), (18, 10), (15, 24), (15, 14), (11, 29), (12, 28), (30, 18), (17, 29), (29, 1), (11, 4), (12, 26), (22, 18), (26, 21), (24, 31), (25, 4), (0, 22), (15, 20), (21, 6), (12, 21), (9, 5), (0, 6), (27, 28), (17, 11), (20, 11), (25, 5), (30, 16), (1, 15), (24, 9), (30, 19), (3, 11), (4, 14), (19, 4), (7, 21), (21, 16), (1, 1), (19, 3), (16, 7), (19, 23), (0, 12), (24, 0), (10, 14), (24, 7), (0, 29), (7, 1), (9, 8), (11, 30), (20, 6), (14, 31), (19, 18), (4, 26), (19, 24), (5, 30), (4, 0), (12, 7), (18, 29), (18, 14), (18, 22), (23, 3), (30, 24), (19, 20), (13, 28), (0, 21), (27, 16), (6, 11), (6, 19), (10, 0), (5, 29), (6, 20), (6, 3), (26, 17), (28, 28), (11, 2), (15, 7), (28, 25), (30, 7), (15, 30), (10, 12), (13, 0), (22, 23), (27, 13), (5, 23), (2, 10), (3, 6), (30, 2), (24, 28), (16, 6), (19, 7), (27, 29), (23, 20), (22, 16), (27, 27), (5, 21), (25, 6), (27, 30), (3, 26), (29, 11), (25, 21), (3, 2), (13, 26), (27, 18), (21, 2), (28, 23), (25, 14), (9, 12), (4, 24), (19, 30), (8, 18), (23, 18), (1, 5), (0, 9), (24, 11), (10, 27), (27, 8), (2, 6), (8, 2), (25, 24), (0, 28), (24, 27), (23, 15), (13, 21), (27, 14), (23, 9), (6, 13), (19, 6), (1, 20), (30, 17), (5, 14), (25, 17), (25, 12), (6, 26), (12, 9), (8, 28), (12, 5), (14, 25), (12, 3), (9, 31), (10, 24), (2, 23), (16, 3), (8, 14), (21, 24), (2, 9), (16, 22), (13, 11), (7, 3), (24, 21), (3, 10), (18, 30), (7, 9), (21, 5), (27, 7), (11, 26), (8, 16), (15, 21), (14, 28), (22, 13), (2, 31), (11, 13), (28, 8), (29, 18), (1, 0), (10, 18), (11, 9), (9, 10), (23, 27), (25, 8), (25, 15), (16, 27), (20, 0), (4, 9), (3, 14), (14, 3), (14, 4), (2, 8), (7, 8), (25, 22), (8, 27), (0, 19), (4, 31), (3, 30), (16, 17), (6, 16), (11, 1), (14, 22), (7, 5), (8, 4), (26, 15), (8, 21), (9, 11), (4, 29), (20, 25), (1, 8), (23, 10), (12, 8), (28, 18), (18, 15), (22, 20), (11, 20), (17, 24), (2, 18), (13, 18), (30, 28), (17, 23), (20, 29), (22, 3), (16, 8), (2, 21), (27, 12), (3, 23), (26, 19), (16, 25), (27, 4), (17, 13), (7, 0), (19, 9), (7, 15), (15, 19), (15, 1), (15, 8), (7, 10), (29, 13), (1, 16), (26, 27), (16, 13), (6, 22), (15, 6), (16, 26), (14, 30), (17, 16), (26, 1), (19, 15), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 34), (15, 20), (3, 22), (4, 20), (19, 27), (0, 19), (30, 19), (11, 19), (1, 5), (24, 9), (4, 35), (27, 7), (17, 22), (18, 31), (13, 6), (5, 24), (12, 25), (21, 26), (8, 13), (28, 24), (30, 26), (0, 29), (10, 34), (21, 32), (14, 22), (15, 18), (11, 1), (19, 23), (20, 0), (16, 26), (29, 34), (22, 1), (8, 2), (18, 17), (30, 23), (28, 4), (25, 28), (11, 21), (26, 28), (9, 14), (4, 22), (4, 27), (6, 1), (26, 8), (21, 17), (6, 19), (17, 25), (5, 7), (19, 3), (21, 12), (14, 3), (2, 22), (13, 15), (12, 18), (0, 10), (5, 22), (20, 15), (26, 32), (23, 2), (11, 32), (24, 27), (28, 9), (30, 33), (7, 7), (13, 8), (22, 31), (18, 24), (15, 33), (12, 6), (19, 1), (8, 29), (22, 12), (9, 3), (22, 4), (27, 35), (30, 8), (9, 9), (1, 10), (13, 5), (20, 16), (19, 22), (29, 33), (22, 16), (13, 14), (9, 10), (0, 17), (12, 33), (2, 12), (19, 2), (27, 8), (24, 16), (26, 23), (11, 3), (1, 23), (17, 2), (21, 29), (17, 29), (11, 7), (6, 13), (28, 10), (17, 8), (11, 2), (11, 4), (30, 29), (10, 1), (14, 10), (16, 4), (7, 33), (20, 22), (28, 16), (18, 3), (1, 13), (19, 21), (17, 23), (2, 17), (4, 33), (4, 6), (11, 20), (4, 14), (29, 17), (14, 25), (30, 0), (1, 2), (13, 26), (24, 30), (30, 6), (30, 32), (19, 34), (2, 8), (18, 7), (16, 31), (30, 28), (25, 25), (27, 15), (25, 31), (6, 27), (16, 28), (3, 28), (9, 33), (15, 13), (22, 27), (28, 25), (17, 24), (7, 20), (17, 21), (4, 17), (27, 13), (15, 34), (19, 15), (5, 19), (13, 25), (25, 24), (3, 8), (16, 27), (1, 24), (25, 14), (4, 24), (27, 22), (9, 31), (20, 3), (17, 12), (22, 6), (21, 4), (12, 10), (14, 32), (10, 10), (25, 19), (0, 25), (23, 13), (14, 31), (22, 30), (26, 21), (3, 14), (18, 11), (22, 26), (13, 1), (14, 29), (2, 3), (30, 13), (0, 23), (9, 16), (0, 6), (2, 23), (9, 26), (5, 16), (21, 27), (28, 0), (13, 20), (9, 20), (19, 0), (9, 13), (26, 26), (30, 3), (9, 28), (29, 6), (0, 32), (5, 2), (17, 32), (12, 32), (13, 9), (23, 31), (29, 19), (22, 14), (21, 34), (4, 9), (4, 26), (22, 28), (23, 25), (0, 20), (26, 18), (19, 31), (24, 0), (14, 11), (21, 19), (7, 30), (9, 32), (29, 30), (28, 23), (1, 15), (18, 4), (12, 14), (3, 19), (19, 16), (12, 20), (18, 35), (14, 8), (6, 33), (9, 5), (10, 29), (28, 1), (29, 3), (11, 18), (22, 29), (23, 29), (22, 35), (1, 19), (18, 9), (5, 30), (30, 22), (15, 26), (16, 32), (22, 20), (13, 35), (14, 30), (9, 25), (4, 2), (5, 6), (26, 20), (11, 33), (11, 24), (2, 35), (5, 32), (0, 7), (25, 10), (18, 14), (22, 18), (20, 2), (10, 5), (2, 25), (5, 14), (10, 7), (26, 19), (26, 35), (4, 34), (23, 10), (3, 15), (8, 23), (2, 0), (23, 19), (1, 21), (25, 26), (18, 13), (29, 12), (4, 15), (1, 31), (11, 5), (16, 6), (6, 35), (8, 21), (27, 12), (19, 14), (5, 0), (11, 35), (1, 29), (19, 11), (23, 7), (16, 17), (25, 17), (15, 32), (6, 25), (29, 7), (23, 35), (12, 17), (29, 32), (14, 9), (3, 13), (9, 19), (17, 3), (5, 21), (3, 5), (12, 19), (20, 8), (16, 12), (21, 24), (14, 24), (15, 19), (25, 2), (4, 3), (17, 16), (8, 31), (16, 9), (7, 4), (5, 34), (21, 10), (19, 32), (9, 30), (25, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "481248", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 24), (29, 4), (38, 14), (2, 17), (27, 2), (26, 36), (1, 33), (4, 10), (7, 5), (9, 33), (30, 9), (33, 35), (20, 25), (19, 3), (22, 9), (34, 15), (4, 15), (10, 15), (15, 8), (12, 3), (38, 9), (3, 31), (38, 15), (28, 28), (22, 8), (37, 30), (33, 24), (23, 3), (28, 7), (13, 4), (32, 11), (13, 26), (6, 17), (6, 31), (24, 2), (2, 27), (17, 12), (16, 34), (30, 4), (18, 33), (5, 4), (13, 16), (37, 24), (3, 1), (1, 29), (21, 27), (1, 16), (18, 16), (26, 3), (24, 16), (27, 26), (22, 26), (32, 28), (14, 1), (3, 28), (17, 7), (6, 14), (10, 34), (28, 3), (5, 15), (14, 26), (27, 15), (6, 2), (23, 2), (16, 16), (13, 23), (34, 31), (32, 24), (12, 15), (32, 31), (4, 23), (34, 32), (2, 15), (19, 31), (20, 21), (17, 24), (6, 15), (14, 0), (35, 14), 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(16, 8), (7, 23), (29, 20), (0, 8), (11, 2), (13, 3), (6, 12), (8, 1), (9, 31), (11, 15), (32, 18), (27, 30), (7, 17), (15, 1), (14, 27), (37, 2), (31, 8), (22, 23), (11, 9), (23, 22), (11, 3), (7, 37), (20, 4), (13, 1), (27, 4), (15, 10), (28, 12), (33, 28), (18, 31), (30, 21), (30, 14), (16, 20), (33, 6), (14, 15), (33, 11), (25, 10), (31, 34), (35, 17), (34, 19), (19, 17), (33, 1), (29, 28), (17, 32), (3, 16), (7, 29), (31, 21), (21, 16), (32, 2), (38, 22), (10, 10), (28, 31), (11, 35), (16, 2), (10, 22), (32, 33), (14, 19), (12, 37), (37, 12), (18, 24), (30, 15), (15, 18), (21, 20), (13, 11), (35, 5), (30, 36), (33, 25), (14, 16), (29, 12), (38, 18), (33, 4), (5, 32), (17, 23), (13, 9), (5, 22), (16, 18), (29, 29), (3, 4), (36, 0), (9, 24), (26, 31), (18, 10), (2, 4), (36, 32), (34, 12), (13, 10), (7, 8), (37, 37), (2, 19), (0, 32), (6, 34), (34, 0), (8, 10), (29, 36), (2, 7), (32, 37), (37, 8), (38, 25), (18, 18), (2, 13), (18, 3), (1, 6), (8, 28), (22, 27), (18, 36), (28, 18), (33, 34), (34, 24), (3, 3), (15, 25), (5, 26), (23, 21), (26, 35), (21, 29), (12, 35), (28, 11), (26, 34), (23, 37), (14, 34), (26, 20), (37, 23), (29, 19), (34, 8), (23, 0), (24, 32), (15, 11), (14, 28), (1, 37), (17, 21), (21, 14), (15, 28), (7, 32), (2, 22), (34, 27), (3, 33), (24, 14), (10, 30), (17, 27), (11, 23), (24, 35), (36, 33), (2, 29), (20, 26), (16, 31), (5, 7), (26, 11), (6, 5), (23, 10), (32, 6), (37, 29), (2, 10), (24, 21), (0, 35), (19, 11), (13, 6), (14, 29), (22, 16), (2, 26), (22, 20), (9, 26), (11, 29), (17, 22), (15, 6), (23, 20), (32, 14), (26, 33), (1, 22), (15, 9), (34, 36), (28, 34), (32, 5), (26, 13), (12, 1), (23, 9), (16, 24), (9, 15), (31, 1), (17, 25), (28, 19), (26, 1), (6, 9), (16, 3), (17, 6), (25, 13), (18, 2), (13, 2), (17, 3), (15, 37), (30, 18), (19, 34), (33, 10), (4, 0), (34, 28), (23, 17), (18, 37), (20, 27), (11, 13), (0, 23), (11, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246240", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 27), (10, 3), (17, 28), (37, 14), (37, 30), (34, 20), (22, 3), (18, 9), (11, 11), (7, 21), (18, 17), (0, 27), (31, 32), (30, 21), (19, 32), (24, 10), (13, 28), (9, 29), (21, 11), (4, 18), (23, 18), (7, 7), (1, 31), (11, 7), (14, 9), (23, 29), (32, 19), (36, 11), (1, 25), (20, 3), (5, 33), (15, 3), (37, 26), (8, 32), (24, 17), (23, 7), (0, 17), (25, 8), (6, 33), (21, 28), (34, 18), (21, 23), (32, 8), (6, 8), (21, 10), (15, 0), (7, 12), (30, 20), (18, 20), (14, 12), (18, 3), (8, 17), (8, 2), (0, 12), (14, 25), (36, 5), (23, 10), (15, 23), (35, 5), (11, 14), (22, 4), (17, 5), (33, 12), (27, 21), (12, 10), (2, 29), (18, 34), (11, 9), (11, 27), (28, 1), (28, 6), (1, 10), (20, 11), (36, 7), (15, 31), (35, 1), (19, 0), (14, 20), (2, 12), (4, 23), (2, 31), (28, 8), (21, 14), (28, 11), (11, 4), (8, 25), (13, 22), (32, 30), (30, 18), (16, 19), (13, 3), (10, 30), (29, 30), (3, 33), (16, 11), (16, 21), (25, 34), (19, 20), (28, 29), (4, 29), (37, 33), (31, 15), (10, 14), (30, 9), (20, 6), (21, 29), (29, 20), (10, 33), (20, 27), (34, 24), (19, 33), (20, 10), (35, 4), (15, 15), (35, 33), (26, 13), (15, 13), (31, 2), (4, 20), (0, 30), (16, 26), (1, 30), (6, 4), (12, 32), (37, 19), (23, 3), (0, 3), (11, 8), (13, 9), (35, 10), (2, 13), (9, 4), (7, 15), (36, 32), (28, 9), (30, 11), (12, 34), (10, 23), (24, 0), (3, 20), (29, 11), (15, 28), (4, 11), (0, 21), (11, 31), (8, 5), (19, 21), (9, 21), (17, 24), (11, 23), (34, 2), (18, 13), (12, 24), (22, 28), (22, 20), (18, 27), (2, 3), (36, 21), (20, 9), (3, 30), (20, 12), (27, 0), (8, 29), (0, 24), (33, 26), (13, 25), (23, 15), (1, 33), (16, 2), (3, 24), (12, 11), (18, 22), (24, 15), (11, 24), (2, 7), (5, 0), (15, 14), (1, 13), (13, 8), (10, 28), (27, 16), (33, 10), (23, 20), (31, 20), (35, 20), (0, 14), (21, 32), (34, 3), (7, 9), (4, 15), (36, 13), (35, 14), (23, 8), (6, 14), (12, 25), (36, 8), (11, 22), (25, 22), (18, 15), (18, 23), (18, 30), (18, 25), (16, 14), (19, 15), (29, 15), (15, 8), (13, 15), (5, 22), (1, 7), (35, 2), (1, 20), (35, 12), (3, 22), (5, 2), (29, 29), (28, 22), (14, 19), (6, 7), (27, 24), (8, 10), (35, 7), (12, 21), (23, 16), (34, 22), (19, 4), (22, 22), (13, 33), (26, 19), (27, 34), (17, 31), (4, 8), (12, 13), (3, 4), (37, 11), (36, 26), (9, 13), (30, 26), (3, 12), (4, 30), (8, 28), (34, 32), (19, 18), (10, 21), (22, 14), (4, 4), (19, 22), (6, 20), (12, 0), (35, 19), (36, 28), (16, 9), (37, 7), (21, 12), (4, 21), (31, 31), (1, 22), (14, 22), (20, 23), (30, 24), (16, 4), (33, 13), (1, 9), (18, 1), (31, 1), (28, 5), (27, 12), (27, 1), (17, 21), (22, 1), (4, 6), (27, 15), (29, 28), (9, 31), (20, 0), (0, 31), (33, 1), (13, 12), (10, 13), (23, 12), (15, 21), (18, 28), (22, 18), (2, 15), (14, 5), (27, 17), (19, 19), (17, 25), (27, 13), (14, 28), (2, 20), (28, 14), (34, 26), (12, 14), (34, 8), (10, 2), (22, 0), (32, 13), (20, 22), (34, 23), (29, 4), (18, 32), (29, 33), (3, 17), (26, 15), (34, 1), (33, 5), (28, 31), (12, 5), (27, 33), (5, 11), (36, 2), (11, 15), (19, 31), (28, 4), (24, 31), (18, 8), (26, 30), (2, 34), (6, 10), (36, 23), (26, 14), (12, 17), (7, 14), (27, 3), (10, 29), (26, 10), (31, 7), (8, 22), (5, 32), (19, 29), (28, 3), (20, 7), (21, 5), (16, 15), (19, 17), (28, 19), (37, 21), (7, 31), (3, 13), (4, 33), (21, 31), (22, 2), (23, 5), (15, 10), (6, 0), (24, 20), (4, 3), (30, 29), (12, 28), (8, 20), (2, 6), (21, 19), (30, 16), (33, 18), (5, 19), (1, 17), (16, 12), (17, 27), (5, 10), (1, 16), (30, 4), (4, 1), (11, 21), (3, 31), (25, 32), (16, 13), (35, 13), (12, 22), (20, 21), (0, 9), (34, 33), (25, 21), (24, 19), (36, 18), (34, 10), (37, 20), (32, 33), (21, 34), (22, 19), (28, 0), (13, 30), (0, 10), (24, 3), (13, 27), (20, 24), (17, 10), (14, 31), (18, 19), (1, 11), (20, 34), (21, 8), (32, 21), (5, 18), (10, 9), (6, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551088", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 30), (1, 26), (28, 32), (22, 28), (13, 6), (13, 24), (23, 6), (1, 27), (31, 26), (31, 27), (35, 10), (31, 25), (31, 21), (24, 24), (27, 17), (35, 11), (12, 24), (5, 10), (20, 19), (28, 28), (13, 7), (37, 7), (3, 12), (26, 27), (12, 29), (28, 19), (0, 20), (20, 26), (17, 16), (23, 5), (18, 21), (3, 17), (23, 23), (1, 24), (9, 11), (29, 13), (6, 4), (3, 27), (6, 21), (33, 14), (22, 4), (34, 22), (22, 7), (13, 14), (9, 23), (31, 12), (31, 13), (0, 21), (3, 14), (20, 15), (4, 25), (8, 11), (13, 12), (30, 20), (4, 17), (26, 26), (14, 21), (23, 9), (13, 11), (9, 17), (21, 23), (28, 12), (7, 22), (30, 16), (1, 32), (31, 4), (27, 19), (22, 8), (13, 30), (7, 13), (5, 29), (5, 6), (34, 28), (9, 26), (5, 22), (16, 23), (2, 16), (18, 25), (10, 31), (21, 15), (15, 4), (25, 30), (6, 22), (15, 13), (6, 7), (24, 9), (29, 32), (33, 23), (16, 0), (32, 26), (25, 28), (21, 4), (21, 13), (0, 7), (20, 0), (16, 22), (5, 15), (18, 17), (10, 22), (27, 30), (30, 29), (33, 3), (18, 14), (3, 31), (37, 9), (8, 2), (17, 1), (10, 20), (18, 1), (34, 32), (1, 3), (36, 26), (17, 5), (12, 3), (11, 14), (21, 17), (28, 24), (5, 8), (2, 11), (35, 30), (33, 22), (5, 25), (10, 23), (26, 18), (25, 25), (15, 31), (28, 26), (22, 24), (17, 2), (21, 3), (10, 8), (32, 16), (36, 15), (24, 5), (5, 14), (15, 5), (21, 1), (0, 26), (13, 5), (27, 18), (7, 11), (30, 27), (0, 19), (20, 32), (27, 1), (2, 21), (16, 2), (13, 31), (9, 0), (22, 10), (28, 21), (15, 15), (27, 24), (20, 17), (37, 1), (12, 16), (12, 25), (7, 17), (0, 2), (11, 21), (34, 16), (3, 9), (17, 13), (26, 14), (0, 3), (18, 3), (16, 16), (23, 16), (26, 0), (0, 28), (5, 20), (31, 3), (31, 11), (37, 24), (17, 9), (16, 12), (26, 19), (15, 9), (11, 20), (3, 20), (31, 32), (11, 18), (20, 21), (18, 30), (10, 13), (25, 23), (5, 3), (17, 21), (12, 26), (7, 3), (13, 20), (20, 8), (16, 19), (28, 18), (5, 32), (3, 26), (7, 15), (19, 21), (1, 17), (18, 7), (20, 2), (5, 4), (8, 29), (25, 13), (16, 3), (10, 1), (11, 27), (30, 12), (4, 14), (37, 14), (23, 8), (32, 4), (34, 1), (0, 31), (37, 15), (12, 31), (16, 1), (25, 11), (24, 31), (22, 1), (2, 27), (34, 30), (30, 13), (24, 15), (12, 1), (19, 32), (6, 2), (28, 29), (25, 22), (23, 17), (18, 8), (8, 28), (37, 27), (19, 31), (34, 6), (4, 31), (34, 13), (34, 12), (28, 8), (15, 19), (3, 2), (9, 21), (23, 11), (4, 3), (1, 8), (16, 28), (33, 10), (5, 21), (13, 0), (24, 3), (17, 29), (9, 31), (35, 3), (36, 28), (32, 10), (28, 23), (27, 29), (35, 27), (21, 9), (7, 8), (2, 7), (1, 25), (14, 16), (30, 3), (14, 6), (31, 23), (12, 27), (20, 10), (20, 24), (11, 16), (0, 4), (11, 17), (27, 25), (4, 1), (26, 15), (30, 9), (22, 22), (28, 1), (21, 2), (26, 13), (35, 21), (29, 0), (10, 17), (23, 32), (32, 17), (5, 19), (9, 12), (26, 8), (18, 6), (15, 2), (11, 9), (30, 6), (19, 12), (3, 3), (8, 12), (1, 9), (6, 0), (0, 14), (28, 9), (19, 27), (31, 7), (2, 18), (31, 16), (29, 6), (20, 7), (20, 20), (2, 31), (5, 5), (11, 11), (5, 17), (11, 7), (30, 10), (1, 5), (15, 29), (16, 4), (0, 1), (21, 8), (33, 24), (23, 29), (38, 11), (37, 30), (7, 26), (18, 27), (13, 21), (25, 19), (25, 31), (7, 20), (37, 23), (12, 17), (12, 5), (31, 15), (26, 29), (33, 1), (9, 24), (9, 30), (8, 17), (30, 32), (9, 4), (2, 4), (24, 6), (8, 19), (19, 17), (21, 22), (32, 2), (19, 16), (10, 7), (1, 18), (14, 13), (14, 30), (24, 16), (17, 15), (16, 10), (36, 24), (31, 31), (25, 20), (26, 20), (16, 26), (35, 18), (38, 19), (34, 7), (22, 16), (36, 21), (33, 2), (22, 3), (8, 8), (36, 8), (4, 27), (24, 21), (12, 32), (18, 32), (3, 19), (34, 18), (5, 24), (14, 31), (3, 8), (1, 10), (32, 0), (32, 21), (22, 32), (36, 32), (6, 27), (10, 6), (7, 24), (37, 32), (20, 5), (3, 25), (4, 7), (30, 22), (36, 17), (14, 20), (16, 29), (19, 2), (37, 28), (12, 20), (24, 27), (29, 21), (27, 20), (30, 23), (28, 20), (10, 10), (25, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "746172", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), 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), (17, 36), (24, 10), (10, 22), (8, 25), (1, 16), (11, 4), (1, 21), (0, 2), (2, 10), (19, 19), (26, 20), (26, 33), (31, 11), (5, 0), (4, 16), (13, 12), (30, 27), (1, 37), (26, 24), (23, 22), (8, 5), (4, 12), (10, 28), (10, 9), (11, 36), (8, 35), (2, 31), (20, 25), (20, 2), (25, 31), (16, 0), (9, 8), (5, 18), (22, 37), (25, 19), (15, 32), (27, 36), (11, 26), (21, 30), (2, 32), (31, 0), (2, 6), (13, 22), (29, 23), (0, 20), (13, 28), (3, 37), (14, 31), (17, 6), (21, 16), (17, 14), (24, 2), (17, 0), (2, 0), (24, 15), (11, 7), (9, 5), (15, 0), (27, 29), (18, 3), (1, 30), (15, 16), (15, 2), (6, 36), (2, 2), (21, 13), (16, 3), (10, 0), (20, 7), (10, 17), (14, 33), (4, 27), (25, 37), (24, 6), (18, 23), (12, 31), (3, 20), (21, 28), (22, 24), (11, 21), (12, 3), (6, 4), (11, 13), (24, 36), (29, 19), (30, 3), (20, 16), (9, 20), (5, 16), (14, 29), (31, 9), (31, 23), (18, 9), (10, 10), (25, 17), (4, 2), (1, 12), (16, 27), (3, 7), (17, 4), (2, 4), (30, 22), (28, 2), (9, 32), (21, 14), (17, 15), (1, 3), (16, 28), (27, 12), (1, 13), (11, 22), (26, 4), (15, 35), (0, 7), (11, 9), (20, 12), (22, 36), (19, 5), (31, 35), (20, 19), (7, 9), (18, 17), (9, 7), (12, 0), (31, 34), (16, 34), (0, 25), (20, 14), (22, 27), (28, 23), (2, 5), (4, 21), (1, 31), (11, 20), (19, 1), (19, 22), (13, 8), (25, 25), (0, 30), (23, 27), (19, 3), (12, 28), (9, 29), (1, 10), (24, 20), (17, 25), (17, 20), (16, 31), (6, 37), (28, 27), (28, 14), (5, 12), (23, 0), (13, 33), (29, 15), (18, 37), (28, 12), (7, 11), (26, 22), (27, 0), (10, 34), (2, 3), (5, 13), (20, 31), (12, 1), (7, 22), (29, 5), (5, 14), (19, 30), (27, 18), (0, 10), (31, 29), (7, 6), (24, 19), (14, 23), (31, 12), (8, 3), (17, 5), (22, 5), (10, 25), (24, 14), (1, 33), (21, 33), (27, 13), (27, 30), (16, 25), (2, 30), (6, 31), (5, 34), (13, 35), (26, 34), (15, 19), (29, 0), (2, 7), (14, 2), (1, 7), (19, 29), (3, 11), (1, 5), (19, 12), (8, 10), (28, 37), (25, 30), (21, 6), (7, 25), (2, 37), (23, 31), (31, 24), (23, 3), (13, 5), (12, 37), (26, 7), (9, 24), (2, 34), (25, 9), (6, 14), (8, 19), (3, 24), (15, 24), (19, 32), (26, 1), (25, 4), (3, 35), (8, 27), (22, 15), (20, 21), (19, 23), (16, 16), (4, 17), (21, 11), (13, 37), (2, 17), (24, 0), (6, 32), (15, 22), (13, 15), (2, 8), (26, 26), (4, 19), (26, 35), (29, 34), (3, 26), (3, 10), (31, 22), (27, 33), (18, 27), (12, 16), (5, 11), (4, 22), (9, 11), (15, 23), (29, 21), (5, 3), (15, 1), (1, 22), (24, 28), (3, 18), (28, 11), (8, 14), (5, 9), (6, 17), (12, 36), (19, 17), (25, 14), (7, 15), (19, 18), (3, 27), (15, 6), (8, 21), (6, 15), (0, 26), (24, 8), (16, 37), (15, 33), (13, 13), (26, 36), (20, 18), (1, 18), (7, 3), (28, 28), (27, 21), (22, 35), (21, 7), (12, 19), (5, 6), (22, 30), (13, 3), (7, 2), (10, 19), (20, 13), (8, 33), (29, 4), (12, 20), (11, 33), (20, 37), (21, 32), (1, 27), (3, 33), (3, 16), (6, 8), (13, 16), (15, 13), (28, 25), (30, 28), (25, 20), (14, 17), (19, 25), (25, 11), (4, 37), (30, 21), (0, 4), (3, 23), (7, 8), (25, 5), (4, 36), (10, 20), (19, 34), (20, 29), (2, 29), (24, 1), (30, 23), (8, 18), (17, 21), (11, 8), (16, 35), (9, 31), (21, 17), (25, 24), (11, 32), (27, 22), (10, 27), (9, 34), (7, 34), (8, 37), (29, 36), (18, 35), (17, 24), (4, 29), (25, 13), (4, 11), (1, 36), (31, 36), (3, 14), (2, 12), (22, 25), (10, 1), (17, 1), (9, 27), (13, 30), (18, 2), (29, 37), (24, 33), (3, 5), (28, 9), (17, 22), (31, 16), (24, 27), (29, 32), (31, 6), (29, 7), (12, 11), (22, 26), (9, 6), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "655182", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 8), (30, 30), (12, 11), (13, 26), (18, 32), (16, 6), (5, 27), (24, 24), (33, 31), (29, 3), (18, 4), (18, 30), (2, 4), (6, 4), (28, 21), (13, 12), (16, 32), (26, 32), (22, 18), (7, 23), (30, 1), (9, 4), (24, 19), (25, 14), (33, 3), (20, 2), (5, 11), (1, 9), (5, 19), (35, 6), (15, 21), (10, 18), (21, 15), (17, 12), (18, 26), (10, 16), (17, 6), (13, 22), (28, 30), (19, 17), (11, 24), (18, 7), (24, 5), (35, 5), (28, 32), (24, 2), (30, 19), (32, 1), (6, 1), (25, 19), (3, 20), (16, 24), (19, 12), (5, 24), (34, 31), (34, 20), (27, 18), (29, 24), (23, 13), (17, 15), (14, 6), (25, 32), (26, 7), (36, 2), (1, 27), (1, 5), (2, 3), (35, 32), (20, 0), (22, 3), (33, 17), (12, 17), (13, 10), (7, 27), (18, 9), (13, 25), (9, 9), (14, 15), (20, 3), (28, 11), (26, 12), (12, 5), (27, 6), (0, 24), (2, 8), (36, 26), (8, 25), (8, 5), (7, 17), (35, 27), (27, 27), (27, 28), (23, 16), (11, 10), (2, 13), (16, 7), (11, 31), (33, 28), (29, 29), (4, 27), (0, 15), (7, 14), (9, 14), (25, 26), (27, 19), (18, 12), (16, 10), (20, 23), (22, 15), (35, 18), (34, 13), (29, 11), (10, 3), (10, 4), (36, 11), (15, 16), (21, 17), (28, 31), (7, 3), (23, 21), (7, 21), (2, 32), (18, 2), (13, 32), (31, 9), (28, 22), (27, 31), (26, 28), (32, 28), (8, 6), (36, 4), (12, 15), (27, 21), (7, 15), (22, 26), (11, 16), (25, 8), (15, 31), (24, 13), (5, 21), (9, 26), (25, 0), (27, 9), (32, 19), (22, 21), (21, 18), (22, 27), (10, 30), (10, 12), (3, 10), (31, 1), (17, 28), (21, 24), (12, 0), (1, 19), (15, 25), (20, 24), (17, 25), (3, 30), (25, 15), (20, 31), (9, 21), (27, 4), (30, 32), (9, 29), (5, 5), (29, 20), (11, 28), (16, 4), (15, 6), (7, 20), (3, 13), (4, 16), (7, 18), (21, 10), (33, 9), (25, 4), (10, 10), (35, 23), (35, 21), (36, 8), (26, 25), (23, 12), (22, 6), (14, 0), (3, 23), (31, 4), (6, 18), (22, 9), (4, 10), (32, 17), (8, 13), (21, 9), (0, 23), (24, 8), (20, 26), (27, 10), (27, 32), (9, 18), (13, 30), (29, 19), (34, 22), (3, 3), (32, 21), (33, 27), (33, 8), (11, 6), (9, 28), (1, 29), (2, 19), (16, 14), (11, 4), (13, 18), (23, 11), (5, 1), (25, 29), (24, 25), (13, 19), (25, 17), (18, 20), (2, 12), (12, 26), (11, 0), (30, 10), (24, 30), (20, 11), (30, 21), (21, 4), (34, 7), (24, 28), (15, 0), (7, 32), (18, 15), (4, 28), (30, 6), (12, 7), (9, 3), (12, 14), (8, 29), (5, 6), (33, 13), (18, 23), (26, 17), (4, 3), (6, 19), (9, 0), (30, 12), (2, 7), (19, 21), (25, 13), (7, 5), (29, 27), (7, 1), (29, 22), (17, 5), (25, 3), (13, 29), (12, 28), (35, 3), (17, 31), (14, 20), (18, 27), (34, 28), (16, 5), (4, 26), (9, 31), (17, 7), (2, 9), (10, 32), (13, 5), (12, 19), (28, 0), (30, 22), (4, 19), (24, 16), (32, 11), (20, 25), (30, 3), (13, 3), (16, 17), (20, 4), (17, 22), (3, 2), (33, 7), (19, 10), (17, 32), (1, 25), (33, 24), (13, 27), (19, 22), (31, 5), (12, 27), (29, 18), (20, 14), (34, 8), (16, 19), (30, 17), (0, 21), (36, 14), (25, 20), (33, 1), (32, 15), (3, 16), (21, 2), (8, 32), (26, 5), (19, 26), (16, 23), (17, 23), (7, 31), (28, 1), (22, 30), (3, 32), (20, 9), (8, 18), (17, 9), (15, 26), (27, 14), (5, 13), (19, 7), (34, 2), (24, 29), (33, 23), (1, 0), (32, 2), (32, 12), (7, 8), (20, 30), (33, 16), (16, 0), (17, 13), (23, 17), (19, 14), (10, 26), (25, 24), (8, 2), (7, 12), (15, 24), (17, 3), (28, 3), (19, 11), (21, 13), (35, 1), (22, 4), (16, 15), (19, 19), (26, 6), (17, 4), (34, 26), (35, 30), (8, 26), (16, 12), (34, 19), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3600", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (23, 32), (2, 22), (23, 13), (11, 11), (29, 30), (4, 9), (17, 27), (29, 10), (20, 6), (7, 18), (4, 6), (31, 28), (27, 16), (24, 19), (10, 1), (30, 10), (3, 2), (10, 19), (0, 21), (26, 32), (23, 6), (16, 7), (15, 23), (13, 8), (24, 1), (12, 18), (8, 10), (2, 17), (6, 30), (12, 29), (12, 16), (2, 18), (27, 26), (19, 6), (24, 18), (16, 4), (9, 17), (8, 18), (2, 10), (3, 22), (4, 15), (3, 6), (15, 17), (4, 30), (5, 17), (11, 15), (28, 31), (14, 8), (27, 6), (0, 27), (3, 9), (0, 31), (2, 32), (13, 21), (25, 27), (29, 18), (18, 6), (23, 22), (22, 21), (18, 12), (4, 5), (0, 7), (20, 2), (26, 6), (17, 18), (4, 21), (30, 3), (30, 33), (29, 27), (10, 34), (27, 11), (0, 32), (22, 14), (12, 35), (14, 5), (31, 33), (2, 13), (25, 18), (23, 8), (9, 10), (13, 13), (0, 22), (16, 34), (15, 34), (11, 26), (29, 5), (12, 19), (13, 31), (6, 34), (7, 25), (7, 34), (28, 23), (12, 11), (28, 14), (1, 15), (32, 30), (15, 33), (0, 23), (1, 29), (22, 6), (26, 30), (6, 28), (17, 9), (8, 27), (25, 14), (4, 17), (13, 3), (31, 16), (4, 20), (20, 29), (18, 3), (15, 4), (28, 11), (9, 3), (18, 22), (10, 11), (19, 31), (5, 9), (23, 16), (13, 11), (5, 6), (32, 16), (25, 26), (14, 18), (31, 18), (21, 30), (20, 27), (10, 30), (22, 12), (22, 9), (31, 32), (19, 25), (15, 15), (11, 28), (11, 31), (6, 13), (3, 25), (28, 32), (26, 2), (23, 2), (1, 14), (13, 30), (23, 21), (21, 23), (13, 14), (22, 34), (31, 29), (7, 9), (32, 1), (9, 26), (22, 28), (13, 24), (5, 34), (29, 0), (8, 13), (27, 15), (15, 1), (25, 1), (17, 30), (3, 26), (25, 12), (31, 26), (7, 21), (10, 3), (7, 3), (14, 34), (16, 5), (24, 26), (0, 20), (21, 0), (11, 8), (9, 19), (1, 6), (11, 12), (22, 15), (7, 5), (17, 12), (19, 16), (20, 3), (3, 8), (2, 15), (4, 1), (22, 29), (9, 35), (1, 1), (11, 32), (18, 33), (20, 18), (29, 33), (26, 34), (7, 12), (17, 26), (27, 25), (4, 35), (15, 28), (29, 2), (28, 12), (3, 31), (14, 28), (12, 28), (8, 34), (31, 4), (11, 0), (9, 15), (2, 2), (31, 7), (10, 9), (16, 11), (28, 18), (23, 7), (13, 26), (15, 32), (23, 25), (23, 26), (1, 22), (15, 10), (17, 15), (30, 9), (10, 27), (28, 26), (12, 6), (21, 28), (22, 8), (8, 35), (32, 27), (16, 20), (12, 21), (2, 28), (16, 24), (4, 10), (17, 7), (25, 6), (23, 30), (30, 20), (3, 34), (21, 22), (27, 1), (22, 3), (21, 18), (15, 19), (2, 5), (24, 35), (26, 21), (22, 18), (0, 4), (4, 16), (1, 23), (2, 19), (28, 35), (10, 35), (15, 21), (23, 23), (6, 6), (21, 31), (22, 26), (24, 6), (7, 13), (11, 19), (26, 12), (2, 20), (12, 22), (23, 18), (5, 28), (15, 25), (26, 20), (25, 4), (29, 29), (19, 9), (5, 35), (10, 5), (17, 8), (7, 6), (20, 31), (31, 6), (3, 19), (24, 22), (26, 29), (31, 15), (12, 1), (16, 0), (18, 24), (1, 31), (24, 24), (5, 20), (23, 14), (26, 24), (0, 33), (0, 34), (32, 4), (11, 13), (11, 10), (29, 35), (15, 11), (22, 27), (0, 30), (2, 29), (0, 26), (17, 2), (24, 17), (14, 20), (22, 20), (26, 22), (22, 11), (28, 2), (21, 24), (21, 29), (24, 34), (9, 32), (8, 12), (22, 33), (25, 13), (0, 35), (15, 8), (0, 1), (10, 24), (32, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "915840", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), 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), (20, 28), (2, 1), (31, 19), (11, 26), (7, 25), (11, 27), (7, 5), (18, 2), (0, 9), (29, 16), (6, 29), (3, 8), (27, 29), (16, 2), (20, 1), (27, 3), (18, 19), (34, 5), (7, 2), (2, 3), (18, 17), (18, 26), (32, 23), (22, 25), (24, 14), (20, 6), (8, 20), (30, 28), (17, 1), (24, 2), (20, 17), (2, 10), (23, 26), (8, 2), (10, 26), (13, 13), (28, 19), (34, 11), (1, 26), (6, 8), (2, 29), (10, 13), (28, 16), (11, 12), (11, 16), (32, 10), (1, 7), (21, 8), (13, 15), (3, 9), (15, 7), (15, 26), (21, 16), (31, 11), (34, 9), (31, 14), (12, 27), (26, 21), (14, 24), (0, 25), (8, 22), (15, 23), (32, 2), (14, 1), (2, 24), (31, 12), (32, 0), (29, 6), (25, 18), (15, 21), (26, 10), (11, 14), (33, 18), (17, 6), (31, 6), (30, 24), (33, 24), (23, 24), (9, 5), (25, 11), (21, 7), (10, 1), (29, 25), (1, 15), (18, 18), (17, 9), (5, 10), (0, 2), (5, 13), (25, 3), (31, 20), (26, 2), (7, 7), (4, 27), (8, 9), (21, 28), (17, 15), (14, 29), (25, 13), (34, 21), (2, 11), (6, 5), (17, 20), (16, 0), (4, 6), (24, 23), (28, 17), (4, 20), (34, 20), (12, 9), (0, 16), (24, 29), (9, 16), (22, 26), (24, 0), (14, 21), (11, 18), (7, 1), (20, 9), (0, 14), (15, 29), (8, 21), (22, 24), (29, 22), (22, 21), (22, 15), (25, 28), (15, 2), (9, 2), (22, 9), (27, 10), (9, 18), (13, 12), (15, 15), (7, 19), (30, 20), (14, 0), (18, 14), (27, 12), (9, 28), (32, 4), (22, 23), (17, 10), (2, 5), (6, 6), (7, 10), (9, 17), (23, 5), (26, 8), (11, 25), (18, 28), (24, 24), (4, 19), (34, 8), (4, 9), (34, 3), (16, 24), (3, 14), (27, 17), (28, 26), (4, 18), (12, 23), (27, 16), (29, 11), (22, 19), (26, 12), (12, 29), (6, 23), (29, 23), (0, 18), (10, 4), (24, 21), (29, 8), (5, 6), (26, 29), (16, 12), (17, 24), (1, 2), (10, 18), (19, 19), (18, 15), (15, 20), (29, 5), (16, 4), (30, 1), (28, 5), (17, 4), (19, 26), (6, 0), (31, 8), (7, 6), (12, 4), (16, 25), (0, 24), (30, 3), (26, 0), (27, 7), (25, 12), (17, 7), (14, 25), (17, 18), (26, 25), (32, 17), (32, 28), (17, 8), (24, 18), (21, 18), (14, 16), (34, 0), (2, 14), (30, 17), (2, 25), (15, 6), (16, 3), (23, 4), (20, 24), (26, 5), (8, 23), (9, 23), (0, 1), (28, 4), (33, 29), (20, 18), (23, 18), (22, 28), (9, 3), (30, 22), (26, 4), (20, 19), (6, 3), (22, 10), (13, 25), (33, 26), (16, 26), (2, 28), (8, 13), (28, 23), (24, 22), (13, 1), (20, 16), (25, 29), (8, 14), (28, 29), (14, 17), (27, 6), (3, 28), (18, 12), (33, 12), (13, 6), (3, 20), (9, 13), (22, 20), (0, 17), (1, 14), (22, 8), (32, 25), (29, 0), (5, 3), (33, 13), (27, 9), (8, 27), (28, 7), (34, 2), (21, 22), (32, 16), (8, 26), (16, 23), (24, 10), (19, 14), (32, 26), (26, 18), (28, 15), (18, 10), (12, 14), (18, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427980", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 7), (9, 11), (23, 30), (17, 4), (18, 15), (27, 7), (21, 17), (31, 29), (36, 19), (19, 2), (29, 13), (21, 20), (11, 24), (17, 8), (19, 26), (25, 8), (9, 9), (36, 13), (19, 22), (7, 2), (14, 15), (30, 30), (9, 6), (2, 10), (20, 4), (16, 26), (35, 9), (12, 21), (2, 28), (29, 11), (35, 7), (31, 13), (37, 26), (1, 30), (31, 28), (11, 28), (31, 25), (11, 18), (13, 11), (34, 18), (29, 12), (20, 28), (14, 25), (6, 5), (1, 14), (32, 4), (7, 17), (18, 9), (18, 28), (7, 11), (24, 4), (4, 15), (22, 3), (19, 12), (20, 22), (12, 18), (22, 25), (13, 1), (15, 3), (33, 3), (15, 10), (26, 15), (22, 30), (1, 7), (18, 16), (17, 30), (24, 22), (25, 29), (8, 28), (5, 23), (14, 0), (9, 29), (14, 23), (38, 22), (0, 21), (17, 23), (34, 19), (22, 16), (10, 18), (34, 7), (4, 27), (0, 22), (25, 0), (19, 27), (6, 8), (28, 19), (14, 19), (34, 8), (33, 6), (6, 11), (18, 11), (33, 13), (30, 9), (11, 2), (18, 22), (31, 7), (34, 3), (2, 20), (18, 13), (6, 16), (32, 30), (17, 20), (26, 27), (29, 20), (21, 5), (25, 2), (37, 3), (9, 20), (31, 12), (25, 16), (23, 7), (35, 1), (26, 6), (20, 1), (36, 24), (38, 0), (1, 13), (27, 22), (34, 1), (28, 9), (2, 30), (2, 29), (12, 27), (17, 22), (32, 11), (1, 25), (8, 15), (13, 28), (25, 10), (1, 26), (15, 6), (36, 16), (9, 25), (7, 27), (1, 6), (14, 22), (18, 5), (20, 20), (20, 21), (15, 28), (14, 29), (27, 8), (11, 1), (26, 10), (28, 21), (15, 24), (33, 18), (13, 0), (12, 2), (16, 22), (24, 23), (8, 6), (28, 13), (20, 29), (13, 9), (17, 12), (36, 1), (15, 1), (2, 13), (1, 12), (32, 14), (36, 2), (37, 11), (6, 29), (13, 21), (24, 7), (4, 4), (18, 20), (25, 21), (6, 20), (10, 26), (27, 27), (4, 17), (34, 30), (35, 30), (17, 9), (22, 11), (8, 3), (30, 26), (18, 30), (18, 0), (38, 6), (33, 21), (36, 18), (28, 29), (35, 4), (38, 10), (5, 29), (37, 17), (18, 2), (38, 24), (10, 0), (24, 8), (27, 18), (1, 2), (5, 21), (13, 2), (5, 20), (36, 5), (23, 24), (15, 17), (22, 26), (10, 20), (11, 16), (10, 24), (26, 23), (3, 21), (11, 3), (7, 8), (21, 28), (18, 19), (19, 19), (19, 1), (16, 14), (10, 4), (25, 1), (23, 27), (30, 7), (31, 15), (4, 19), (23, 17), (32, 26), (23, 12), (26, 29), (37, 0), (24, 2), (32, 9), (27, 14), (28, 8), (18, 26), (35, 10), (29, 16), (3, 1), (4, 20), (37, 10), (11, 29), (7, 14), (5, 3), (21, 13), (12, 29), (10, 12), (1, 16), (25, 28), (11, 8), (32, 16), (17, 18), (28, 22), (27, 6), (20, 14), (2, 17), (0, 25), (22, 22), (31, 26), (24, 10), (23, 2), (29, 25), (21, 2), (20, 9), (29, 6), (29, 19), (28, 3), (15, 18), (37, 8), (32, 29), (17, 3), (17, 19), (13, 14), (31, 16), (6, 22), (30, 12), (9, 1), (18, 10), (2, 1), (22, 8), (9, 0), (29, 24), (26, 30), (13, 8), (9, 17), (2, 12), (33, 26), (5, 12), (9, 22), (24, 16), (23, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82000", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 14), (23, 5), (4, 26), (29, 22), (18, 29), (3, 18), (15, 11), (6, 10), (24, 28), (18, 4), (1, 2), (19, 2), (13, 20), (8, 11), (24, 17), (22, 23), (1, 27), (10, 20), (12, 28), (11, 11), (25, 19), (4, 29), (20, 22), (1, 16), (28, 3), (1, 20), (28, 27), (13, 7), (26, 2), (25, 22), (7, 15), (8, 27), (25, 13), (0, 25), (6, 27), (17, 13), (11, 5), (18, 6), (1, 29), (19, 22), (23, 26), (15, 18), (15, 14), (3, 25), (25, 21), (12, 27), (1, 4), (9, 21), (5, 30), (12, 14), (18, 30), (1, 7), (14, 1), (19, 12), (4, 17), (28, 13), (22, 13), (23, 30), (22, 26), (21, 27), (14, 4), (24, 13), (9, 10), (4, 7), (0, 26), (13, 21), (15, 30), (27, 16), (24, 9), (11, 4), (22, 15), (15, 4), (5, 18), (10, 4), (29, 10), (4, 23), (8, 8), (29, 3), (17, 18), (7, 1), (14, 26), (11, 21), (9, 9), (23, 2), (26, 6), (28, 16), (19, 29), (26, 5), (19, 16), (18, 12), (8, 19), (6, 7), (29, 15), (11, 17), (25, 8), (8, 18), (24, 6), (26, 16), (16, 16), (22, 24), (0, 30), (25, 29), (1, 19), (2, 26), (4, 8), (11, 15), (23, 29), (12, 29), (26, 30), (15, 2), (11, 27), (6, 17), (8, 16), (0, 17), (13, 14), (13, 23), (9, 11), (3, 5), (28, 1), (11, 19), (25, 10), (24, 19), (18, 28), (27, 0), (18, 27), (5, 13), (11, 0), (0, 22), (17, 26), (16, 23), (20, 21), (4, 10), (0, 4), (9, 27), (20, 1), (6, 9), (5, 9), (14, 22), (24, 24), (24, 10), (25, 6), (22, 27), (5, 12), (19, 5), (2, 16), (8, 29), (4, 1), (25, 28), (23, 16), (11, 8), (23, 0), (14, 21), (7, 16), (11, 23), (8, 26), (5, 20), (16, 15), (21, 29), (5, 5), (5, 14), (1, 24), (19, 19), (28, 11), (27, 9), (27, 1), (20, 2), (1, 28), (26, 3), (28, 2), (28, 7), (21, 5), (10, 26), (13, 10), (25, 5), (25, 12), (10, 3), (26, 13), (24, 7), (9, 23), (24, 0), (15, 20), (5, 19), (0, 24), (17, 16), (2, 20), (28, 6), (21, 18), (22, 28), (12, 6), (7, 4), (5, 22), (28, 25), (21, 23), (20, 25), (20, 0), (22, 18), (7, 7), (12, 8), (27, 12), (24, 16), (21, 28), (11, 30), (0, 20), (9, 19), (9, 7), (27, 13), (19, 3), (28, 10), (8, 25), (18, 14), (19, 15), (3, 15), (14, 23), (16, 3), (17, 20), (25, 0), (14, 2), (27, 18), (27, 2), (27, 30), (22, 20), (15, 3), (7, 19), (0, 10), (2, 2), (7, 28), (9, 26), (3, 21), (10, 13), (10, 30), (15, 8), (28, 28), (22, 14), (17, 14), (17, 1), (14, 24), (8, 17), (10, 23), (14, 18), (21, 8), (1, 26), (10, 28), (1, 8), (14, 30), (9, 18), (17, 2), (4, 2), (0, 3), (28, 15), (9, 4), (2, 29), (8, 9), (0, 11), (13, 3), (13, 2), (7, 30), (13, 16), (28, 14), (1, 17), (26, 24), (16, 9), (29, 4), (16, 7), (1, 6), (19, 8), (11, 13), (26, 25), (13, 29), (11, 20), (29, 7), (21, 26), (24, 30), (19, 24), (12, 5), (2, 25), (14, 29), (11, 6), (2, 28), (7, 3), (26, 10), (15, 16), (8, 2), (14, 14), (26, 20), (6, 30), (29, 25), (3, 12), (17, 4), (27, 20), (3, 8), (8, 3), (1, 1), (7, 25), (2, 13), (14, 7), (20, 12), (9, 12), (20, 4), (12, 16), (25, 9), (24, 8), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948240", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 3), (10, 14), (20, 24), (26, 1), (21, 19), (2, 21), (26, 9), (15, 2), (17, 32), (7, 27), (12, 5), (0, 10), (19, 2), (10, 18), (26, 4), (31, 32), (4, 6), (0, 32), (20, 29), (17, 31), (29, 8), (8, 27), (2, 0), (28, 24), (30, 12), (4, 0), (9, 24), (19, 34), (23, 3), (18, 4), (28, 19), (28, 35), (16, 34), (2, 27), (31, 11), (13, 13), (21, 11), (15, 25), (1, 4), (18, 34), (14, 9), (2, 28), (22, 32), (27, 21), (5, 0), (1, 23), (8, 5), (32, 18), (29, 20), (1, 31), (26, 12), (17, 29), (8, 29), (11, 35), (11, 12), (28, 30), (4, 34), (2, 10), (27, 13), (27, 29), (31, 35), (5, 1), (10, 30), (30, 21), (11, 10), (15, 32), (5, 7), (8, 35), (11, 31), (29, 24), (1, 35), (23, 16), (14, 18), (16, 33), (30, 5), (28, 23), (17, 9), (27, 31), (18, 6), (14, 27), (3, 0), (1, 14), (9, 5), (4, 18), (8, 4), (28, 3), (20, 32), (7, 29), (4, 1), (26, 28), (14, 32), (0, 7), (8, 30), (11, 29), (3, 19), (16, 13), (24, 19), (21, 3), (16, 24), (4, 15), (12, 4), (16, 15), (12, 16), (11, 20), (3, 17), (15, 35), (3, 18), (16, 29), (27, 2), (13, 26), (26, 3), (4, 17), (31, 7), (30, 27), (6, 16), (25, 7), (12, 12), (25, 0), (9, 10), (0, 23), (17, 4), (7, 35), (10, 5), (8, 10), (0, 9), (5, 11), (10, 10), (29, 34), (30, 10), (6, 23), (13, 21), (27, 3), (22, 9), (4, 23), (0, 2), (22, 34), (6, 9), (32, 31), (12, 15), (31, 27), (9, 12), (19, 20), (0, 12), (32, 10), (5, 21), (24, 32), (4, 26), (15, 4), (12, 28), (25, 5), (17, 35), (25, 11), (12, 21), (10, 21), (8, 31), (28, 17), (16, 16), (22, 24), (18, 13), (13, 16), (21, 35), (24, 30), (27, 18), (9, 28), (16, 12), (9, 4), (32, 0), (18, 7), (12, 8), (29, 32), (17, 13), (21, 1), (25, 8), (13, 33), (18, 20), (19, 22), (28, 0), (26, 35), (22, 27), (29, 15), (25, 18), (9, 19), (19, 12), (9, 9), (22, 2), (22, 0), (30, 30), (16, 5), (14, 6), (20, 12), (22, 7), (28, 7), (6, 0), (6, 28), (32, 29), (21, 6), (28, 25), (1, 34), (6, 15), (2, 25), (6, 32), (13, 34), (25, 30), (21, 22), (24, 15), (14, 34), (8, 12), (31, 14), (2, 26), (29, 17), (5, 22), (10, 33), (10, 19), (8, 21), (31, 0), (13, 6), (25, 31), (17, 11), (30, 16), (3, 35), (9, 8), (7, 32), (20, 1), (23, 35), (27, 16), (1, 0), (18, 27), (4, 3), (22, 29), (24, 14), (16, 25), (24, 24), (15, 24), (31, 17), (17, 10), (15, 3), (22, 1), (30, 8), (27, 32), (9, 26), (15, 5), (0, 25), (12, 22), (6, 1), (22, 26), (6, 22), (14, 10), (31, 29), (30, 15), (16, 23), (23, 25), (24, 27), (12, 26), (28, 8), (26, 6), (19, 29), (30, 34), (6, 5), (9, 17), (8, 16), (27, 0), (29, 23), (2, 11), (31, 8), (3, 1), (32, 20), (19, 27), (21, 18), (5, 15), (6, 33), (24, 21), (30, 28), (8, 1), (0, 26), (14, 5), (20, 5), (13, 14), (22, 21), (14, 4), (8, 14), (30, 18), (4, 11), (2, 30), (32, 22), (22, 11), (18, 28), (26, 0), (2, 24), (9, 16), (26, 25), (18, 10), (4, 10), (12, 30), (19, 16), (19, 31), (25, 2), (20, 35), (5, 9), (4, 2), (24, 17), (17, 22), (18, 21), (5, 35), (30, 29), (27, 4), (4, 9), (12, 13), (7, 10), (13, 35), (11, 14), (23, 22), (10, 2), (20, 6), (20, 10), (22, 22), (5, 20), (25, 16), (30, 0), (14, 13), (31, 10), (24, 4), (25, 20), (17, 12), (28, 28), (9, 22), (21, 32), (19, 28), (14, 28), (0, 34), (5, 3), (22, 28), (10, 35), (4, 29), (29, 25), (12, 18), (3, 2), (3, 16), (8, 22), (29, 31), (15, 33), (19, 15), (21, 15), (1, 20), (31, 30), (10, 22), (16, 31), (24, 5), (3, 5), (21, 8), (10, 20), (0, 16), (22, 14), (15, 26), (0, 13), (10, 3), (23, 1), (28, 2), (12, 27), (3, 27), (0, 4), (31, 4), (14, 26), (28, 34), (0, 29), (20, 13), (3, 8), (27, 34), (13, 19), (5, 19), (15, 0), (30, 13), (23, 5), (4, 35), (14, 23), (31, 31), (3, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30240", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (25, 19), (21, 4), (21, 15), (13, 9), (24, 35), (28, 1), (10, 30), (10, 18), (15, 17), (21, 31), (3, 1), (26, 32), (24, 7), (23, 1), (25, 14), (8, 27), (31, 22), (19, 20), (16, 5), (24, 5), (6, 19), (6, 9), (2, 0), (25, 22), (21, 21), (1, 16), (2, 23), (20, 11), (29, 22), (22, 29), (14, 15), (3, 10), (31, 13), (2, 16), (19, 29), (7, 15), (12, 12), (4, 27), (8, 12), (9, 17), (12, 14), (25, 28), (10, 32), (13, 30), (12, 6), (13, 27), (23, 23), (1, 1), (27, 29), (25, 17), (18, 34), (9, 10), (1, 0), (29, 3), (2, 27), (29, 1), (8, 21), (7, 6), (3, 4), (16, 10), (14, 36), (2, 5), (21, 35), (5, 18), (20, 14), (12, 34), (8, 1), (22, 7), (7, 30), (11, 0), (24, 1), (30, 5), (27, 12), (20, 5), (5, 11), (2, 25), (7, 18), (0, 35), (29, 20), (2, 34), (22, 11), (19, 33), (3, 18), (12, 11), (3, 30), (29, 23), (22, 4), (8, 36), (26, 30), (20, 0), (14, 14), (21, 32), (14, 28), (15, 35), (31, 8), (0, 29), (1, 7), (0, 24), (12, 25), (4, 15), (7, 12), (5, 7), (31, 33), (18, 10), (29, 16), (11, 6), (24, 34), (13, 24), (9, 6), (10, 27), (21, 30), (11, 31), (21, 3), (28, 34), (26, 36), (22, 14), (0, 30), (27, 10), (15, 28), (20, 17), (17, 19), (10, 21), (30, 15), (7, 11), (19, 15), (4, 3), (0, 13), (8, 14), (6, 30), (5, 23), (23, 18), (11, 17), (28, 9), (30, 35), (27, 9), (0, 10), (16, 23), (22, 33), (29, 15), (9, 14), (21, 28), (3, 9), (4, 16), (24, 14), (16, 16), (9, 24), (29, 25), (4, 10), (20, 19), (15, 12), (13, 10), (18, 30), (7, 13), (26, 0), (18, 32), (24, 12), (9, 20), (15, 20), (7, 2), (28, 29), (7, 25), (10, 2), (3, 33), (17, 33), (7, 29), (13, 22), (13, 28), (1, 26), (9, 2), (31, 19), (7, 28), (9, 19), (31, 23), (5, 27), (21, 8), (11, 32), (4, 35), (20, 13), (17, 8), (21, 2), (29, 28), (18, 5), (9, 3), (30, 36), (5, 1), (25, 10), (14, 22), (29, 17), (29, 7), (14, 12), (5, 17), (2, 10), (29, 10), (28, 35), (28, 33), (13, 18), (14, 31), (16, 26), (5, 28), (23, 20), (20, 8), (18, 31), (14, 10), (15, 29), (11, 19), (6, 32), (28, 22), (30, 19), (30, 32), (28, 19), (12, 19), (29, 6), (31, 9), (16, 31), (3, 14), (3, 13), (14, 17), (26, 11), (17, 15), (28, 12), (1, 21), (20, 4), (5, 12), (12, 30), (17, 3), (9, 11), (17, 30), (9, 9), (27, 21), (18, 24), (26, 18), (14, 13), (7, 14), (17, 34), (10, 13), (15, 14), (21, 5), (8, 24), (23, 32), (12, 21), (29, 31), (21, 26), (15, 9), (14, 23), (19, 35), (15, 2), (22, 26), (11, 30), (3, 23), (11, 11), (24, 9), (8, 3), (2, 35), (17, 22), (21, 24), (29, 35), (22, 21), (26, 23), (18, 21), (9, 30), (23, 36), (30, 4), (12, 28), (14, 30), (0, 20), (30, 12), (18, 28), (13, 6), (30, 25), (16, 3), (31, 27), (8, 22), (27, 17), (5, 4), (12, 2), (18, 2), (6, 8), (25, 29), (24, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "147200", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 31), (4, 29), (15, 9), (0, 20), (17, 27), (6, 17), (10, 7), (2, 24), (18, 16), (3, 25), (16, 35), (15, 17), (6, 35), (24, 22), (33, 18), (17, 6), (13, 19), (20, 19), (13, 18), (3, 17), (14, 19), (21, 27), (14, 16), (22, 16), (25, 29), (20, 32), (10, 15), (1, 0), (12, 10), (34, 10), (24, 34), (1, 31), (27, 10), (27, 3), (13, 25), (29, 12), (30, 34), (28, 30), (28, 7), (5, 5), (21, 7), (0, 18), (9, 30), (28, 10), (34, 1), (5, 34), (2, 15), (10, 30), (27, 25), (14, 26), (33, 27), (0, 22), (21, 30), (30, 33), (16, 30), (35, 19), (23, 19), (30, 12), (28, 13), (9, 34), (6, 18), (23, 18), (24, 10), (30, 13), (10, 18), (29, 20), (22, 5), (22, 31), (25, 9), (13, 5), (0, 11), (5, 21), (9, 26), (15, 24), (16, 3), (3, 23), (17, 2), (3, 34), (30, 10), (5, 14), (8, 20), (19, 17), (15, 14), (13, 14), (2, 6), (23, 22), (3, 18), (34, 24), (9, 16), (11, 32), (33, 14), (7, 5), (5, 19), (0, 13), (26, 0), (7, 1), (17, 29), (20, 9), (3, 26), (35, 33), (6, 29), (9, 0), (14, 14), (3, 6), (22, 29), (35, 8), (19, 18), (26, 21), (33, 13), (12, 16), (12, 24), (25, 17), (13, 7), (28, 0), (3, 29), (5, 3), (27, 34), (19, 28), (9, 6), (29, 0), (21, 25), (16, 8), (27, 11), (25, 16), (18, 20), (35, 7), (17, 30), (23, 23), (11, 8), (15, 4), (19, 8), (19, 19), (23, 20), (18, 1), (21, 26), (18, 18), (10, 31), (4, 7), (3, 5), (4, 8), (17, 34), (35, 3), (8, 31), (25, 23), (10, 20), (27, 6), (25, 5), (32, 6), (15, 12), (2, 12), (34, 35), (0, 23), (4, 21), (0, 31), (22, 21), (32, 20), (21, 29), (22, 3), (22, 12), (22, 15), (12, 11), (3, 32), (22, 27), (28, 28), (33, 16), (3, 1), (13, 26), (4, 31), (17, 5), (32, 23), (31, 20), (15, 34), (14, 22), (13, 34), (18, 29), (11, 34), (29, 15), (12, 5), (33, 4), (21, 4), (26, 25), (14, 20), (3, 14), (24, 19), (27, 26), (28, 4), (26, 35), (26, 27), (10, 34), (25, 25), (2, 25), (32, 34), (24, 13), (21, 3), (16, 4), (9, 1), (29, 3), (8, 19), (28, 20), (11, 21), (34, 12), (27, 18), (22, 24), (21, 19), (22, 14), (25, 22), (20, 2), (31, 9), (28, 26), (35, 20), (0, 8), (33, 5), (0, 3), (16, 15), (17, 32), (4, 26), (27, 15), (5, 4), (16, 17), (3, 31), (13, 2), (2, 1), (14, 25), (14, 2), (18, 8), (4, 17), (24, 17), (11, 9), (14, 23), (29, 18), (2, 13), (12, 23), (2, 3), (11, 24), (22, 6), (24, 30), (8, 17), (22, 0), (0, 25), (34, 31), (26, 16), (7, 3), (9, 12), (11, 17), (7, 27), (11, 6), (29, 23), (34, 22), (4, 27), (5, 7), (20, 18), (5, 22), (12, 15), (32, 17), (34, 29), (7, 16), (12, 21), (4, 16), (5, 25), (33, 24), (30, 18), (30, 22), (11, 19), (12, 3), (3, 20), (35, 32), (23, 28), (3, 28), (19, 5), (26, 3), (10, 33), (23, 27), (24, 4), (16, 33), (35, 14), (9, 22), (30, 0), (3, 24), (15, 35), (27, 5), (6, 4), (2, 32), (2, 2), (18, 15), (9, 15), (20, 21), (33, 12), (1, 5), (2, 16), (16, 16), (28, 16), (10, 12), (20, 0), (31, 22), (33, 20), (34, 16), (3, 16), (25, 27), (6, 31), (31, 5), (11, 2), (6, 9), (18, 30), (17, 28), (31, 31), (22, 35), (20, 8), (21, 23), (25, 1), (32, 15), (12, 9), (8, 1), (29, 5), (5, 9), (21, 12), (32, 30), (9, 20), (33, 2), (2, 19), (9, 17), (2, 35), (30, 25), (27, 16), (26, 2), (33, 30), (34, 26), (15, 2), (30, 9), (33, 0), (11, 35), (26, 26), (26, 30), (9, 14), (22, 18), (23, 12), (11, 18), (12, 34), (33, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215496", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 11), (20, 29), (3, 17), (5, 6), (12, 7), (21, 18), (8, 31), (17, 7), (2, 12), (17, 31), (5, 15), (12, 11), (22, 7), (20, 18), (25, 8), (29, 28), (22, 20), (2, 15), (8, 16), (12, 31), (13, 20), (22, 26), (9, 24), (11, 22), (10, 22), (10, 1), (25, 6), (2, 14), (25, 17), (7, 24), (2, 10), (29, 18), (25, 16), (3, 31), (5, 3), (11, 14), (2, 1), (7, 3), (29, 20), (3, 4), (1, 23), (9, 30), (14, 28), (29, 16), (25, 15), (23, 17), (12, 21), (24, 13), (12, 27), (6, 12), (23, 9), (15, 6), (28, 32), (17, 32), (10, 0), (26, 12), (1, 3), (3, 13), (14, 20), (21, 23), (5, 8), (10, 4), (21, 4), (27, 18), (15, 11), (10, 10), (4, 10), (21, 16), (4, 22), (16, 15), (27, 7), (21, 15), (19, 16), (0, 5), (0, 4), (13, 0), (14, 29), (4, 6), (20, 23), (15, 22), (1, 9), (9, 0), (7, 14), (9, 14), (21, 12), (6, 9), (28, 5), (1, 31), (9, 8), (27, 27), (18, 12), (23, 15), (28, 19), (14, 0), (15, 4), (9, 3), (23, 11), (13, 10), (14, 19), (16, 12), (13, 18), (0, 11), (9, 21), (2, 13), (0, 21), (0, 7), (4, 15), (15, 20), (19, 17), (14, 5), (2, 21), (16, 23), (17, 6), (17, 26), (13, 22), (24, 6), (20, 21), (25, 3), (27, 10), (23, 25), (14, 27), (19, 8), (18, 25), (7, 30), (18, 29), (7, 28), (8, 25), (10, 30), (3, 30), (19, 32), (8, 10), (15, 3), (13, 25), (8, 19), (10, 19), (2, 32), (22, 8), (8, 13), (5, 5), (26, 25), (0, 27), (17, 29), (5, 14), (15, 18), (29, 25), (11, 8), (12, 24), (1, 21), (22, 2), (7, 11), (14, 3), (9, 23), (23, 2), (10, 6), (8, 17), (13, 3), (17, 28), (18, 9), (14, 15), (23, 18), (18, 32), (16, 31), (15, 29), (4, 19), (22, 3), (16, 13), (2, 28), (1, 7), (18, 5), (2, 30), (12, 28), (0, 20), (19, 28), (12, 4), (23, 1), (15, 25), (26, 28), (23, 4), (17, 3), (10, 12), (23, 20), (18, 24), (3, 14), (23, 10), (20, 2), (9, 26), (5, 2), (17, 30), (3, 10), (16, 7), (11, 31), (3, 20), (14, 9), (11, 2), (0, 12), (10, 27), (27, 31), (20, 31), (29, 27), (12, 6), (29, 11), (19, 27), (10, 20), (14, 16), (5, 18), (8, 0), (25, 27), (22, 15), (3, 11), (16, 28), (28, 1), (2, 4), (16, 21), (25, 12), (22, 17), (13, 31), (8, 15), (20, 19), (20, 3), (21, 24), (25, 14), (16, 4), (10, 14), (15, 28), (11, 4), (15, 30), (14, 17), (26, 15), (12, 16), (0, 8), (4, 3), (8, 30), (17, 13), (25, 22), (22, 28), (4, 17), (25, 29), (5, 21), (11, 23), (10, 3), (11, 28), (10, 31), (23, 30), (8, 7), (25, 9), (20, 7), (5, 30), (7, 20), (27, 24), (0, 16), (6, 30), (28, 4), (19, 31), (8, 24), (20, 12), (7, 19), (22, 1), (0, 30), (24, 5), (4, 16), (13, 5), (22, 13), (2, 18), (15, 16), (12, 25), (4, 8), (24, 11), (4, 31), (18, 13), (5, 22), (28, 17), (13, 23), (20, 30), (20, 14), (17, 2), (11, 19), (2, 7), (6, 27), (0, 10), (5, 7), (4, 23), (6, 7), (7, 32), (23, 3), (5, 17), (21, 32), (19, 7), (9, 31), (15, 5), (23, 32), (12, 22), (28, 11), (20, 9), (7, 15), (25, 1), (22, 11), (22, 5), (24, 12), (9, 12), (8, 18), (0, 23), (8, 12), (18, 4), (28, 23), (21, 26), (6, 2), (1, 25), (28, 15), (16, 20), (21, 1), (15, 31), (17, 27), (8, 21), (5, 25), (1, 20), (9, 17), (27, 32), (13, 21), (29, 30), (14, 26), (14, 11), (24, 31), (10, 5), (5, 24), (18, 23), (9, 11), (9, 15), (10, 25), (0, 18), (27, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739620", "dataset": "MATH"}
{"messages": [{"content": "In a 31x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 27), (5, 21), (8, 5), (28, 11), (0, 17), (22, 1), (15, 2), (6, 16), (13, 8), (25, 6), (30, 3), (4, 20), (11, 12), (5, 24), (12, 12), (21, 22), (9, 5), (21, 12), (21, 20), (15, 29), (29, 12), (7, 17), (17, 10), (16, 31), (19, 12), (15, 17), (11, 21), (28, 17), (11, 27), (5, 16), (18, 25), (12, 3), (1, 31), (29, 16), (17, 30), (13, 25), (28, 4), (23, 29), (29, 32), (9, 1), (22, 19), (19, 2), (0, 12), (4, 25), (19, 18), (8, 19), (15, 6), (10, 27), (24, 5), (14, 27), (22, 2), (26, 14), (29, 2), (11, 11), (16, 29), (23, 22), (7, 0), (27, 24), (28, 12), (5, 15), (14, 11), (9, 16), (26, 4), (24, 9), (0, 9), (14, 14), (20, 19), (17, 6), (23, 13), (21, 19), (29, 11), (7, 2), (10, 31), (14, 20), (30, 24), (24, 22), (4, 6), (28, 29), (7, 28), (30, 26), (7, 16), (24, 4), (15, 11), (1, 29), (13, 24), (8, 0), (0, 31), (23, 17), (27, 12), (3, 25), (5, 5), (15, 1), (30, 15), (8, 13), (2, 24), (20, 6), (14, 10), (16, 7), (6, 28), (0, 5), (28, 8), (28, 6), (22, 21), (10, 0), (17, 18), (28, 20), (2, 27), (23, 30), (4, 24), (12, 10), (12, 29), (9, 15), (4, 14), (23, 10), (25, 4), (19, 11), (8, 15), (11, 22), (29, 6), (23, 32), (14, 5), (27, 23), (24, 32), (3, 6), (12, 24), (11, 24), (20, 13), (23, 14), (8, 26), (19, 26), (10, 4), (27, 29), (4, 13), (9, 25), (17, 8), (0, 6), (20, 11), (23, 4), (29, 5), (7, 15), (23, 16), (30, 8), (28, 25), (17, 32), (21, 13), (26, 6), (20, 2), (16, 4), (30, 1), (22, 11), (4, 16), (18, 10), (22, 5), (26, 10), (27, 17), (8, 25), (22, 24), (20, 10), (21, 18), (12, 1), (2, 5), (25, 12), (13, 5), (11, 1), (8, 20), (4, 11), (16, 28), (1, 3), (19, 20), (1, 7), (4, 31), (28, 32), (23, 15), (7, 32), (28, 13), (24, 30), (25, 27), (2, 32), (25, 5), (9, 28), (15, 4), (24, 21), (7, 25), (17, 7), (13, 22), (12, 15), (27, 31), (19, 24), (26, 16), (6, 31), (1, 17), (26, 31), (18, 28), (14, 19), (28, 26), (15, 13), (26, 2), (19, 4), (25, 1), (18, 1), (2, 9), (24, 24), (6, 10), (7, 12), (27, 8), (14, 15), (0, 24), (4, 17), (24, 11), (27, 16), (23, 12), (14, 30), (26, 29), (28, 18), (12, 25), (7, 3), (5, 19), (23, 26), (1, 26), (4, 3), (17, 13), (0, 16), (15, 7), (10, 26), (23, 20), (29, 19), (21, 11), (17, 0), (10, 6), (28, 24), (29, 26), (29, 21), (23, 2), (30, 10), (24, 15), (1, 2), (6, 3), (22, 18), (21, 7), (21, 24), (11, 6), (15, 12), (26, 15), (9, 2), (25, 21), (7, 6), (8, 32), (6, 17), (19, 3), (26, 24), (5, 12), (20, 26), (12, 27), (3, 10), (21, 25), (27, 9), (13, 21), (13, 4), (26, 22), (4, 5), (14, 18), (27, 26), (29, 23), (11, 19), (12, 17), (3, 19), (16, 5), (0, 13), (22, 27), (18, 9), (16, 16), (19, 32), (11, 32), (24, 14), (3, 27), (16, 2), (20, 27), (25, 7), (11, 3), (0, 7), (26, 26), (30, 5), (12, 6), (21, 1), (21, 16), (26, 23), (20, 15), (0, 27), (15, 18), (18, 14), (17, 17), (2, 25), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "958010", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 23), (6, 7), (27, 31), (9, 3), (9, 35), (6, 8), (17, 5), (13, 31), (17, 13), (26, 5), (24, 28), (8, 5), (9, 31), (6, 9), (15, 35), (18, 15), (13, 24), (2, 24), (25, 24), (8, 29), (4, 9), (29, 23), (22, 36), (4, 29), (20, 15), (12, 16), (19, 27), (19, 5), (22, 26), (24, 29), (3, 32), (26, 24), (24, 6), (15, 17), (24, 8), (8, 33), (17, 27), (20, 7), (0, 17), (28, 20), (21, 0), (0, 28), (8, 9), (11, 30), (21, 29), (19, 6), (19, 16), (29, 5), (21, 8), (11, 21), (2, 23), (21, 18), (23, 15), (21, 30), (6, 19), (22, 27), (6, 3), (8, 13), (4, 36), (24, 21), (6, 15), (27, 22), (14, 16), (16, 17), (20, 23), (1, 7), (11, 18), (13, 0), (24, 16), (20, 35), (2, 9), (5, 22), (24, 35), (3, 28), (11, 23), (0, 6), (12, 10), (29, 2), (6, 10), (6, 2), (16, 24), (24, 32), (3, 26), (4, 4), (7, 10), (16, 13), (19, 12), (21, 12), (25, 11), (0, 20), (14, 11), (3, 0), (5, 7), (9, 19), (10, 30), (21, 17), (1, 12), (1, 31), (29, 33), (8, 11), (22, 1), (14, 31), (25, 33), (18, 25), (24, 34), (25, 13), (13, 34), (12, 23), (15, 23), (1, 3), (13, 3), (20, 27), (11, 0), (2, 4), (3, 14), (18, 31), (1, 1), (6, 27), (24, 13), (14, 4), (20, 0), (16, 7), (9, 17), (12, 25), (27, 3), (10, 6), (10, 7), (9, 11), (9, 13), (25, 14), (23, 27), (22, 11), (21, 25), (23, 24), (4, 19), (4, 18), (15, 19), (21, 27), (22, 19), (9, 23), (0, 4), (13, 27), (23, 10), (20, 21), (23, 20), (1, 21), (16, 29), (7, 36), (25, 27), (23, 0), (15, 31), (20, 16), (27, 18), (11, 26), (21, 10), (14, 29), (3, 13), (4, 11), (14, 0), (14, 14), (19, 8), (18, 23), (11, 16), (26, 22), (0, 3), (2, 35), (1, 34), (16, 33), (28, 23), (22, 21), (9, 21), (3, 19), (9, 25), (16, 22), (29, 16), (23, 31), (10, 25), (15, 22), (17, 21), (10, 21), (27, 6), (28, 4), (0, 36), (27, 4), (1, 18), (29, 22), (20, 13), (12, 18), (24, 33), (28, 22), (6, 33), (2, 26), (8, 6), (0, 18), (13, 12), (3, 20), (20, 8), (24, 31), (7, 9), (16, 18), (21, 32), (28, 7), (18, 28), (12, 0), (28, 31), (15, 30), (16, 27), (16, 0), (17, 31), (7, 23), (21, 24), (26, 2), (11, 32), (26, 31), (10, 0), (26, 35), (4, 8), (4, 7), (24, 19), (5, 16), (23, 22), (18, 26), (11, 15), (5, 20), (5, 21), (22, 20), (25, 6), (26, 26), (11, 34), (16, 6), (19, 10), (23, 7), (10, 10), (12, 28), (5, 17), (18, 6), (20, 6), (28, 18), (19, 4), (29, 1), (11, 13), (6, 34), (26, 28), (5, 15), (12, 19), (26, 16), (17, 14), (1, 23), (9, 28), (19, 31), (22, 34), (11, 20), (23, 23), (27, 11), (26, 17), (21, 31), (11, 22), (4, 13), (18, 35), (23, 11), (16, 8), (14, 28), (9, 15), (25, 1), (14, 34), (6, 23), (28, 10), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898560", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 9), (21, 16), (33, 28), (16, 23), (6, 22), (24, 4), (4, 31), (36, 20), (19, 1), (32, 0), (5, 24), (19, 3), (33, 27), (13, 22), (2, 11), (14, 21), (21, 27), (3, 4), (12, 9), (13, 0), (14, 5), (2, 7), (31, 2), (35, 22), (24, 24), (13, 26), (9, 32), (4, 2), (7, 23), (28, 7), (3, 17), (1, 20), (25, 21), (24, 0), (20, 11), (2, 17), (30, 20), (1, 2), (3, 20), (12, 33), (29, 17), (34, 27), (16, 31), (14, 13), (0, 25), (5, 14), (35, 2), (17, 6), (17, 32), (26, 18), (18, 21), (9, 9), (18, 17), (24, 15), (29, 14), (8, 1), (6, 4), (30, 2), (34, 9), (10, 28), (21, 15), (4, 5), (38, 26), (21, 13), (21, 33), (16, 12), (14, 26), (25, 6), (27, 9), (32, 17), (20, 17), (33, 15), (25, 1), (36, 26), (1, 28), (31, 5), (29, 28), (35, 21), (37, 0), (18, 27), (28, 17), (1, 31), (24, 32), (24, 5), (4, 15), (7, 27), (33, 8), (34, 8), (11, 17), (22, 19), (34, 2), (32, 32), (4, 23), (7, 4), (34, 16), (34, 30), (5, 21), (17, 15), (35, 13), (26, 15), (16, 9), (30, 21), (22, 25), (14, 27), (35, 27), (38, 2), (22, 5), (10, 27), (36, 31), (25, 26), (12, 3), (29, 24), (26, 13), (35, 23), (32, 2), (36, 18), (12, 14), (22, 6), (17, 0), (26, 1), (27, 8), (9, 28), (29, 12), (12, 25), (23, 30), (22, 29), (25, 30), (17, 8), (4, 29), (18, 24), (25, 11), (7, 19), (5, 32), (15, 26), (37, 33), (32, 30), (32, 12), (26, 7), (13, 21), (21, 24), (4, 4), (37, 17), (33, 11), (19, 22), (23, 1), (33, 29), (25, 14), (11, 18), (38, 27), (3, 6), (37, 9), (17, 14), (17, 16), (12, 23), (26, 28), (11, 16), (23, 8), (5, 28), (24, 25), (19, 25), (9, 17), (31, 29), (18, 26), (28, 27), (18, 15), (7, 6), (34, 1), (8, 0), (33, 21), (18, 8), (35, 0), (37, 19), (30, 16), (37, 24), (2, 32), (23, 23), (20, 32), (29, 20), (3, 7), (16, 25), (1, 11), (19, 24), (6, 18), (24, 28), (15, 28), (35, 31), (28, 11), (22, 32), (0, 21), (20, 6), (29, 13), (3, 24), (6, 21), (24, 26), (16, 15), (0, 7), (35, 29), (2, 23), (10, 10), (31, 32), (2, 28), (1, 26), (12, 21), (2, 5), (4, 24), (5, 11), (30, 5), (11, 8), (0, 14), (7, 21), (20, 3), (22, 0), (1, 5), (5, 19), (32, 22), (1, 12), (33, 30), (0, 5), (18, 28), (2, 12), (10, 33), (14, 1), (13, 16), (4, 28), (21, 2), (9, 29), (8, 23), (20, 4), (27, 5), (13, 30), (36, 7), (12, 13), (12, 4), (11, 31), (16, 5), (13, 12), (0, 33), (30, 3), (5, 6), (36, 23), (23, 4), (32, 29), (6, 31), (34, 5), (37, 29), (14, 18), (14, 25), (3, 12), (26, 14), (15, 3), (17, 1), (34, 0), (1, 23), (11, 22), (17, 27), (27, 27), (22, 12), (22, 4), (3, 2), (4, 1), (16, 2), (13, 28), (19, 27), (37, 12), (3, 9), (31, 33), (29, 25), (24, 13), (6, 5), (38, 31), (25, 31), (25, 10), (21, 8), (24, 7), (15, 30), (9, 18), (3, 0), (30, 8), (1, 24), (3, 10), (23, 22), (8, 30), (18, 9), (16, 13), (5, 13), (5, 16), (36, 1), (33, 9), (22, 23), (11, 19), (11, 13), (22, 17), (27, 26), (25, 5), (33, 0), (19, 31), (2, 0), (34, 14), (18, 11), (15, 20), (34, 12), (38, 9), (38, 11), (18, 7), (24, 31), (22, 30), (31, 17), (10, 20), (1, 9), (11, 2), (12, 18), (2, 21), (17, 17), (9, 3), (9, 20), (31, 8), (27, 3), (1, 17), (9, 25), (32, 24), (2, 2), (12, 10), (29, 16), (32, 11), (20, 14), (2, 22), (24, 18), (38, 16), (1, 10), (38, 13), (3, 16), (13, 27), (19, 2), (15, 17), (23, 3), (28, 13), (28, 14), (19, 19), (10, 6), (11, 9), (7, 28), (10, 5), (18, 12), (19, 14), (37, 13), (17, 30), (20, 0), (6, 23), (8, 24), (22, 24), (36, 11), (11, 27), (10, 32), (2, 10), (36, 6), (26, 4), (3, 15), (14, 11), (15, 13), (34, 22), (10, 12), (30, 24), (38, 15), (8, 12), (17, 9), (27, 7), (0, 28), (8, 15), (24, 19), (22, 28), (27, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "937768", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 24), (34, 7), (1, 30), (28, 26), (12, 25), (4, 8), (31, 0), (23, 2), (27, 19), (17, 6), (7, 20), (30, 28), (8, 4), (17, 21), (0, 27), (9, 10), (5, 12), (1, 13), (29, 13), (20, 23), (32, 3), (24, 15), (19, 25), (6, 12), (13, 2), (4, 26), (14, 2), (18, 4), (16, 18), (20, 18), (27, 8), (12, 19), (27, 9), (2, 5), (28, 11), (12, 1), (15, 29), (4, 0), (4, 5), (17, 22), (11, 30), (10, 22), (8, 20), (9, 24), (4, 11), (28, 16), (13, 11), (34, 3), (20, 22), (4, 21), (34, 5), (13, 28), (20, 3), (9, 19), (3, 30), (18, 12), (28, 19), (5, 5), (32, 1), (30, 1), (13, 14), (30, 14), (25, 25), (7, 28), (21, 28), (23, 16), (28, 2), (13, 22), (19, 26), (11, 2), (30, 23), (6, 6), (17, 29), (5, 16), (9, 11), (25, 26), (19, 5), (31, 28), (2, 16), (8, 27), (29, 16), (16, 28), (24, 13), (5, 6), (29, 1), (3, 2), (23, 3), (6, 28), (30, 10), (0, 1), (34, 11), (27, 22), (24, 19), (5, 4), (26, 30), (34, 18), (15, 7), (10, 27), (31, 20), (19, 1), (31, 18), (29, 22), (4, 23), (1, 8), (18, 3), (17, 13), (10, 2), (26, 0), (9, 30), (3, 29), (5, 27), (8, 10), (21, 4), (11, 9), (26, 18), (5, 23), (33, 5), (23, 5), (28, 7), (33, 0), (21, 26), (9, 25), (1, 28), (29, 29), (28, 18), (22, 10), (29, 15), (33, 22), (34, 2), (27, 5), (17, 15), (31, 5), (5, 30), (24, 17), (18, 23), (30, 6), (24, 29), (23, 7), (3, 25), (16, 21), (23, 29), (30, 3), (11, 3), (24, 8), (3, 16), (10, 13), (12, 30), (26, 17), (4, 17), (21, 6), (31, 7), (10, 25), (32, 20), (2, 19), (1, 9), (5, 15), (12, 15), (26, 10), (27, 15), (13, 18), (16, 17), (2, 10), (7, 10), (30, 17), (32, 9), (29, 14), (13, 1), (34, 15), (29, 11), (7, 7), (0, 30), (27, 6), (2, 27), (29, 24), (1, 19), (7, 18), (2, 24), (27, 23), (15, 9), (29, 4), (17, 10), (6, 15), (27, 3), (25, 7), (0, 23), (12, 27), (21, 16), (1, 15), (25, 10), (15, 8), (28, 5), (4, 7), (31, 27), (27, 24), (2, 20), (1, 17), (14, 7), (2, 30), (12, 0), (26, 28), (18, 28), (2, 29), (2, 17), (32, 2), (26, 23), (0, 13), (6, 26), (0, 20), (20, 0), (33, 9), (31, 10), (23, 4), (22, 20), (0, 28), (22, 6), (18, 10), (27, 17), (4, 20), (24, 25), (12, 22), (16, 25), (28, 3), (31, 14), (21, 17), (2, 2), (20, 27), (32, 0), (5, 19), (24, 11), (25, 14), (9, 4), (23, 15), (32, 22), (34, 20), (1, 6), (17, 8), (23, 30), (14, 16), (30, 15), (1, 24), (5, 25), (25, 18), (17, 12), (30, 13), (25, 3), (15, 30), (11, 22), (2, 4), (22, 29), (15, 20), (16, 27), (29, 19), (11, 13), (2, 12), (27, 11), (6, 11), (11, 24), (3, 14), (15, 13), (33, 4), (7, 13), (21, 11), (4, 6), (13, 20), (9, 5), (28, 25), (8, 14), (11, 16), (7, 30), (17, 30), (15, 28), (12, 6), (22, 26), (10, 12), (33, 26), (14, 4), (5, 29), (0, 2), (32, 16), (24, 12), (31, 13), (6, 16), (16, 1), (13, 9), (18, 14), (18, 21), (23, 25), (2, 13), (3, 20), (6, 21), (26, 5), (0, 14), (22, 2), (7, 12), (30, 9), (15, 3), (14, 19), (19, 23), (13, 25), (18, 7), (11, 5), (30, 0), (4, 13), (10, 11), (18, 26), (21, 21), (5, 3), (29, 12), (34, 14), (26, 3), (12, 24), (14, 20), (33, 6), (20, 17), (1, 26), (32, 17), (2, 15), (34, 12), (6, 14), (11, 1), (13, 7), (16, 16), (5, 22), (31, 11), (18, 9), (5, 13), (19, 12), (27, 0), (31, 22), (34, 8), (22, 21), (25, 28), (23, 6), (16, 14), (8, 19), (18, 0), (32, 24), (32, 23), (22, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242560", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), 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), (23, 7), (17, 5), (28, 24), (18, 7), (18, 20), (5, 27), (26, 10), (18, 26), (20, 29), (31, 22), (4, 17), (11, 16), (6, 26), (2, 7), (28, 0), (7, 13), (15, 5), (12, 20), (14, 26), (22, 33), (0, 25), (8, 26), (29, 9), (32, 21), (22, 14), (9, 32), (32, 31), (26, 13), (12, 33), (10, 30), (32, 26), (7, 20), (35, 2), (3, 27), (26, 22), (0, 23), (29, 2), (22, 21), (21, 2), (34, 28), (35, 14), (33, 26), (15, 32), (0, 9), (12, 7), (30, 0), (12, 23), (28, 5), (27, 17), (32, 6), (31, 12), (17, 23), (11, 31), (19, 1), (22, 32), (3, 30), (1, 19), (10, 20), (15, 23), (8, 11), (4, 7), (31, 18), (19, 33), (28, 19), (30, 25), (31, 13), (4, 32), (35, 27), (31, 29), (21, 28), (29, 24), (32, 10), (1, 12), (14, 1), (14, 23), (26, 18), (23, 24), (15, 22), (16, 24), (32, 9), (14, 18), (7, 28), (0, 4), (3, 24), (25, 17), (1, 4), (34, 33), (30, 4), (5, 22), (7, 27), (4, 2), (15, 8), (6, 25), (30, 31), (33, 18), (34, 6), (29, 1), (20, 1), (8, 7), (2, 24), (29, 6), (4, 10), (4, 6), (18, 29), (20, 30), (29, 12), (18, 19), (19, 16), (21, 4), (22, 23), (3, 28), (13, 0), (24, 18), (6, 24), (19, 28), (25, 32), (27, 28), (17, 29), (7, 3), (6, 19), (7, 30), (17, 10), (1, 13), (15, 27), (20, 11), (32, 28), (9, 13), (31, 0), (2, 17), (23, 11), (3, 31), (6, 9), (22, 30), (19, 9), (10, 23), (20, 25), (19, 11), (31, 31), (8, 27), (12, 29), (11, 1), (24, 23), (35, 10), (0, 12), (35, 17), (5, 10), (25, 16), (30, 23), (17, 6), (10, 26), (22, 15), (0, 27), (28, 32), (34, 21), (33, 27), (13, 10), (26, 6), (5, 8), (7, 19), (35, 19), (6, 21), (2, 5), (20, 8), (3, 2), (22, 16), (28, 26), (18, 2), (7, 10), (25, 3), (6, 5), (0, 26), (3, 16), (27, 12), (31, 19), (13, 22), (24, 30), (7, 2), (2, 33), (30, 12), (17, 0), (34, 0), (13, 17), (20, 5), (5, 12), (17, 12), (23, 23), (13, 18), (29, 11), (30, 17), (7, 24), (33, 8), (8, 4), (1, 1), (15, 28), (24, 33), (16, 4), (32, 12), (10, 25), (13, 15), (8, 23), (9, 4), (6, 15), (3, 15), (28, 13), (22, 22), (11, 17), (22, 17), (17, 3), (30, 11), (17, 1), (30, 7), (9, 12), (33, 13), (32, 1), (2, 22), (25, 2), (6, 3), (14, 10), (16, 16), (31, 1), (8, 6), (6, 13), (34, 22), (0, 17), (7, 21), (19, 25), (35, 21), (33, 7), (30, 10), (6, 29), (0, 33), (3, 11), (16, 6), (15, 3), (4, 16), (7, 16), (31, 32), (3, 14), (31, 17), (12, 8), (31, 21), (6, 20), (21, 27), (1, 26), (21, 10), (14, 30), (31, 15), (3, 21), (7, 5), (25, 21), (8, 5), (35, 20), (34, 11), (7, 18), (23, 15), (5, 13), (33, 20), (26, 32), (30, 13), (10, 22), (20, 3), (10, 1), (14, 19), (26, 31), (21, 23), (23, 1), (32, 3), (16, 33), (10, 6), (12, 16), (11, 20), (0, 6), (24, 21), (16, 22), (33, 31), (34, 7), (24, 7), (1, 9), (26, 25), (27, 18), (35, 18), (26, 19), (27, 20), (5, 5), (5, 32), (5, 1), (16, 9), (3, 33), (11, 10), (19, 31), (11, 5), (33, 33), (24, 29), (3, 5), (21, 30), (24, 15), (28, 23), (29, 27), (34, 31), (20, 28), (7, 1), (20, 10), (31, 23), (4, 29), (14, 2), (9, 7), (1, 2), (29, 10), (24, 32), (23, 4), (25, 8), (16, 32), (32, 4), (6, 10), (28, 4), (22, 31), (10, 33), (6, 6), (32, 22), (10, 31), (15, 25), (35, 1), (35, 24), (17, 26), (29, 31), (11, 28), (2, 28), (0, 5), (22, 8), (25, 5), (14, 5), (15, 4), (18, 25), (0, 21), (8, 1), (15, 9), (9, 28), (1, 31), (19, 3), (11, 2), (0, 31), (6, 1), (28, 8), (26, 11), (9, 2), (31, 20), (35, 23), (6, 18), (23, 6), (10, 29), (27, 5), (25, 15), (21, 19), (5, 7), (14, 17), (27, 0), (9, 19), (17, 7), (1, 29), (4, 28), (8, 14), (4, 8), (2, 2), (28, 9), (15, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904320", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 2), (20, 3), (1, 31), (4, 7), (10, 23), (20, 1), (28, 24), (26, 27), (7, 7), (24, 30), (33, 32), (15, 15), (33, 17), (17, 8), (29, 7), (4, 15), (17, 20), (33, 20), (8, 31), (6, 16), (10, 24), (17, 0), (19, 18), (24, 2), (15, 10), (30, 16), (7, 30), (7, 22), (32, 4), (22, 21), (14, 8), (4, 9), (29, 25), (30, 28), (2, 29), (1, 26), (3, 7), (13, 8), (9, 3), (21, 12), (19, 29), (27, 24), (21, 16), (0, 17), (10, 12), (6, 3), (33, 0), (28, 6), (16, 6), (31, 5), (21, 7), (17, 30), (5, 3), (3, 11), (9, 26), (15, 20), (5, 25), (19, 30), (22, 8), (12, 14), (7, 25), (12, 17), (24, 27), (23, 27), (10, 16), (0, 30), (28, 8), (5, 18), (10, 8), (9, 18), (13, 4), (11, 19), (8, 10), (30, 31), (17, 27), (12, 27), (33, 2), (18, 13), (2, 32), (18, 33), (28, 18), (4, 11), (17, 7), (28, 28), (27, 2), (8, 8), (21, 19), (17, 16), (3, 5), (11, 3), (14, 1), (16, 14), (27, 12), (24, 17), (29, 12), (2, 19), (26, 14), (16, 13), (2, 25), (16, 22), (28, 5), (2, 20), (2, 28), (15, 27), (29, 32), (8, 7), (12, 20), (17, 2), (32, 10), (0, 14), (8, 2), (5, 7), (24, 18), (3, 18), (8, 6), (18, 32), (4, 6), (6, 17), (14, 18), (6, 33), (26, 22), (22, 0), (9, 0), (10, 3), (15, 31), (11, 32), (7, 18), (23, 30), (22, 9), (13, 17), (16, 31), (8, 32), (3, 24), (7, 8), (19, 23), (2, 11), (18, 1), (31, 20), (26, 10), (32, 1), (0, 22), (15, 16), (0, 5), (22, 25), (23, 10), (6, 31), (23, 4), (9, 12), (32, 16), (20, 4), (6, 23), (19, 25), (27, 5), (13, 19), (10, 7), (25, 31), (21, 28), (7, 26), (23, 12), (28, 27), (30, 8), (16, 16), (19, 5), (10, 26), (18, 10), (2, 14), (29, 15), (0, 6), (20, 23), (20, 9), (19, 22), (4, 23), (26, 1), (1, 4), (11, 23), (15, 12), (28, 33), (10, 30), (23, 25), (21, 32), (17, 9), (31, 13), (9, 30), (6, 24), (25, 1), (27, 26), (31, 7), (28, 4), (24, 0), (21, 29), (24, 25), (33, 1), (22, 14), (12, 21), (3, 9), (2, 3), (12, 19), (1, 16), (1, 6), (7, 12), (23, 21), (15, 14), (1, 12), (13, 13), (8, 23), (32, 6), (7, 17), (4, 25), (22, 3), (9, 21), (24, 13), (22, 5), (26, 30), (16, 28), (31, 10), (14, 29), (0, 31), (9, 9), (15, 2), (30, 27), (24, 28), (0, 29), (21, 17), (8, 28), (31, 9), (11, 30), (22, 22), (1, 29), (21, 26), (0, 7), (2, 33), (31, 24), (22, 33), (12, 31), (4, 10), (33, 31), (29, 1), (12, 2), (1, 15), (17, 31), (12, 28), (28, 32), (21, 31), (2, 5), (1, 19), (20, 20), (2, 9), (8, 17), (28, 19), (3, 10), (24, 19), (25, 19), (33, 28), (7, 16), (31, 16), (27, 18), (30, 11), (30, 24), (19, 11), (14, 27), (13, 15), (20, 2), (33, 3), (22, 16), (23, 24), (8, 24), (31, 15), (1, 24), (9, 17), (31, 6), (17, 25), (21, 33), (1, 14), (28, 29), (5, 17), (23, 7), (3, 27), (25, 14), (0, 13), (29, 33), (30, 23), (0, 16), (5, 24), (33, 14), (30, 7), (29, 5), (11, 24), (24, 3), (30, 0), (9, 10), (18, 7), (14, 25), (30, 1), (18, 3), (2, 1), (10, 14), (1, 28), (6, 9), (8, 12), (4, 31), (10, 20), (9, 14), (27, 13), (2, 10), (16, 11), (30, 30), (28, 9), (27, 28), (30, 33), (30, 4), (22, 1), (9, 6), (12, 10), (25, 26), (17, 21), (29, 16), (20, 16), (8, 20), (12, 15), (32, 30), (23, 20), (20, 22), (11, 20), (17, 23), (23, 28), (4, 8), (1, 22), (11, 6), (13, 26), (2, 30), (0, 11), (30, 17), (16, 3), (14, 2), (21, 27), (11, 2), (3, 3), (19, 17), (0, 23), (15, 25), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "493560", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 28), (3, 3), (23, 14), (7, 10), (22, 0), (3, 6), (8, 11), (28, 17), (24, 16), (25, 35), (9, 31), (8, 31), (9, 25), (24, 9), (15, 20), (2, 10), (18, 32), (0, 9), (31, 4), (18, 28), (11, 17), (0, 28), (32, 16), (24, 15), (32, 8), (3, 4), (16, 20), (2, 14), (30, 20), (17, 3), (3, 26), (19, 23), (21, 18), (22, 15), (31, 31), (0, 31), (20, 15), (15, 19), (27, 13), (25, 23), (9, 26), (20, 6), (6, 21), (10, 34), (33, 16), (28, 11), (4, 5), (25, 24), (9, 35), (23, 33), (31, 12), (20, 7), (29, 17), (1, 34), (5, 27), (9, 5), (4, 16), (17, 8), (13, 20), (23, 4), (27, 27), (19, 13), (21, 22), (15, 4), (21, 8), (13, 5), (16, 14), (4, 6), (1, 3), (2, 37), (5, 2), (5, 0), (13, 15), (32, 29), (23, 23), (17, 35), (32, 25), (9, 37), (20, 25), (5, 24), (9, 33), (2, 27), (32, 17), (15, 30), (17, 11), (7, 0), (0, 37), (14, 26), (25, 20), (33, 34), (12, 24), (8, 28), (18, 1), (15, 23), (9, 15), (1, 15), (24, 18), (26, 32), (23, 19), (21, 29), (24, 34), (0, 21), (12, 12), (24, 27), (14, 35), (26, 7), (23, 30), (15, 34), (14, 12), (13, 2), (21, 0), (2, 22), (20, 36), (14, 10), (3, 2), (10, 9), (21, 23), (11, 34), (20, 30), (14, 0), (16, 26), (1, 9), (24, 19), (0, 35), (13, 36), (12, 27), (30, 12), (31, 17), (4, 15), (26, 0), (28, 1), (29, 18), (24, 0), (33, 1), (33, 20), (11, 26), (2, 20), (13, 27), (9, 24), (13, 33), (31, 21), (26, 12), (19, 4), (23, 17), (30, 27), (29, 1), (28, 23), (24, 11), (7, 35), (16, 5), (10, 11), (33, 9), (23, 21), (11, 1), (10, 30), (14, 3), (33, 36), (26, 2), (20, 2), (33, 0), (2, 28), (0, 33), (25, 30), (10, 12), (29, 11), (9, 18), (0, 36), (17, 31), (11, 29), (27, 22), (9, 27), (29, 9), (1, 35), (27, 24), (3, 8), (17, 15), (32, 14), (13, 8), (30, 22), (23, 34), (31, 6), (4, 26), (23, 8), (7, 7), (29, 22), (33, 29), (10, 27), (28, 5), (33, 11), (23, 35), (31, 9), (1, 5), (26, 13), (6, 31), (24, 35), (3, 7), (9, 6), (20, 18), (32, 27), (11, 15), (11, 36), (18, 21), (29, 3), (18, 4), (26, 17), (14, 4), (6, 23), (31, 29), (11, 27), (5, 35), (20, 16), (22, 3), (10, 17), (26, 19), (23, 28), (21, 28), (33, 25), (24, 28), (2, 1), (27, 8), (4, 31), (17, 21), (25, 12), (28, 30), (4, 19), (8, 2), (13, 24), (23, 37), (1, 21), (29, 20), (17, 29), (1, 31), (5, 37), (21, 19), (30, 4), (29, 7), (23, 9), (11, 19), (7, 23), (28, 8), (16, 6), (31, 19), (33, 19), (19, 31), (16, 13), (10, 6), (9, 2), (23, 25), (13, 4), (32, 0), (14, 19), (0, 15), (4, 36), (16, 17), (14, 20), (19, 32), (7, 3), (25, 25), (10, 7), (24, 32), (9, 4), (12, 1), (16, 19), (14, 29), (11, 37), (20, 5), (28, 10), (15, 8), (24, 12), (33, 7), (16, 15), (7, 24), (28, 12), (24, 25), (11, 14), (8, 26), (5, 31), (19, 30), (19, 5), (25, 5), (31, 18), (3, 1), (1, 11), (10, 28), (12, 6), (18, 34), (18, 12), (31, 7), (11, 4), (12, 37), (8, 3), (24, 29), (19, 37), (9, 32), (2, 25), (21, 33), (28, 19), (19, 6), (7, 37), (3, 37), (6, 20), (5, 13), (3, 22), (7, 11), (18, 8), (31, 5), (21, 16), (1, 8), (7, 34), (6, 30), (7, 12), (0, 17), (9, 30), (21, 15), (27, 7), (26, 1), (29, 8), (33, 13), (16, 21), (0, 13), (11, 10), (32, 20), (15, 35), (26, 16), (27, 20), (14, 28), (2, 19), (27, 10), (11, 9), (8, 13), (17, 33), (4, 34), (24, 1), (18, 36), (20, 26), (1, 22), (8, 29), (25, 28), (31, 15), (16, 25), (10, 14), (23, 27), (19, 14), (20, 33), (2, 30), (23, 20), (20, 24), (30, 28), (11, 23), (13, 31), (30, 1), (31, 28), (5, 14), (10, 29), (21, 14), (14, 27), (27, 2), (20, 8), (4, 10), (6, 0), (23, 10), (19, 21), (27, 5), (14, 23), (23, 16), (29, 34), (10, 19), (14, 32), (22, 14), (24, 3), (15, 22), (16, 16), (25, 3), (33, 3), (30, 5), (4, 37), (13, 9), (33, 6), (29, 32), (23, 7), (3, 29), (27, 29), (12, 19), (23, 3), (7, 25), (15, 7), (18, 6), (31, 27), (10, 10), (1, 7), (19, 29), (22, 18), (30, 33), (10, 26), (31, 33), (31, 1), (15, 5), (4, 30), (1, 29), (16, 4), (0, 23), (1, 0), (23, 36), (10, 31), (27, 21), (2, 11), (16, 2), (29, 30), (1, 2), (18, 25), (26, 25), (19, 8), (12, 7), (26, 14), (14, 8), (14, 9), (32, 34), (6, 36), (14, 5), (27, 0), (30, 19), (5, 6), (16, 0), (29, 36), (3, 35), (28, 7), (17, 36), (18, 35), (6, 18), (19, 12), (30, 37), (28, 21), (23, 6), (25, 34), (3, 14), (33, 12), (1, 25), (30, 14), (0, 32), (22, 2), (15, 24), (23, 2), (32, 32), (24, 20), (33, 5), (16, 10), (31, 26), (15, 1), (32, 2), (13, 13), (12, 26), (28, 31), (21, 11), (7, 9), (11, 32), (7, 29), (29, 13), (27, 3), (17, 6), (15, 29), (30, 24), (8, 35), (13, 34), (11, 11), (24, 4), (5, 25), (32, 36), (29, 16), (28, 29), (29, 27), (3, 18), (26, 30), (14, 21), (14, 6), (2, 2), (12, 13), (8, 7), (8, 23), (0, 24), (3, 28), (7, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "354560", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), 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), (12, 13), (16, 28), (4, 31), (28, 31), (32, 0), (10, 22), (16, 19), (33, 19), (10, 12), (17, 7), (21, 1), (18, 22), (6, 1), (1, 4), (11, 9), (13, 16), (11, 20), (31, 25), (14, 10), (14, 21), (19, 16), (9, 22), (7, 12), (34, 8), (12, 31), (16, 25), (15, 1), (5, 6), (6, 6), (0, 27), (13, 22), (31, 22), (23, 5), (12, 7), (7, 14), (35, 16), (1, 17), (18, 15), (15, 14), (22, 11), (0, 8), (18, 29), (26, 1), (33, 11), (14, 25), (29, 13), (35, 21), (2, 24), (6, 22), (10, 1), (3, 28), (3, 25), (1, 28), (22, 30), (22, 21), (21, 20), (19, 21), (13, 27), (4, 15), (28, 17), (8, 29), (28, 16), (6, 32), (20, 9), (7, 32), (23, 2), (21, 21), (12, 19), (34, 21), (19, 27), (31, 15), (1, 26), (25, 28), (17, 27), (4, 10), (12, 25), (34, 19), (30, 22), (29, 26), (34, 10), (4, 1), (16, 26), (16, 13), (33, 26), (13, 21), (27, 24), (15, 32), (15, 9), (25, 29), (27, 12), (6, 20), (19, 6), (27, 13), (13, 9), (4, 11), (13, 20), (12, 17), (19, 3), (6, 2), (7, 29), (29, 18), (5, 3), (23, 20), (29, 21), (12, 22), (8, 8), (2, 20), (10, 19), (7, 7), (3, 20), (6, 26), (33, 32), (10, 28), (12, 8), (25, 31), (18, 11), (2, 13), (2, 5), (20, 27), (34, 6), (18, 12), (0, 30), (8, 13), (29, 24), (26, 20), (10, 17), (24, 23), (25, 5), (7, 18), (1, 25), (3, 27), (31, 27), (8, 31), (31, 29), (7, 10), (26, 4), (11, 25), (29, 19), (6, 12), (11, 24), (9, 9), (19, 29), (17, 16), (4, 7), (31, 11), (27, 28), (3, 19), (24, 6), (14, 20), (2, 22), (27, 19), (28, 1), (12, 4), (6, 15), (30, 26), (4, 21), (29, 25), (35, 5), (1, 1), (17, 20), (28, 29), (12, 27), (23, 19), (5, 26), (9, 17), (33, 21), (26, 16), (23, 31), (5, 32), (24, 20), (5, 7), (2, 1), (12, 6), (6, 23), (6, 24), (29, 23), (10, 6), (13, 15), (34, 29), (17, 21), (24, 19), (3, 11), (1, 14), (32, 17), (13, 18), (1, 6), (33, 27), (13, 29), (13, 19), (9, 31), (18, 30), (24, 12), (8, 28), (30, 24), (34, 22), (30, 19), (19, 0), (17, 17), (24, 22), (10, 14), (26, 9), (9, 0), (28, 14), (3, 23), (18, 18), (20, 19), (8, 23), (34, 1), (15, 4), (23, 11), (2, 29), (17, 28), (31, 24), (11, 22), (8, 6), (1, 11), (31, 1), (6, 14), (16, 16), (0, 16), (35, 6), (7, 6), (34, 12), (7, 11), (16, 23), (9, 11), (22, 17), (7, 15), (31, 2), (16, 8), (28, 8), (16, 14), (2, 11), (35, 31), (10, 16), (2, 2), (4, 20), (19, 7), (12, 16), (15, 28), (1, 12), (12, 32), (33, 12), (31, 23), (8, 5), (3, 10), (2, 26), (25, 12), (5, 29), (23, 14), (29, 30), (7, 28), (8, 1), (3, 21), (14, 9), (26, 6), (30, 9), (5, 8), (35, 28), (28, 13), (13, 14), (13, 26), (19, 32), (5, 9), (11, 29), (22, 9), (0, 5), (5, 5), (18, 24), (28, 7), (1, 22), (4, 3), (25, 25), (30, 29), (25, 22), (23, 15), (6, 27), (4, 27), (0, 22), (28, 30), (33, 30), (18, 26), (33, 2), (35, 26), (27, 1), (2, 25), (3, 17), (0, 11), (31, 5), (1, 21), (20, 7), (17, 4), (1, 32), (29, 12), (19, 10), (3, 30), (27, 17), (23, 25), (0, 28), (22, 18), (2, 9), (10, 15), (4, 25), (22, 0), (12, 30), (26, 32), (11, 28), (24, 8), (1, 19), (11, 3), (25, 2), (9, 6), (22, 6), (19, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979604", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), 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), (1, 31), (21, 28), (36, 10), (32, 17), (36, 14), (31, 25), (21, 9), (17, 12), (17, 9), (5, 19), (30, 28), (16, 27), (33, 15), (7, 11), (18, 18), (18, 13), (25, 2), (32, 10), (18, 29), (3, 6), (31, 0), (30, 29), (18, 3), (21, 27), (0, 2), (11, 19), (15, 16), (24, 33), (18, 20), (24, 11), (3, 23), (1, 32), (3, 21), (21, 14), (32, 28), (11, 17), (11, 35), (36, 4), (17, 4), (14, 36), (34, 6), (26, 10), (19, 28), (5, 2), (13, 7), (4, 32), (28, 15), (32, 7), (18, 27), (27, 8), (29, 3), (3, 7), (8, 11), (1, 19), (2, 30), (25, 11), (21, 30), (15, 8), (35, 4), (18, 8), (24, 19), (15, 17), (6, 22), (37, 15), (9, 25), (1, 4), (10, 13), (26, 36), (3, 0), (7, 17), (2, 3), (29, 15), (18, 16), (0, 1), (7, 25), (0, 8), (19, 24), (26, 28), (32, 5), (35, 34), (31, 36), (3, 25), (12, 4), (1, 10), (16, 20), (30, 15), (30, 30), (18, 25), (37, 11), (4, 21), (10, 19), (13, 30), (34, 0), (6, 11), (4, 13), (28, 5), (18, 12), (15, 22), (15, 26), (26, 30), (1, 15), (6, 0), (9, 27), (11, 36), (17, 3), (2, 16), (9, 6), (23, 14), (17, 19), (23, 29), (5, 33), (6, 4), (38, 13), (17, 16), (19, 5), (7, 6), (27, 35), (12, 3), (26, 13), (5, 6), (1, 23), (31, 16), (20, 31), (34, 21), (24, 35), (32, 4), (38, 21), (6, 36), (31, 2), (15, 6), (37, 23), (33, 22), (6, 31), (10, 7), (14, 11), (32, 26), (38, 1), (13, 14), (31, 28), (26, 2), (37, 31), (8, 15), (2, 25), (36, 25), (22, 19), (10, 31), (7, 16), (6, 23), (36, 13), (25, 15), (14, 14), (10, 12), (17, 25), (3, 17), (31, 9), (37, 7), (16, 7), (20, 10), (26, 5), (30, 11), (25, 1), (8, 5), (34, 36), (33, 11), (22, 7), (29, 22), (21, 22), (12, 11), (13, 10), (37, 20), (33, 23), (23, 35), (26, 27), (7, 36), (20, 26), (33, 1), (19, 13), (37, 29), (23, 2), (11, 34), (9, 22), (33, 14), (25, 0), (37, 4), (7, 30), (20, 36), (33, 27), (13, 2), (16, 24), (37, 30), (0, 22), (31, 5), (25, 20), (9, 14), (27, 5), (36, 22), (24, 8), (17, 22), (3, 30), (12, 18), (18, 11), (21, 19), (21, 2), (20, 34), (34, 13), (15, 30), (33, 2), (23, 27), (36, 15), (22, 21), (26, 7), (20, 25), (16, 8), (7, 31), (26, 21), (38, 23), (18, 22), (8, 25), (7, 15), (2, 5), (16, 19), (12, 34), (12, 5), (26, 26), (37, 28), (12, 24), (30, 32), (27, 34), (17, 27), (10, 23), (37, 36), (24, 18), (38, 29), (4, 22), (8, 30), (18, 35), (29, 13), (0, 18), (29, 30), (35, 23), (1, 20), (13, 13), (37, 25), (15, 11), (7, 8), (30, 7), (8, 22), (12, 15), (4, 23), (31, 27), (1, 36), (8, 13), (29, 25), (11, 5), (4, 9), (17, 5), (14, 2), (24, 27), (34, 34), (27, 12), (23, 24), (5, 14), (10, 30), (16, 6), (22, 14), (13, 34), (19, 26), (30, 34), (5, 0), (30, 31), (26, 22), (29, 6), (2, 1), (35, 2), (25, 21), (26, 33), (36, 27), (25, 16), (13, 0), (3, 22), (12, 2), (1, 35), (18, 9), (17, 20), (18, 15), (31, 35), (23, 31), (17, 7), (26, 9), (16, 25), (8, 16), (5, 10), (26, 15), (31, 10), (8, 12), (19, 9), (23, 17), (6, 35), (22, 9), (0, 31), (21, 10), (25, 17), (15, 28), (38, 33), (4, 15), (22, 4), (8, 2), (31, 20), (21, 32), (27, 13), (6, 8), (1, 34), (22, 29), (4, 24), (13, 6), (21, 4), (3, 24), (25, 26), (15, 9), (20, 3), (14, 8), (9, 9), (19, 20), (6, 14), (28, 34), (16, 11), (30, 19), (6, 30), (30, 23), (28, 17), (4, 6), (35, 24), (28, 36), (11, 23), (10, 17), (33, 3), (36, 26), (13, 12), (6, 32), (4, 1), (20, 19), (26, 19), (23, 20), (3, 8), (33, 7), (31, 29), (25, 12), (25, 33), (37, 9), (4, 27), (26, 18), (33, 18), (21, 36), (11, 24), (30, 9), (16, 16), (18, 6), (36, 3), (7, 21), (32, 24), (18, 7), (7, 2), (32, 22), (37, 0), (11, 18), (20, 9), (7, 5), (3, 1), (32, 31), (18, 34), (29, 4), (35, 25), (28, 4), (24, 25), (14, 18), (36, 30), (22, 13), (21, 3), (21, 31), (37, 16), (1, 6), (23, 32), (27, 33), (14, 24), (34, 15), (11, 20), (37, 18), (25, 36), (14, 9), (8, 33), (37, 35), (25, 9), (25, 27), (8, 23), (4, 4), (37, 13), (20, 0), (9, 2), (30, 25), (19, 16), (6, 34), (20, 15), (31, 31), (7, 4), (16, 32), (20, 32), (35, 8), (32, 9), (13, 20), (11, 27), (38, 12), (26, 8), (15, 35), (28, 0), (28, 14), (31, 24), (28, 10), (8, 14), (38, 25), (6, 17), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634296", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (9, 10), (3, 22), (8, 18), (18, 28), (15, 25), (18, 3), (1, 23), (22, 11), (25, 25), (25, 19), (17, 18), (12, 0), (23, 0), (12, 24), (10, 31), (13, 18), (3, 13), (30, 4), (16, 27), (8, 7), (21, 0), (21, 26), (30, 23), (4, 9), (23, 12), (29, 20), (6, 10), (5, 20), (4, 7), (12, 4), (2, 21), (11, 19), (6, 6), (19, 2), (4, 19), (28, 18), (30, 3), (14, 33), (13, 33), (5, 16), (29, 4), (5, 2), (19, 11), (19, 3), (18, 0), (28, 16), (12, 7), (29, 15), (25, 9), (24, 25), (7, 29), (3, 35), (23, 9), (27, 2), (22, 26), (23, 23), (5, 12), (26, 30), (9, 27), (24, 24), (9, 34), (29, 13), (26, 18), (22, 8), (15, 27), (32, 30), (1, 25), (0, 24), (8, 32), (0, 3), (1, 5), (10, 30), (29, 8), (8, 24), (27, 34), (2, 0), (8, 16), (6, 1), (24, 1), (1, 8), (32, 20), (17, 26), (6, 17), (3, 32), (19, 19), (13, 20), (16, 31), (28, 29), (11, 28), (30, 21), (13, 35), (9, 12), (10, 27), (22, 31), (20, 34), (5, 34), (26, 2), (32, 23), (11, 21), (1, 2), (9, 16), (28, 20), (7, 4), (15, 15), (11, 33), (3, 26), (26, 19), (10, 8), (7, 20), (16, 29), (18, 16), (28, 19), (4, 28), (21, 32), (21, 17), (7, 25), (31, 20), (27, 3), (8, 29), (18, 10), (17, 17), (26, 13), (16, 32), (11, 14), (30, 11), (12, 26), (26, 29), (8, 4), (18, 26), (30, 24), (8, 33), (2, 14), (10, 16), (12, 35), (9, 2), (3, 3), (2, 32), (27, 7), (25, 8), (18, 14), (10, 12), (20, 5), (11, 12), (23, 5), (1, 9), (31, 16), (26, 26), (22, 23), (4, 33), (7, 14), (26, 6), (19, 29), (12, 16), (1, 11), (15, 31), (4, 29), (9, 7), (28, 32), (0, 16), (18, 25), (1, 35), (25, 2), (2, 22), (4, 22), (15, 5), (22, 2), (27, 8), (32, 6), (8, 25), (17, 7), (29, 22), (13, 16), (20, 31), (6, 35), (18, 27), (16, 20), (30, 35), (17, 25), (27, 28), (3, 6), (17, 13), (17, 0), (1, 29), (7, 9), (1, 3), (18, 17), (11, 4), (15, 30), (26, 0), (1, 30), (20, 4), (0, 10), (31, 23), (3, 18), (27, 11), (31, 11), (9, 30), (0, 5), (0, 28), (31, 1), (9, 14), (19, 34), (23, 10), (31, 31), (4, 34), (3, 1), (9, 29), (17, 29), (30, 22), (19, 13), (5, 4), (8, 9), (15, 6), (12, 17), (10, 33), (8, 1), (24, 34), (6, 27), (31, 34), (1, 24), (16, 9), (4, 1), (12, 6), (7, 21), (31, 25), (10, 10), (19, 7), (14, 30), (7, 3), (10, 3), (18, 33), (13, 15), (30, 10), (13, 30), (29, 24), (26, 28), (18, 18), (1, 15), (20, 23), (16, 4), (16, 28), (5, 23), (19, 27), (25, 34), (10, 14), (25, 11), (22, 34), (26, 23), (20, 2), (31, 14), (1, 13), (6, 12), (21, 11), (32, 32), (5, 33), (26, 7), (0, 23), (21, 22), (19, 24), (2, 24), (10, 13), (21, 20), (28, 12), (12, 2), (17, 10), (13, 26), (0, 17), (3, 31), (17, 19), (6, 13), (28, 33), (5, 9), (10, 20), (28, 22), (22, 0), (2, 18), (12, 9), (23, 2), (2, 4), (12, 14), (26, 25), (1, 7), (2, 11), (24, 8), (20, 1), (11, 8), (21, 14), (30, 7), (9, 32), (0, 34), (14, 16), (14, 18), (30, 28), (8, 22), (19, 32), (22, 7), (6, 14), (28, 30), (26, 27), (27, 20), (20, 30), (27, 16), (17, 1), (15, 18), (9, 21), (32, 26), (32, 2), (3, 10), (17, 9), (24, 18), (16, 35), (8, 34), (17, 34), (1, 4), (11, 20), (6, 2), (19, 22), (26, 3), (2, 7), (23, 1), (27, 26), (9, 9), (5, 1), (6, 11), (9, 0), (23, 11), (17, 32), (6, 20), (17, 5), (13, 22), (30, 0), (18, 8), (6, 22), (25, 28), (5, 26), (26, 11), (22, 5), (25, 22), (7, 34), (16, 34), (6, 33), (28, 1), (29, 31), (19, 28), (28, 11), (14, 4), (14, 32), (27, 14), (1, 10), (25, 30), (6, 23), (24, 17), (2, 16), (13, 6), (14, 14), (22, 4), (11, 6), (30, 25), (26, 10), (26, 20), (29, 10), (27, 5), (1, 28), (30, 27), (24, 12), (26, 35), (12, 27), (10, 26), (32, 8), (21, 2), (23, 28), (20, 10), (6, 26), (21, 16), (25, 10), (15, 20), (32, 4), (24, 28), (4, 0), (26, 32), (4, 27), (19, 35), (18, 35), (6, 3), (19, 23), (1, 14), (31, 12), (27, 6), (21, 1), (20, 15), (19, 14), (4, 10), (24, 19), (20, 13), (23, 7), (24, 11), (24, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851328", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 11), (12, 11), (36, 2), (7, 10), (3, 1), (27, 34), (38, 14), (13, 24), (7, 12), (5, 31), (23, 37), (33, 34), (22, 21), (27, 27), (0, 23), (19, 2), (28, 23), (1, 5), (10, 30), (28, 9), (38, 11), (23, 21), (3, 16), (5, 29), (33, 27), (37, 24), (37, 12), (34, 35), (23, 18), (17, 36), (22, 30), (36, 7), (4, 12), (17, 8), (28, 2), (17, 34), (20, 0), (38, 26), (38, 9), (19, 30), (7, 7), (15, 21), (15, 4), (37, 23), (9, 14), (23, 1), (9, 6), (4, 26), (17, 31), (21, 11), (7, 36), (12, 36), (18, 20), (0, 36), (27, 4), (24, 6), (29, 22), (14, 11), (37, 33), (23, 30), (15, 16), (25, 24), (6, 27), (20, 5), (11, 37), (17, 37), (19, 32), (32, 36), (35, 9), (8, 24), (3, 35), (32, 19), (16, 35), (19, 5), (12, 17), (30, 37), (12, 34), (1, 21), (9, 28), (17, 5), (1, 24), (29, 15), (38, 31), (8, 2), (14, 15), (11, 14), (23, 10), (23, 24), (26, 17), (3, 17), (18, 26), (12, 3), (33, 1), (27, 20), (35, 17), (23, 36), (7, 8), (7, 9), (15, 18), (2, 11), (32, 11), (37, 14), (37, 9), (14, 9), (31, 19), (0, 4), (6, 16), (14, 5), (18, 9), (13, 28), (15, 5), (18, 11), (4, 8), (22, 8), (14, 24), (27, 16), (16, 8), (31, 36), (32, 30), (0, 24), (28, 30), (24, 8), (26, 16), (5, 8), (31, 9), (37, 29), (12, 12), (35, 15), (19, 19), (25, 21), (6, 4), (26, 20), (32, 18), (9, 1), (36, 0), (29, 23), (28, 12), (34, 20), (7, 31), (21, 10), (11, 17), (24, 27), (4, 3), (25, 29), (31, 7), (33, 7), (19, 7), (7, 11), (36, 16), (37, 27), (0, 25), (33, 37), (25, 25), (5, 17), (33, 9), (36, 21), (30, 30), (35, 1), (11, 27), (7, 6), (13, 33), (22, 19), (17, 16), (34, 32), (28, 7), (23, 29), (31, 17), (21, 19), (5, 9), (4, 24), (36, 8), (20, 34), (32, 5), (16, 19), (19, 37), (34, 29), (16, 28), (6, 30), (15, 23), (30, 7), (17, 15), (6, 5), (12, 24), (0, 32), (5, 22), (26, 19), (6, 36), (33, 25), (30, 26), (0, 20), (12, 23), (12, 8), (30, 32), (9, 34), (0, 35), (5, 32), (19, 29), (19, 17), (0, 2), (31, 15), (19, 28), (13, 31), (29, 26), (3, 22), (8, 12), (0, 5), (8, 27), (16, 26), (19, 10), (11, 34), (35, 22), (8, 31), (6, 12), (37, 10), (13, 23), (36, 6), (9, 16), (27, 6), (32, 10), (32, 14), (7, 5), (12, 16), (29, 0), (25, 28), (6, 23), (26, 28), (32, 6), (15, 17), (17, 14), (1, 4), (30, 23), (14, 26), (23, 22), (17, 28), (31, 13), (24, 4), (29, 16), (31, 8), (15, 11), (35, 19), (10, 31), (10, 22), (31, 27), (5, 27), (25, 36), (16, 20), (25, 17), (21, 20), (18, 19), (20, 30), (16, 29), (5, 5), (28, 37), (10, 19), (23, 31), (38, 8), (14, 17), (21, 6), (36, 9), (32, 29), (26, 23), (0, 3), (14, 16), (26, 35), (29, 29), (3, 28), (7, 2), (6, 7), (5, 6), (26, 5), (11, 10), (10, 6), (27, 28), (27, 10), (0, 28), (15, 25), (37, 11), (15, 13), (37, 25), (24, 17), (22, 16), (33, 32), (24, 10), (12, 5), (23, 9), (23, 7), (32, 23), (12, 1), (6, 17), (18, 23), (32, 7), (1, 30), (11, 5), (19, 3), (2, 17), (25, 27), (26, 7), (3, 23), (13, 15), (7, 35), (24, 18), (15, 34), (21, 28), (31, 37), (2, 28), (25, 22), (0, 33), (17, 17), (33, 30), (14, 7), (24, 30), (18, 32), (21, 1), (3, 27), (4, 9), (8, 22), (15, 20), (38, 6), (3, 29), (0, 11), (32, 3), (2, 19), (13, 34), (37, 37), (6, 29), (33, 12), (18, 27), (20, 25), (8, 28), (9, 23), (38, 0), (6, 14), (38, 32), (18, 12), (9, 0), (1, 25), (11, 12), (38, 30), (12, 25), (20, 13), (14, 10), (27, 12), (18, 28), (32, 9), (22, 25), (33, 8), (2, 1), (36, 37), (30, 2), (16, 36), (35, 21), (25, 9), (16, 24), (7, 27), (19, 35), (19, 12), (32, 27), (5, 15), (10, 33), (11, 16), (30, 13), (26, 21), (38, 1), (27, 0), (28, 6), (29, 10), (38, 7), (34, 11), (1, 7), (17, 12), (7, 19), (10, 32), (25, 5), (16, 14), (34, 16), (18, 5), (0, 27), (31, 21), (22, 9), (34, 12), (11, 6), (3, 37), (38, 17), (38, 19), (25, 3), (7, 25), (32, 28), (19, 24), (21, 31), (31, 2), (14, 25), (33, 35), (14, 8), (12, 35), (20, 6), (23, 2), (31, 5), (27, 8), (1, 13), (6, 26), (38, 12), (20, 22), (7, 18), (25, 14), (14, 31), (32, 17), (2, 0), (9, 27), (3, 30), (16, 21), (16, 13), (27, 24), (33, 5), (7, 33), (28, 35), (25, 20), (4, 5), (25, 8), (26, 24), (28, 25), (9, 18), (1, 37), (19, 6), (5, 10), (34, 8), (12, 33), (37, 8), (7, 17), (29, 3), (29, 33), (19, 34), (17, 13), (33, 31), (28, 29), (28, 24), (31, 23), (24, 9), (37, 35), (28, 8), (25, 16), (37, 20), (33, 14), (20, 2), (15, 0), (19, 18), (4, 34), (30, 16), (11, 8), (31, 12), (30, 8), (10, 16), (19, 14), (24, 33), (8, 17), (22, 37), (25, 10), (36, 18), (2, 16), (27, 35), (27, 31), (0, 8), (32, 25), (20, 3), (33, 19), (25, 30), (28, 34), (7, 29), (37, 21), (25, 12), (31, 18), (13, 7), (23, 13), (6, 0), (4, 15), (5, 28), (19, 22), (2, 30), (30, 9), (8, 3), (0, 10), (4, 6), (14, 0), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "675000", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (1, 25), (13, 25), (7, 27), (11, 23), (12, 8), (27, 5), (2, 2), (12, 29), (9, 16), (6, 22), (18, 27), (22, 24), (17, 16), (8, 12), (6, 9), (19, 30), (21, 2), (4, 12), (29, 21), (25, 22), (25, 9), (18, 16), (13, 12), (10, 11), (17, 27), (10, 24), (1, 22), (9, 17), (5, 24), (14, 15), (18, 13), (12, 16), (9, 15), (9, 24), (8, 8), (1, 14), (11, 30), (23, 13), (18, 5), (11, 26), (6, 18), (22, 22), (21, 5), (6, 2), (2, 12), (5, 17), (18, 23), (18, 20), (25, 19), (21, 21), (26, 4), (2, 25), (20, 18), (27, 18), (9, 22), (13, 17), (15, 15), (6, 1), (10, 28), (6, 0), (10, 26), (23, 7), (14, 24), (19, 19), (8, 21), (11, 27), (21, 17), (6, 28), (0, 16), (17, 3), (12, 24), (8, 2), (0, 15), (14, 3), (21, 11), (14, 5), (16, 15), (3, 24), (26, 12), (29, 5), (27, 1), (24, 20), (21, 15), (7, 30), (20, 9), (16, 5), (15, 23), (4, 18), (5, 15), (2, 0), (28, 12), (22, 21), (15, 9), (10, 12), (8, 9), (25, 3), (22, 3), (18, 7), (19, 18), (28, 28), (12, 30), (18, 12), (0, 21), (0, 30), (8, 10), (23, 22), (24, 13), (25, 25), (21, 18), (17, 6), (28, 10), (5, 11), (10, 10), (9, 7), (22, 26), (25, 15), (10, 23), (29, 18), (3, 8), (25, 1), (24, 19), (26, 2), (7, 1), (15, 7), (22, 14), (19, 12), (12, 6), (9, 20), (23, 14), (7, 25), (14, 16), (22, 4), (27, 3), (27, 10), (29, 8), (25, 10), (20, 23), (14, 19), (23, 6), (6, 26), (20, 16), (2, 9), (12, 12), (14, 13), (25, 23), (2, 4), (9, 3), (14, 8), (21, 25), (5, 23), (28, 25), (11, 10), (27, 15), (3, 7), (28, 9), (24, 27), (14, 22), (24, 3), (14, 18), (16, 24), (2, 24), (3, 14), (3, 0), (3, 3), (24, 12), (9, 21), (26, 6), (25, 29), (0, 7), (17, 17), (7, 15), (10, 17), (29, 20), (7, 11), (17, 22), (23, 1), (5, 20), (15, 4), (8, 25), (8, 22), (12, 13), (13, 10), (4, 25), (8, 26), (9, 26), (26, 25), (18, 29), (6, 27), (22, 19), (22, 0), (15, 29), (7, 23), (11, 1), (11, 19), (10, 25), (13, 26), (14, 10), (5, 16), (0, 12), (1, 3), (1, 10), (24, 21), (3, 22), (28, 6), (11, 5), (10, 20), (21, 14), (23, 17), (15, 14), (16, 26), (28, 1), (4, 0), (1, 15), (19, 29), (9, 5), (22, 8), (7, 29), (18, 3), (3, 2), (20, 29), (5, 1), (6, 5), (13, 14), (6, 14), (21, 10), (2, 14), (26, 11), (8, 20), (14, 28), (19, 14), (10, 9), (14, 25), (7, 21), (15, 8), (28, 4), (11, 14), (19, 5), (9, 19), (26, 29), (10, 21), (1, 26), (7, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83808", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), 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), (8, 0), (9, 1), (6, 2), (24, 19), (2, 11), (28, 30), (14, 32), (23, 26), (11, 31), (28, 4), (7, 3), (11, 18), (17, 12), (15, 26), (2, 10), (31, 26), (15, 27), (27, 14), (11, 8), (0, 25), (26, 24), (5, 9), (17, 5), (25, 6), (6, 22), (12, 21), (19, 16), (2, 12), (6, 7), (18, 21), (29, 21), (6, 12), (20, 4), (1, 4), (27, 31), (9, 17), (4, 12), (18, 15), (4, 15), (7, 6), (18, 29), (26, 21), (1, 1), (2, 30), (24, 14), (20, 7), (24, 13), (25, 32), (18, 0), (0, 12), (6, 20), (8, 12), (9, 12), (28, 20), (17, 24), (8, 25), (22, 26), (29, 25), (25, 20), (0, 9), (14, 24), (25, 5), (17, 26), (20, 31), (32, 1), (24, 17), (1, 24), (29, 12), (5, 11), (31, 18), (28, 9), (0, 20), (19, 28), (27, 21), (30, 2), (11, 26), (10, 24), (7, 15), (19, 25), (25, 2), (21, 0), (29, 10), (31, 5), (14, 26), (2, 7), (5, 0), (0, 27), (32, 7), (24, 31), (21, 8), (15, 29), (13, 11), (0, 29), (11, 30), (20, 12), (1, 20), (18, 18), (31, 7), (10, 6), (30, 7), (31, 1), (1, 12), (5, 7), (0, 1), (30, 9), (27, 19), (29, 11), (12, 25), (7, 18), (4, 21), (8, 20), (28, 31), (15, 18), (10, 5), (3, 31), (14, 4), (9, 0), (17, 7), (28, 12), (16, 32), (29, 29), (26, 26), (11, 15), (14, 20), (32, 18), (29, 6), (8, 16), (23, 2), (12, 24), (26, 13), (22, 24), (30, 13), (23, 23), (21, 12), (30, 8), (22, 12), (7, 10), (11, 25), (21, 25), (13, 9), (31, 29), (4, 2), (28, 25), (16, 21), (22, 0), (18, 23), (27, 27), (0, 15), (5, 17), (16, 22), (0, 22), (21, 19), (7, 17), (5, 20), (15, 6), (29, 17), (30, 15), (12, 13), (15, 22), (0, 26), (10, 28), (25, 25), (25, 16), (9, 31), (17, 25), (13, 27), (4, 7), (21, 20), (16, 2), (28, 15), (10, 27), (11, 23), (29, 7), (27, 26), (22, 29), (10, 11), (16, 4), (12, 10), (32, 22), (31, 23), (9, 18), (32, 26), (0, 8), (11, 3), (3, 27), (5, 24), (0, 23), (16, 17), (24, 30), (0, 3), (23, 27), (13, 24), (32, 11), (11, 20), (3, 11), (20, 23), (23, 24), (0, 11), (23, 4), (29, 28), (2, 20), (16, 23), (18, 9), (13, 10), (5, 16), (6, 10), (17, 3), (6, 9), (7, 1), (28, 28), (2, 24), (31, 24), (20, 28), (2, 1), (26, 17), (4, 23), (8, 21), (10, 9), (3, 29), (20, 9), (25, 26), (5, 30), (24, 11), (30, 22), (30, 0), (25, 8), (30, 23), (22, 4), (28, 22), (0, 19), (17, 16), (28, 23), (19, 23), (1, 17), (26, 15), (0, 5), (26, 25), (23, 16), (19, 31), (25, 13), (2, 26), (24, 16), (1, 14), (25, 10), (16, 13), (19, 0), (31, 8), (11, 12), (7, 19), (4, 29), (17, 31), (22, 10), (12, 4), (11, 27), (2, 13), (28, 2), (19, 20), (8, 11), (30, 12), (11, 22), (21, 4), (19, 17), (11, 19), (6, 0), (8, 1), (29, 5), (25, 28), (20, 26), (18, 30), (14, 7), (27, 18), (14, 15), (8, 13), (12, 16), (13, 12), (15, 21), (12, 5), (29, 24), (9, 26), (13, 18), (26, 5), (9, 24), (4, 25), (22, 18), (10, 18), (23, 13), (18, 11), (16, 1), (31, 21), (10, 14), (13, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "653760", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 27), (7, 22), (19, 25), (33, 30), (25, 30), (15, 9), (19, 26), (17, 35), (28, 29), (2, 25), (19, 24), (0, 31), (17, 24), (9, 13), (33, 29), (19, 4), (12, 28), (31, 12), (13, 21), (13, 27), (24, 3), (4, 3), (14, 19), (0, 26), (30, 12), (21, 30), (2, 14), (13, 4), (19, 13), (35, 1), (32, 30), (13, 17), (27, 37), (30, 16), (21, 22), (2, 12), (24, 5), (6, 32), (18, 14), (26, 17), (8, 23), (16, 0), (1, 18), (8, 30), (2, 2), (32, 19), (13, 26), (11, 22), (23, 2), (0, 19), (20, 23), (29, 24), (23, 11), (0, 25), (31, 36), (23, 25), (9, 0), (20, 9), (29, 6), (21, 15), (15, 30), (26, 33), (3, 26), (25, 33), (19, 23), (31, 24), (28, 11), (5, 27), (17, 16), (13, 28), (5, 34), (33, 34), (27, 12), (25, 5), (35, 4), (10, 29), (24, 23), (2, 7), (2, 24), (11, 19), (15, 11), (6, 37), (2, 15), (1, 26), (3, 11), (34, 37), (18, 4), (24, 27), (4, 33), (29, 0), (10, 2), (17, 28), (17, 27), (10, 18), (18, 2), (17, 9), (35, 15), (26, 26), (27, 21), (32, 31), (26, 8), (9, 34), (1, 22), (31, 33), (2, 18), (21, 11), (3, 13), (0, 5), (7, 36), (35, 13), (1, 36), (32, 2), (3, 3), (7, 5), (6, 9), (7, 33), (15, 20), (12, 32), (21, 7), (24, 12), (4, 4), (34, 17), (22, 28), (21, 32), (6, 11), (29, 25), (4, 18), (20, 16), (21, 8), (15, 1), (8, 4), (8, 16), (11, 3), (19, 3), (11, 28), (1, 7), (15, 13), (27, 24), (23, 32), (3, 23), (9, 6), (18, 24), (27, 31), (29, 16), (18, 26), (20, 5), (30, 30), (26, 35), (23, 34), (32, 26), (9, 5), (21, 19), (23, 16), (25, 37), (12, 10), (28, 0), (32, 25), (20, 34), (25, 17), (2, 34), (13, 31), (31, 2), (11, 5), (6, 10), (20, 18), (26, 24), (21, 21), (6, 7), (14, 33), (12, 14), (16, 29), (33, 32), (29, 5), (8, 17), (24, 19), (10, 28), (4, 22), (30, 21), (12, 8), (34, 29), (4, 29), (20, 36), (31, 26), (23, 35), (27, 20), (32, 8), (13, 32), (35, 20), (26, 0), (23, 15), (11, 34), (9, 26), (5, 0), (18, 11), (10, 25), (11, 10), (1, 10), (2, 37), (24, 34), (16, 14), (34, 7), (33, 7), (27, 22), (29, 2), (27, 29), (27, 34), (22, 20), (19, 31), (5, 28), (1, 24), (5, 9), (13, 13), (3, 2), (18, 13), (5, 36), (12, 2), (18, 33), (2, 19), (9, 7), (6, 17), (9, 35), (35, 6), (8, 22), (1, 6), (24, 14), (10, 34), (12, 16), (27, 26), (19, 18), (12, 30), (7, 20), (32, 7), (25, 12), (8, 11), (10, 30), (0, 7), (14, 4), (34, 8), (32, 10), (27, 7), (15, 10), (16, 31), (16, 4), (6, 31), (13, 6), (26, 18), (1, 20), (19, 8), (26, 32), (34, 2), (32, 24), (13, 12), (8, 34), (28, 3), (23, 10), (35, 5), (12, 36), (3, 18), (31, 21), (7, 23), (13, 2), (33, 24), (23, 4), (27, 32), (22, 9), (30, 3), (31, 17), (10, 17), (0, 21), (22, 36), (33, 10), (14, 1), (6, 36), (16, 33), (1, 23), (35, 2), (1, 2), (11, 9), (24, 32), (30, 23), (22, 33), (35, 19), (21, 31), (17, 2), (1, 8), (16, 35), (33, 3), (4, 37), (4, 20), (13, 7), (7, 6), (19, 10), (22, 27), (6, 15), (3, 8), (3, 20), (13, 18), (4, 0), (11, 18), (28, 20), (35, 30), (8, 29), (16, 25), (0, 23), (34, 28), (30, 28), (15, 15), (8, 9), (28, 24), (34, 14), (11, 27), (3, 15), (12, 26), (5, 4), (26, 27), (28, 25), (22, 17), (26, 11), (18, 15), (5, 23), (31, 19), (0, 15), (32, 0), (8, 3), (10, 8), (31, 28), (2, 13), (27, 5), (24, 17), (26, 29), (30, 24), (7, 29), (23, 7), (29, 20), (3, 24), (33, 18), (14, 36), (16, 23), (10, 3), (21, 4), (2, 29), (5, 5), (2, 32), (19, 33), (27, 35), (3, 37), (14, 24), (30, 35), (30, 32), (22, 5), (20, 24), (10, 14), (1, 17), (34, 25), (32, 36), (5, 29), (35, 29), (19, 11), (4, 15), (15, 31), (0, 29), (30, 2), (34, 4), (15, 16), (23, 29), (2, 8), (10, 5), (1, 0), (26, 5), (27, 19), (35, 11), (11, 32), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2964", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), 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), (9, 8), (3, 8), (36, 24), (13, 8), (20, 0), (3, 22), (36, 9), (12, 27), (35, 8), (25, 8), (5, 23), (9, 10), (11, 6), (6, 18), (20, 30), (19, 21), (20, 11), (4, 21), (12, 17), (9, 3), (35, 6), (7, 23), (22, 9), (23, 23), (10, 21), (2, 8), (2, 23), (24, 17), (25, 5), (27, 21), (2, 24), (15, 0), (25, 11), (0, 22), (11, 16), (35, 19), (29, 19), (20, 24), (34, 24), (30, 3), (26, 29), (36, 15), (32, 22), (14, 0), (8, 27), (29, 17), (19, 3), (28, 22), (24, 13), (35, 23), (5, 2), (2, 20), (17, 21), (25, 0), (32, 1), (2, 30), (6, 2), (19, 14), (0, 21), (36, 0), (0, 25), (27, 22), (7, 21), (26, 23), (8, 28), (0, 26), (23, 19), (6, 30), (32, 30), (14, 20), (22, 22), (29, 9), (29, 0), (5, 0), (12, 18), (13, 20), (36, 1), (22, 24), (22, 14), (34, 19), (26, 17), (0, 18), (32, 19), (36, 21), (6, 12), (25, 18), (33, 27), (8, 2), (21, 29), (17, 17), (4, 7), (10, 29), (11, 27), (17, 4), (27, 4), (25, 13), (36, 27), (14, 13), (6, 1), (26, 8), (14, 19), (12, 2), (36, 11), (30, 25), (32, 2), (10, 14), (16, 30), (31, 16), (22, 6), (25, 26), (7, 26), (6, 17), (2, 12), (19, 24), (8, 1), (13, 7), (6, 9), (17, 3), (35, 17), (17, 28), (14, 25), (25, 15), (30, 1), (10, 17), (15, 19), (35, 29), (0, 29), (18, 15), (8, 8), (8, 9), (16, 14), (20, 23), (21, 30), (12, 7), (31, 13), (10, 26), (16, 16), (5, 8), (20, 27), (7, 2), (15, 26), (16, 7), (29, 18), (23, 29), (1, 17), (32, 28), (11, 29), (14, 5), (13, 18), (18, 5), (21, 28), (36, 3), (10, 1), (32, 29), (7, 5), (25, 27), (9, 11), (19, 27), (16, 27), (34, 14), (27, 13), (17, 1), (0, 12), (35, 13), (5, 19), (20, 16), (4, 22), (23, 28), (28, 16), (4, 18), (22, 8), (8, 10), (23, 11), (11, 19), (21, 2), (27, 10), (0, 30), (18, 27), (14, 22), (1, 9), (28, 9), (5, 17), (18, 8), (21, 11), (6, 25), (23, 5), (27, 26), (4, 0), (12, 4), (10, 10), (14, 11), (28, 26), (33, 10), (19, 7), (18, 29), (6, 8), (30, 0), (9, 26), (23, 8), (5, 25), (30, 8), (6, 11), (3, 19), (36, 4), (36, 23), (33, 30), (29, 12), (28, 27), (16, 26), (35, 12), (8, 5), (26, 5), (19, 4), (27, 20), (29, 8), (1, 27), (21, 6), (4, 16), (24, 14), (21, 5), (2, 17), (14, 8), (20, 9), (6, 16), (4, 15), (8, 17), (31, 24), (22, 2), (32, 12), (5, 7), (22, 19), (7, 29), (35, 2), (15, 17), (6, 13), (30, 2), (23, 26), (24, 18), (9, 13), (20, 18), (0, 16), (9, 1), (28, 5), (9, 5), (4, 19), (16, 17), (24, 19), (25, 4), (5, 5), (11, 25), (11, 5), (0, 9), (3, 30), (17, 11), (2, 21), (20, 19), (11, 12), (18, 13), (25, 7), (18, 23), (19, 1), (25, 17), (22, 3), (9, 12), (34, 15), (15, 5), (23, 24), (26, 10), (32, 16), (0, 6), (33, 15), (15, 23), (17, 27), (35, 0), (1, 12), (11, 14), (2, 0), (33, 0), (24, 28), (13, 15), (10, 20), (11, 2), (34, 16), (33, 28), (26, 11), (12, 14), (35, 28), (20, 20), (21, 13), (28, 25), (12, 25), (22, 29), (15, 25), (9, 17), (13, 30), (29, 4), (25, 3), (33, 26), (23, 12), (2, 29), (18, 2), (30, 14), (4, 25), (32, 24), (28, 17), (32, 14), (8, 29), (29, 29), (3, 25), (35, 7), (18, 9), (34, 22), (24, 15), (1, 2), (16, 2), (33, 16), (29, 27), (17, 7), (16, 19), (28, 29), (22, 11), (18, 18), (5, 14), (1, 28), (17, 14), (11, 23), (17, 18), (33, 14), (10, 11), (29, 28), (26, 20), (17, 23), (3, 15), (21, 9), (3, 10), (11, 30), (13, 9), (8, 21), (24, 26), (12, 9), (23, 3), (11, 0), (30, 26), (31, 23), (29, 10), (0, 23), (12, 13), (1, 10), (11, 13), (28, 30), (1, 24), (17, 2), (35, 16), (1, 30), (8, 12), (18, 0), (3, 9), (10, 13), (14, 28), (24, 8), (35, 26), (6, 10), (17, 26), (14, 18), (24, 2), (10, 24), (22, 0), (31, 14), (12, 0), (35, 1), (29, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "860472", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 12), (15, 9), (9, 13), (19, 23), (31, 27), (28, 14), (3, 1), (11, 19), (17, 14), (6, 7), (13, 22), (2, 21), (21, 15), (10, 21), (15, 27), (2, 31), (26, 2), (4, 27), (29, 8), (18, 33), (0, 20), (31, 25), (1, 7), (4, 14), (7, 6), (0, 24), (23, 25), (13, 12), (4, 13), (8, 13), (3, 21), (21, 13), (18, 16), (6, 29), (23, 18), (0, 28), (6, 20), (8, 18), (16, 0), (30, 6), (14, 18), (9, 20), (12, 6), (22, 31), (27, 24), (21, 8), (23, 33), (11, 15), (24, 10), (20, 15), (26, 31), (7, 7), (6, 17), (2, 27), (18, 32), (26, 26), (2, 26), (23, 12), (14, 23), (7, 5), (0, 29), (3, 17), (26, 27), (24, 20), (29, 15), (22, 14), (14, 30), (29, 29), (11, 26), (5, 31), (5, 18), (19, 16), (19, 17), (6, 13), (14, 16), (4, 20), (25, 20), (5, 11), (0, 8), (12, 34), (20, 11), (7, 29), (21, 14), (24, 6), (1, 32), (9, 26), (7, 17), (15, 28), (28, 25), (25, 7), (3, 33), (9, 30), (25, 27), (18, 17), (31, 4), (5, 17), (5, 2), (23, 29), (19, 10), (3, 34), (14, 3), (10, 1), (22, 15), (16, 9), (13, 13), (1, 1), (23, 32), (30, 18), (20, 32), (5, 9), (14, 11), (27, 4), (8, 24), (4, 24), (10, 5), (11, 16), (19, 3), (23, 2), (13, 10), (31, 19), (5, 10), (17, 0), (2, 12), (19, 7), (21, 16), (11, 22), (15, 20), (6, 24), (3, 13), (31, 33), (17, 25), (12, 33), (9, 29), (28, 19), (16, 24), (0, 14), (2, 13), (17, 19), (21, 0), (28, 24), (20, 4), (11, 9), (29, 13), (13, 30), (20, 5), (29, 27), (19, 34), (7, 34), (0, 3), (18, 11), (27, 31), (10, 12), (10, 6), (28, 22), (22, 23), (1, 17), (3, 25), (2, 6), (18, 20), (26, 13), (1, 30), (17, 17), (10, 26), (5, 30), (8, 10), (27, 1), (31, 2), (18, 27), (1, 9), (10, 22), (24, 17), (2, 30), (5, 21), (25, 32), (22, 7), (27, 10), (6, 32), (3, 20), (22, 6), (12, 11), (21, 7), (1, 15), (26, 11), (11, 5), (22, 8), (30, 32), (26, 3), (6, 28), (19, 5), (28, 9), (20, 0), (21, 33), (17, 28), (15, 19), (24, 2), (11, 6), (30, 12), (1, 5), (11, 8), (27, 7), (17, 9), (15, 21), (24, 33), (15, 34), (7, 8), (20, 7), (31, 22), (18, 2), (26, 19), (21, 30), (28, 5), (11, 14), (0, 6), (16, 12), (23, 21), (10, 16), (24, 29), (26, 12), (24, 0), (23, 27), (6, 9), (4, 25), (3, 12), (15, 1), (28, 17), (23, 10), (20, 30), (7, 12), (1, 21), (15, 14), (28, 16), (28, 29), (30, 19), (6, 12), (15, 25), (28, 13), (3, 26), (25, 11), (10, 25), (6, 3), (11, 30), (19, 15), (16, 8), (7, 1), (25, 25), (20, 12), (4, 1), (30, 16), (9, 0), (2, 22), (2, 20), (4, 8), (8, 29), (28, 20), (9, 21), (10, 18), (10, 10), (21, 17), (25, 34), (20, 25), (7, 25), (5, 7), (27, 9), (1, 14), (30, 8), (25, 28), (18, 24), (16, 21), (6, 19), (9, 11), (7, 32), (14, 19), (3, 32), (6, 33), (27, 5), (18, 15), (3, 22), (25, 23), (13, 4), (27, 18), (6, 26), (8, 11), (25, 2), (10, 23), (17, 18), (14, 1), (31, 20), (14, 31), (24, 25), (19, 29), (0, 21), (30, 29), (21, 31), (13, 25), (5, 34), (29, 30), (9, 16), (10, 31), (24, 12), (14, 4), (21, 25), (25, 19), (14, 26), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682500", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 35), (1, 17), (2, 26), (2, 6), (3, 23), (7, 34), (7, 28), (30, 7), (18, 15), (21, 19), (26, 35), (2, 19), (6, 31), (4, 31), (10, 3), (34, 26), (18, 27), (2, 24), (15, 22), (13, 8), (28, 0), (14, 16), (30, 25), (1, 11), (32, 26), (6, 20), (17, 12), (23, 12), (13, 1), (16, 16), (14, 11), (19, 29), (11, 35), (30, 16), (29, 26), (26, 36), (27, 3), (20, 19), (26, 0), (8, 34), (25, 11), (13, 11), (2, 16), (5, 36), (25, 1), (18, 35), (17, 25), (15, 14), (5, 9), (10, 10), (22, 30), (32, 0), (10, 24), (30, 15), (19, 30), (29, 35), (21, 35), (7, 5), (6, 27), (1, 2), (18, 5), (29, 9), (30, 9), (24, 7), (32, 21), (12, 19), (9, 36), (18, 32), (33, 9), (30, 18), (22, 31), (26, 13), (15, 0), (27, 35), (21, 12), (10, 26), (30, 27), (28, 3), (20, 32), (20, 33), (23, 5), (31, 31), (4, 6), (31, 18), (10, 27), (31, 6), (6, 33), (26, 29), (25, 21), (34, 25), (3, 12), (12, 7), (23, 33), (32, 33), (5, 16), (16, 35), (7, 29), (15, 15), (18, 4), (23, 14), (1, 7), (4, 24), (5, 15), (7, 17), (33, 13), (22, 11), (12, 15), (29, 30), (29, 11), (29, 24), (14, 24), (32, 20), (14, 5), (15, 20), (2, 32), (16, 25), (4, 9), (28, 21), (19, 15), (32, 4), (18, 14), (19, 16), (33, 20), (2, 36), (7, 19), (26, 20), (26, 14), (26, 9), (13, 34), (34, 3), (32, 18), (18, 33), (6, 0), (32, 6), (1, 24), (11, 19), (11, 23), (34, 16), (21, 16), (4, 1), (22, 25), (1, 1), (17, 23), (25, 7), (13, 22), (0, 13), (17, 15), (14, 36), (28, 6), (7, 32), (7, 23), (2, 9), (3, 22), (27, 17), (5, 6), (15, 11), (16, 33), (16, 30), (18, 0), (26, 28), (22, 2), (4, 29), (26, 25), (34, 22), (24, 31), (30, 24), (32, 34), (6, 8), (7, 1), (23, 4), (10, 9), (28, 26), (8, 27), (3, 25), (31, 29), (25, 29), (33, 22), (8, 15), (33, 6), (19, 7), (31, 28), (14, 14), (28, 27), (28, 14), (2, 12), (11, 10), (25, 12), (4, 2), (26, 24), (8, 14), (28, 2), (10, 4), (8, 17), (6, 6), (26, 32), (32, 2), (11, 25), (25, 23), (14, 26), (32, 3), (14, 31), (16, 27), (31, 14), (24, 12), (10, 1), (20, 27), (29, 32), (30, 13), (18, 30), (29, 22), (10, 34), (19, 31), (28, 28), (8, 22), (32, 17), (11, 11), (17, 27), (23, 2), (20, 18), (0, 4), (16, 29), (8, 1), (20, 16), (3, 5), (26, 19), (30, 22), (24, 18), (9, 8), (8, 11), (34, 19), (33, 19), (16, 14), (16, 34), (7, 20), (30, 31), (33, 31), (24, 32), (20, 6), (21, 22), (17, 35), (34, 10), (12, 12), (5, 28), (7, 6), (8, 36), (17, 18), (8, 35), (6, 2), (29, 25), (32, 8), (29, 18), (29, 7), (2, 4), (7, 7), (14, 17), (22, 28), (6, 24), (5, 27), (4, 22), (8, 32), (3, 8), (28, 10), (21, 24), (15, 8), (20, 2), (34, 5), (34, 30), (1, 29), (30, 32), (27, 13), (19, 14), (15, 35), (1, 34), (33, 2), (30, 33), (34, 13), (5, 30), (10, 15), (10, 18), (7, 14), (19, 24), (31, 11), (0, 16), (25, 13), (5, 3), (30, 29), (5, 5), (24, 10), (0, 22), (19, 25), (4, 19), (34, 4), (29, 19), (6, 17), (3, 18), (18, 34), (25, 20), (15, 27), (33, 0), (0, 32), (34, 12), (10, 19), (21, 26), (19, 5), (28, 30), (2, 13), (16, 6), (1, 28), (11, 1), (25, 0), (34, 32), (15, 24), (26, 16), (34, 28), (12, 23), (16, 10), (24, 24), (12, 32), (25, 25), (27, 34), (14, 9), (7, 24), (1, 12), (5, 29), (28, 25), (5, 31), (24, 14), (23, 13), (22, 15), (7, 8), (8, 29), (13, 5), (31, 33), (18, 6), (29, 15), (19, 35), (4, 34), (22, 6), (27, 5), (3, 28), (20, 12), (9, 1), (21, 27), (31, 13), (19, 32), (7, 3), (11, 18), (4, 3), (11, 16), (0, 12), (25, 22), (15, 19), (11, 7), (24, 26), (9, 4), (13, 18), (12, 14), (29, 14), (15, 29), (19, 8), (1, 19), (34, 11), (3, 0), (3, 6), (6, 36), (34, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947968", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 1), (4, 33), (28, 16), (15, 31), (26, 35), (9, 22), (6, 3), (35, 11), (13, 1), (19, 33), (19, 16), (30, 2), (26, 17), (38, 9), (17, 2), (11, 10), (9, 29), (27, 29), (5, 2), (37, 31), (33, 37), (3, 16), (2, 2), (17, 31), (5, 7), (7, 26), (0, 8), (21, 24), (0, 5), (20, 4), (10, 1), (22, 30), (2, 1), (24, 5), (1, 6), (8, 1), (17, 0), (22, 28), (30, 28), (23, 10), (17, 5), (13, 12), (2, 34), (8, 30), (27, 33), (17, 19), (1, 0), (21, 19), (36, 7), (9, 18), (8, 7), (20, 28), (14, 21), (11, 6), (20, 19), (2, 32), (17, 33), (33, 29), (32, 12), (20, 32), (15, 0), (29, 26), (10, 27), (38, 16), (13, 26), (13, 15), (7, 33), (26, 25), (9, 32), (5, 8), (13, 6), (24, 16), (26, 2), (24, 27), (16, 2), (5, 34), (23, 20), (27, 11), (23, 7), (35, 1), (12, 10), (9, 15), (17, 29), (0, 11), (30, 26), (29, 17), (33, 36), (8, 25), (2, 23), (1, 26), (16, 28), (16, 25), (34, 29), (12, 33), (34, 5), (8, 2), (7, 35), (25, 11), (11, 4), (13, 13), (9, 17), (36, 15), (21, 25), (32, 31), (18, 21), (27, 27), (18, 28), (37, 21), (0, 37), (31, 2), (2, 14), (17, 16), (24, 4), (2, 9), (32, 32), (0, 19), (8, 17), (6, 19), (11, 29), (14, 15), (7, 29), (33, 4), (16, 7), (27, 10), (34, 16), (33, 3), (37, 22), (13, 36), (31, 7), (12, 2), (21, 12), (25, 33), (12, 4), (28, 7), (19, 25), (6, 17), (28, 24), (12, 11), (10, 33), (34, 27), (22, 3), (2, 10), (17, 27), (34, 3), (4, 36), (26, 37), (20, 26), (0, 17), (5, 28), (27, 12), (21, 28), (20, 2), (5, 24), (36, 33), (2, 15), (21, 33), (28, 8), (29, 23), (36, 36), (10, 17), (31, 34), (7, 32), (31, 12), (2, 29), (1, 8), (26, 10), (32, 24), (0, 3), (16, 13), (18, 8), (2, 13), (32, 16), (21, 31), (29, 18), (5, 12), (25, 8), (23, 17), (14, 14), (25, 16), (4, 35), (13, 23), (15, 18), (31, 26), (37, 1), (16, 1), (33, 11), (0, 29), (8, 18), (31, 11), (16, 20), (19, 10), (4, 15), (2, 0), (9, 19), (36, 9), (6, 15), (14, 9), (10, 24), (18, 10), (7, 15), (33, 22), (35, 4), (21, 29), (11, 13), (21, 16), (21, 21), (29, 27), (27, 19), (29, 21), (3, 34), (11, 25), (12, 1), (28, 32), (9, 2), (17, 34), (7, 17), (24, 33), (31, 17), (25, 4), (20, 7), (21, 35), (26, 31), (7, 9), (29, 31), (33, 14), (4, 18), (19, 30), (38, 14), (31, 13), (12, 35), (32, 23), (36, 4), (30, 5), (37, 32), (25, 21), (0, 6), (16, 32), (32, 14), (21, 5), (26, 28), (26, 1), (2, 17), (37, 28), (26, 33), (24, 9), (7, 19), (25, 0), (23, 29), (21, 9), (0, 35), (3, 32), (22, 9), (25, 23), (13, 25), (9, 16), (38, 36), (12, 31), (13, 4), (29, 13), (28, 2), (0, 28), (17, 12), (6, 35), (25, 15), (36, 20), (33, 33), (38, 2), (22, 27), (29, 29), (11, 5), (30, 35), (3, 3), (34, 31), (19, 26), (15, 27), (12, 13), (37, 15), (32, 35), (11, 30), (34, 33), (27, 13), (13, 11), (28, 12), (15, 15), (0, 32), (33, 13), (27, 9), (19, 8), (8, 32), (13, 16), (28, 27), (7, 7), (20, 25), (5, 5), (15, 29), (22, 19), (18, 19), (34, 26), (1, 37), (33, 15), (0, 31), (15, 22), (26, 21), (2, 7), (37, 19), (20, 18), (24, 24), (2, 28), (28, 14), (7, 24), (11, 8), (38, 3), (34, 28), (3, 0), (8, 4), (13, 27), (22, 33), (16, 37), (26, 22), (30, 4), (30, 22), (11, 32), (5, 9), (12, 28), (9, 26), (38, 28), (14, 13), (20, 37), (11, 14), (31, 21), (26, 32), (21, 17), (21, 1), (10, 28), (23, 37), (19, 21), (10, 16), (10, 30), (38, 11), (37, 26), (26, 9), (2, 5), (15, 12), (0, 2), (11, 22), (34, 4), (18, 13), (28, 31), (8, 6), (8, 15), (16, 26), (34, 11), (35, 16), (21, 36), (13, 30), (32, 0), (14, 4), (34, 12), (11, 16), (30, 11), (9, 37), (33, 9), (3, 36), (26, 12), (31, 3), (36, 19), (18, 33), (30, 19), (27, 14), (12, 16), (4, 31), (23, 26), (32, 5), (14, 6), (4, 10), (36, 14), (7, 30), (8, 20), (9, 27), (25, 5), (24, 15), (26, 27), (31, 23), (20, 31), (18, 11), (17, 15), (6, 13), (4, 20), (32, 34), (21, 14), (9, 4), (17, 17), (13, 24), (24, 22), (4, 26), (30, 16), (30, 3), (30, 25), (7, 37), (32, 30), (33, 32), (36, 11), (35, 35), (38, 27), (25, 18), (36, 6), (25, 6), (37, 7), (3, 23), (4, 8), (32, 21), (17, 23), (2, 21), (25, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931392", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 33), (26, 0), (25, 34), (14, 24), (4, 15), (7, 33), (3, 27), (2, 5), (9, 22), (21, 21), (24, 34), (26, 37), (21, 24), (25, 38), (11, 10), (4, 17), (1, 32), (6, 7), (11, 17), (2, 17), (27, 11), (21, 6), (8, 26), (28, 21), (22, 33), (10, 37), (12, 17), (2, 16), (9, 30), (16, 12), (2, 13), (24, 8), (21, 7), (29, 38), (15, 34), (18, 21), (27, 17), (13, 21), (28, 27), (10, 22), (8, 15), (14, 12), (18, 37), (27, 3), (3, 12), (30, 6), (21, 12), (18, 25), (23, 37), (30, 15), (24, 6), (8, 31), (10, 31), (24, 11), (14, 36), (30, 9), (26, 28), (29, 10), (13, 12), (0, 10), (27, 16), (21, 19), (7, 32), (29, 35), (33, 26), (33, 31), (17, 27), (20, 21), (22, 12), (21, 37), (6, 24), (14, 14), (12, 14), (29, 11), (23, 38), (33, 25), (31, 35), (4, 4), (8, 38), (16, 35), (4, 12), (3, 20), (11, 33), (1, 37), (20, 2), (27, 32), (4, 8), (18, 31), (31, 21), (0, 24), (31, 13), (23, 33), (30, 11), (23, 10), (27, 18), (4, 18), (32, 19), (16, 13), (1, 15), (1, 35), (25, 31), (32, 4), (25, 27), (22, 7), (25, 1), (12, 12), (28, 10), (0, 35), (17, 21), (33, 2), (2, 37), (24, 19), (25, 28), (8, 18), (5, 6), (20, 30), (2, 21), (28, 3), (0, 29), (5, 10), (31, 2), (16, 20), (27, 27), (14, 2), (7, 1), (8, 1), (9, 23), (27, 26), (9, 33), (9, 24), (2, 28), (9, 3), (11, 38), (22, 20), (31, 1), (29, 30), (17, 13), (28, 16), (5, 15), (13, 25), (6, 18), (17, 1), (28, 0), (15, 15), (23, 13), (9, 18), (22, 1), (7, 25), (23, 14), (24, 29), (10, 25), (19, 6), (9, 32), (1, 6), (31, 23), (31, 28), (17, 23), (22, 23), (15, 37), (1, 38), (22, 11), (20, 10), (1, 9), (21, 32), (19, 35), (7, 11), (20, 11), (9, 21), (8, 23), (5, 3), (24, 4), (3, 7), (27, 7), (24, 10), (9, 28), (21, 10), (9, 2), (11, 30), (30, 12), (8, 16), (19, 5), (12, 13), (0, 1), (5, 5), (0, 16), (0, 7), (32, 9), (23, 19), (19, 23), (22, 34), (8, 13), (2, 1), (25, 23), (22, 38), (4, 11), (8, 5), (4, 32), (10, 27), (4, 24), (12, 2), (26, 9), (25, 6), (11, 28), (19, 34), (30, 1), (8, 37), (5, 37), (14, 38), (17, 29), (32, 29), (16, 1), (31, 3), (6, 38), (20, 20), (31, 10), (17, 25), (16, 33), (6, 36), (25, 17), (2, 6), (1, 23), (20, 3), (11, 11), (9, 7), (13, 33), (33, 12), (13, 1), (31, 15), (4, 0), (21, 23), (29, 34), (8, 2), (23, 23), (10, 13), (15, 19), (8, 22), (6, 4), (20, 24), (23, 26), (30, 32), (25, 12), (17, 34), (16, 3), (27, 31), (24, 2), (30, 2), (32, 5), (2, 0), (15, 30), (2, 9), (32, 14), (2, 27), (18, 26), (11, 16), (13, 15), (28, 1), (13, 26), (11, 14), (15, 24), (15, 23), (22, 9), (15, 8), (33, 24), (32, 17), (3, 2), (26, 18), (4, 9), (19, 7), (31, 27), (19, 4), (10, 38), (22, 2), (17, 9), (31, 32), (30, 20), (25, 26), (1, 5), (33, 32), (18, 18), (13, 0), (31, 6), (29, 36), (16, 9), (7, 27), (3, 14), (23, 36), (33, 8), (27, 13), (15, 14), (3, 32), (8, 4), (32, 3), (15, 20), (29, 29), (12, 34), (6, 32), (13, 4), (31, 19), (3, 9), (22, 17), (19, 13), (18, 32), (12, 9), (23, 35), (16, 4), (15, 21), (28, 20), (4, 31), (4, 3), (2, 8), (29, 14), (0, 6), (0, 21), (16, 2), (26, 21), (18, 23), (25, 20), (33, 19), (2, 26), (29, 19), (16, 36), (7, 37), (23, 31), (15, 26), (32, 36), (17, 24), (29, 37), (15, 7), (13, 18), (29, 22), (11, 1), (11, 27), (6, 16), (4, 10), (18, 15), (18, 16), (4, 1), (14, 25), (26, 15), (19, 30), (24, 14), (31, 16), (32, 37), (19, 15), (17, 26), (27, 9), (16, 28), (9, 10), (31, 36), (29, 7), (14, 31), (6, 10), (6, 14), (7, 22), (26, 22), (1, 34), (11, 21), (6, 37), (24, 23), (23, 20), (25, 10), (31, 14), (13, 35), (22, 35), (11, 8), (16, 18), (32, 21), (12, 31), (10, 30), (15, 10), (21, 1), (5, 1), (21, 34), (6, 17), (3, 0), (2, 36), (17, 32), (5, 14), (0, 8), (15, 5), (10, 8), (18, 29), (20, 0), (28, 37), (17, 20), (0, 33), (5, 20), (1, 26), (22, 0), (14, 1), (6, 3), (7, 24), (14, 11), (18, 36), (13, 37), (12, 19), (22, 25), (23, 5), (27, 34), (26, 14), (2, 3), (3, 34), (6, 19), (31, 4), (31, 26), (30, 37), (9, 5), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "693000", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), 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, 21), (24, 12), (1, 3), (16, 10), (0, 24), (0, 19), (6, 27), (31, 22), (7, 11), (4, 28), (2, 10), (23, 17), (27, 13), (17, 21), (26, 11), (27, 19), (2, 3), (32, 12), (15, 14), (26, 27), (13, 20), (17, 24), (12, 16), (10, 17), (16, 7), (6, 24), (16, 15), (26, 6), (1, 5), (7, 9), (1, 2), (25, 17), (32, 11), (2, 5), (19, 19), (9, 22), (19, 9), (1, 13), (6, 2), (5, 2), (12, 22), (2, 17), (20, 17), (19, 22), (23, 22), (4, 22), (13, 9), (25, 14), (2, 20), (18, 12), (26, 1), (8, 26), (28, 25), (23, 28), (17, 11), (17, 3), (0, 10), (21, 7), (20, 33), (24, 0), (11, 10), (1, 12), (17, 18), (25, 31), (22, 20), (18, 7), (21, 32), (16, 22), (10, 16), (9, 28), (26, 26), (14, 3), (5, 31), (22, 3), (9, 32), (9, 18), (4, 26), (17, 33), (11, 28), (24, 5), (9, 26), (10, 18), (4, 15), (23, 31), (14, 9), (10, 29), (12, 2), (3, 12), (30, 27), (13, 10), (4, 12), (19, 5), (32, 2), (28, 5), (17, 1), (21, 33), (9, 8), (3, 9), (18, 28), (5, 0), (7, 31), (6, 11), (19, 30), (20, 9), (29, 9), (15, 7), (27, 28), (7, 4), (15, 19), (20, 5), (22, 22), (1, 11), (23, 26), (23, 4), (0, 8), (19, 3), (14, 2), (2, 16), (4, 0), (30, 33), (1, 23), (18, 9), (22, 9), (20, 10), (21, 8), (3, 28), (10, 24), (25, 25), (17, 16), (14, 0), (8, 12), (14, 1), (31, 14), (29, 29), (11, 24), (0, 31), (30, 8), (4, 33), (20, 6), (18, 30), (23, 23), (19, 1), (25, 15), (30, 9), (20, 1), (10, 19), (20, 19), (23, 7), (21, 12), (13, 19), (1, 20), (31, 15), (19, 15), (23, 13), (14, 25), (17, 5), (30, 6), (24, 17), (30, 13), (25, 30), (1, 33), (21, 6), (18, 25), (17, 12), (21, 9), (0, 17), (8, 5), (31, 3), (7, 22), (8, 4), (26, 4), (7, 25), (25, 18), (31, 20), (19, 25), (11, 11), (27, 33), (4, 20), (3, 26), (32, 16), (13, 2), (20, 32), (25, 7), (20, 28), (23, 15), (18, 21), (8, 3), (15, 24), (31, 26), (20, 24), (25, 5), (2, 0), (28, 8), (18, 19), (13, 14), (15, 33), (24, 28), (20, 21), (10, 22), (2, 8), (24, 19), (3, 32), (13, 5), (8, 8), (11, 20), (8, 32), (0, 11), (30, 2), (9, 17), (27, 7), (23, 21), (10, 14), (28, 15), (29, 16), (5, 5), (18, 17), (30, 32), (22, 5), (0, 32), (28, 17), (6, 30), (22, 16), (5, 33), (29, 8), (15, 20), (14, 10), (22, 4), (26, 10), (20, 23), (5, 18), (14, 20), (13, 23), (2, 33), (26, 16), (24, 31), (25, 16), (9, 24), (30, 20), (23, 32), (22, 30), (7, 6), (11, 2), (23, 24), (13, 1), (15, 1), (3, 15), (12, 26), (2, 29), (16, 18), (18, 6), (3, 5), (1, 30), (24, 24), (25, 26), (29, 1), (9, 12), (20, 3), (32, 26), (24, 15), (27, 4), (24, 10), (15, 18), (31, 33), (27, 2), (28, 16), (8, 7), (21, 5), (30, 15), (0, 6), (14, 15), (13, 3), (5, 4), (5, 32), (22, 0), (25, 6), (11, 15), (27, 11), (27, 26), (25, 22), (21, 15), (29, 6), (16, 14), (18, 4), (30, 4), (23, 3), (10, 12), (16, 4), (1, 19), (14, 26), (6, 8), (8, 16), (13, 12), (12, 14), (12, 6), (11, 8), (21, 13), (4, 11), (32, 19), (27, 15), (29, 12), (30, 25), (15, 5), (27, 9), (7, 23), (2, 7), (2, 24), (31, 16), (19, 28), (26, 14), (22, 23), (0, 1), (32, 28), (18, 2), (0, 7), (20, 13), (17, 0), (30, 1), (6, 10), (19, 12), (32, 27), (22, 25), (7, 18), (7, 17), (23, 20), (27, 10), (25, 24), (4, 8), (3, 0), (19, 2), (13, 28), (12, 1), (3, 33), (10, 10), (0, 26), (12, 8), (1, 6), (22, 24), (10, 2), (8, 13), (8, 24), (10, 33), (1, 7), (29, 28), (22, 18), (18, 10), (16, 32), (2, 31), (20, 16), (20, 25), (8, 31), (26, 30), (12, 13), (30, 24), (0, 21), (3, 31), (22, 12), (11, 31), (7, 30), (12, 0), (31, 21), (19, 32), (14, 21), (16, 16), (4, 19), (16, 0), (8, 6), (21, 11), (3, 30), (14, 7), (3, 21), (2, 21), (30, 3), (4, 24), (3, 1), (10, 6), (21, 29), (28, 26), (16, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103680", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), 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), (13, 32), (12, 5), (21, 19), (1, 9), (4, 27), (1, 12), (30, 24), (26, 3), (15, 10), (2, 24), (20, 10), (36, 30), (35, 28), (36, 21), (17, 14), (20, 19), (36, 1), (31, 17), (15, 6), (30, 8), (35, 0), (2, 23), (9, 15), (14, 27), (32, 7), (2, 17), (36, 10), (9, 21), (35, 17), (23, 0), (25, 1), (19, 31), (30, 26), (23, 10), (32, 20), (31, 5), (7, 20), (9, 10), (31, 9), (12, 15), (29, 31), (15, 7), (16, 8), (13, 14), (17, 9), (26, 5), (28, 16), (33, 15), (17, 26), (22, 24), (28, 28), (20, 5), (18, 31), (24, 30), (15, 24), (18, 12), (0, 22), (13, 13), (10, 20), (13, 33), (29, 4), (25, 26), (20, 0), (1, 25), (31, 14), (22, 0), (15, 29), (3, 3), (34, 21), (32, 2), (5, 10), (12, 25), (9, 19), (35, 24), (15, 4), (30, 25), (20, 1), (33, 8), (8, 4), (15, 14), (19, 4), (17, 11), (16, 14), (22, 23), (19, 28), (20, 14), (2, 18), (25, 8), (1, 14), (22, 29), (3, 0), (33, 20), (22, 25), (13, 1), (9, 7), (8, 30), (9, 1), (2, 14), (31, 20), (0, 9), (20, 22), (16, 2), (13, 6), (30, 13), (11, 32), (2, 3), (13, 26), (36, 17), (28, 19), (3, 33), (30, 15), (20, 3), (22, 28), (15, 25), (15, 20), (14, 17), (34, 17), (22, 6), (18, 10), (12, 10), (32, 31), (32, 27), (5, 26), (6, 25), (10, 6), (5, 9), (6, 7), (8, 1), (34, 8), (17, 15), (6, 27), (26, 23), (15, 13), (21, 12), (36, 27), (33, 26), (14, 29), (30, 9), (14, 22), (23, 8), (7, 23), (3, 24), (30, 18), (18, 24), (13, 28), (28, 3), (7, 3), (30, 31), (8, 5), (6, 29), (4, 2), (2, 22), (31, 6), (32, 30), (3, 31), (22, 17), (31, 27), (14, 19), (20, 20), (16, 20), (2, 13), (22, 2), (8, 20), (27, 20), (7, 18), (15, 1), (24, 26), (28, 5), (3, 9), (6, 16), (4, 7), (2, 27), (7, 1), (15, 31), (16, 27), (4, 16), (22, 10), (29, 14), (36, 7), (27, 2), (28, 18), (5, 4), (18, 27), (23, 11), (25, 16), (21, 28), (6, 23), (23, 15), (13, 16), (36, 9), (6, 33), (16, 0), (15, 0), (9, 27), (6, 30), (10, 21), (28, 31), (36, 32), (33, 9), (24, 13), (12, 20), (3, 14), (35, 2), (5, 3), (4, 11), (11, 25), (9, 2), (7, 16), (12, 18), (3, 8), (22, 15), (11, 33), (9, 32), (29, 17), (14, 33), (9, 9), (23, 9), (32, 16), (35, 10), (5, 30), (16, 9), (26, 30), (4, 21), (27, 8), (32, 26), (4, 28), (16, 26), (2, 20), (35, 4), (18, 11), (24, 0), (24, 6), (20, 25), (12, 2), (20, 30), (3, 26), (34, 23), (33, 29), (34, 26), (21, 30), (11, 12), (23, 33), (24, 28), (18, 15), (20, 17), (36, 19), (7, 26), (19, 16), (19, 32), (10, 7), (2, 7), (7, 22), (19, 0), (34, 7), (11, 4), (34, 6), (30, 5), (23, 23), (31, 16), (6, 13), (3, 19), (6, 4), (5, 12), (14, 20), (24, 9), (0, 26), (26, 31), (24, 12), (26, 29), (27, 30), (17, 33), (32, 4), (8, 16), (6, 6), (35, 18), (27, 13), (12, 1), (21, 26), (21, 14), (1, 6), (3, 32), (11, 3), (28, 21), (2, 29), (17, 8), (34, 16), (31, 30), (31, 24), (28, 0), (27, 0), (11, 9), (16, 3), (32, 6), (14, 25), (5, 8), (16, 29), (36, 5), (15, 16), (27, 5), (15, 5), (12, 19), (36, 28), (4, 25), (17, 19), (23, 29), (18, 13), (10, 26), (14, 30), (25, 18), (30, 0), (30, 21), (22, 14), (1, 16), (2, 26), (0, 16), (1, 24), (28, 24), (7, 24), (10, 18), (11, 31), (7, 5), (2, 21), (33, 21), (5, 5), (20, 15), (21, 22), (6, 2), (28, 32), (11, 17), (9, 11), (35, 23), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "491040", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (4, 23), (28, 29), (4, 19), (2, 26), (24, 3), (15, 29), (21, 24), (9, 22), (21, 11), (26, 7), (5, 23), (4, 2), (13, 28), (25, 18), (17, 2), (8, 12), (9, 5), (16, 27), (17, 14), (22, 20), (20, 15), (11, 23), (29, 18), (18, 26), (18, 4), (18, 27), (15, 22), (0, 14), (25, 3), (5, 2), (25, 10), (20, 13), (4, 3), (28, 13), (19, 22), (24, 17), (23, 17), (13, 20), (23, 22), (7, 8), (3, 13), (3, 22), (10, 12), (15, 2), (3, 6), (3, 7), (4, 15), (21, 3), (15, 10), (27, 29), (7, 1), (16, 4), (18, 22), (25, 12), (1, 9), (8, 5), (15, 25), (28, 15), (14, 13), (9, 9), (22, 11), (13, 15), (0, 5), (0, 19), (20, 9), (17, 20), (3, 24), (28, 26), (0, 29), (26, 13), (2, 0), (3, 23), (8, 27), (26, 21), (29, 12), (28, 10), (21, 10), (2, 5), (10, 14), (17, 26), (28, 28), (9, 16), (22, 27), (15, 14), (3, 14), (17, 22), (20, 6), (13, 6), (11, 21), (22, 6), (1, 4), (15, 8), (28, 7), (26, 9), (16, 2), (12, 27), (7, 11), (14, 20), (28, 16), (21, 20), (15, 15), (10, 4), (26, 2), (0, 13), (19, 0), (25, 14), (9, 11), (19, 21), (22, 12), (18, 29), (13, 9), (8, 17), (9, 26), (18, 20), (12, 20), (24, 1), (3, 20), (9, 18), (28, 1), (23, 9), (27, 14), (1, 22), (28, 27), (24, 5), (20, 11), (21, 21), (6, 14), (24, 24), (17, 6), (10, 7), (0, 8), (11, 12), (3, 1), (26, 4), (27, 17), (1, 28), (1, 19), (25, 0), (7, 16), (11, 11), (19, 12), (9, 24), (6, 28), (4, 20), (19, 29), (10, 22), (0, 16), (25, 1), (28, 4), (1, 21), (8, 22), (16, 13), (0, 2), (6, 4), (3, 5), (0, 22), (19, 24), (27, 10), (20, 24), (9, 3), (0, 15), (11, 9), (20, 23), (22, 29), (3, 18), (6, 10), (16, 10), (29, 17), (5, 18), (18, 11), (18, 17), (11, 19), (11, 8), (25, 15), (18, 1), (1, 16), (24, 16), (16, 11), (24, 20), (27, 3), (23, 6), (26, 16), (5, 3), (13, 29), (16, 8), (21, 12), (23, 24), (2, 24), (24, 15), (3, 12), (5, 22), (12, 5), (18, 23), (20, 12), (26, 26), (4, 27), (2, 20), (22, 21), (15, 4), (26, 19), (11, 27), (0, 27), (0, 3), (1, 14), (9, 6), (8, 23), (23, 1), (10, 23), (17, 15), (18, 3), (16, 9), (25, 13), (13, 10), (19, 25), (19, 5), (28, 2), (14, 19), (14, 25), (0, 4), (20, 17), (29, 8), (29, 10), (0, 7), (2, 15), (13, 8), (3, 26), (7, 14), (5, 9), (0, 26), (3, 8), (4, 7), (23, 19), (0, 12), (16, 28), (23, 14), (13, 23), (24, 6), (21, 19), (0, 17), (25, 27), (19, 26), (27, 20), (26, 23), (25, 29), (0, 6), (26, 18), (12, 13), (8, 0), (16, 7), (5, 6), (8, 26), (19, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757248", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 1), (0, 6), (24, 34), (2, 19), (29, 17), (26, 17), (13, 8), (30, 6), (23, 18), (28, 17), (25, 32), (6, 29), (23, 21), (0, 34), (16, 5), (25, 36), (19, 32), (0, 19), (28, 14), (2, 25), (24, 27), (27, 37), (2, 28), (5, 9), (22, 1), (27, 4), (15, 4), (12, 14), (7, 7), (22, 9), (12, 21), (24, 8), (29, 18), (19, 3), (29, 11), (15, 3), (18, 32), (0, 25), (4, 33), (1, 1), (0, 5), (19, 8), (0, 20), (19, 4), (13, 3), (0, 28), (13, 1), (4, 14), (18, 27), (17, 32), (31, 15), (23, 34), (10, 23), (0, 22), (21, 25), (28, 6), (11, 11), (21, 10), (18, 37), (29, 19), (13, 21), (5, 8), (20, 11), (4, 11), (23, 32), (6, 36), (25, 7), (14, 26), (25, 8), (30, 12), (14, 3), (24, 2), (31, 21), (0, 15), (8, 5), (18, 22), (24, 6), (22, 33), (12, 17), (28, 19), (4, 27), (13, 27), (31, 22), (3, 5), (14, 33), (28, 0), (20, 6), (16, 16), (4, 17), (30, 25), (27, 22), (3, 27), (11, 29), (25, 17), (7, 31), (25, 10), (27, 9), (8, 9), (17, 16), (15, 37), (23, 8), (8, 7), (0, 35), (2, 1), (14, 29), (3, 17), (23, 16), (29, 2), (24, 18), (7, 32), (15, 29), (8, 23), (25, 19), (15, 16), (31, 1), (17, 35), (8, 32), (16, 37), (22, 30), (20, 33), (18, 18), (25, 22), (31, 20), (1, 15), (20, 35), (0, 1), (31, 33), (9, 15), (24, 11), (24, 1), (17, 5), (6, 30), (9, 33), (30, 3), (12, 0), (12, 26), (0, 29), (13, 29), (29, 25), (30, 29), (13, 31), (21, 23), (29, 6), (23, 14), (27, 26), (7, 4), (9, 27), (17, 12), (0, 26), (29, 30), (17, 34), (10, 15), (9, 23), (13, 11), (23, 15), (12, 34), (3, 33), (16, 7), (0, 30), (2, 16), (29, 26), (24, 16), (8, 25), (24, 17), (28, 2), (24, 37), (12, 15), (11, 12), (29, 4), (22, 22), (26, 18), (15, 7), (29, 23), (14, 11), (29, 22), (7, 21), (6, 0), (14, 17), (14, 0), (8, 24), (15, 20), (9, 6), (4, 10), (7, 20), (23, 29), (6, 1), (11, 16), (16, 24), (18, 34), (27, 14), (20, 10), (28, 11), (14, 8), (26, 9), (3, 24), (16, 27), (20, 37), (1, 10), (16, 11), (16, 2), (20, 2), (18, 12), (20, 15), (14, 25), (9, 8), (15, 24), (9, 24), (27, 5), (10, 11), (5, 14), (21, 36), (3, 22), (3, 35), (16, 13), (19, 34), (19, 16), (12, 8), (0, 21), (24, 9), (2, 34), (20, 4), (11, 37), (5, 2), (10, 4), (4, 24), (17, 14), (25, 5), (4, 23), (9, 14), (30, 15), (3, 12), (3, 16), (15, 0), (30, 9), (19, 0), (3, 30), (11, 9), (25, 20), (29, 20), (12, 4), (30, 14), (24, 33), (21, 35), (15, 11), (9, 9), (23, 26), (15, 30), (22, 2), (23, 7), (27, 2), (11, 5), (30, 5), (24, 19), (13, 16), (10, 35), (7, 13), (19, 36), (28, 28), (17, 18), (25, 29), (25, 12), (3, 28), (26, 10), (22, 23), (23, 4), (16, 36), (15, 5), (23, 12), (14, 15), (14, 13), (14, 16), (1, 31), (27, 33), (20, 24), (18, 8), (14, 6), (2, 12), (18, 3), (5, 15), (2, 5), (28, 37), (27, 12), (29, 31), (10, 31), (18, 33), (14, 18), (10, 20), (1, 34), (5, 24), (27, 35), (26, 15), (30, 32), (14, 12), (9, 18), (19, 15), (11, 13), (10, 26), (21, 6), (17, 28), (4, 6), (13, 17), (31, 0), (6, 13), (28, 20), (11, 3), (7, 22), (30, 24), (9, 13), (16, 14), (23, 28), (29, 3), (28, 18), (22, 21), (5, 6), (26, 26), (20, 0), (26, 28), (29, 35), (7, 37), (16, 29), (23, 27), (24, 5), (4, 8), (26, 21), (11, 28), (3, 13), (30, 4), (0, 8), (5, 21), (28, 12), (11, 21), (22, 32), (27, 16), (20, 17), (20, 22), (21, 33), (28, 36), (18, 23), (10, 34), (3, 20), (13, 22), (17, 19), (2, 20), (5, 13), (3, 21), (26, 29), (20, 7), (16, 25), (20, 27), (21, 31), (25, 9), (9, 7), (22, 20), (14, 31), (28, 33), (25, 13), (31, 3), (1, 3), (25, 23), (13, 18), (13, 7), (9, 19), (24, 32), (23, 3), (6, 26), (19, 1), (13, 32), (6, 14), (10, 13), (13, 26), (13, 37), (17, 7), (7, 17), (22, 5), (25, 11), (15, 33), (14, 19), (18, 20), (10, 17), (5, 35), (9, 2), (12, 5), (28, 35), (4, 16), (6, 18), (9, 1), (5, 0), (21, 27), (24, 35), (2, 9), (23, 13), (0, 33), (22, 26), (19, 9), (17, 2), (11, 4), (17, 25), (14, 5), (18, 4), (6, 34), (30, 31), (0, 24), (4, 7), (3, 26), (12, 25), (25, 31), (6, 33), (28, 8), (31, 8), (13, 20), (6, 22), (19, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68352", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 3), (12, 7), (25, 25), (25, 16), (13, 20), (15, 6), (8, 14), (20, 13), (29, 21), (21, 17), (11, 20), (0, 11), (15, 13), (13, 13), (28, 13), (26, 25), (10, 16), (10, 27), (15, 19), (4, 15), (13, 0), (11, 29), (27, 29), (28, 24), (10, 19), (25, 26), (23, 26), (33, 18), (9, 23), (20, 8), (24, 10), (11, 24), (23, 9), (14, 19), (4, 26), (25, 1), (7, 24), (22, 16), (4, 27), (3, 14), (25, 10), (26, 6), (3, 19), (10, 17), (0, 21), (32, 17), (18, 20), (23, 28), (9, 11), (12, 0), (6, 14), (33, 22), (14, 17), (19, 19), (20, 24), (19, 5), (5, 19), (6, 11), (20, 11), (14, 11), (9, 1), (30, 1), (16, 24), (20, 14), (3, 26), (0, 20), (16, 29), (11, 11), (26, 20), (10, 10), (7, 23), (34, 15), (27, 21), (30, 23), (3, 25), (34, 18), (3, 16), (6, 19), (22, 9), (3, 4), (4, 2), (15, 20), (27, 2), (8, 8), (34, 27), (17, 7), (2, 15), (24, 22), (32, 14), (24, 12), (3, 28), (21, 7), (34, 9), (24, 3), (23, 4), (2, 7), (26, 10), (15, 16), (10, 2), (4, 20), (19, 6), (8, 11), (14, 26), (9, 15), (26, 14), (23, 17), (10, 6), (4, 7), (28, 4), (13, 10), (3, 13), (23, 11), (3, 10), (0, 29), (2, 22), (25, 22), (10, 8), (23, 22), (3, 8), (3, 6), (21, 28), (25, 19), (27, 20), (25, 21), (17, 19), (2, 23), (2, 21), (30, 20), (31, 11), (25, 8), (6, 9), (13, 1), (21, 3), (8, 28), (14, 18), (28, 27), (13, 16), (34, 26), (3, 18), (2, 12), (8, 12), (11, 0), (28, 7), (0, 9), (13, 19), (34, 11), (34, 6), (8, 13), (32, 13), (29, 29), (16, 8), (1, 2), (21, 26), (5, 17), (5, 7), (16, 1), (32, 12), (31, 6), (31, 26), (7, 2), (21, 27), (11, 26), (5, 25), (14, 21), (31, 14), (9, 20), (32, 26), (5, 5), (32, 16), (15, 2), (16, 5), (30, 3), (0, 13), (31, 1), (26, 28), (8, 16), (2, 6), (15, 15), (5, 27), (12, 22), (10, 13), (15, 29), (11, 28), (31, 13), (25, 9), (23, 15), (22, 13), (14, 28), (12, 23), (19, 22), (33, 19), (2, 3), (2, 16), (19, 17), (21, 20), (12, 11), (34, 23), (17, 4), (15, 7), (27, 19), (6, 6), (7, 26), (12, 27), (2, 26), (19, 29), (7, 22), (3, 11), (26, 1), (29, 13), (3, 24), (25, 28), (16, 9), (4, 8), (29, 23), (31, 20), (26, 13), (28, 5), (31, 8), (1, 5), (28, 2), (33, 1), (20, 7), (34, 25), (0, 15), (18, 3), (12, 8), (8, 0), (22, 21), (23, 0), (14, 4), (11, 7), (19, 21), (22, 19), (6, 7), (23, 8), (10, 5), (21, 18), (18, 13), (7, 7), (24, 13), (28, 15), (6, 27), (6, 26), (24, 0), (15, 18), (5, 0), (7, 5), (25, 14), (12, 15), (7, 12), (0, 22), (29, 9), (1, 4), (13, 14), (17, 15), (22, 25), (3, 17), (17, 6), (12, 21), (31, 10), (6, 3), (25, 11), (14, 14), (12, 12), (25, 27), (25, 5), (26, 18), (25, 0), (18, 1), (18, 17), (3, 20), (34, 16), (16, 11), (30, 8), (20, 23), (8, 19), (5, 24), (25, 18), (33, 5), (20, 15), (2, 28), (3, 5), (28, 6), (10, 7), (32, 8), (30, 28), (1, 25), (25, 17), (5, 4), (5, 10), (20, 18), (14, 25), (9, 14), (9, 27), (23, 6), (28, 18), (12, 4), (14, 8), (1, 8), (19, 24), (20, 0), (31, 12), (1, 6), (19, 13), (29, 7), (29, 5), (29, 16), (11, 3), (15, 3), (4, 17), (2, 29), (2, 10), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437400", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 27), (24, 10), (33, 13), (3, 17), (35, 33), (10, 17), (28, 25), (4, 33), (9, 30), (23, 13), (25, 24), (2, 3), (16, 29), (14, 20), (19, 10), (6, 19), (17, 27), (13, 1), (30, 10), (14, 14), (8, 6), (36, 28), (8, 13), (11, 18), (14, 11), (35, 5), (31, 20), (36, 29), (19, 8), (0, 6), (18, 16), (35, 19), (19, 25), (27, 2), (28, 23), (28, 10), (14, 26), (37, 3), (10, 2), (12, 11), (21, 21), (31, 16), (22, 19), (3, 1), (11, 14), (29, 24), (2, 17), (21, 1), (31, 5), (11, 34), (26, 4), (20, 11), (37, 16), (6, 14), (13, 30), (33, 30), (17, 16), (6, 2), (5, 13), (21, 25), (37, 0), (3, 29), (4, 5), (7, 2), (35, 16), (0, 30), (28, 31), (21, 2), (14, 0), (14, 29), (15, 5), (16, 0), (12, 27), (10, 24), (22, 1), (27, 8), (33, 20), (31, 32), (37, 5), (6, 13), (18, 22), (36, 4), (4, 9), (23, 21), (32, 1), (11, 22), (14, 3), (24, 6), (24, 25), (27, 1), (27, 7), (28, 22), (17, 32), (30, 13), (9, 9), (19, 34), (5, 15), (32, 11), (33, 18), (32, 28), (26, 31), (16, 3), (7, 10), (27, 10), (34, 0), (12, 13), (25, 1), (6, 17), (31, 31), (8, 7), (13, 6), (2, 23), (30, 28), (4, 34), (29, 25), (16, 17), (30, 20), (0, 29), (16, 15), (17, 31), (29, 20), (36, 23), (1, 34), (9, 12), (22, 2), (22, 10), (8, 21), (20, 3), (22, 16), (1, 3), (8, 8), (25, 3), (21, 6), (18, 4), (35, 22), (10, 26), (13, 28), (27, 12), (5, 14), (13, 29), (29, 15), (34, 28), (19, 32), (15, 9), (1, 1), (1, 21), (29, 19), (11, 33), (29, 29), (16, 20), (8, 32), (19, 18), (3, 22), (4, 31), (20, 9), (9, 7), (35, 13), (28, 6), (6, 24), (7, 5), (10, 16), (3, 25), (36, 13), (18, 15), (33, 32), (26, 0), (14, 30), (23, 22), (25, 9), (26, 3), (26, 14), (33, 29), (24, 26), (11, 0), (3, 3), (6, 31), (3, 14), (35, 20), (8, 17), (29, 22), (30, 5), (12, 22), (23, 3), (13, 21), (32, 3), (11, 32), (18, 14), (9, 3), (34, 13), (9, 1), (36, 8), (28, 19), (22, 31), (3, 8), (33, 3), (12, 7), (9, 24), (34, 15), (5, 17), (26, 33), (19, 5), (12, 1), (32, 22), (15, 25), (17, 10), (6, 10), (13, 4), (32, 13), (36, 33), (3, 21), (10, 4), (34, 32), (14, 7), (15, 3), (19, 31), (35, 3), (15, 27), (36, 30), (14, 2), (7, 4), (23, 34), (33, 5), (15, 29), (27, 29), (21, 14), (34, 29), (35, 21), (9, 5), (6, 12), (6, 1), (10, 34), (14, 4), (15, 31), (12, 10), (37, 9), (32, 10), (1, 4), (33, 25), (23, 14), (27, 6), (13, 33), (12, 34), (32, 30), (2, 25), (30, 32), (21, 19), (14, 18), (18, 7), (18, 23), (3, 18), (12, 29), (31, 6), (30, 3), (11, 23), (25, 28), (30, 21), (37, 11), (14, 5), (37, 2), (14, 21), (24, 5), (3, 27), (29, 26), (22, 8), (3, 12), (1, 11), (27, 25), (17, 18), (11, 5), (23, 29), (14, 9), (15, 18), (15, 8), (9, 27), (6, 21), (8, 1), (34, 33), (28, 17), (7, 13), (21, 12), (33, 7), (26, 25), (37, 10), (19, 27), (4, 15), (18, 24), (15, 1), (3, 32), (29, 11), (1, 23), (20, 8), (16, 12), (15, 28), (15, 24), (15, 19), (36, 11), (23, 31), (7, 14), (15, 4), (24, 29), (29, 1), (4, 32), (26, 21), (36, 16), (18, 27), (28, 14), (20, 6), (34, 19), (28, 32), (31, 27), (14, 6), (34, 26), (3, 31), (4, 6), (35, 27), (33, 16), (15, 22), (31, 18), (11, 2), (19, 11), (13, 14), (8, 16), (34, 21), (23, 8), (17, 1), (1, 2), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "771984", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 28), (21, 16), (34, 32), (23, 1), (11, 34), (26, 25), (22, 0), (7, 11), (12, 30), (34, 9), (35, 20), (14, 30), (12, 7), (29, 2), (12, 23), (3, 27), (15, 9), (21, 14), (31, 38), (22, 25), (11, 23), (8, 26), (27, 28), (20, 3), (36, 3), (17, 26), (37, 20), (7, 5), (16, 18), (9, 28), (18, 11), (24, 3), (14, 28), (29, 12), (29, 3), (13, 16), (31, 26), (35, 18), (35, 7), (33, 5), (25, 20), (24, 6), (0, 26), (12, 33), (36, 6), (3, 18), (19, 18), (19, 0), (5, 10), (23, 32), (30, 38), (4, 26), (11, 18), (38, 6), (3, 1), (7, 32), (32, 24), (20, 32), (32, 18), (17, 16), (0, 31), (28, 7), (11, 36), (1, 5), (31, 27), (28, 32), (37, 33), (26, 23), (20, 25), (2, 32), (27, 2), (32, 0), (14, 13), (36, 27), (14, 10), (17, 5), (3, 17), (7, 33), (32, 32), (8, 24), (3, 14), (11, 9), (6, 20), (0, 36), (0, 13), (6, 10), (21, 1), (31, 10), (3, 37), (32, 29), (2, 0), (26, 19), (5, 12), (27, 5), (37, 34), (26, 16), (4, 32), (0, 2), (14, 6), (36, 31), (26, 12), (15, 25), (28, 37), (22, 7), (18, 0), (8, 13), (13, 0), (11, 19), (5, 11), (37, 38), (15, 12), (33, 35), (2, 36), (4, 14), (35, 38), (23, 38), (7, 16), (21, 27), (1, 30), (14, 9), (22, 11), (33, 38), (31, 11), (10, 18), (27, 32), (8, 14), (13, 22), (29, 17), (26, 29), (17, 35), (21, 34), (38, 32), (21, 20), (23, 12), (10, 8), (36, 29), (26, 18), (9, 37), (4, 2), (34, 3), (15, 33), (4, 33), (13, 15), (28, 26), (18, 33), (33, 19), (0, 38), (14, 20), (25, 30), (0, 12), (20, 18), (37, 2), (31, 7), (36, 14), (20, 22), (23, 10), (24, 9), (10, 2), (37, 23), (13, 10), (19, 4), (22, 9), (20, 29), (7, 1), (38, 17), (7, 31), (3, 5), (30, 37), (4, 7), (9, 25), (25, 16), (23, 16), (18, 19), (33, 31), (6, 11), (10, 32), (13, 1), (11, 12), (16, 26), (5, 17), (35, 10), (6, 34), (26, 32), (20, 23), (36, 22), (23, 36), (1, 12), (29, 14), (17, 23), (0, 23), (33, 3), (9, 14), (15, 8), (29, 1), (3, 2), (35, 3), (38, 26), (26, 26), (2, 37), (20, 24), (18, 31), (13, 24), (26, 38), (38, 12), (31, 22), (24, 21), (5, 9), (1, 21), (38, 16), (4, 18), (5, 38), (34, 21), (7, 26), (14, 16), (18, 5), (36, 34), (5, 33), (10, 30), (36, 26), (26, 11), (1, 6), (15, 2), (12, 29), (19, 22), (21, 4), (33, 1), (30, 26), (17, 29), (34, 17), (32, 38), (33, 23), (8, 31), (2, 23), (35, 4), (6, 31), (11, 32), (5, 35), (0, 9), (5, 13), (19, 27), (4, 24), (15, 36), (21, 15), (21, 8), (16, 11), (22, 23), (22, 35), (19, 10), (38, 30), (37, 3), (30, 20), (6, 0), (11, 38), (19, 12), (10, 5), (30, 0), (13, 12), (20, 13), (32, 7), (21, 13), (3, 35), (26, 7), (21, 17), (17, 38), (30, 3), (27, 31), (28, 6), (9, 23), (4, 34), (32, 19), (18, 18), (29, 34), (28, 17), (27, 34), (3, 34), (33, 28), (7, 29), (18, 34), (6, 25), (28, 15), (6, 32), (21, 36), (21, 26), (16, 19), (15, 14), (21, 0), (20, 15), (5, 28), (29, 35), (9, 31), (4, 8), (32, 23), (37, 27), (3, 22), (32, 15), (38, 9), (25, 2), (7, 21), (23, 33), (5, 32), (30, 1), (10, 1), (18, 35), (6, 19), (10, 19), (4, 37), (3, 6), (28, 2), (32, 11), (7, 38), (29, 21), (36, 13), (23, 28), (34, 26), (31, 16), (33, 24), (26, 10), (8, 28), (24, 31), (20, 9), (34, 25), (17, 28), (7, 37), (8, 12), (24, 19), (32, 37), (29, 30), (15, 28), (29, 29), (33, 37), (18, 32), (35, 2), (13, 23), (37, 16), (37, 24), (6, 30), (38, 14), (28, 9), (6, 27), (30, 25), (28, 31), (0, 17), (29, 8), (12, 14), (29, 23), (13, 2), (6, 26), (6, 6), (33, 2), (25, 22), (16, 8), (33, 26), (26, 33), (6, 38), (12, 1), (12, 19), (18, 38), (0, 10), (2, 3), (22, 17), (15, 15), (35, 9), (30, 12), (31, 0), (8, 2), (34, 1), (32, 10), (32, 31), (34, 36), (8, 1), (14, 25), (12, 24), (12, 15), (30, 5), (9, 16), (33, 0), (5, 18), (9, 26), (5, 37), (37, 18), (10, 12), (8, 22), (0, 25), (37, 28), (15, 13), (4, 6), (38, 11), (27, 38), (15, 21), (1, 16), (10, 6), (3, 23), (14, 11), (37, 37), (12, 10), (21, 30), (24, 8), (4, 16), (20, 34), (36, 28), (26, 3), (26, 30), (28, 33), (2, 13), (3, 26), (17, 11), (0, 22), (3, 19), (5, 5), (33, 11), (33, 18), (16, 4), (35, 28), (7, 13), (14, 27), (9, 6), (26, 28), (14, 29), (12, 17), (8, 7), (14, 19), (17, 17), (4, 27), (14, 14), (35, 13), (4, 9), (17, 19), (17, 8), (1, 24), (2, 12), (15, 38), (32, 2), (9, 3), (4, 36), (20, 27), (28, 5), (21, 23), (4, 3), (20, 8), (22, 31), (25, 4), (35, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "594000", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 6), (15, 27), (18, 33), (22, 38), (34, 8), (13, 22), (32, 33), (1, 28), (29, 31), (25, 28), (19, 28), (34, 24), (29, 27), (14, 14), (11, 29), (24, 23), (30, 26), (28, 14), (21, 23), (29, 8), (7, 23), (27, 16), (24, 0), (30, 5), (25, 17), (25, 14), (31, 36), (2, 12), (5, 17), (23, 37), (26, 23), (20, 1), (6, 18), (28, 35), (7, 30), (27, 0), (17, 15), (20, 21), (25, 16), (7, 37), (30, 31), (11, 24), (21, 25), (22, 9), (34, 2), (1, 10), (28, 5), (19, 12), (8, 19), (0, 36), (1, 33), (6, 22), (35, 27), (2, 5), (27, 37), (7, 14), (31, 27), (6, 2), (19, 3), (10, 18), (6, 5), (19, 32), (23, 35), (31, 16), (30, 19), (23, 21), (13, 15), (30, 6), (8, 22), (3, 32), (12, 34), (27, 3), (30, 8), (32, 4), (22, 27), (35, 7), (16, 37), (17, 30), (20, 6), (4, 12), (22, 33), (0, 28), (30, 4), (7, 28), (35, 15), (35, 33), (29, 19), (21, 22), (23, 6), (30, 23), (16, 6), (8, 38), (5, 25), (31, 8), (8, 29), (10, 8), (18, 22), (32, 36), (8, 12), (12, 3), (2, 34), (8, 23), (4, 8), (20, 31), (18, 0), (12, 22), (35, 36), (6, 26), (27, 8), (29, 33), (29, 22), (36, 37), (16, 35), (5, 4), (30, 15), (20, 3), (14, 31), (34, 15), (35, 8), (2, 7), (35, 0), (5, 24), (19, 35), (21, 12), (16, 22), (21, 6), (11, 13), (27, 28), (33, 7), (11, 16), (35, 19), (16, 38), (18, 23), (0, 30), (34, 37), (17, 25), (16, 28), (13, 14), (4, 1), (23, 38), (24, 20), (5, 22), (5, 26), (22, 28), (33, 11), (15, 35), (18, 26), (12, 1), (18, 36), (3, 1), (3, 4), (8, 9), (20, 0), (29, 9), (36, 16), (10, 2), (33, 31), (31, 6), (22, 23), (12, 29), (17, 34), (36, 4), (12, 4), (32, 30), (20, 33), (0, 21), (13, 9), (33, 1), (26, 19), (27, 24), (12, 10), (21, 3), (29, 3), (19, 4), (30, 24), (2, 23), (14, 8), (32, 29), (14, 11), (20, 24), (25, 31), (7, 33), (27, 21), (11, 31), (9, 19), (21, 10), (4, 14), (35, 17), (28, 9), (29, 28), (17, 4), (12, 6), (18, 37), (21, 0), (24, 34), (7, 29), (4, 15), (3, 35), (37, 8), (11, 34), (32, 6), (13, 21), (14, 1), (22, 26), (18, 4), (10, 10), (36, 28), (2, 14), (5, 35), (17, 26), (13, 28), (32, 28), (28, 26), (21, 24), (11, 15), (28, 19), (32, 12), (32, 0), (9, 26), (0, 38), (6, 33), (33, 19), (30, 30), (19, 11), (18, 11), (22, 22), (2, 21), (30, 37), (25, 27), (13, 1), (22, 11), (37, 28), (31, 13), (36, 9), (35, 28), (11, 19), (16, 5), (11, 37), (24, 21), (27, 14), (9, 12), (8, 28), (4, 30), (32, 7), (4, 0), (28, 2), (12, 24), (2, 2), (37, 15), (22, 4), (2, 27), (21, 8), (12, 8), (19, 22), (7, 38), (33, 29), (21, 33), (25, 13), (33, 4), (23, 31), (28, 36), (35, 14), (33, 17), (7, 36), (15, 12), (37, 6), (30, 29), (37, 21), (31, 19), (1, 27), (26, 13), (1, 34), (13, 12), (19, 20), (2, 18), (9, 34), (11, 38), (28, 1), (20, 12), (7, 34), (32, 9), (32, 24), (13, 13), (21, 4), (5, 30), (33, 2), (14, 20), (36, 20), (34, 25), (22, 5), (15, 34), (24, 29), (34, 16), (8, 11), (30, 17), (17, 16), (23, 17), (12, 32), (11, 5), (34, 11), (29, 16), (6, 34), (4, 9), (7, 7), (0, 35), (6, 37), (10, 27), (4, 13), (24, 37), (14, 21), (6, 12), (31, 12), (11, 22), (3, 31), (17, 32), (31, 11), (24, 12), (19, 2), (27, 17), (20, 25), (3, 6), (13, 27), (21, 7), (28, 34), (3, 29), (22, 6), (3, 18), (11, 26), (9, 36), (24, 36), (37, 5), (0, 33), (26, 25), (36, 18), (5, 12), (11, 18), (34, 5), (36, 3), (19, 19), (5, 32), (25, 0), (33, 10), (16, 10), (32, 22), (21, 35), (36, 38), (6, 6), (22, 3), (0, 22), (21, 9), (25, 33), (25, 15), (16, 17), (37, 17), (14, 28), (3, 21), (21, 27), (7, 13), (2, 10), (1, 11), (27, 35), (7, 19), (30, 38), (27, 7), (15, 10), (0, 10), (4, 31), (8, 3), (32, 1), (4, 3), (23, 28), (32, 5), (17, 2), (26, 27), (3, 33), (14, 9), (17, 1), (30, 11), (23, 20), (20, 23), (19, 38), (15, 7), (24, 10), (14, 16), (24, 13), (6, 21), (24, 14), (13, 36), (36, 23), (2, 17), (35, 32), (28, 29), (8, 21), (34, 26), (0, 31), (2, 33), (6, 20), (18, 12), (5, 1), (26, 11), (36, 35), (24, 4), (33, 9), (29, 24), (8, 30), (36, 15), (8, 37), (36, 0), (22, 12), (11, 32), (16, 32), (24, 35), (16, 13), (31, 9), (5, 16), (18, 25), (14, 19), (1, 29), (7, 17), (33, 15), (5, 27), (0, 20), (13, 32), (22, 36), (1, 22), (2, 30), (0, 17), (12, 15), (14, 33), (26, 17), (21, 36), (19, 9), (11, 36), (18, 21), (10, 32), (9, 7), (37, 32), (28, 4), (0, 19), (0, 14), (11, 17), (37, 19), (10, 0), (20, 26), (29, 5), (14, 7), (8, 10), (1, 20), (30, 34), (25, 29), (17, 14), (13, 18), (13, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "315000", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 27), (7, 28), (3, 24), (17, 6), (30, 12), (19, 18), (15, 7), (23, 12), (25, 7), (21, 30), (8, 18), (30, 24), (18, 0), (28, 24), (30, 10), (33, 20), (7, 15), (17, 23), (28, 18), (14, 26), (1, 21), (34, 8), (6, 17), (33, 13), (31, 27), (28, 21), (3, 23), (25, 23), (1, 12), (0, 7), (3, 15), (5, 16), (26, 28), (30, 21), (32, 25), (32, 6), (14, 4), (34, 22), (31, 8), (22, 26), (35, 28), (1, 26), (33, 17), (9, 12), (23, 7), (22, 7), (32, 13), (33, 6), (24, 5), (24, 2), (3, 7), (11, 29), (31, 7), (34, 16), (30, 26), (1, 17), (10, 7), (9, 22), (17, 14), (27, 24), (14, 16), (33, 24), (21, 25), (7, 29), (14, 7), (2, 29), (24, 25), (15, 24), (3, 11), (30, 4), (31, 14), (4, 28), (3, 12), (32, 19), (30, 0), (30, 7), (13, 28), (18, 21), (8, 17), (35, 11), (10, 12), (21, 2), (35, 14), (1, 6), (17, 28), (31, 6), (34, 6), (21, 13), (31, 23), (19, 11), (18, 3), (13, 21), (19, 19), (26, 12), (28, 5), (29, 8), (34, 0), (19, 21), (28, 28), (34, 21), (28, 8), (10, 9), (33, 5), (8, 30), (17, 15), (20, 3), (4, 26), (14, 21), (19, 5), (12, 25), (17, 2), (24, 1), (20, 17), (0, 28), (19, 13), (35, 18), (15, 14), (19, 25), (15, 28), (11, 30), (17, 19), (26, 26), (2, 20), (16, 15), (20, 21), (28, 2), (13, 2), (25, 8), (17, 20), (14, 15), (34, 7), (1, 9), (3, 3), (5, 5), (11, 19), (20, 12), (22, 14), (6, 26), (14, 19), (19, 14), (15, 2), (32, 27), (30, 20), (0, 10), (32, 28), (3, 17), (30, 30), (9, 16), (2, 6), (23, 5), (15, 26), (20, 2), (18, 17), (27, 30), (22, 29), (13, 1), (6, 28), (7, 23), (31, 17), (16, 19), (16, 30), (29, 1), (7, 19), (21, 19), (21, 3), (20, 6), (28, 13), (24, 23), (11, 7), (22, 13), (14, 18), (10, 13), (9, 7), (7, 9), (8, 20), (25, 6), (33, 8), (3, 21), (30, 6), (29, 7), (4, 27), (7, 8), (17, 10), (35, 22), (5, 19), (16, 9), (15, 22), (7, 17), (9, 4), (23, 17), (6, 14), (11, 5), (12, 16), (6, 20), (30, 17), (2, 24), (24, 0), (21, 22), (7, 21), (25, 9), (24, 21), (23, 20), (23, 6), (32, 8), (12, 5), (21, 21), (8, 16), (4, 11), (13, 0), (7, 2), (11, 18), (3, 20), (7, 5), (28, 23), (32, 30), (20, 30), (26, 25), (8, 26), (7, 6), (14, 22), (1, 7), (26, 13), (16, 5), (13, 20), (23, 14), (12, 13), (0, 21), (30, 8), (3, 30), (7, 24), (35, 6), (32, 22), (20, 20), (17, 9), (5, 22), (9, 2), (32, 3), (15, 3), (30, 22), (20, 16), (1, 22), (8, 22), (6, 30), (4, 30), (33, 11), (15, 16), (6, 7), (13, 3), (23, 2), (15, 8), (28, 11), (8, 14), (12, 23), (21, 20), (2, 12), (29, 29), (35, 17), (8, 8), (23, 16), (12, 29), (15, 9), (9, 18), (23, 15), (3, 1), (30, 27), (18, 25), (33, 14), (34, 17), (34, 27), (3, 5), (28, 29), (31, 16), (0, 12), (6, 27), (3, 22), (11, 23), (28, 20), (12, 6), (23, 11), (5, 8), (27, 14), (27, 22), (35, 5), (2, 0), (11, 3), (29, 18), (27, 25), (7, 12), (13, 12), (9, 0), (22, 23), (35, 0), (16, 16), (1, 2), (0, 30), (11, 27), (27, 12), (9, 27), (18, 1), (3, 2), (23, 19), (29, 6), (3, 6), (20, 7), (1, 28), (25, 15), (25, 24), (19, 3), (10, 8), (17, 30), (31, 11), (10, 10), (29, 24), (11, 21), (32, 11), (17, 0), (15, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "593160", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (5, 4), (17, 9), (18, 0), (19, 6), (1, 19), (25, 28), (17, 7), (17, 26), (30, 1), (11, 31), (6, 22), (0, 14), (22, 27), (12, 9), (30, 17), (14, 17), (28, 2), (22, 10), (30, 13), (17, 1), (28, 15), (29, 15), (21, 31), (15, 3), (22, 14), (20, 27), (8, 10), (31, 3), (18, 14), (16, 12), (7, 31), (31, 24), (14, 25), (15, 24), (32, 25), (9, 28), (2, 17), (11, 21), (25, 0), (11, 19), (10, 5), (24, 9), (31, 30), (17, 25), (3, 24), (17, 10), (9, 0), (15, 27), (13, 5), (28, 30), (6, 6), (1, 7), (30, 31), (19, 5), (26, 12), (24, 22), (7, 7), (30, 15), (12, 31), (22, 22), (4, 1), (8, 14), (23, 16), (24, 20), (29, 5), (26, 0), (17, 2), (10, 9), (21, 13), (11, 18), (7, 5), (22, 7), (9, 18), (6, 21), (34, 1), (7, 25), (24, 28), (9, 12), (30, 27), (14, 14), (4, 19), (6, 2), (15, 13), (19, 8), (8, 9), (19, 31), (1, 1), (14, 6), (10, 4), (10, 18), (20, 22), (5, 5), (22, 1), (26, 23), (21, 10), (16, 9), (33, 27), (3, 26), (15, 0), (30, 26), (0, 20), (11, 2), (15, 2), (32, 7), (4, 30), (30, 12), (16, 0), (1, 22), (4, 27), (4, 2), (19, 28), (6, 10), (4, 13), (2, 22), (24, 11), (6, 11), (8, 22), (29, 22), (20, 26), (33, 7), (18, 5), (21, 14), (27, 27), (16, 3), (27, 4), (10, 15), (10, 11), (28, 5), (21, 0), (22, 26), (26, 3), (25, 17), (3, 1), (12, 25), (3, 25), (21, 15), (7, 30), (21, 12), (7, 23), (23, 29), (3, 13), (22, 18), (2, 3), (23, 10), (32, 18), (0, 30), (21, 16), (24, 32), (0, 17), (12, 2), (33, 6), (28, 24), (30, 30), (33, 32), (16, 21), (14, 27), (27, 17), (34, 26), (12, 27), (10, 1), (13, 13), (7, 29), (27, 28), (31, 21), (12, 30), (10, 8), (15, 18), (23, 9), (14, 18), (4, 18), (30, 18), (29, 24), (25, 11), (30, 8), (11, 7), (26, 1), (6, 31), (7, 17), (7, 12), (13, 11), (21, 23), (22, 5), (34, 18), (29, 28), (26, 32), (16, 22), (9, 31), (13, 1), (25, 32), (10, 17), (4, 16), (5, 27), (21, 18), (23, 0), (16, 26), (16, 25), (9, 11), (16, 32), (29, 1), (21, 25), (5, 18), (30, 28), (34, 14), (34, 19), (15, 32), (4, 26), (6, 24), (9, 16), (0, 1), (20, 6), (20, 1), (4, 14), (31, 14), (9, 9), (19, 19), (2, 31), (12, 17), (8, 11), (13, 20), (15, 14), (0, 16), (31, 31), (26, 22), (10, 6), (7, 19), (11, 27), (11, 1), (29, 32), (24, 19), (6, 19), (29, 13), (25, 23), (13, 8), (31, 28), (25, 12), (24, 29), (12, 26), (20, 4), (32, 31), (11, 12), (9, 30), (17, 28), (22, 16), (29, 9), (0, 22), (26, 14), (18, 32), (20, 20), (9, 20), (12, 1), (32, 20), (11, 8), (9, 8), (23, 20), (28, 6), (15, 4), (34, 8), (9, 25), (12, 8), (23, 31), (14, 26), (2, 26), (33, 1), (30, 0), (17, 21), (28, 10), (6, 26), (28, 28), (18, 28), (28, 12), (2, 30), (3, 4), (27, 18), (0, 7), (12, 3), (33, 12), (4, 6), (2, 11), (20, 2), (20, 14), (32, 6), (14, 1), (2, 29), (31, 1), (22, 31), (30, 19), (20, 32), (22, 30), (24, 5), (3, 10), (4, 24), (18, 22), (31, 0), (32, 21), (24, 10), (24, 17), (29, 30), (18, 16), (25, 2), (11, 20), (6, 13), (33, 0), (12, 29), (11, 10), (30, 20), (4, 20), (19, 17), (13, 6), (22, 23), (14, 12), (23, 27), (12, 21), (9, 27), (5, 22), (0, 29), (20, 21), (14, 9), (2, 12), (29, 11), (2, 5), (22, 25), (21, 21), (15, 25), (6, 32), (9, 26), (10, 7), (11, 29), (6, 25), (5, 15), (5, 30), (8, 25), (3, 14), (19, 2), (30, 6), (31, 19), (23, 18), (18, 23), (13, 31), (29, 18), (22, 21), (19, 24), (5, 26), (16, 31), (6, 0), (32, 23), (2, 4), (4, 4), (1, 11), (12, 12), (18, 4), (17, 14), (14, 22), (23, 22), (10, 19), (12, 4), (2, 18), (17, 16), (4, 9), (26, 27), (17, 24), (33, 28), (3, 17), (2, 20), (18, 17), (0, 28), (12, 28), (5, 9), (8, 0), (8, 5), (3, 3), (2, 21), (9, 14), (2, 27), (3, 15), (23, 28), (29, 3), (20, 15), (4, 3), (4, 29), (27, 10), (22, 20), (4, 23), (25, 31), (8, 6), (30, 2), (11, 26), (18, 13), (15, 7), (0, 15), (14, 0), (7, 3), (0, 21), (19, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "876960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 7), (17, 0), (22, 26), (9, 14), (4, 12), (8, 10), (6, 15), (33, 8), (0, 4), (11, 16), (27, 11), (10, 19), (31, 8), (1, 8), (14, 4), (33, 22), (33, 25), (2, 2), (19, 29), (27, 0), (27, 29), (9, 7), (2, 11), (21, 13), (33, 6), (15, 13), (21, 3), (15, 5), (24, 1), (9, 3), (29, 21), (20, 24), (15, 20), (12, 22), (19, 23), (26, 6), (7, 21), (27, 27), (2, 27), (17, 1), (24, 11), (9, 0), (7, 0), (0, 16), (22, 8), (4, 29), (31, 13), (18, 28), (32, 18), (26, 2), (32, 4), (24, 5), (25, 13), (30, 8), (9, 25), (15, 19), (11, 25), (20, 27), (12, 18), (9, 13), (2, 23), (12, 29), (28, 5), (32, 3), (12, 7), (24, 21), (8, 16), (7, 8), (14, 26), (28, 8), (7, 12), (29, 16), (9, 2), (10, 25), (10, 5), (17, 29), (19, 28), (15, 12), (31, 23), (9, 23), (5, 15), (16, 27), (28, 17), (17, 2), (1, 17), (28, 20), (33, 16), (2, 6), (13, 5), (17, 25), (8, 14), (20, 7), (16, 18), (30, 17), (22, 5), (26, 24), (6, 24), (22, 12), (8, 8), (6, 12), (14, 8), (1, 2), (26, 5), (26, 28), (33, 1), (8, 21), (15, 9), (31, 27), (11, 14), (29, 10), (24, 16), (17, 26), (23, 15), (31, 7), (2, 22), (3, 4), (23, 4), (1, 12), (29, 15), (7, 3), (18, 9), (2, 16), (25, 12), (19, 8), (20, 4), (26, 23), (32, 22), (10, 0), (24, 4), (26, 13), (18, 1), (30, 0), (6, 22), (12, 20), (24, 18), (21, 12), (28, 26), (12, 3), (2, 8), (33, 0), (6, 4), (3, 10), (11, 2), (16, 4), (0, 8), (3, 14), (24, 23), (24, 28), (25, 21), (11, 0), (27, 8), (1, 20), (18, 20), (14, 24), (25, 10), (33, 7), (34, 23), (16, 24), (31, 18), (21, 0), (29, 18), (7, 15), (19, 7), (2, 0), (0, 15), (1, 18), (17, 7), (15, 15), (28, 0), (33, 3), (24, 13), (10, 9), (28, 15), (11, 21), (16, 20), (9, 9), (20, 18), (5, 8), (12, 11), (31, 12), (21, 18), (0, 23), (6, 29), (30, 21), (23, 19), (33, 10), (15, 11), (5, 25), (27, 6), (13, 24), (14, 27), (13, 26), (27, 26), (5, 28), (34, 25), (2, 24), (31, 21), (31, 6), (6, 8), (5, 2), (27, 10), (11, 20), (5, 10), (25, 1), (16, 10), (19, 24), (5, 9), (11, 6), (6, 16), (5, 3), (33, 29), (8, 17), (29, 9), (11, 11), (19, 0), (32, 24), (25, 4), (9, 5), (9, 26), (19, 15), (30, 9), (12, 21), (23, 11), (5, 26), (26, 10), (1, 27), (28, 23), (28, 19), (33, 15), (33, 12), (6, 10), (7, 6), (18, 23), (31, 22), (3, 21), (14, 11), (13, 27), (12, 4), (33, 18), (1, 29), (25, 7), (2, 5), (15, 27), (12, 10), (20, 29), (8, 9), (24, 9), (1, 28), (6, 23), (16, 1), (3, 27), (3, 9), (21, 19), (13, 20), (32, 28), (4, 13), (7, 7), (0, 9), (26, 21), (12, 1), (18, 17), (33, 26), (34, 9), (23, 9), (10, 1), (2, 13), (22, 9), (29, 20), (18, 11), (19, 10), (18, 16), (28, 21), (3, 13), (34, 10), (10, 6), (10, 8), (32, 21), (18, 6), (26, 27), (13, 17), (29, 4), (9, 16), (8, 25), (14, 18), (30, 15), (2, 7), (7, 25), (0, 11), (14, 6), (3, 23), (25, 24), (14, 22), (10, 3), (2, 20), (14, 12), (32, 17), (30, 24), (12, 27), (20, 9), (3, 28), (16, 25), (12, 19), (18, 29), (23, 5), (4, 0), (13, 25), (15, 22), (28, 25), (28, 29), (9, 10), (16, 7), (16, 17), (15, 0), (0, 13), (21, 16), (14, 3), (6, 0), (17, 9), (11, 1), (34, 20), (24, 12), (0, 29), (12, 14), (33, 2), (3, 25), (19, 16), (11, 17), (28, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872352", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 7), (21, 2), (8, 21), (14, 26), (22, 21), (6, 3), (18, 28), (21, 0), (13, 10), (0, 1), (8, 22), (33, 30), (6, 10), (10, 17), (4, 6), (32, 24), (18, 33), (19, 19), (3, 6), (5, 15), (16, 37), (28, 3), (24, 20), (26, 18), (16, 7), (9, 27), (23, 1), (15, 27), (19, 20), (23, 37), (10, 7), (18, 31), (11, 1), (18, 12), (15, 28), (28, 35), (11, 36), (6, 34), (28, 24), (7, 10), (28, 10), (9, 11), (33, 18), (29, 9), (31, 13), (10, 22), (15, 16), (32, 15), (5, 29), (15, 20), (15, 2), (10, 20), (16, 14), (5, 19), (17, 18), (8, 28), (26, 9), (5, 6), (3, 16), (29, 19), (23, 32), (3, 38), (7, 12), (33, 33), (30, 15), (2, 26), (5, 2), (4, 38), (1, 26), (26, 23), (9, 37), (9, 34), (18, 9), (12, 3), (19, 9), (8, 29), (19, 34), (22, 28), (22, 29), (4, 10), (22, 24), (18, 10), (29, 10), (16, 17), (17, 24), (31, 4), (18, 7), (18, 6), (32, 20), (9, 6), (30, 14), (4, 20), (23, 5), (3, 18), (29, 21), (33, 13), (8, 7), (11, 27), (1, 25), (0, 11), (33, 27), (26, 8), (2, 19), (6, 18), (21, 23), (25, 6), (8, 35), (21, 11), (28, 4), (27, 8), (19, 8), (10, 24), (26, 32), (8, 13), (17, 13), (29, 0), (9, 0), (9, 15), (26, 35), (24, 35), (25, 36), (5, 36), (22, 32), (2, 31), (7, 9), (2, 20), (2, 10), (15, 4), (5, 4), (22, 14), (3, 25), (17, 20), (14, 9), (16, 10), (0, 31), (6, 23), (7, 35), (19, 17), (25, 12), (33, 14), (33, 5), (15, 35), (6, 33), (31, 25), (3, 4), (30, 37), (11, 11), (32, 22), (18, 34), (3, 37), (31, 36), (14, 4), (26, 6), (31, 17), (12, 31), (2, 30), (23, 38), (6, 8), (17, 9), (20, 24), (1, 15), (22, 15), (12, 8), (31, 23), (22, 30), (15, 13), (12, 37), (12, 12), (10, 2), (29, 29), (2, 17), (14, 16), (9, 35), (24, 32), (2, 18), (8, 27), (0, 3), (26, 20), (0, 32), (30, 35), (13, 38), (5, 32), (28, 13), (25, 3), (26, 7), (15, 5), (24, 2), (7, 37), (20, 25), (23, 13), (26, 22), (12, 20), (15, 12), (31, 31), (32, 0), (30, 1), (32, 17), (24, 21), (27, 14), (20, 7), (19, 6), (28, 8), (27, 28), (24, 25), (10, 9), (1, 38), (14, 10), (17, 5), (12, 35), (7, 26), (20, 0), (29, 22), (28, 19), (1, 9), (31, 35), (12, 26), (33, 19), (24, 1), (20, 21), (3, 34), (16, 33), (0, 15), (12, 21), (23, 24), (20, 9), (19, 11), (31, 15), (17, 30), (30, 5), (2, 28), (13, 18), (18, 8), (13, 23), (31, 11), (18, 4), (22, 18), (29, 14), (23, 27), (33, 7), (3, 12), (10, 14), (16, 9), (5, 5), (11, 5), (17, 2), (4, 18), (20, 18), (13, 8), (18, 5), (6, 2), (6, 4), (11, 35), (33, 10), (5, 22), (22, 8), (23, 19), (13, 22), (30, 32), (4, 33), (16, 15), (27, 21), (0, 8), (30, 12), (28, 28), (17, 7), (27, 24), (9, 18), (13, 34), (25, 14), (17, 32), (28, 38), (20, 34), (19, 24), (27, 16), (25, 11), (31, 37), (30, 26), (21, 30), (6, 20), (0, 21), (30, 38), (8, 12), (2, 33), (24, 38), (23, 30), (20, 2), (5, 0), (4, 32), (20, 26), (9, 20), (1, 16), (24, 16), (25, 9), (17, 38), (15, 3), (27, 18), (0, 38), (4, 0), (2, 21), (6, 13), (19, 23), (5, 16), (3, 9), (10, 15), (14, 21), (24, 33), (1, 32), (30, 20), (33, 8), (12, 29), (15, 32), (22, 19), (22, 17), (9, 19), (33, 12), (24, 3), (8, 31), (16, 22), (20, 6), (12, 14), (3, 11), (15, 9), (14, 1), (28, 37), (29, 32), (12, 36), (18, 14), (3, 24), (24, 7), (8, 30), (13, 2), (14, 38), (16, 24), (23, 31), (5, 38), (12, 17), (3, 26), (5, 20), (4, 34), (31, 24), (28, 0), (25, 2), (20, 20), (11, 28), (10, 25), (20, 14), (11, 7), (2, 16), (7, 5), (14, 34), (23, 10), (0, 10), (24, 12), (11, 33), (15, 37), (6, 31), (32, 35), (7, 33), (22, 16), (8, 0), (1, 37), (12, 9), (9, 1), (27, 5), (24, 31), (2, 3), (17, 36), (15, 33), (14, 17), (17, 23), (0, 28), (30, 0), (28, 7), (27, 0), (1, 17), (29, 18), (16, 21), (8, 9), (18, 29), (17, 14), (15, 10), (19, 7), (20, 30), (23, 35), (29, 26), (11, 21), (22, 37), (30, 28), (8, 25), (13, 7), (23, 6), (6, 35), (21, 31), (8, 2), (4, 7), (0, 4), (3, 30), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925344", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), 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), (5, 25), (14, 7), (10, 25), (15, 28), (9, 11), (13, 17), (9, 9), (17, 22), (20, 8), (24, 29), (22, 6), (4, 31), (29, 18), (30, 33), (0, 16), (7, 31), (5, 5), (23, 34), (27, 26), (11, 8), (0, 10), (25, 5), (29, 11), (19, 34), (13, 34), (14, 14), (22, 27), (26, 15), (2, 10), (22, 13), (11, 18), (1, 35), (10, 32), (5, 17), (19, 17), (9, 10), (11, 2), (14, 24), (14, 10), (28, 34), (29, 16), (23, 20), (24, 30), (29, 26), (15, 31), (5, 32), (15, 20), (22, 29), (13, 4), (16, 25), (15, 6), (28, 13), (11, 5), (31, 23), (17, 27), (8, 15), (23, 28), (8, 5), (30, 21), (29, 9), (5, 6), (18, 33), (15, 22), (5, 4), (26, 12), (21, 22), (1, 34), (19, 31), (10, 12), (1, 18), (21, 21), (17, 10), (23, 25), (15, 32), (3, 25), (13, 23), (17, 12), (20, 0), (12, 30), (22, 32), (4, 19), (17, 1), (25, 31), (31, 10), (25, 26), (19, 9), (2, 2), (16, 15), (6, 2), (1, 32), (24, 25), (4, 21), (8, 6), (24, 20), (16, 0), (22, 9), (10, 1), (17, 18), (10, 9), (17, 26), (20, 24), (14, 0), (1, 7), (12, 32), (9, 15), (18, 1), (2, 17), (25, 16), (27, 23), (16, 34), (17, 35), (10, 8), (26, 30), (19, 21), (31, 8), (16, 14), (13, 33), (25, 9), (2, 7), (8, 12), (4, 12), (12, 18), (24, 11), (10, 3), (3, 11), (12, 13), (7, 30), (12, 19), (31, 5), (24, 5), (6, 14), (28, 21), (3, 33), (17, 16), (28, 4), (2, 1), (15, 16), (8, 8), (21, 18), (16, 3), (20, 14), (20, 11), (13, 15), (13, 19), (14, 22), (24, 33), (21, 16), (7, 3), (0, 13), (14, 23), (9, 31), (8, 24), (10, 23), (23, 18), (19, 14), (5, 19), (25, 6), (3, 13), (0, 3), (0, 29), (16, 33), (26, 35), (12, 14), (29, 30), (23, 12), (17, 4), (28, 0), (4, 2), (10, 11), (2, 29), (14, 21), (21, 17), (12, 5), (17, 9), (28, 8), (13, 11), (19, 11), (23, 32), (5, 35), (6, 30), (20, 10), (20, 15), (9, 21), (16, 17), (27, 29), (20, 2), (31, 14), (3, 18), (12, 31), (7, 16), (21, 25), (0, 14), (5, 21), (5, 30), (6, 28), (7, 17), (14, 13), (20, 26), (11, 13), (15, 7), (13, 25), (10, 24), (30, 15), (30, 30), (29, 5), (11, 33), (31, 1), (14, 5), (7, 27), (3, 4), (8, 20), (8, 17), (12, 34), (3, 26), (16, 2), (28, 2), (20, 34), (31, 12), (4, 35), (19, 32), (18, 0), (6, 26), (15, 25), (10, 6), (19, 19), (17, 21), (7, 7), (10, 2), (7, 11), (7, 28), (13, 6), (19, 5), (23, 35), (21, 14), (26, 25), (26, 16), (31, 22), (29, 1), (3, 32), (23, 1), (0, 24), (28, 23), (1, 30), (29, 25), (9, 12), (31, 24), (21, 31), (18, 27), (12, 12), (17, 30), (18, 8), (25, 23), (1, 20), (22, 0), (6, 3), (29, 8), (1, 5), (5, 33), (5, 22), (26, 32), (6, 5), (18, 2), (1, 13), (18, 16), (11, 10), (29, 12), (1, 27), (23, 4), (4, 14), (11, 7), (15, 12), (11, 31), (27, 22), (15, 34), (7, 21), (15, 35), (23, 10), (18, 9), (30, 1), (2, 4), (21, 3), (27, 24), (17, 13), (10, 16), (3, 29), (1, 9), (26, 22), (30, 34), (15, 30), (3, 31), (11, 32), (7, 15), (14, 3), (28, 27), (12, 6), (12, 7), (6, 22), (1, 31), (23, 19), (24, 34), (8, 14), (9, 4), (6, 18), (20, 5), (28, 19), (5, 26), (25, 35), (8, 9), (29, 13), (26, 0), (7, 9), (8, 29), (25, 21), (3, 2), (25, 15), (30, 17), (25, 20), (1, 6), (13, 29), (17, 2), (11, 23), (24, 7), (22, 28), (1, 17), (9, 28), (20, 29), (11, 16), (0, 35), (24, 3), (8, 7), (11, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "247280", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 14), (19, 9), (31, 18), (16, 2), (12, 13), (23, 0), (35, 22), (26, 11), (36, 11), (7, 16), (3, 31), (19, 32), (4, 19), (36, 21), (18, 13), (24, 11), (2, 11), (34, 26), (21, 29), (20, 14), (37, 10), (10, 9), (9, 7), (0, 4), (10, 19), (9, 23), (1, 2), (16, 29), (2, 23), (33, 28), (17, 26), (27, 14), (4, 15), (29, 1), (2, 22), (37, 8), (27, 1), (35, 24), (29, 24), (27, 26), (30, 25), (21, 30), (0, 23), (14, 22), (3, 19), (13, 15), (0, 9), (24, 24), (23, 5), (17, 4), (3, 30), (17, 3), (33, 11), (3, 29), (17, 19), (29, 11), (19, 34), (28, 16), (17, 32), (26, 15), (11, 14), (34, 14), (36, 1), (35, 8), (16, 10), (21, 4), (31, 10), (1, 24), (3, 5), (15, 9), (3, 17), (35, 6), (11, 22), (6, 21), (29, 29), (30, 30), (8, 1), (9, 22), (29, 21), (28, 25), (20, 19), (21, 9), (11, 18), (25, 30), (2, 16), (21, 26), (0, 16), (14, 21), (11, 20), (3, 23), (27, 15), (10, 31), (24, 9), (8, 11), (8, 32), (18, 18), (5, 16), (12, 15), (0, 34), (21, 14), (14, 29), (26, 17), (14, 33), (30, 5), (0, 10), (18, 30), (9, 18), (36, 28), (32, 24), (34, 27), (1, 17), (31, 29), (8, 27), (1, 12), (9, 33), (31, 12), (9, 14), (18, 26), (5, 17), (25, 14), (23, 15), (0, 30), (15, 4), (9, 25), (31, 17), (31, 8), (2, 34), (27, 17), (35, 17), (7, 22), (25, 12), (30, 23), (34, 18), (4, 32), (24, 18), (25, 15), (11, 15), (16, 9), (22, 2), (12, 22), (37, 17), (13, 1), (24, 2), (9, 4), (10, 5), (27, 20), (35, 14), (2, 32), (18, 23), (10, 12), (17, 0), (26, 9), (16, 27), (2, 33), (1, 29), (15, 16), (16, 16), (22, 33), (24, 5), (18, 4), (20, 13), (25, 13), (2, 26), (3, 3), (32, 27), (36, 30), (33, 23), (36, 20), (17, 6), (13, 12), (27, 10), (31, 27), (32, 7), (10, 22), (10, 16), (22, 25), (2, 10), (14, 17), (33, 26), (1, 8), (4, 28), (14, 27), (14, 8), (1, 18), (17, 34), (16, 6), (5, 18), (23, 13), (29, 6), (11, 28), (11, 33), (17, 17), (17, 14), (22, 1), (10, 25), (19, 16), (3, 22), (29, 3), (30, 2), (29, 22), (26, 4), (21, 22), (34, 8), (30, 14), (7, 30), (22, 13), (18, 25), (30, 7), (6, 26), (37, 25), (11, 30), (35, 29), (0, 26), (7, 3), (37, 30), (3, 12), (26, 26), (4, 6), (24, 4), (12, 27), (28, 24), (23, 22), (35, 3), (2, 14), (16, 13), (16, 15), (0, 6), (13, 29), (9, 10), (31, 15), (19, 29), (0, 11), (4, 13), (21, 28), (29, 14), (31, 3), (3, 26), (37, 7), (24, 22), (17, 1), (35, 27), (21, 15), (12, 5), (37, 12), (11, 6), (22, 0), (36, 18), (25, 26), (23, 16), (6, 32), (9, 31), (26, 30), (34, 17), (23, 29), (24, 27), (20, 12), (9, 21), (33, 17), (19, 15), (19, 7), (18, 3), (23, 14), (15, 3), (33, 0), (34, 33), (29, 19), (17, 10), (17, 18), (15, 7), (34, 5), (15, 31), (27, 5), (1, 31), (22, 14), (18, 32), (14, 26), (8, 26), (10, 14), (6, 28), (29, 17), (16, 17), (33, 9), (15, 24), (25, 6), (2, 6), (11, 2), (23, 17), (6, 11), (14, 10), (1, 1), (22, 19), (12, 20), (29, 13), (21, 34), (25, 11), (28, 12), (6, 2), (33, 10), (19, 27), (23, 21), (5, 5), (15, 6), (10, 30), (28, 18), (6, 25), (8, 6), (24, 23), (2, 29), (33, 19), (34, 31), (18, 28), (4, 12), (0, 27), (37, 22), (15, 23), (27, 28), (10, 3), (30, 10), (32, 18), (26, 6), (11, 25), (11, 1), (8, 12), (5, 31), (5, 29), (26, 25), (19, 1), (9, 0), (4, 1), (13, 16), (37, 6), (0, 18), (28, 34), (36, 23), (9, 24), (35, 9), (11, 4), (5, 15), (34, 4), (30, 11), (17, 15), (25, 28), (19, 24), (23, 6), (10, 13), (37, 28), (15, 11), (0, 22), (1, 15), (17, 24), (9, 9), (11, 16), (13, 0), (18, 14), (8, 20), (18, 9), (30, 32), (14, 14), (26, 22), (2, 20), (7, 20), (8, 33), (32, 20), (22, 10), (2, 7), (13, 3), (8, 22), (27, 24), (12, 12), (25, 20), (24, 8), (15, 34), (31, 25), (15, 25), (5, 30), (15, 14), (22, 34), (22, 17), (12, 6), (3, 21), (2, 3), (5, 24), (20, 18), (9, 6), (34, 30), (4, 29), (8, 10), (7, 26), (27, 31), (36, 16), (30, 26), (20, 10), (25, 3), (31, 9), (16, 32), (34, 24), (21, 2), (26, 0), (23, 3), (37, 33), (4, 11), (9, 1), (12, 32), (14, 7), (4, 20), (26, 33), (27, 21), (12, 10), (16, 12), (0, 2), (34, 10), (19, 13), (31, 2), (20, 15), (12, 7), (23, 32), (33, 8), (9, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48195", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 3), (8, 14), (23, 8), (33, 9), (19, 30), (3, 27), (26, 32), (0, 20), (4, 19), (32, 7), (32, 26), (20, 12), (33, 1), (35, 8), (38, 31), (38, 10), (4, 37), (20, 14), (11, 12), (17, 30), (13, 37), (10, 22), (38, 25), (25, 7), (10, 27), (24, 4), (21, 24), (24, 0), (20, 6), (19, 14), (11, 19), (2, 31), (20, 34), (3, 0), (34, 2), (22, 20), (17, 5), (10, 4), (12, 28), (27, 10), (15, 28), (13, 15), (22, 2), (24, 37), (31, 33), (0, 9), (27, 29), (8, 32), (6, 16), (32, 21), (32, 8), (16, 35), (22, 28), (34, 3), (18, 18), (22, 25), (34, 18), (18, 34), (36, 9), (31, 1), (5, 26), (8, 15), (4, 36), (20, 36), (11, 34), (16, 31), (32, 35), (38, 4), (30, 36), (27, 12), (27, 33), (36, 19), (25, 35), (32, 11), (37, 30), (30, 5), (36, 35), (25, 37), (32, 12), (24, 12), (10, 32), (27, 4), (25, 22), (33, 30), (14, 27), (38, 32), (16, 14), (22, 6), (29, 9), (30, 16), (38, 2), (14, 24), (23, 33), (30, 7), (5, 27), (36, 33), (38, 21), (23, 35), (8, 13), (9, 14), (7, 3), (38, 26), (21, 18), (22, 9), (14, 13), (19, 22), (34, 6), (17, 24), (15, 1), (7, 29), (22, 36), (0, 6), (27, 17), (13, 1), (24, 15), (11, 37), (31, 24), (23, 12), (1, 1), (6, 2), (12, 13), (35, 15), (12, 10), (15, 4), (37, 6), (32, 23), (5, 3), (6, 31), (8, 28), (23, 30), (32, 25), (24, 33), (8, 16), (6, 28), (28, 0), (19, 0), (10, 0), (33, 6), (6, 25), (26, 33), (3, 20), (12, 30), (30, 12), (3, 1), (24, 11), (9, 37), (25, 34), (21, 28), (27, 19), (5, 5), (2, 14), (9, 1), (26, 28), (1, 25), (14, 30), (16, 2), (10, 11), (11, 15), (21, 30), (13, 24), (19, 27), (18, 8), (21, 1), (36, 0), (30, 1), (28, 8), (12, 23), (0, 36), (37, 15), (34, 35), (7, 16), (22, 7), (8, 18), (12, 4), (10, 18), (1, 9), (23, 27), (12, 25), (5, 11), (14, 20), (1, 13), (10, 8), (36, 14), (25, 21), (17, 23), (10, 16), (23, 32), (31, 37), (33, 36), (27, 9), (6, 18), (20, 22), (25, 24), (35, 12), (37, 24), (18, 16), (32, 0), (5, 20), (13, 16), (16, 20), (12, 21), (32, 32), (20, 21), (6, 26), (19, 15), (31, 35), (14, 18), (16, 33), (9, 36), (7, 14), (31, 36), (24, 18), (14, 15), (2, 23), (38, 12), (19, 11), (11, 18), (35, 32), (5, 18), (33, 37), (9, 2), (34, 5), (29, 15), (10, 26), (24, 22), (15, 14), (4, 27), (3, 3), (28, 2), (24, 24), (37, 27), (32, 16), (29, 29), (27, 26), (28, 13), (19, 7), (21, 0), (15, 23), (7, 9), (29, 18), (37, 8), (36, 12), (22, 32), (17, 15), (4, 34), (6, 4), (18, 23), (23, 19), (37, 28), (19, 20), (17, 1), (5, 19), (6, 35), (12, 20), (1, 33), (24, 21), (37, 23), (27, 22), (3, 8), (21, 15), (19, 29), (24, 27), (24, 26), (37, 25), (18, 2), (6, 29), (0, 23), (15, 2), (3, 34), (29, 7), (7, 22), (13, 35), (24, 35), (20, 8), (38, 36), (9, 3), (38, 1), (12, 34), (8, 17), (14, 23), (7, 34), (14, 19), (7, 36), (32, 1), (22, 4), (8, 34), (15, 24), (5, 16), (31, 7), (11, 7), (23, 7), (36, 25), (27, 15), (20, 17), (30, 37), (36, 13), (33, 3), (4, 9), (21, 26), (35, 18), (26, 2), (19, 2), (10, 37), (9, 4), (1, 11), (26, 11), (9, 23), (26, 25), (25, 23), (29, 11), (27, 25), (20, 28), (26, 37), (5, 36), (30, 2), (14, 10), (22, 23), (27, 34), (31, 11), (18, 17), (29, 14), (33, 12), (22, 29), (11, 11), (0, 21), (32, 29), (1, 31), (7, 11), (22, 27), (0, 24), (20, 29), (16, 27), (10, 9), (29, 34), (11, 3), (21, 34), (11, 4), (6, 11), (34, 24), (28, 3), (5, 25), (34, 29), (15, 12), (25, 14), (25, 5), (2, 3), (37, 22), (2, 29), (36, 23), (25, 1), (29, 23), (22, 24), (19, 17), (2, 26), (31, 19), (8, 25), (18, 32), (30, 24), (29, 21), (6, 0), (8, 0), (33, 2), (10, 24), (27, 13), (36, 37), (31, 22), (7, 10), (20, 3), (7, 20), (4, 25), (3, 4), (16, 0), (11, 20), (2, 32), (33, 27), (29, 20), (28, 25), (30, 0), (31, 23), (18, 33), (30, 29), (2, 33), (37, 4), (34, 36), (23, 23), (30, 10), (10, 21), (19, 19), (14, 1), (22, 12), (9, 34), (3, 24), (9, 13), (11, 6), (38, 22), (8, 22), (17, 21), (4, 35), (31, 18), (4, 31), (29, 19), (36, 36), (20, 25), (28, 7), (1, 24), (34, 30), (17, 2), (1, 0), (4, 3), (12, 22), (26, 20), (6, 37), (12, 26), (31, 29), (9, 19), (7, 33), (30, 19), (1, 5), (22, 5), (25, 16), (8, 36), (7, 30), (34, 37), (34, 9), (29, 30), (30, 14), (13, 31), (36, 21), (34, 15), (25, 27), (38, 17), (32, 3), (29, 17), (6, 10), (15, 27), (25, 20), (10, 2), (9, 7), (33, 18), (1, 30), (33, 5), (36, 27), (28, 30), (14, 3), (6, 30), (23, 28), (2, 27), (3, 33), (10, 23), (9, 17), (6, 5), (19, 1), (12, 8), (29, 28), (34, 27), (2, 22), (5, 29), (6, 6), (25, 26), (26, 35), (15, 36), (16, 11), (27, 30), (0, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "993384", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 30), (0, 29), (24, 19), (4, 20), (23, 18), (15, 5), (1, 21), (25, 16), (1, 0), (34, 8), (22, 9), (32, 27), (28, 11), (32, 21), (7, 27), (24, 15), (12, 1), (5, 26), (30, 1), (9, 9), (21, 21), (18, 13), (25, 29), (26, 8), (2, 7), (1, 3), (25, 6), (22, 28), (24, 26), (3, 25), (29, 4), (3, 5), (1, 7), (0, 4), (24, 30), (28, 7), (30, 2), (7, 13), (6, 9), (3, 29), (26, 3), (22, 22), (23, 30), (24, 4), (21, 8), (30, 11), (15, 3), (7, 12), (20, 27), (18, 29), (23, 9), (33, 0), (8, 25), (11, 12), (5, 30), (30, 20), (0, 10), (5, 25), (12, 13), (33, 27), (19, 10), (10, 3), (16, 2), (29, 29), (11, 7), (16, 17), (34, 18), (24, 20), (5, 16), (5, 12), (1, 11), (8, 15), (14, 18), (17, 5), (17, 17), (22, 14), (22, 24), (0, 28), (20, 24), (29, 7), (16, 9), (2, 10), (1, 23), (19, 3), (29, 8), (27, 2), (34, 2), (33, 21), (23, 21), (16, 11), (19, 23), (0, 26), (18, 20), (32, 7), (11, 20), (21, 5), (26, 0), (28, 30), (34, 10), (22, 29), (18, 15), (6, 26), (7, 0), (12, 6), (24, 18), (20, 16), (19, 19), (24, 25), (8, 1), (13, 9), (31, 30), (29, 11), (9, 6), (2, 22), (5, 17), (3, 6), (17, 0), (20, 7), (11, 14), (5, 7), (18, 8), (30, 18), (4, 5), (32, 15), (13, 27), (19, 0), (11, 27), (13, 15), (17, 21), (20, 6), (27, 21), (9, 26), (27, 6), (14, 13), (12, 29), (0, 5), (9, 14), (34, 16), (6, 0), (23, 11), (32, 1), (25, 18), (0, 25), (2, 29), (6, 5), (32, 4), (31, 23), (16, 5), (11, 4), (26, 10), (18, 4), (13, 1), (23, 25), (8, 21), (15, 26), (27, 25), (12, 11), (26, 7), (2, 24), (14, 0), (1, 29), (12, 18), (18, 7), (34, 25), (23, 8), (25, 8), (1, 20), (23, 28), (10, 19), (6, 14), (18, 24), (0, 12), (3, 8), (15, 9), (4, 4), (31, 24), (26, 17), (12, 3), (19, 11), (5, 9), (15, 29), (1, 2), (10, 27), (4, 8), (17, 25), (33, 28), (20, 14), (13, 18), (31, 21), (6, 28), (14, 29), (22, 15), (1, 6), (14, 3), (23, 5), (31, 4), (7, 24), (11, 15), (9, 27), (11, 29), (4, 2), (6, 6), (31, 2), (23, 13), (2, 26), (32, 17), (16, 8), (29, 13), (29, 21), (23, 6), (11, 30), (17, 27), (0, 27), (18, 18), (7, 22), (34, 12), (25, 15), (1, 17), (24, 13), (23, 16), (22, 8), (3, 18), (20, 19), (19, 15), (6, 16), (27, 13), (14, 24), (19, 18), (29, 24), (22, 19), (29, 20), (5, 13), (19, 25), (6, 24), (9, 11), (21, 1), (25, 11), (7, 29), (19, 24), (26, 22), (18, 16), (16, 13), (10, 14), (22, 1), (14, 12), (13, 19), (22, 17), (29, 27), (27, 28), (4, 13), (31, 26), (17, 28), (22, 11), (20, 21), (10, 10), (14, 14), (9, 24), (34, 22), (33, 18), (1, 14), (31, 20), (20, 17), (25, 28), (16, 19), (3, 13), (4, 30), (20, 28), (12, 23), (21, 28), (24, 27), (5, 28), (3, 2), (24, 9), (22, 30), (28, 10), (20, 26), (27, 15), (7, 20), (27, 7), (20, 15), (27, 1), (6, 17), (1, 15), (25, 24), (4, 28), (5, 21), (27, 20), (28, 6), (30, 13), (32, 10), (3, 28), (2, 18), (6, 18), (26, 12), (11, 22), (18, 28), (12, 14), (9, 15), (18, 23), (10, 4), (19, 28), (1, 8), (12, 8), (14, 17), (6, 27), (31, 1), (30, 24), (3, 23), (26, 21), (9, 1), (19, 13), (28, 17), (12, 9), (20, 30), (1, 18), (18, 22), (28, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269460", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 6), (34, 29), (4, 26), (17, 23), (4, 33), (34, 16), (13, 29), (4, 25), (20, 9), (28, 10), (14, 2), (10, 23), (12, 19), (4, 36), (31, 19), (14, 6), (14, 36), (22, 3), (5, 17), (28, 11), (37, 19), (37, 29), (17, 29), (34, 17), (9, 32), (17, 26), (29, 19), (28, 25), (20, 6), (23, 12), (27, 32), (8, 34), (29, 20), (27, 13), (9, 22), (1, 3), (7, 17), (22, 32), (35, 9), (31, 5), (6, 33), (35, 5), (24, 18), (26, 18), (28, 36), (6, 6), (35, 3), (4, 16), (5, 34), (7, 1), (19, 14), (13, 18), (21, 2), (6, 1), (16, 28), (23, 36), (19, 12), (1, 32), (2, 16), (16, 11), (31, 6), (10, 33), (11, 30), (10, 14), (0, 4), (36, 9), (30, 12), (27, 30), (9, 24), (25, 23), (15, 1), (5, 28), (31, 20), (16, 24), (14, 34), (32, 14), (8, 14), (29, 8), (36, 30), (28, 21), (11, 5), (3, 15), (12, 1), (31, 34), (37, 35), (36, 0), (31, 9), (18, 26), (27, 28), (21, 10), (19, 11), (3, 14), (11, 0), (37, 4), (7, 14), (0, 26), (16, 0), (35, 20), (23, 14), (22, 10), (38, 11), (34, 1), (22, 15), (7, 6), (16, 23), (22, 14), (5, 9), (26, 21), (31, 29), (3, 6), (2, 21), (22, 24), (15, 9), (36, 33), (27, 16), (10, 2), (6, 0), (35, 21), (21, 15), (37, 16), (7, 20), (21, 13), (25, 31), (22, 26), (4, 6), (27, 17), (33, 8), (32, 3), (5, 0), (24, 22), (10, 22), (11, 19), (3, 12), (4, 28), (6, 21), (2, 20), (2, 31), (34, 4), (4, 30), (0, 17), (6, 11), (25, 9), (37, 32), (18, 13), (25, 2), (18, 31), (24, 15), (25, 10), (4, 32), (27, 8), (13, 5), (8, 19), (26, 24), (14, 5), (31, 13), (24, 14), (11, 31), (30, 35), (2, 8), (12, 22), (6, 12), (34, 2), (36, 3), (9, 7), (26, 4), (14, 8), (16, 21), (24, 3), (7, 3), (35, 35), (34, 34), (31, 18), (15, 3), (17, 13), (18, 28), (3, 24), (33, 4), (36, 31), (7, 24), (30, 8), (20, 36), (30, 7), (17, 21), (17, 30), (4, 8), (20, 26), (1, 36), (6, 22), (3, 35), (3, 13), (24, 7), (36, 36), (30, 0), (2, 32), (26, 20), (24, 36), (3, 23), (9, 29), (0, 31), (28, 31), (26, 6), (32, 13), (31, 8), (32, 19), (20, 33), (11, 8), (8, 12), (9, 16), (22, 17), (34, 33), (8, 30), (16, 14), (31, 7), (28, 5), (35, 10), (24, 1), (24, 24), (16, 36), (8, 27), (22, 0), (19, 7), (4, 23), (37, 11), (16, 8), (25, 16), (12, 5), (35, 19), (16, 12), (36, 5), (13, 25), (15, 31), (3, 28), (26, 32), (9, 34), (8, 17), (35, 22), (26, 0), (9, 31), (37, 26), (16, 19), (8, 5), (32, 28), (13, 19), (27, 20), (37, 1), (10, 29), (30, 9), (2, 22), (26, 33), (34, 3), (23, 3), (32, 29), (15, 12), (6, 5), (4, 13), (26, 29), (6, 14), (25, 4), (36, 10), (9, 17), (12, 0), (19, 16), (33, 3), (31, 10), (24, 17), (14, 29), (4, 7), (26, 25), (6, 17), (10, 7), (28, 16), (35, 33), (29, 13), (30, 33), (2, 1), (15, 14), (1, 33), (14, 33), (24, 26), (23, 26), (30, 23), (36, 32), (10, 13), (30, 24), (37, 24), (29, 29), (15, 34), (16, 30), (16, 1), (36, 28), (0, 20), (21, 32), (33, 13), (27, 26), (12, 7), (11, 11), (34, 28), (23, 20), (20, 24), (21, 17), (2, 7), (1, 13), (0, 36), (33, 32), (9, 13), (36, 22), (14, 9), (11, 28), (16, 5), (12, 21), (3, 26), (22, 4), (24, 6), (14, 12), (19, 19), (0, 15), (12, 16), (21, 23), (15, 26), (7, 29), (7, 5), (6, 23), (1, 0), (16, 27), (5, 27), (22, 7), (11, 24), (1, 25), (5, 11), (9, 27), (12, 26), (3, 21), (24, 8), (3, 8), (8, 6), (10, 3), (3, 11), (30, 28), (21, 36), (31, 28), (6, 24), (0, 19), (6, 10), (21, 26), (5, 29), (6, 34), (13, 23), (23, 31), (18, 0), (20, 27), (17, 20), (24, 34), (7, 7), (27, 25), (25, 13), (11, 26), (20, 3), (5, 16), (25, 28), (8, 26), (29, 9), (18, 21), (22, 1), (11, 2), (4, 18), (21, 14), (34, 35), (2, 27), (22, 36), (38, 14), (29, 23), (5, 7), (28, 18), (9, 30), (27, 31), (20, 13), (33, 14), (15, 22), (31, 23), (6, 15), (12, 2), (17, 27), (22, 27), (12, 20), (28, 12), (30, 16), (30, 29), (33, 0), (12, 17), (30, 30), (25, 5), (18, 10), (37, 2), (35, 29), (4, 0), (5, 30), (11, 13), (1, 27), (11, 15), (24, 35), (31, 33), (38, 15), (22, 16), (33, 10), (36, 1), (28, 6), (24, 16), (12, 23), (15, 27), (28, 8), (12, 8), (16, 33), (17, 3), (28, 28), (8, 24), (3, 2), (2, 4), (33, 27), (6, 30), (19, 18), (2, 0), (33, 11), (24, 2), (17, 5), (13, 33), (14, 0), (4, 24), (25, 17), (22, 8), (33, 28), (25, 21), (33, 25), (33, 18), (27, 34), (36, 7), (23, 33), (6, 35), (32, 17), (17, 7), (36, 27), (34, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851904", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), 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), (4, 22), (10, 20), (18, 23), (12, 24), (23, 34), (1, 29), (25, 29), (9, 20), (1, 19), (10, 19), (5, 15), (15, 19), (13, 21), (15, 27), (14, 0), (22, 24), (2, 25), (9, 8), (5, 11), (10, 5), (16, 25), (0, 4), (13, 16), (12, 33), (23, 8), (3, 0), (19, 33), (10, 17), (18, 14), (15, 29), (25, 30), (22, 17), (10, 34), (27, 8), (27, 34), (27, 12), (8, 32), (4, 14), (15, 25), (26, 5), (17, 14), (30, 15), (0, 6), (30, 3), (27, 20), (23, 22), (12, 15), (22, 2), (17, 18), (5, 19), (15, 4), (10, 16), (25, 23), (11, 22), (1, 22), (19, 25), (4, 3), (27, 6), (24, 2), (21, 14), (1, 26), (0, 5), (13, 0), (16, 3), (10, 6), (25, 8), (28, 34), (13, 28), (4, 13), (2, 0), (29, 2), (17, 29), (6, 1), (15, 21), (6, 0), (25, 11), (21, 5), (20, 1), (29, 12), (16, 28), (20, 23), (30, 19), (0, 24), (10, 1), (22, 19), (29, 9), (24, 10), (21, 29), (9, 6), (23, 33), (28, 32), (1, 5), (22, 6), (8, 2), (19, 15), (6, 16), (11, 18), (24, 25), (28, 20), (22, 21), (9, 10), (12, 4), (22, 25), (3, 6), (25, 9), (30, 9), (1, 27), (13, 17), (26, 20), (2, 34), (30, 26), (27, 24), (24, 33), (9, 1), (19, 7), (10, 14), (26, 18), (1, 21), (28, 17), (24, 23), (10, 27), (6, 22), (23, 21), (7, 27), (5, 1), (7, 19), (15, 16), (18, 9), (30, 27), (2, 29), (7, 7), (28, 7), (23, 11), (2, 16), (9, 25), (5, 23), (28, 14), (17, 5), (27, 14), (14, 10), (25, 7), (18, 4), (0, 9), (13, 22), (20, 7), (11, 1), (0, 17), (5, 31), (21, 15), (19, 11), (7, 34), (25, 27), (15, 15), (4, 8), (8, 16), (3, 13), (3, 31), (14, 26), (29, 34), (9, 27), (2, 12), (7, 10), (16, 1), (13, 12), (0, 3), (13, 7), (19, 23), (21, 7), (29, 19), (28, 27), (20, 17), (8, 15), (7, 23), (21, 23), (17, 0), (27, 2), (5, 17), (13, 9), (17, 13), (11, 10), (3, 10), (5, 21), (8, 31), (13, 24), (0, 29), (26, 34), (29, 1), (3, 4), (9, 26), (4, 16), (21, 20), (29, 6), (6, 7), (30, 23), (14, 17), (6, 4), (16, 4), (3, 21), (25, 2), (1, 32), (29, 8), (4, 30), (26, 10), (11, 34), (14, 2), (12, 20), (8, 17), (0, 2), (24, 34), (22, 1), (0, 28), (7, 8), (7, 16), (27, 3), (25, 22), (19, 32), (27, 13), (15, 13), (28, 33), (19, 18), (28, 6), (25, 25), (16, 8), (5, 18), (25, 16), (5, 16), (14, 3), (1, 13), (14, 15), (29, 30), (25, 19), (27, 1), (23, 1), (27, 23), (26, 26), (14, 12), (17, 6), (29, 16), (14, 33), (10, 28), (23, 30), (30, 8), (12, 31), (23, 5), (10, 24), (17, 23), (3, 5), (9, 5), (4, 29), (15, 14), (4, 1), (22, 3), (20, 29), (8, 19), (8, 23), (30, 12), (30, 1), (18, 3), (15, 33), (22, 30), (11, 31), (16, 23), (16, 17), (28, 19), (12, 11), (8, 12), (23, 20), (24, 5), (0, 1), (19, 22), (9, 33), (7, 15), (0, 31), (16, 11), (27, 9), (22, 8), (5, 30), (6, 15), (12, 13), (10, 9), (29, 24), (9, 2), (28, 2), (18, 20), (26, 19), (1, 34), (7, 13), (20, 31), (18, 15), (30, 25), (21, 34), (2, 33), (4, 34), (1, 17), (21, 6), (13, 18), (30, 16), (17, 26), (10, 33), (9, 13), (26, 13), (13, 2), (14, 34), (20, 25), (27, 32), (20, 15), (28, 10), (14, 19), (6, 2), (4, 33), (26, 27), (2, 26), (4, 21), (21, 10), (13, 6), (7, 25), (22, 23), (11, 21), (12, 28), (25, 4), (23, 26), (17, 21), (27, 16), (30, 2), (6, 12), (0, 21), (15, 6), (3, 25), (9, 16), (24, 19), (23, 27), (16, 29), (12, 3), (8, 21), (6, 26), (1, 9), (14, 13), (0, 23), (21, 22), (13, 27), (19, 24), (24, 29), (1, 20), (13, 30), (24, 27), (21, 2), (19, 0), (9, 29), (0, 13), (23, 23), (7, 30), (2, 14), (11, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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), (26, 30), (6, 29), (14, 7), (3, 12), (12, 8), (29, 30), (26, 11), (16, 22), (0, 29), (12, 30), (11, 5), (1, 2), (23, 26), (11, 10), (13, 32), (29, 19), (1, 19), (4, 4), (11, 26), (3, 7), (10, 24), (26, 24), (19, 1), (22, 19), (23, 23), (9, 4), (1, 15), (1, 9), (26, 18), (29, 14), (14, 10), (21, 8), (13, 13), (24, 0), (13, 29), (14, 28), (18, 12), (16, 6), (13, 21), (12, 26), (0, 20), (15, 9), (5, 27), (11, 17), (13, 20), (27, 16), (17, 11), (5, 25), (12, 13), (14, 18), (25, 13), (19, 23), (23, 16), (18, 26), (14, 20), (21, 6), (11, 8), (27, 5), (29, 5), (24, 5), (20, 32), (7, 24), (19, 5), (8, 23), (10, 15), (6, 7), (1, 24), (29, 13), (23, 31), (17, 19), (26, 28), (21, 21), (28, 3), (19, 16), (3, 27), (14, 25), (21, 29), (12, 5), (29, 15), (27, 15), (20, 1), (14, 6), (22, 0), (24, 24), (14, 16), (10, 13), (20, 24), (5, 6), (10, 5), (3, 13), (27, 6), (20, 6), (8, 6), (6, 2), (3, 18), (16, 7), (0, 27), (10, 18), (9, 31), (23, 7), (4, 2), (12, 9), (8, 14), (22, 27), (21, 11), (14, 32), (2, 10), (28, 5), (2, 15), (19, 18), (14, 22), (0, 26), (26, 32), (18, 0), (2, 27), (8, 21), (7, 13), (0, 11), (8, 15), (5, 21), (17, 26), (1, 20), (17, 15), (4, 28), (2, 30), (12, 1), (12, 6), (13, 6), (2, 18), (0, 4), (8, 4), (12, 31), (1, 5), (25, 7), (25, 27), (9, 18), (27, 21), (28, 4), (15, 12), (28, 24), (26, 4), (23, 29), (21, 9), (3, 32), (17, 20), (13, 8), (20, 22), (22, 5), (25, 18), (2, 7), (17, 10), (28, 30), (7, 2), (0, 21), (2, 31), (27, 7), (21, 20), (14, 9), (22, 21), (10, 22), (4, 14), (23, 28), (4, 16), (15, 13), (14, 5), (26, 12), (19, 32), (21, 30), (15, 27), (10, 0), (21, 2), (7, 10), (0, 15), (5, 18), (18, 25), (17, 1), (9, 8), (11, 31), (27, 10), (17, 8), (8, 8), (19, 17), (29, 23), (26, 1), (25, 4), (2, 23), (7, 31), (21, 25), (29, 0), (7, 15), (22, 11), (29, 6), (26, 14), (22, 1), (18, 14), (28, 21), (7, 5), (16, 10), (4, 13), (18, 31), (18, 27), (7, 22), (10, 29), (19, 9), (21, 16), (10, 4), (16, 32), (15, 31), (12, 25), (2, 19), (10, 11), (26, 21), (15, 20), (9, 0), (25, 23), (10, 23), (18, 8), (27, 14), (15, 25), (11, 0), (5, 15), (20, 19), (24, 26), (7, 32), (14, 12), (22, 18), (12, 11), (22, 22), (9, 6), (28, 22), (12, 0), (0, 8), (28, 6), (15, 18), (16, 16), (9, 15), (25, 17), (19, 6), (4, 27), (15, 21), (10, 17), (24, 2), (11, 18), (26, 3), (1, 10), (0, 23), (1, 7), (21, 19), (17, 3), (25, 9), (9, 26), (14, 4), (23, 19), (1, 4), (8, 26), (9, 17), (9, 24), (1, 25), (19, 15), (11, 11), (15, 0), (1, 26), (3, 14), (2, 4), (10, 6), (11, 22), (15, 16), (5, 24), (3, 22), (25, 10), (19, 2), (5, 1), (7, 7), (9, 14), (8, 17), (23, 2), (25, 19), (22, 15), (16, 1), (20, 8), (9, 12), (19, 31), (20, 18), (9, 11), (5, 14), (18, 20), (14, 21), (15, 19), (24, 29), (28, 0), (22, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882792", "dataset": "MATH"}
{"messages": [{"content": "In a 32x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 24), (24, 1), (4, 3), (21, 14), (14, 23), (31, 7), (9, 30), (28, 19), (9, 9), (0, 31), (3, 9), (26, 4), (6, 18), (8, 30), (4, 29), (16, 6), (17, 6), (9, 25), (11, 26), (17, 20), (29, 27), (12, 11), (7, 5), (3, 17), (10, 24), (28, 13), (29, 16), (28, 15), (13, 8), (26, 31), (13, 10), (0, 22), (8, 12), (15, 22), (13, 11), (7, 6), (30, 24), (22, 2), (28, 6), (12, 0), (5, 31), (24, 6), (9, 14), (2, 19), (31, 8), (12, 18), (11, 11), (1, 19), (23, 29), (9, 3), (29, 0), (12, 9), (7, 26), (21, 27), (18, 31), (7, 20), (7, 23), (6, 22), (21, 15), (19, 21), (10, 13), (1, 16), (26, 13), (20, 31), (10, 25), (2, 11), (17, 19), (26, 14), (17, 8), (22, 13), (28, 3), (15, 20), (29, 29), (0, 30), (11, 24), (29, 7), (12, 4), (24, 5), (11, 7), (4, 11), (23, 3), (20, 1), (25, 13), (5, 28), (16, 25), (21, 24), (15, 5), (10, 16), (31, 15), (6, 16), (7, 22), (19, 27), (8, 6), (1, 27), (11, 28), (26, 10), (5, 10), (3, 11), (28, 21), (24, 22), (19, 23), (10, 19), (2, 23), (11, 23), (16, 14), (3, 10), (15, 1), (28, 5), (17, 27), (12, 23), (17, 13), (13, 13), (1, 9), (8, 31), (17, 4), (19, 2), (11, 13), (15, 31), (1, 7), (0, 18), (19, 19), (2, 10), (8, 5), (4, 13), (10, 0), (13, 31), (27, 9), (19, 12), (22, 7), (8, 4), (2, 16), (5, 18), (18, 5), (2, 1), (7, 1), (13, 12), (11, 25), (1, 4), (24, 28), (25, 17), (9, 26), (27, 6), (26, 24), (0, 27), (24, 24), (7, 15), (4, 4), (7, 12), (22, 19), (14, 28), (18, 16), (6, 13), (9, 5), (17, 29), (26, 29), (30, 0), (31, 23), (16, 24), (25, 2), (18, 22), (16, 3), (15, 4), (5, 9), (10, 20), (6, 29), (17, 17), (18, 10), (6, 1), (2, 21), (30, 19), (7, 28), (5, 5), (14, 31), (20, 22), (14, 21), (18, 17), (27, 27), (16, 8), (22, 17), (3, 16), (18, 26), (24, 16), (20, 3), (13, 4), (1, 28), (4, 17), (10, 30), (23, 27), (27, 14), (5, 17), (4, 14), (15, 16), (27, 8), (5, 6), (19, 6), (13, 21), (16, 27), (4, 12), (9, 12), (25, 12), (21, 1), (1, 30), (25, 26), (7, 25), (16, 9), (13, 3), (25, 30), (28, 25), (3, 27), (6, 14), (0, 10), (6, 20), (5, 16), (8, 10), (12, 22), (26, 2), (18, 24), (21, 7), (6, 4), (2, 9), (27, 0), (21, 11), (23, 17), (10, 29), (27, 18), (29, 25), (11, 6), (10, 1), (6, 15), (30, 22), (4, 15), (30, 16), (16, 1), (13, 15), (12, 8), (16, 20), (24, 23), (9, 7), (0, 7), (26, 19), (31, 3), (14, 15), (30, 11), (20, 25), (8, 11), (28, 20), (11, 5), (10, 14), (7, 17), (16, 26), (24, 20), (3, 31), (3, 1), (28, 14), (26, 23), (2, 12), (14, 8), (23, 12), (31, 11), (13, 7), (3, 18), (30, 3), (17, 3), (28, 4), (15, 12), (0, 11), (18, 28), (3, 2), (24, 19), (23, 4), (18, 12), (14, 5), (11, 21), (13, 16), (17, 9), (3, 30), (12, 16), (25, 10), (22, 30), (31, 21), (4, 6), (22, 8), (12, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352488", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), 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), (29, 5), (4, 25), (4, 29), (9, 2), (28, 23), (16, 24), (27, 11), (23, 13), (15, 2), (24, 26), (20, 13), (25, 24), (0, 31), (4, 2), (32, 1), (17, 10), (25, 16), (12, 18), (29, 21), (13, 26), (2, 5), (31, 10), (23, 29), (24, 8), (4, 11), (23, 16), (11, 10), (10, 21), (25, 3), (22, 6), (16, 21), (5, 30), (23, 8), (4, 10), (18, 5), (32, 8), (19, 8), (25, 9), (19, 6), (11, 14), (14, 11), (13, 25), (33, 17), (19, 4), (15, 31), (5, 12), (23, 12), (14, 19), (11, 6), (31, 2), (12, 19), (26, 6), (16, 30), (2, 30), (6, 20), (33, 2), (10, 13), (15, 12), (19, 12), (25, 0), (10, 1), (0, 29), (5, 11), (31, 29), (13, 15), (19, 0), (33, 24), (13, 30), (24, 7), (27, 30), (32, 22), (6, 4), (28, 7), (1, 27), (29, 10), (23, 11), (12, 1), (13, 18), (31, 16), (6, 8), (2, 16), (8, 27), (16, 31), (16, 0), (3, 11), (11, 23), (23, 25), (28, 22), (10, 6), (31, 21), (3, 2), (29, 6), (31, 0), (2, 12), (10, 20), (3, 7), (4, 4), (9, 8), (21, 18), (8, 1), (31, 30), (14, 27), (32, 4), (5, 31), (5, 7), (21, 19), (3, 4), (9, 18), (32, 17), (31, 8), (19, 7), (23, 21), (11, 28), (31, 7), (28, 20), (29, 30), (31, 13), (12, 11), (5, 3), (14, 12), (26, 18), (13, 14), (17, 22), (29, 17), (16, 3), (14, 10), (7, 28), (18, 11), (29, 26), (0, 30), (9, 24), (6, 30), (6, 6), (5, 0), (12, 15), (17, 26), (13, 13), (12, 25), (9, 7), (26, 14), (1, 25), (31, 11), (19, 21), (26, 29), (30, 22), (9, 25), (26, 30), (12, 30), (5, 27), (23, 3), (33, 19), (3, 29), (30, 12), (7, 3), (25, 31), (32, 29), (4, 18), (30, 3), (29, 20), (25, 5), (2, 24), (10, 30), (17, 5), (24, 15), (7, 18), (16, 29), (8, 5), (17, 14), (30, 14), (8, 26), (33, 13), (29, 31), (14, 14), (23, 5), (24, 22), (1, 11), (14, 1), (1, 26), (27, 2), (27, 13), (4, 21), (10, 9), (11, 18), (6, 10), (19, 16), (23, 4), (11, 0), (24, 2), (20, 31), (27, 31), (27, 10), (27, 22), (10, 16), (6, 3), (4, 0), (29, 22), (1, 5), (7, 2), (2, 17), (13, 29), (27, 0), (1, 16), (22, 8), (27, 26), (26, 31), (29, 0), (13, 9), (20, 14), (31, 14), (16, 16), (5, 19), (8, 10), (10, 19), (5, 29), (5, 13), (24, 9), (11, 29), (31, 17), (6, 13), (17, 20), (2, 14), (0, 24), (26, 10), (33, 3), (19, 11), (17, 11), (29, 8), (17, 16), (27, 12), (15, 3), (32, 6), (11, 15), (7, 10), (4, 30), (3, 10), (9, 5), (30, 4), (11, 20), (15, 29), (22, 0), (16, 1), (19, 14), (8, 23), (20, 28), (28, 2), (20, 5), (26, 9), (19, 30), (27, 27), (20, 19), (26, 12), (21, 7), (26, 11), (21, 21), (16, 26), (7, 23), (8, 20), (29, 25), (14, 0), (27, 14), (3, 12), (32, 19), (7, 21), (29, 27), (32, 12), (3, 28), (17, 8), (2, 23), (6, 9), (19, 31), (26, 28), (18, 16), (9, 6), (30, 26), (33, 25), (28, 29), (13, 20), (17, 1), (19, 27), (0, 27), (11, 2), (21, 8), (4, 23), (30, 11), (2, 3), (13, 0), (29, 11), (10, 0), (11, 26), (8, 24), (21, 6), (24, 19), (9, 13), (3, 13), (27, 8), (2, 20), (22, 13), (22, 2), (14, 23), (3, 14), (9, 26), (2, 9), (9, 30), (18, 3), (28, 12), (11, 4), (17, 28), (7, 13), (28, 5), (22, 20), (22, 22), (13, 5), (21, 26), (8, 12), (5, 18), (28, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400278", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), 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), (0, 17), (31, 15), (11, 3), (7, 14), (21, 11), (23, 30), (9, 6), (1, 14), (19, 22), (22, 9), (22, 5), (31, 26), (2, 14), (5, 26), (17, 23), (23, 12), (0, 27), (26, 20), (5, 24), (15, 1), (6, 15), (16, 25), (23, 24), (0, 19), (30, 18), (26, 1), (3, 3), (12, 30), (6, 27), (16, 6), (30, 27), (6, 8), (23, 19), (24, 25), (23, 16), (17, 26), (11, 12), (9, 24), (11, 6), (31, 23), (18, 6), (22, 28), (3, 16), (18, 18), (28, 26), (31, 28), (2, 28), (24, 24), (15, 10), (9, 30), (8, 22), (30, 20), (26, 29), (3, 8), (7, 28), (7, 9), (28, 12), (30, 19), (23, 26), (16, 12), (20, 5), (18, 4), (3, 1), (16, 18), (12, 17), (15, 9), (20, 27), (1, 15), (28, 9), (28, 13), (11, 14), (16, 21), (10, 10), (31, 14), (28, 28), (25, 25), (30, 3), (29, 13), (19, 0), (12, 6), (16, 19), (16, 13), (3, 22), (15, 28), (24, 7), (23, 25), (10, 2), (23, 3), (2, 21), (29, 21), (25, 18), (27, 11), (30, 8), (6, 6), (13, 24), (15, 30), (6, 19), (23, 1), (31, 6), (15, 16), (10, 14), (0, 29), (7, 8), (16, 3), (10, 20), (0, 8), (2, 18), (10, 28), (25, 17), (19, 2), (26, 30), (15, 3), (16, 30), (3, 14), (21, 21), (0, 11), (14, 11), (4, 24), (27, 24), (17, 7), (18, 16), (6, 29), (20, 28), (16, 22), (0, 1), (31, 3), (0, 10), (13, 2), (12, 23), (5, 12), (23, 14), (27, 17), (26, 8), (29, 17), (11, 24), (21, 8), (5, 4), (17, 10), (1, 20), (10, 29), (8, 9), (23, 29), (11, 28), (12, 2), (30, 28), (4, 13), (21, 27), (0, 21), (9, 19), (18, 5), (31, 8), (29, 25), (17, 18), (21, 22), (30, 5), (20, 7), (30, 11), (24, 11), (1, 12), (14, 26), (22, 17), (9, 10), (26, 18), (2, 1), (11, 22), (23, 15), (5, 0), (3, 4), (18, 2), (26, 28), (19, 6), (1, 7), (24, 0), (28, 23), (24, 14), (29, 9), (29, 1), (18, 0), (5, 13), (22, 1), (17, 30), (26, 4), (24, 3), (20, 14), (9, 4), (26, 7), (0, 15), (27, 1), (17, 15), (23, 20), (2, 10), (30, 7), (30, 14), (24, 10), (31, 1), (12, 19), (8, 1), (10, 21), (2, 24), (6, 12), (6, 22), (8, 7), (19, 16), (8, 27), (1, 18), (14, 1), (12, 27), (14, 22), (4, 8), (17, 9), (19, 29), (21, 3), (4, 14), (24, 13), (1, 3), (4, 5), (29, 24), (22, 4), (30, 17), (11, 26), (22, 25), (31, 25), (4, 22), (2, 2), (20, 22), (26, 10), (8, 17), (19, 13), (4, 10), (23, 7), (12, 3), (8, 3), (15, 29), (8, 21), (26, 15), (13, 23), (5, 8), (7, 6), (14, 6), (24, 5), (11, 0), (7, 18), (12, 29), (31, 18), (15, 11), (16, 1), (0, 16), (14, 30), (15, 13), (21, 12), (4, 4), (24, 21), (2, 19), (2, 17), (13, 17), (19, 20), (24, 27), (1, 29), (12, 4), (8, 15), (29, 5), (2, 5), (19, 7), (13, 26), (22, 10), (2, 25), (14, 21), (24, 2), (27, 5), (19, 17), (25, 22), (27, 8), (18, 22), (9, 18), (17, 20), (20, 9), (8, 28), (14, 2), (16, 26), (8, 12), (5, 18), (27, 28), (9, 8), (10, 13), (13, 22), (12, 5), (2, 26), (22, 26), (7, 23), (19, 4), (18, 15), (29, 19), (11, 23), (13, 11), (11, 16), (1, 2), (27, 13), (17, 11), (12, 13), (27, 10), (15, 22), (12, 7), (24, 26), (16, 23), (1, 19), (30, 1), (17, 6), (29, 8), (24, 6), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "680184", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 34), (10, 17), (20, 15), (2, 36), (29, 6), (4, 13), (29, 9), (16, 3), (15, 30), (3, 5), (28, 23), (18, 18), (26, 24), (25, 33), (1, 30), (10, 11), (0, 29), (0, 7), (6, 11), (5, 0), (9, 22), (7, 3), (16, 9), (23, 5), (18, 7), (11, 32), (3, 15), (23, 28), (5, 7), (6, 26), (7, 33), (26, 30), (10, 16), (4, 26), (8, 33), (15, 3), (26, 9), (30, 31), (15, 32), (23, 29), (13, 0), (11, 36), (31, 22), (2, 34), (25, 27), (13, 3), (18, 25), (17, 13), (31, 11), (31, 24), (5, 32), (29, 12), (11, 34), (21, 3), (29, 1), (9, 19), (14, 21), (31, 3), (18, 21), (10, 0), (14, 0), (14, 15), (9, 24), (19, 6), (25, 32), (24, 8), (30, 0), (17, 4), (5, 4), (31, 5), (27, 19), (18, 1), (0, 34), (17, 11), (2, 15), (1, 16), (11, 2), (7, 0), (15, 33), (27, 35), (24, 7), (24, 1), (26, 14), (15, 31), (0, 8), (5, 1), (11, 7), (29, 29), (6, 17), (13, 26), (13, 21), (20, 10), (1, 22), (26, 3), (28, 29), (2, 26), (7, 12), (22, 6), (14, 34), (4, 9), (28, 1), (31, 28), (26, 17), (5, 17), (31, 6), (14, 9), (11, 19), (6, 27), (6, 23), (12, 35), (3, 35), (2, 13), (20, 17), (13, 2), (23, 31), (18, 10), (8, 24), (12, 12), (27, 34), (5, 9), (22, 16), (14, 5), (10, 6), (1, 10), (8, 3), (23, 26), (28, 34), (25, 11), (24, 24), (11, 29), (0, 5), (13, 30), (24, 10), (23, 9), (18, 34), (1, 31), (16, 24), (3, 4), (0, 27), (3, 25), (9, 2), (23, 30), (31, 18), (11, 35), (26, 4), (11, 5), (14, 23), (24, 30), (23, 24), (28, 10), (26, 35), (22, 26), (24, 26), (4, 3), (25, 19), (20, 12), (11, 26), (17, 34), (23, 25), (7, 34), (2, 18), (24, 5), (21, 2), (25, 24), (30, 11), (6, 33), (24, 28), (21, 26), (12, 25), (23, 7), (24, 4), (1, 24), (26, 33), (9, 16), (4, 2), (7, 5), (21, 6), (3, 30), (20, 4), (20, 6), (17, 8), (9, 14), (20, 8), (17, 30), (26, 26), (2, 0), (9, 17), (26, 18), (26, 25), (30, 33), (20, 13), (13, 22), (20, 24), (22, 14), (4, 27), (8, 20), (29, 4), (1, 7), (7, 27), (23, 35), (16, 19), (24, 25), (3, 9), (13, 8), (30, 7), (4, 19), (19, 1), (31, 23), (28, 22), (30, 4), (26, 19), (12, 13), (18, 22), (15, 14), (24, 0), (19, 33), (5, 28), (3, 1), (27, 22), (11, 24), (10, 28), (17, 35), (29, 8), (20, 9), (10, 14), (21, 25), (12, 27), (0, 14), (28, 8), (1, 26), (15, 34), (11, 0), (30, 1), (19, 18), (8, 30), (9, 9), (16, 20), (2, 28), (10, 20), (21, 20), (15, 19), (28, 25), (18, 20), (15, 9), (27, 20), (21, 24), (9, 36), (24, 35), (9, 20), (14, 18), (15, 7), (1, 11), (27, 5), (20, 14), (21, 13), (10, 2), (14, 19), (16, 4), (23, 16), (19, 8), (9, 25), (12, 31), (1, 28), (27, 15), (25, 36), (28, 36), (1, 35), (17, 5), (4, 8), (8, 32), (3, 18), (8, 18), (22, 13), (27, 8), (31, 10), (15, 26), (11, 17), (10, 3), (4, 31), (23, 36), (16, 1), (7, 28), (22, 30), (31, 21), (11, 22), (26, 34), (23, 34), (4, 10), (31, 27), (30, 19), (14, 1), (2, 27), (4, 0), (8, 27), (16, 28), (10, 7), (13, 16), (25, 10), (15, 23), (30, 14), (18, 17), (8, 4), (28, 24), (6, 7), (26, 13), (24, 27), (14, 30), (4, 16), (12, 17), (11, 16), (16, 29), (15, 12), (24, 21), (17, 23), (22, 35), (17, 1), (5, 19), (18, 0), (22, 34), (27, 13), (31, 13), (17, 31), (3, 22), (19, 36), (21, 33), (12, 29), (0, 4), (11, 18), (9, 30), (28, 35), (25, 26), (12, 4), (22, 20), (11, 23), (13, 10), (9, 26), (1, 27), (20, 19), (21, 30), (29, 23), (3, 32), (21, 28), (0, 1), (7, 1), (14, 6), (23, 11), (28, 27), (30, 16), (6, 4), (8, 28), (2, 12), (20, 29), (2, 35), (1, 25), (24, 36), (17, 3), (26, 29), (16, 27), (25, 18), (17, 15), (4, 20), (22, 25), (4, 23), (28, 18), (14, 4), (26, 32), (1, 33), (25, 16), (11, 30), (16, 8), (0, 16), (30, 17), (16, 7), (17, 36), (29, 25), (11, 9), (4, 34), (18, 31), (11, 33), (20, 16), (7, 24), (21, 16), (27, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "628992", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 3), (8, 28), (16, 20), (19, 19), (15, 16), (24, 21), (22, 36), (11, 21), (11, 22), (11, 26), (10, 5), (27, 22), (3, 19), (20, 20), (5, 22), (30, 14), (1, 17), (17, 31), (3, 7), (30, 28), (22, 24), (1, 1), (9, 14), (20, 13), (9, 37), (16, 4), (28, 10), (12, 31), (8, 7), (29, 2), (28, 5), (9, 4), (17, 27), (13, 31), (2, 11), (26, 5), (18, 14), (22, 11), (0, 23), (28, 37), (0, 8), (18, 0), (8, 20), (10, 28), (22, 1), (20, 37), (4, 27), (0, 28), (26, 33), (2, 10), (27, 2), (25, 1), (31, 30), (11, 10), (7, 7), (21, 32), (17, 0), (16, 15), (25, 26), (5, 18), (11, 0), (27, 0), (21, 0), (24, 33), (5, 4), (20, 8), (31, 21), (21, 27), (20, 6), (1, 18), (7, 33), (9, 5), (8, 21), (8, 22), (19, 27), (9, 21), (5, 34), (31, 4), (3, 9), (14, 1), (3, 26), (31, 29), (21, 33), (28, 2), (14, 32), (21, 26), (30, 11), (22, 8), (27, 7), (28, 1), (17, 8), (16, 24), (12, 7), (8, 18), (2, 17), (0, 32), (7, 30), (16, 13), (25, 25), (30, 35), (14, 7), (30, 26), (4, 24), (15, 14), (31, 25), (30, 34), (2, 16), (1, 23), (20, 36), (31, 3), (26, 10), (23, 15), (19, 29), (10, 24), (12, 30), (27, 16), (2, 20), (17, 20), (17, 33), (23, 16), (9, 12), (25, 7), (1, 7), (11, 13), (3, 8), (24, 14), (1, 21), (21, 25), (25, 13), (0, 4), (18, 23), (14, 18), (25, 11), (4, 2), (0, 7), (28, 28), (20, 34), (3, 0), (26, 24), (4, 31), (17, 30), (22, 14), (3, 24), (24, 17), (3, 28), (11, 20), (19, 9), (2, 31), (27, 11), (29, 11), (14, 20), (26, 1), (6, 28), (17, 1), (1, 14), (23, 17), (27, 13), (17, 2), (4, 0), (8, 1), (1, 8), (17, 18), (24, 10), (7, 32), (1, 3), (12, 36), (27, 37), (9, 34), (30, 21), (5, 28), (26, 23), (30, 0), (22, 30), (6, 22), (21, 1), (27, 25), (17, 24), (15, 30), (20, 15), (12, 11), (12, 15), (22, 15), (2, 5), (9, 13), (23, 6), (21, 19), (6, 36), (3, 15), (23, 12), (4, 4), (31, 12), (7, 29), (18, 22), (26, 28), (10, 1), (10, 36), (29, 22), (18, 31), (31, 31), (20, 14), (31, 35), (18, 30), (24, 15), (18, 2), (18, 28), (18, 1), (3, 27), (11, 18), (8, 32), (9, 22), (4, 20), (0, 30), (2, 0), (14, 2), (24, 32), (17, 4), (6, 27), (9, 33), (19, 23), (26, 26), (8, 36), (20, 31), (30, 20), (30, 29), (9, 27), (4, 12), (20, 18), (8, 15), (21, 29), (6, 5), (15, 32), (10, 10), (29, 20), (13, 9), (28, 18), (2, 24), (16, 6), (30, 25), (13, 4), (26, 21), (9, 28), (18, 13), (0, 24), (13, 6), (9, 9), (8, 34), (15, 20), (20, 5), (18, 36), (8, 5), (0, 34), (18, 21), (28, 12), (0, 31), (12, 16), (3, 32), (23, 19), (24, 12), (17, 37), (24, 34), (3, 17), (27, 31), (24, 7), (15, 21), (11, 6), (9, 16), (13, 24), (19, 15), (4, 33), (23, 23), (18, 26), (2, 32), (7, 23), (3, 14), (23, 1), (29, 28), (29, 27), (3, 5), (10, 32), (22, 27), (25, 31), (22, 13), (27, 27), (17, 17), (0, 14), (17, 15), (13, 26), (3, 35), (19, 4), (5, 37), (18, 34), (23, 7), (0, 19), (10, 23), (12, 5), (10, 4), (22, 10), (6, 1), (19, 7), (8, 17), (17, 28), (0, 21), (4, 15), (28, 29), (24, 35), (9, 26), (6, 2), (15, 4), (11, 25), (31, 19), (6, 15), (12, 26), (8, 6), (8, 2), (18, 16), (1, 32), (22, 33), (24, 28), (15, 19), (28, 27), (10, 26), (20, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "870264", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 10), (0, 29), (12, 3), (8, 15), (22, 15), (6, 18), (11, 2), (14, 22), (18, 3), (35, 5), (26, 14), (22, 29), (26, 20), (3, 1), (21, 27), (3, 13), (8, 11), (4, 12), (35, 14), (6, 0), (6, 27), (13, 9), (24, 10), (23, 22), (8, 21), (12, 11), (7, 17), (13, 0), (21, 13), (3, 4), (25, 0), (9, 4), (19, 21), (5, 7), (5, 10), (5, 14), (33, 13), (8, 26), (3, 30), (32, 15), (32, 26), (9, 26), (6, 26), (35, 28), (13, 24), (3, 27), (5, 21), (28, 18), (7, 10), (28, 27), (8, 9), (14, 1), (24, 6), (2, 7), (6, 2), (31, 10), (23, 21), (9, 14), (8, 8), (9, 18), (27, 5), (7, 3), (33, 4), (17, 20), (12, 21), (11, 20), (31, 6), (25, 19), (5, 27), (36, 16), (10, 23), (12, 7), (12, 30), (2, 14), (20, 6), (30, 28), (14, 10), (0, 8), (21, 8), (8, 18), (7, 5), (3, 20), (29, 16), (16, 10), (23, 13), (30, 17), (3, 2), (8, 30), (13, 23), (33, 12), (24, 4), (5, 29), (25, 25), (26, 8), (20, 30), (31, 2), (6, 12), (8, 6), (4, 8), (29, 28), (8, 19), (34, 7), (6, 6), (26, 9), (30, 24), (19, 17), (30, 5), (24, 30), (9, 22), (14, 23), (35, 13), (25, 28), (32, 28), (11, 11), (0, 21), (15, 5), (9, 16), (27, 29), (18, 18), (12, 4), (16, 3), (6, 14), (29, 29), (21, 12), (22, 17), (31, 20), (4, 18), (31, 26), (3, 5), (26, 28), (13, 25), (21, 6), (14, 29), (24, 3), (1, 24), (4, 10), (28, 20), (23, 25), (20, 13), (1, 10), (3, 10), (25, 14), (24, 21), (8, 22), (22, 25), (30, 9), (18, 12), (9, 23), (8, 10), (24, 13), (5, 6), (36, 24), (14, 27), (18, 10), (15, 13), (29, 9), (20, 4), (11, 19), (20, 1), (7, 0), (33, 10), (2, 10), (16, 22), (29, 0), (21, 29), (27, 23), (8, 0), (11, 10), (6, 30), (8, 3), (30, 0), (29, 12), (13, 4), (34, 18), (15, 21), (33, 15), (25, 11), (15, 9), (26, 21), (21, 16), (28, 1), (4, 30), (1, 2), (11, 1), (32, 17), (22, 2), (32, 22), (8, 24), (14, 2), (7, 7), (3, 16), (27, 19), (26, 29), (29, 7), (15, 18), (9, 19), (13, 17), (32, 8), (7, 6), (30, 12), (1, 9), (34, 3), (29, 2), (36, 10), (2, 13), (8, 28), (5, 24), (10, 28), (4, 21), (36, 12), (13, 18), (6, 16), (19, 25), (24, 22), (28, 6), (15, 24), (35, 8), (28, 15), (25, 15), (25, 17), (5, 25), (34, 16), (36, 8), (28, 5), (21, 20), (33, 24), (5, 19), (34, 24), (21, 14), (24, 26), (5, 15), (26, 15), (31, 9), (20, 18), (27, 9), (19, 24), (29, 27), (13, 26), (36, 6), (27, 2), (19, 26), (12, 0), (1, 30), (19, 14), (30, 8), (11, 23), (15, 8), (21, 9), (33, 17), (17, 0), (21, 7), (11, 15), (22, 27), (2, 21), (25, 13), (12, 26), (18, 9), (14, 26), (34, 8), (19, 10), (24, 12), (25, 20), (25, 9), (13, 21), (7, 4), (19, 9), (27, 16), (15, 19), (17, 26), (29, 30), (21, 11), (13, 22), (29, 17), (19, 1), (14, 12), (22, 28), (29, 13), (21, 1), (29, 26), (13, 5), (7, 15), (19, 22), (35, 6), (2, 20), (10, 10), (33, 25), (20, 2), (10, 30), (30, 3), (8, 5), (16, 15), (19, 6), (12, 8), (10, 26), (11, 26), (36, 1), (15, 25), (11, 9), (13, 8), (16, 5), (36, 18), (12, 10), (0, 14), (1, 15), (19, 18), (36, 15), (20, 27), (2, 19), (13, 20), (14, 19), (15, 12), (9, 20), (32, 4), (9, 12), (31, 25), (10, 12), (7, 29), (24, 7), (8, 13), (18, 8), (20, 17), (21, 15), (28, 12), (1, 23), (27, 15), (24, 16), (16, 29), (33, 18), (26, 1), (22, 23), (16, 13), (25, 4), (11, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866320", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), 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), (21, 1), (14, 13), (19, 10), (4, 11), (27, 20), (7, 0), (24, 0), (4, 23), (11, 26), (16, 10), (7, 16), (26, 10), (21, 24), (13, 32), (23, 18), (14, 17), (27, 26), (14, 29), (3, 10), (23, 22), (15, 28), (13, 26), (17, 33), (20, 12), (10, 12), (30, 20), (11, 14), (23, 17), (26, 7), (5, 12), (29, 19), (6, 9), (20, 29), (22, 32), (11, 27), (23, 13), (8, 33), (28, 8), (8, 28), (12, 30), (4, 13), (19, 27), (10, 25), (26, 22), (3, 18), (6, 4), (4, 9), (21, 22), (7, 4), (24, 16), (0, 14), (15, 15), (15, 2), (21, 28), (11, 31), (8, 17), (27, 7), (3, 16), (14, 9), (6, 1), (16, 13), (28, 10), (20, 8), (12, 5), (8, 20), (29, 0), (7, 20), (15, 31), (0, 29), (30, 25), (28, 25), (5, 27), (25, 25), (24, 7), (7, 28), (9, 25), (24, 22), (10, 27), (3, 27), (23, 14), (4, 8), (11, 16), (28, 7), (18, 13), (27, 14), (27, 5), (3, 24), (26, 17), (3, 6), (6, 0), (20, 27), (10, 31), (29, 11), (10, 22), (20, 24), (27, 3), (10, 13), (18, 21), (15, 10), (2, 2), (2, 29), (26, 27), (11, 19), (1, 1), (3, 17), (8, 7), (11, 28), (4, 5), (21, 27), (9, 18), (8, 26), (6, 13), (26, 23), (10, 17), (19, 0), (12, 25), (11, 4), (28, 3), (27, 10), (12, 18), (27, 32), (11, 25), (24, 20), (10, 20), (27, 27), (24, 18), (25, 33), (29, 17), (25, 24), (2, 14), (25, 16), (22, 1), (14, 28), (30, 12), (18, 27), (9, 0), (5, 11), (6, 7), (6, 26), (19, 13), (17, 19), (3, 1), (22, 20), (14, 12), (13, 31), (13, 20), (12, 20), (5, 15), (15, 30), (5, 3), (14, 26), (7, 32), (19, 32), (23, 21), (20, 26), (11, 2), (18, 28), (18, 17), (22, 15), (22, 0), (22, 17), (7, 21), (24, 30), (12, 2), (28, 6), (9, 6), (18, 0), (6, 16), (8, 32), (25, 3), (25, 13), (0, 22), (26, 3), (22, 4), (26, 13), (19, 18), (21, 20), (20, 15), (13, 16), (7, 23), (10, 6), (5, 16), (20, 28), (6, 24), (3, 20), (24, 11), (26, 1), (19, 24), (21, 10), (29, 28), (26, 20), (2, 20), (17, 27), (2, 4), (17, 25), (29, 2), (30, 31), (25, 30), (15, 25), (30, 28), (25, 7), (26, 14), (25, 20), (30, 26), (5, 9), (11, 21), (17, 10), (17, 14), (25, 19), (12, 17), (17, 12), (19, 23), (5, 24), (4, 4), (9, 12), (17, 31), (1, 11), (29, 29), (8, 18), (19, 4), (11, 33), (22, 21), (25, 11), (9, 11), (27, 21), (16, 32), (19, 22), (18, 7), (26, 18), (24, 31), (1, 33), (27, 4), (24, 4), (30, 9), (25, 23), (9, 21), (14, 3), (20, 30), (3, 15), (25, 2), (27, 17), (27, 1), (24, 24), (20, 23), (20, 25), (22, 3), (17, 30), (29, 4), (13, 28), (13, 18), (13, 6), (7, 27), (18, 25), (23, 7), (27, 22), (9, 13), (10, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854262", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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, 3), (23, 24), (14, 27), (22, 2), (6, 20), (1, 34), (23, 21), (27, 24), (12, 26), (2, 19), (13, 4), (6, 28), (24, 17), (7, 12), (1, 21), (25, 12), (2, 23), (9, 25), (27, 18), (22, 8), (29, 34), (19, 26), (5, 16), (25, 33), (3, 3), (4, 17), (10, 6), (13, 1), (13, 25), (24, 7), (8, 9), (8, 31), (31, 22), (24, 8), (11, 32), (31, 11), (11, 10), (11, 5), (18, 8), (20, 22), (18, 31), (30, 2), (5, 4), (3, 12), (29, 18), (15, 34), (33, 27), (17, 29), (15, 23), (6, 27), (23, 2), (17, 8), (16, 1), (18, 28), (16, 5), (14, 11), (20, 3), (21, 3), (33, 30), (18, 1), (20, 13), (24, 25), (30, 1), (19, 6), (32, 6), (11, 27), (10, 21), (27, 34), (30, 18), (30, 9), (6, 6), (3, 27), (30, 31), (8, 20), (19, 7), (8, 13), (28, 4), (21, 5), (4, 8), (29, 10), (17, 34), (29, 28), (23, 9), (11, 12), (26, 30), (13, 21), (12, 18), (23, 32), (18, 20), (9, 1), (24, 9), (18, 23), (33, 29), (32, 16), (32, 10), (16, 10), (8, 8), (23, 5), (3, 2), (22, 19), (14, 34), (10, 32), (30, 14), (4, 26), (20, 14), (27, 29), (12, 16), (22, 32), (31, 24), (27, 15), (11, 25), (12, 34), (28, 9), (6, 30), (11, 6), (21, 32), (7, 15), (3, 10), (8, 0), (11, 14), (23, 34), (7, 26), (16, 9), (24, 12), (23, 12), (21, 18), (16, 14), (32, 15), (19, 8), (23, 17), (18, 2), (4, 15), (19, 10), (7, 3), (16, 11), (30, 33), (13, 19), (2, 29), (0, 13), (24, 27), (32, 33), (16, 2), (30, 7), (13, 6), (29, 17), (0, 34), (6, 1), (15, 4), (14, 7), (3, 34), (15, 6), (33, 2), (0, 28), (18, 6), (14, 18), (7, 6), (0, 3), (14, 20), (13, 3), (32, 27), (9, 34), (24, 10), (29, 26), (8, 34), (21, 24), (16, 19), (30, 4), (5, 24), (16, 31), (0, 4), (0, 6), (33, 13), (24, 29), (12, 14), (20, 7), (26, 8), (22, 22), (27, 8), (2, 26), (9, 24), (18, 17), (12, 1), (13, 10), (16, 16), (16, 13), (10, 10), (5, 10), (24, 1), (17, 7), (0, 10), (19, 15), (11, 22), (21, 26), (7, 20), (1, 24), (20, 0), (31, 19), (29, 4), (1, 1), (10, 7), (4, 6), (33, 17), (4, 13), (27, 22), (6, 3), (8, 19), (3, 15), (33, 24), (30, 29), (9, 16), (32, 13), (27, 19), (25, 7), (32, 5), (14, 10), (29, 5), (3, 31), (28, 3), (18, 29), (13, 18), (3, 30), (11, 19), (20, 32), (3, 32), (15, 12), (16, 34), (24, 16), (13, 34), (16, 8), (30, 17), (14, 2), (1, 32), (31, 14), (3, 17), (2, 24), (28, 13), (19, 32), (6, 16), (16, 30), (9, 20), (9, 30), (13, 17), (8, 28), (5, 5), (17, 14), (31, 26), (22, 3), (1, 31), (17, 18), (6, 33), (23, 11), (12, 23), (20, 33), (28, 16), (1, 20), (23, 18), (4, 7), (29, 16), (19, 18), (6, 23), (31, 4), (15, 31), (28, 20), (28, 32), (21, 13), (5, 0), (1, 8), (1, 0), (2, 13), (15, 2), (14, 32), (28, 34), (5, 13), (29, 0), (32, 30), (3, 5), (5, 11), (3, 19), (29, 22), (5, 1), (10, 12), (24, 4), (15, 14), (30, 11), (12, 30), (19, 13), (10, 15), (8, 10), (7, 19), (20, 8), (29, 29), (13, 5), (6, 15), (18, 26), (1, 12), (0, 27), (32, 29), (30, 13), (31, 2), (28, 28), (14, 19), (18, 27), (2, 10), (22, 31), (22, 10), (10, 8), (21, 12), (31, 17), (16, 3), (18, 25), (1, 10), (27, 26), (23, 14), (23, 4), (28, 1), (5, 30), (12, 17), (19, 25), (29, 7), (4, 19), (17, 3), (19, 30), (0, 31), (5, 8), (6, 8), (29, 27), (16, 28), (27, 1), (26, 32), (18, 5), (33, 9), (17, 4), (12, 0), (27, 5), (17, 28), (5, 29), (29, 31), (30, 30), (10, 28), (8, 33), (15, 15), (30, 12), (18, 13), (25, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "728640", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 29), (17, 3), (10, 30), (4, 24), (15, 30), (8, 7), (27, 4), (20, 10), (14, 32), (27, 34), (14, 12), (6, 13), (11, 7), (12, 5), (15, 9), (14, 15), (3, 1), (12, 29), (13, 6), (8, 11), (6, 36), (4, 36), (13, 9), (6, 28), (21, 10), (7, 34), (6, 37), (2, 18), (20, 29), (24, 19), (24, 25), (20, 22), (4, 10), (22, 34), (17, 28), (27, 6), (3, 8), (3, 20), (16, 27), (18, 7), (16, 0), (19, 36), (27, 37), (10, 33), (17, 20), (29, 26), (21, 8), (28, 33), (14, 23), (8, 20), (27, 31), (8, 29), (6, 30), (2, 33), (2, 19), (28, 24), (0, 19), (9, 24), (25, 4), (21, 28), (2, 14), (2, 27), (9, 38), (26, 8), (2, 32), (9, 15), (19, 10), (24, 0), (11, 23), (9, 9), (10, 31), (23, 26), (8, 18), (1, 6), (0, 10), (6, 1), (4, 4), (27, 22), (3, 14), (17, 8), (8, 3), (12, 7), (11, 37), (15, 17), (15, 31), (18, 1), (6, 7), (27, 38), (20, 28), (0, 23), (1, 17), (6, 9), (1, 25), (21, 21), (11, 15), (25, 2), (28, 30), (7, 12), (28, 37), (14, 10), (20, 21), (8, 21), (8, 17), (26, 35), (1, 4), (1, 20), (3, 35), (18, 5), (13, 22), (22, 17), (2, 15), (20, 5), (23, 34), (24, 32), (26, 9), (15, 2), (5, 24), (2, 4), (13, 25), (15, 25), (25, 1), (8, 14), (24, 2), (5, 20), (12, 25), (8, 9), (18, 31), (20, 4), (4, 37), (29, 6), (23, 21), (1, 36), (22, 23), (8, 12), (15, 1), (25, 12), (14, 0), (14, 33), (2, 22), (28, 10), (3, 12), (24, 34), (13, 17), (20, 15), (12, 6), (0, 9), (2, 10), (23, 23), (4, 12), (22, 35), (22, 27), (4, 9), (7, 21), (21, 17), (3, 33), (28, 38), (5, 22), (21, 19), (11, 32), (29, 10), (28, 17), (2, 12), (23, 31), (13, 19), (10, 28), (3, 22), (22, 3), (0, 37), (19, 15), (22, 33), (7, 9), (11, 16), (10, 36), (6, 29), (6, 33), (15, 19), (13, 32), (21, 5), (20, 7), (12, 36), (17, 17), (7, 35), (25, 19), (4, 11), (23, 14), (21, 37), (20, 25), (11, 4), (14, 20), (7, 3), (29, 13), (12, 30), (29, 25), (16, 9), (4, 20), (5, 33), (4, 2), (26, 15), (15, 3), (13, 31), (11, 31), (18, 37), (7, 0), (21, 27), (23, 10), (13, 37), (5, 1), (22, 16), (27, 17), (21, 23), (9, 25), (6, 32), (2, 36), (19, 35), (24, 24), (9, 22), (15, 0), (9, 29), (27, 8), (10, 29), (3, 15), (5, 19), (25, 33), (24, 18), (13, 30), (3, 2), (2, 34), (1, 18), (17, 7), (19, 20), (10, 16), (24, 11), (5, 28), (18, 13), (9, 13), (3, 34), (11, 5), (0, 35), (2, 3), (7, 32), (0, 18), (29, 28), (22, 20), (29, 8), (20, 16), (26, 13), (18, 8), (1, 31), (5, 23), (12, 12), (18, 11), (12, 10), (15, 18), (5, 25), (25, 31), (27, 24), (1, 2), (13, 16), (21, 13), (14, 29), (23, 6), (7, 36), (3, 29), (24, 29), (14, 22), (24, 6), (24, 5), (0, 30), (14, 18), (0, 15), (16, 25), (22, 22), (11, 19), (25, 24), (0, 29), (6, 21), (27, 21), (20, 24), (8, 24), (23, 9), (3, 31), (20, 19), (11, 36), (20, 34), (21, 12), (14, 37), (8, 27), (11, 28), (12, 35), (12, 17), (22, 12), (26, 31), (2, 28), (8, 1), (3, 0), (4, 31), (18, 20), (27, 12), (24, 30), (17, 27), (6, 0), (11, 29), (21, 9), (1, 11), (27, 29), (13, 20), (17, 19), (15, 37), (11, 12), (22, 32), (21, 2), (6, 18), (5, 10), (23, 17), (4, 7), (18, 27), (28, 21), (29, 9), (19, 3), (17, 1), (15, 16), (17, 22), (8, 38), (10, 9), (26, 14), (27, 35), (3, 30), (2, 11), (21, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "310800", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 26), (24, 35), (9, 21), (23, 1), (9, 30), (25, 38), (28, 24), (31, 0), (23, 17), (7, 31), (25, 9), (11, 24), (25, 3), (29, 20), (25, 24), (17, 14), (22, 26), (2, 2), (18, 35), (12, 14), (0, 35), (6, 32), (16, 6), (26, 3), (4, 9), (29, 38), (3, 9), (11, 2), (24, 36), (14, 17), (3, 37), (24, 1), (3, 19), (21, 10), (21, 12), (29, 13), (27, 13), (4, 26), (21, 13), (13, 22), (0, 14), (31, 11), (12, 32), (24, 23), (29, 19), (28, 5), (0, 23), (15, 15), (12, 38), (21, 18), (8, 23), (27, 7), (21, 21), (20, 30), (8, 34), (8, 19), (27, 27), (13, 27), (22, 22), (21, 8), (29, 7), (13, 6), (23, 10), (14, 38), (31, 16), (13, 33), (11, 33), (4, 24), (9, 12), (18, 14), (1, 26), (7, 2), (0, 19), (7, 10), (7, 17), (14, 5), (30, 1), (28, 30), (14, 15), (7, 4), (3, 20), (23, 6), (25, 5), (18, 6), (16, 8), (25, 36), (14, 35), (7, 7), (28, 22), (10, 37), (3, 30), (16, 25), (16, 27), (13, 24), (11, 3), (31, 26), (29, 31), (20, 26), (16, 10), (11, 11), (24, 19), (9, 24), (21, 28), (11, 28), (15, 5), (24, 12), (17, 30), (26, 34), (25, 33), (2, 24), (3, 36), (14, 27), (6, 8), (2, 3), (14, 6), (22, 32), (17, 36), (11, 34), (26, 30), (18, 11), (6, 25), (28, 14), (4, 10), (2, 6), (29, 33), (7, 26), (23, 37), (27, 12), (0, 10), (13, 28), (9, 11), (20, 7), (23, 12), (8, 21), (10, 9), (10, 21), (10, 27), (5, 8), (16, 36), (7, 36), (24, 15), (12, 20), (11, 13), (13, 38), (27, 8), (31, 5), (21, 35), (23, 22), (5, 13), (15, 36), (6, 22), (27, 30), (10, 5), (13, 10), (8, 9), (3, 21), (14, 3), (15, 19), (9, 4), (22, 24), (3, 27), (29, 23), (21, 0), (4, 7), (26, 32), (13, 20), (14, 14), (10, 32), (6, 10), (5, 28), (4, 2), (16, 11), (6, 30), (31, 34), (22, 20), (23, 32), (7, 33), (9, 31), (25, 23), (12, 7), (9, 33), (11, 9), (23, 35), (13, 1), (20, 8), (14, 29), (1, 28), (15, 12), (25, 26), (10, 38), (13, 30), (11, 31), (15, 32), (22, 28), (11, 4), (19, 8), (14, 24), (1, 14), (20, 34), (3, 16), (6, 15), (16, 1), (12, 26), (25, 34), (13, 4), (23, 23), (0, 18), (28, 8), (0, 34), (29, 10), (19, 13), (23, 36), (16, 22), (14, 16), (21, 32), (29, 8), (19, 3), (15, 37), (15, 33), (26, 37), (20, 17), (27, 37), (24, 11), (31, 20), (25, 15), (12, 27), (0, 22), (19, 0), (15, 38), (20, 23), (27, 31), (0, 36), (24, 21), (30, 6), (17, 15), (0, 4), (8, 11), (18, 9), (14, 13), (31, 35), (6, 7), (21, 5), (16, 4), (6, 37), (4, 18), (16, 26), (13, 5), (24, 8), (2, 29), (17, 5), (8, 36), (26, 7), (25, 22), (22, 19), (20, 4), (1, 29), (6, 16), (13, 8), (27, 22), (5, 3), (2, 9), (2, 37), (4, 13), (5, 15), (2, 26), (24, 22), (30, 17), (11, 23), (22, 35), (22, 1), (19, 11), (3, 2), (21, 27), (4, 6), (10, 26), (0, 9), (18, 2), (18, 29), (6, 6), (28, 34), (26, 8), (16, 31), (1, 35), (17, 27), (30, 29), (13, 13), (5, 7), (5, 24), (10, 25), (4, 12), (17, 37), (17, 21), (1, 3), (5, 33), (19, 35), (18, 32), (10, 30), (8, 33), (0, 7), (24, 38), (31, 23), (0, 24), (27, 18), (15, 14), (18, 27), (2, 34), (3, 13), (29, 11), (4, 8), (8, 29), (19, 22), (3, 0), (18, 23), (16, 15), (12, 0), (19, 34), (30, 25), (11, 25), (3, 11), (9, 1), (18, 38), (11, 19), (12, 9), (22, 17), (8, 31), (4, 37), (2, 35), (10, 17), (29, 22), (26, 26), (1, 34), (24, 0), (15, 25), (14, 37), (12, 11), (4, 15), (8, 0), (6, 5), (4, 34), (9, 20), (14, 7), (12, 15), (4, 22), (31, 37), (21, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174960", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 14), (3, 27), (14, 8), (26, 6), (13, 32), (10, 18), (22, 28), (9, 16), (2, 12), (30, 30), (32, 21), (6, 25), (26, 0), (30, 12), (29, 19), (23, 27), (35, 32), (12, 21), (22, 21), (3, 8), (0, 10), (5, 19), (11, 19), (28, 22), (19, 26), (6, 33), (31, 2), (31, 18), (27, 13), (28, 16), (0, 20), (3, 23), (28, 29), (2, 3), (12, 20), (2, 30), (29, 1), (30, 1), (17, 4), (5, 23), (31, 25), (9, 3), (4, 6), (14, 6), (4, 33), (28, 23), (15, 17), (13, 17), (13, 4), (33, 10), (4, 24), (11, 6), (0, 5), (23, 29), (16, 19), (9, 2), (33, 15), (4, 29), (17, 31), (7, 12), (22, 23), (2, 16), (19, 29), (21, 25), (3, 14), (32, 4), (32, 7), (30, 26), (13, 26), (26, 24), (11, 30), (11, 3), (0, 19), (14, 9), (0, 2), (12, 23), (14, 24), (1, 15), (7, 7), (18, 7), (18, 9), (9, 18), (23, 28), (15, 23), (25, 9), (6, 2), (23, 26), (0, 25), (30, 10), (1, 13), (10, 30), (9, 30), (23, 19), (21, 15), (18, 18), (10, 12), (26, 23), (24, 4), (7, 17), (7, 14), (26, 4), (24, 9), (20, 0), (0, 9), (5, 12), (6, 16), (18, 13), (17, 15), (34, 13), (34, 15), (25, 2), (17, 29), (22, 24), (35, 21), (10, 17), (3, 21), (16, 28), (8, 5), (6, 7), (25, 4), (34, 24), (31, 9), (27, 21), (23, 7), (10, 13), (5, 26), (8, 12), (14, 31), (26, 2), (13, 10), (10, 5), (22, 4), (21, 23), (4, 30), (31, 8), (20, 33), (22, 20), (23, 11), (14, 26), (11, 18), (18, 8), (10, 3), (6, 4), (15, 11), (3, 6), (26, 1), (21, 20), (16, 22), (16, 13), (29, 33), (23, 24), (16, 27), (24, 29), (31, 6), (30, 32), (32, 31), (13, 28), (16, 18), (15, 31), (20, 19), (11, 32), (22, 10), (13, 33), (0, 11), (27, 11), (24, 11), (27, 28), (24, 12), (18, 32), (9, 32), (5, 30), (6, 14), (8, 18), (27, 5), (21, 5), (4, 16), (21, 0), (1, 32), (32, 20), (16, 5), (3, 25), (35, 19), (2, 14), (0, 33), (25, 6), (0, 17), (13, 20), (18, 16), (35, 20), (17, 28), (20, 16), (29, 17), (24, 16), (33, 8), (8, 29), (2, 33), (19, 3), (28, 31), (16, 0), (16, 3), (27, 10), (9, 5), (16, 1), (31, 23), (16, 15), (28, 14), (7, 29), (21, 30), (20, 7), (10, 25), (23, 8), (5, 6), (13, 13), (25, 12), (17, 13), (21, 8), (28, 30), (35, 18), (24, 7), (16, 6), (29, 3), (31, 32), (15, 19), (13, 2), (17, 33), (26, 29), (31, 19), (31, 12), (24, 22), (9, 12), (13, 0), (26, 3), (20, 10), (7, 31), (7, 21), (5, 10), (35, 6), (4, 17), (34, 21), (29, 2), (24, 6), (2, 4), (23, 31), (26, 15), (7, 8), (27, 30), (22, 25), (19, 16), (11, 23), (0, 6), (16, 32), (21, 24), (9, 26), (1, 19), (10, 29), (26, 12), (17, 6), (22, 7), (2, 29), (18, 5), (8, 1), (1, 30), (1, 1), (29, 12), (29, 0), (29, 5), (27, 12), (33, 28), (11, 12), (4, 5), (3, 1), (5, 2), (14, 10), (18, 23), (6, 31), (14, 1), (32, 15), (5, 16), (33, 0), (4, 9), (21, 31), (25, 21), (5, 11), (27, 17), (16, 31), (6, 26), (7, 20), (18, 24), (4, 2), (8, 27), (24, 28), (25, 27), (11, 10), (13, 25), (18, 15), (3, 20), (7, 13), (6, 32), (33, 4), (22, 3), (3, 18), (12, 25), (28, 0), (1, 8), (32, 28), (31, 4), (30, 17), (2, 20), (1, 10), (14, 14), (31, 13), (14, 21), (1, 18), (33, 14), (28, 8), (4, 7), (33, 9), (33, 22), (27, 2), (16, 20), (15, 7), (5, 0), (31, 16), (16, 16), (10, 11), (11, 27), (12, 24), (23, 12), (26, 16), (23, 33), (22, 12), (11, 29), (18, 17), (31, 26), (5, 1), (26, 20), (12, 18), (8, 13), (29, 15), (20, 29), (18, 1), (33, 19), (7, 16), (18, 14), (1, 25), (17, 27), (23, 25), (28, 32), (12, 2), (15, 3), (29, 23), (12, 12), (9, 7), (27, 32), (16, 17), (5, 18), (0, 31), (21, 33), (25, 18), (12, 30), (33, 29), (18, 10), (4, 31), (1, 3), (25, 29), (10, 21), (3, 12), (30, 14), (21, 14), (21, 3), (0, 32), (34, 23), (22, 9), (18, 2), (3, 5), (19, 20), (24, 0), (26, 25), (20, 31), (21, 2), (32, 26), (2, 6), (10, 26), (16, 9), (32, 6), (15, 29), (12, 15), (11, 8), (25, 15), (30, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439452", "dataset": "MATH"}
{"messages": [{"content": "In a 35x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 38), 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), (26, 15), (2, 38), (2, 8), (0, 10), (13, 29), (18, 23), (17, 2), (9, 32), (23, 6), (19, 4), (23, 26), (21, 23), (3, 26), (15, 0), (0, 24), (22, 25), (28, 3), (27, 3), (24, 31), (6, 12), (11, 16), (29, 37), (3, 2), (26, 33), (6, 3), (7, 10), (22, 35), (7, 25), (23, 7), (15, 22), (13, 22), (16, 22), (13, 35), (1, 16), (23, 13), (29, 23), (20, 12), (26, 10), (22, 2), (25, 6), (21, 31), (7, 27), (27, 10), (30, 35), (10, 36), (19, 12), (14, 21), (19, 1), (3, 3), (4, 5), (16, 29), (5, 32), (31, 24), (5, 18), (21, 26), (8, 20), (5, 6), (6, 25), (31, 23), (15, 2), (22, 4), (22, 3), (31, 21), (19, 9), (10, 2), (10, 3), (22, 18), (0, 8), (33, 21), (1, 11), (17, 3), (4, 15), (3, 36), (4, 0), (4, 1), (2, 37), (34, 16), (6, 35), (20, 14), (26, 21), (14, 32), (34, 9), (1, 0), (33, 27), (32, 36), (8, 9), (8, 12), (6, 32), (16, 34), (12, 36), (33, 34), (8, 0), (20, 6), (24, 26), (25, 20), (27, 26), (24, 12), (8, 35), (33, 38), (0, 21), (3, 24), (20, 33), (2, 14), (28, 7), (34, 27), (15, 25), (32, 17), (13, 0), (2, 33), (30, 5), (12, 20), (15, 15), (12, 21), (10, 19), (3, 27), (10, 38), (28, 13), (6, 11), (34, 20), (11, 12), (8, 29), (27, 22), (15, 31), (23, 2), (4, 38), (22, 15), (28, 10), (14, 0), (10, 31), (12, 34), (3, 19), (23, 36), (6, 13), (23, 20), (13, 31), (27, 16), (18, 31), (34, 13), (33, 32), (17, 12), (6, 2), (20, 13), (17, 35), (21, 29), (26, 5), (32, 26), (9, 25), (28, 17), (6, 27), (8, 3), (33, 15), (26, 0), (10, 4), (21, 16), (3, 37), (21, 6), (11, 34), (12, 30), (1, 13), (31, 29), (7, 7), (18, 35), (29, 20), (8, 26), (29, 30), (24, 14), (17, 16), (0, 31), (8, 15), (24, 17), (15, 19), (12, 5), (4, 10), (13, 11), (17, 30), (14, 14), (27, 6), (15, 36), (1, 19), (23, 1), (23, 25), (2, 7), (21, 17), (6, 5), (33, 3), (20, 27), (4, 12), (33, 13), (6, 24), (15, 27), (31, 32), (29, 14), (21, 10), (7, 22), (0, 34), (7, 33), (4, 17), (29, 4), (8, 11), (6, 18), (33, 25), (4, 35), (7, 35), (32, 30), (27, 2), (3, 25), (34, 19), (19, 30), (20, 32), (11, 9), (14, 17), (2, 0), (30, 13), (13, 37), (23, 14), (4, 11), (12, 9), (9, 29), (20, 9), (20, 34), (31, 8), (26, 26), (12, 24), (27, 5), (12, 29), (1, 4), (0, 38), (1, 23), (19, 37), (32, 20), (26, 9), (31, 31), (18, 0), (28, 34), (12, 8), (22, 38), (31, 15), (28, 29), (31, 1), (18, 3), (32, 2), (33, 31), (8, 21), (16, 9), (12, 16), (20, 23), (1, 37), (8, 18), (25, 28), (32, 8), (7, 17), (3, 18), (9, 9), (16, 4), (22, 12), (18, 7), (5, 15), (32, 5), (2, 10), (4, 29), (32, 23), (19, 38), (9, 14), (17, 6), (23, 17), (24, 25), (32, 10), (2, 26), (5, 2), (21, 5), (9, 27), (1, 25), (27, 8), (32, 32), (20, 2), (30, 24), (1, 2), (15, 9), (24, 5), (4, 4), (17, 31), (23, 21), (33, 2), (0, 9), (19, 33), (17, 13), (31, 2), (1, 6), (22, 21), (6, 34), (19, 6), (14, 36), (5, 16), (27, 9), (14, 7), (13, 25), (32, 27), (9, 10), (11, 0), (27, 21), (13, 5), (21, 22), (0, 15), (16, 20), (32, 31), (8, 14), (6, 23), (31, 11), (17, 28), (7, 28), (15, 6), (28, 8), (11, 5), (33, 6), (9, 26), (17, 23), (20, 7), (23, 33), (15, 5), (24, 24), (22, 9), (7, 38), (31, 27), (8, 36), (16, 26), (23, 22), (26, 12), (20, 0), (15, 4), (32, 12), (14, 10), (24, 1), (22, 0), (34, 22), (29, 0), (29, 38), (19, 32), (15, 13), (31, 13), (12, 14), (4, 30), (5, 8), (10, 33), (24, 8), (29, 1), (5, 23), (31, 10), (2, 34), (10, 11), (24, 33), (24, 0), (16, 24), (2, 29), (17, 38), (27, 7), (9, 38), (10, 7), (29, 22), (34, 29), (17, 4), (8, 25), (16, 2), (8, 5), (22, 26), (22, 32), (34, 10), (30, 7), (28, 36), (8, 30), (16, 27), (27, 15), (21, 2), (30, 26), (34, 6), (13, 1), (16, 16), (16, 19), (24, 4), (14, 4), (7, 8), (16, 10), (1, 18), (7, 18), (28, 26), (5, 33), (3, 34), (16, 36), (5, 36), (20, 8), (5, 25), (26, 22), (31, 7), (30, 15), (23, 5), (2, 20), (27, 32), (20, 16), (2, 5), (31, 4), (19, 16), (4, 31), (0, 33), (24, 34), (11, 27), (18, 24), (30, 36), (21, 30), (27, 13), (15, 35), (4, 27), (7, 26), (12, 27), (13, 33), (12, 18), (26, 16), (27, 35), (30, 29), (21, 38), (29, 25), (5, 27), (25, 30), (11, 3), (25, 14), (0, 27), (20, 3), (10, 21), (9, 13), (12, 10), (27, 18), (32, 16), (24, 30), (7, 5), (27, 31), (25, 7), (20, 4), (27, 29), (10, 32), (14, 15), (18, 15), (10, 6), (15, 10), (4, 19), (10, 16), (34, 31), (5, 37), (5, 5), (7, 24), (25, 23), (30, 0), (4, 21), (17, 26), (29, 12), (16, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626940", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 25), (32, 29), (15, 21), (11, 13), (11, 31), (8, 35), (6, 34), (26, 14), (27, 7), (8, 6), (17, 16), (34, 1), (22, 13), (33, 26), (5, 7), (9, 34), (30, 34), (15, 25), (20, 27), (23, 9), (30, 28), (0, 36), (12, 25), (2, 13), (26, 31), (23, 26), (27, 10), (20, 33), (11, 30), (24, 27), (7, 4), (34, 28), (35, 5), (34, 32), (14, 5), (36, 24), (13, 4), (9, 6), (38, 4), (28, 9), (30, 8), (4, 12), (14, 23), (20, 19), (23, 20), (37, 0), (34, 4), (6, 7), (17, 34), (1, 8), (12, 17), (17, 27), (19, 24), (31, 35), (9, 5), (16, 9), (5, 30), (7, 6), (12, 28), (34, 12), (5, 20), (23, 8), (15, 19), (31, 29), (31, 20), (18, 26), (10, 3), (33, 0), (32, 16), (26, 1), (26, 6), (33, 19), (26, 27), (28, 4), (35, 23), (17, 2), (0, 4), (18, 32), (27, 0), (20, 6), (22, 8), (4, 9), (30, 29), (35, 27), (32, 27), (0, 28), (14, 22), (11, 32), (11, 11), (37, 18), (2, 15), (12, 10), (18, 1), (8, 19), (10, 13), (1, 6), (28, 1), (13, 21), (9, 32), (6, 8), (5, 18), (30, 23), (16, 11), (7, 12), (16, 29), (17, 0), (11, 1), (32, 3), (2, 12), (22, 4), (34, 34), (31, 18), (24, 23), (33, 1), (10, 31), (26, 8), (36, 2), (14, 9), (29, 24), (2, 30), (5, 27), (3, 28), (25, 2), (8, 36), (18, 36), (15, 1), (23, 7), (36, 35), (25, 1), (26, 25), (38, 25), (8, 7), (4, 33), (28, 26), (31, 34), (12, 31), (38, 13), (38, 22), (25, 11), (16, 7), (24, 20), (9, 15), (29, 8), (13, 23), (16, 13), (32, 9), (19, 23), (0, 25), (10, 15), (10, 7), (6, 13), (5, 10), (2, 24), (15, 24), (8, 29), (28, 20), (28, 35), (10, 6), (18, 30), (28, 24), (38, 19), (23, 25), (8, 11), (4, 21), (13, 0), (14, 33), (7, 28), (24, 22), (2, 23), (3, 31), (33, 7), (5, 4), (37, 21), (37, 9), (21, 15), (31, 36), (37, 34), (29, 14), (0, 13), (27, 28), (21, 3), (33, 14), (15, 11), (25, 35), (16, 28), (9, 22), (1, 11), (9, 13), (3, 10), (11, 8), (2, 14), (9, 30), (34, 2), (23, 31), (23, 3), (25, 25), (37, 13), (11, 12), (0, 12), (6, 27), (25, 24), (33, 34), (1, 34), (12, 16), (9, 1), (19, 11), (9, 18), (2, 25), (29, 10), (36, 8), (21, 13), (21, 31), (1, 28), (22, 15), (2, 18), (33, 3), (17, 15), (29, 7), (28, 16), (10, 2), (14, 4), (29, 19), (18, 28), (37, 8), (24, 6), (0, 35), (0, 23), (30, 0), (25, 15), (35, 1), (4, 18), (10, 33), (22, 35), (36, 14), (18, 21), (29, 12), (1, 3), (3, 1), (2, 19), (36, 5), (16, 34), (12, 18), (25, 28), (14, 34), (14, 16), (37, 16), (20, 29), (33, 36), (7, 19), (31, 27), (24, 19), (5, 1), (35, 12), (12, 0), (2, 32), (31, 11), (33, 20), (26, 12), (27, 5), (36, 26), (0, 26), (2, 4), (14, 27), (30, 16), (21, 9), (3, 17), (36, 19), (26, 11), (18, 23), (13, 6), (30, 31), (20, 9), (20, 0), (12, 26), (31, 30), (30, 27), (18, 27), (1, 13), (1, 27), (19, 21), (2, 0), (20, 8), (22, 10), (3, 7), (6, 12), (32, 23), (24, 30), (11, 36), (18, 8), (26, 21), (11, 2), (6, 32), (9, 21), (16, 22), (19, 28), (4, 6), (4, 26), (16, 8), (35, 13), (30, 3), (28, 18), (38, 7), (24, 21), (34, 3), (1, 4), (28, 28), (10, 18), (36, 11), (32, 5), (20, 24), (22, 18), (17, 17), (7, 29), (19, 19), (20, 26), (23, 18), (6, 9), (10, 12), (6, 16), (16, 25), (37, 6), (23, 0), (16, 5), (37, 10), (29, 11), (17, 5), (27, 29), (25, 3), (22, 36), (25, 29), (5, 15), (10, 16), (34, 10), (23, 32), (23, 12), (37, 4), (17, 1), (12, 19), (7, 23), (19, 35), (16, 33), (28, 23), (16, 23), (0, 1), (27, 25), (26, 15), (4, 27), (35, 8), (1, 30), (29, 26), (2, 22), (20, 23), (11, 24), (21, 17), (33, 13), (33, 33), (23, 22), (32, 17), (17, 9), (4, 5), (22, 17), (29, 18), (18, 12), (9, 23), (25, 32), (16, 24), (17, 32), (12, 30), (32, 28), (30, 14), (6, 6), (26, 0), (38, 35), (8, 18), (18, 16), (10, 19), (6, 31), (8, 17), (27, 36), (38, 28), (26, 28), (16, 36), (38, 12), (26, 26), (19, 20), (34, 26), (22, 24), (23, 35), (11, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "741240", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (16, 0), (15, 4), (37, 23), (8, 27), (16, 22), (22, 22), (7, 15), (7, 6), (36, 2), (35, 28), (30, 5), (22, 38), (14, 32), (4, 10), (32, 11), (26, 4), (23, 13), (1, 37), (32, 25), (30, 25), (3, 9), (34, 36), (22, 23), (22, 27), (5, 3), (9, 30), (33, 10), (5, 28), (29, 21), (5, 38), (7, 2), (24, 29), (34, 25), (7, 34), (36, 5), (12, 26), (22, 37), (23, 34), (28, 8), (15, 13), (14, 1), (36, 38), (12, 11), (3, 27), (10, 28), (4, 20), (14, 0), (10, 10), (0, 31), (29, 19), (20, 24), (12, 5), (21, 28), (13, 5), (21, 24), (12, 7), (18, 8), (25, 26), (34, 19), (0, 24), (21, 15), (11, 17), (15, 14), (23, 28), (25, 22), (26, 10), (24, 24), (22, 18), (27, 36), (33, 20), (23, 2), (2, 34), (3, 38), (30, 18), (21, 32), (35, 29), (17, 13), (16, 4), (18, 28), (11, 31), (10, 15), (34, 30), (1, 28), (8, 29), (20, 18), (35, 30), (17, 11), (6, 29), (13, 20), (13, 38), (0, 10), (29, 0), (31, 26), (23, 20), (23, 37), (31, 8), (9, 5), (0, 27), (35, 27), (13, 16), (2, 8), (16, 9), (4, 33), (14, 36), (19, 14), (22, 5), (3, 2), (22, 14), (31, 27), (35, 37), (27, 38), (5, 6), (32, 19), (8, 19), (2, 33), (37, 26), (3, 33), (4, 23), (9, 21), (3, 25), (7, 26), (26, 5), (16, 32), (11, 37), (17, 9), (9, 29), (0, 25), (12, 9), (0, 21), (33, 3), (34, 7), (18, 38), (27, 24), (33, 21), (2, 26), (15, 2), (19, 34), (15, 20), (30, 15), (23, 29), (26, 14), (20, 35), (15, 11), (31, 31), (9, 14), (15, 5), (9, 0), (5, 21), (2, 7), (14, 30), (38, 35), (11, 16), (25, 21), (1, 4), (16, 15), (22, 32), (3, 22), (30, 4), (27, 19), (14, 31), (8, 0), (35, 25), (20, 12), (2, 20), (38, 12), (34, 3), (25, 15), (29, 5), (35, 31), (33, 30), (30, 20), (3, 35), (11, 32), (17, 10), (18, 37), (33, 1), (33, 36), (28, 7), (9, 7), (4, 19), (27, 18), (31, 9), (13, 15), (16, 23), (15, 10), (24, 3), (38, 29), (28, 0), (31, 19), (34, 15), (5, 7), (35, 7), (19, 6), (15, 0), (23, 33), (7, 7), (8, 8), (30, 7), (3, 30), (24, 28), (32, 27), (11, 27), (27, 34), (2, 17), (32, 2), (13, 14), (30, 22), (36, 11), (35, 8), (21, 2), (25, 24), (36, 16), (16, 25), (4, 7), (26, 8), (4, 25), (22, 7), (1, 12), (38, 33), (18, 24), (3, 18), (23, 5), (2, 5), (16, 16), (36, 19), (3, 13), (25, 14), (0, 13), (25, 0), (37, 16), (11, 25), (34, 12), (27, 26), (31, 36), (28, 13), (7, 16), (1, 27), (18, 17), (2, 1), (23, 14), (18, 14), (38, 5), (19, 9), (19, 13), (12, 14), (7, 32), (19, 33), (3, 16), (37, 11), (30, 34), (32, 38), (5, 19), (32, 24), (25, 29), (30, 2), (13, 28), (15, 38), (19, 22), (20, 11), (28, 18), (29, 7), (14, 38), (29, 33), (23, 7), (7, 24), (20, 7), (9, 9), (26, 16), (25, 25), (32, 15), (6, 38), (35, 13), (7, 8), (6, 9), (11, 8), (18, 33), (5, 30), (0, 28), (24, 13), (27, 0), (1, 18), (22, 20), (17, 32), (8, 1), (10, 30), (31, 25), (6, 1), (18, 35), (1, 1), (27, 6), (31, 15), (16, 7), (38, 19), (29, 36), (20, 2), (27, 4), (32, 12), (4, 21), (34, 38), (36, 21), (23, 21), (20, 38), (38, 8), (22, 8), (5, 18), (35, 33), (27, 15), (1, 10), (27, 3), (16, 18), (9, 10), (6, 17), (30, 24), (13, 35), (1, 16), (16, 5), (18, 21), (8, 14), (12, 33), (4, 36), (2, 11), (24, 31), (1, 2), (3, 32), (9, 22), (2, 24), (30, 17), (7, 3), (25, 11), (10, 17), (11, 12), (24, 5), (22, 2), (19, 0), (3, 14), (3, 36), (4, 15), (1, 24), (25, 31), (37, 32), (19, 19), (10, 0), (32, 6), (20, 28), (1, 32), (3, 0), (10, 1), (27, 25), (14, 9), (15, 30), (15, 31), (3, 20), (7, 19), (36, 37), (8, 35), (4, 11), (19, 25), (32, 30), (10, 12), (15, 26), (34, 1), (11, 21), (28, 12), (31, 6), (18, 2), (5, 31), (25, 23), (27, 17), (14, 23), (16, 30), (6, 28), (9, 13), (6, 14), (29, 37), (12, 6), (33, 16), (10, 16), (20, 33), (23, 16), (22, 12), (10, 33), (14, 25), (33, 7), (26, 19), (18, 34), (38, 25), (15, 27), (36, 4), (21, 38), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "844992", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (2, 12), (24, 36), (19, 29), (14, 22), (13, 23), (3, 11), (6, 19), (16, 24), (17, 36), (1, 29), (12, 12), (16, 19), (10, 25), (17, 18), (7, 31), (29, 22), (13, 25), (7, 21), (28, 0), (13, 0), (13, 20), (34, 20), (18, 7), (34, 22), (14, 21), (0, 5), (13, 22), (27, 2), (10, 4), (31, 2), (16, 27), (17, 13), (26, 8), (12, 26), (1, 4), (4, 12), (6, 9), (12, 7), (27, 7), (33, 33), (13, 26), (27, 15), (29, 23), (24, 9), (13, 7), (23, 20), (26, 23), (4, 29), (28, 1), (29, 36), (13, 31), (18, 29), (15, 25), (11, 2), (11, 18), (33, 15), (5, 22), (4, 15), (6, 15), (11, 15), (10, 8), (17, 2), (4, 9), (31, 4), (1, 33), (34, 28), (10, 20), (2, 26), (10, 27), (29, 15), (32, 10), (23, 29), (27, 9), (13, 5), (21, 15), (29, 2), (21, 8), (2, 5), (9, 28), (33, 27), (21, 12), (20, 9), (14, 8), (12, 0), (2, 14), (18, 21), (3, 6), (26, 24), (1, 18), (19, 22), (4, 3), (14, 35), (23, 10), (6, 14), (25, 24), (16, 1), (10, 11), (6, 27), (25, 33), (8, 35), (26, 7), (15, 30), (34, 1), (31, 7), (20, 10), (22, 16), (4, 28), (25, 30), (17, 15), (2, 17), (32, 7), (25, 9), (4, 10), (25, 23), (20, 3), (2, 16), (12, 35), (32, 18), (28, 28), (10, 19), (16, 0), (11, 4), (6, 28), (32, 12), (1, 3), (4, 17), (17, 17), (14, 0), (10, 32), (17, 16), (18, 2), (30, 17), (3, 10), (9, 18), (3, 16), (28, 6), (13, 17), (19, 7), (24, 30), (13, 13), (1, 7), (25, 4), (33, 35), (0, 31), (6, 25), (0, 11), (33, 17), (29, 34), (13, 35), (23, 4), (0, 16), (17, 3), (26, 14), (30, 34), (0, 32), (32, 22), (31, 22), (10, 29), (29, 8), (12, 9), (26, 15), (22, 5), (14, 13), (25, 28), (8, 34), (33, 21), (13, 9), (25, 14), (7, 9), (21, 24), (2, 34), (25, 2), (22, 32), (27, 1), (22, 29), (4, 27), (33, 6), (7, 0), (25, 35), (14, 15), (11, 9), (31, 27), (19, 25), (19, 5), (13, 16), (21, 25), (34, 2), (34, 27), (8, 28), (31, 0), (3, 33), (28, 24), (6, 13), (0, 24), (19, 0), (4, 6), (29, 9), (10, 0), (2, 20), (6, 23), (28, 20), (29, 11), (33, 1), (5, 11), (15, 16), (13, 6), (11, 0), (8, 32), (3, 28), (15, 28), (12, 10), (23, 28), (28, 7), (21, 17), (0, 35), (32, 0), (22, 2), (13, 19), (21, 31), (33, 25), (4, 13), (31, 28), (23, 16), (8, 12), (10, 7), (15, 35), (5, 35), (14, 28), (1, 6), (28, 27), (26, 6), (11, 13), (6, 6), (33, 11), (9, 26), (18, 25), (21, 16), (1, 12), (31, 24), (31, 26), (9, 19), (11, 24), (12, 4), (0, 2), (27, 31), (10, 23), (13, 3), (1, 8), (12, 2), (16, 18), (3, 7), (6, 10), (5, 20), (11, 16), (29, 35), (28, 15), (18, 28), (32, 28), (1, 24), (27, 22), (3, 17), (27, 24), (19, 23), (0, 25), (21, 5), (17, 6), (27, 14), (5, 9), (10, 2), (32, 17), (16, 15), (13, 27), (18, 17), (1, 2), (23, 13), (19, 35), (13, 18), (16, 31), (19, 24), (8, 33), (5, 17), (16, 10), (19, 32), (4, 4), (17, 9), (5, 30), (33, 26), (28, 32), (2, 27), (29, 32), (8, 19), (1, 20), (19, 21), (31, 18), (33, 20), (20, 6), (2, 6), (30, 29), (7, 26), (34, 11), (3, 12), (2, 13), (31, 14), (2, 22), (32, 13), (9, 4), (4, 30), (13, 21), (31, 11), (22, 20), (4, 32), (14, 33), (32, 24), (3, 23), (17, 24), (4, 18), (33, 0), (25, 16), (33, 29), (24, 35), (25, 17), (30, 18), (18, 10), (3, 32), (5, 12), (34, 25), (34, 15), (19, 13), (33, 7), (3, 30), (21, 23), (4, 33), (32, 11), (30, 6), (20, 2), (16, 30), (2, 35), (5, 25), (3, 3), (14, 26), (3, 15), (25, 8), (20, 18), (0, 13), (33, 9), (29, 27), (14, 30), (10, 18), (22, 30), (8, 0), (29, 30), (24, 8), (25, 0), (8, 2), (24, 32), (3, 18), (10, 10), (26, 12), (15, 2), (0, 36), (30, 8), (27, 19), (2, 21), (8, 30), (5, 13), (3, 22), (19, 3), (4, 35), (20, 13), (5, 4), (9, 17), (12, 3), (31, 19), (15, 13), (34, 31), (11, 8), (10, 6), (22, 25), (4, 36), (8, 9), (23, 15), (28, 21), (26, 4), (18, 19), (28, 17), (26, 27), (25, 10), (12, 33), (1, 25), (24, 24), (22, 34), (31, 35), (9, 2), (32, 16), (34, 4), (3, 8), (6, 31), (19, 14), (30, 32), (8, 25), (29, 21), (17, 8), (14, 25), (34, 16), (19, 11), (21, 33), (20, 35), (15, 36), (30, 28), (9, 23), (21, 6), (16, 23), (30, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "893760", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), 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), (14, 23), (1, 25), (4, 3), (7, 1), (24, 0), (4, 9), (33, 11), (18, 2), (7, 19), (12, 1), (27, 24), (11, 0), (9, 8), (20, 15), (0, 14), (3, 26), (8, 30), (19, 11), (15, 0), (8, 29), (8, 13), (24, 11), (30, 21), (33, 9), (9, 26), (19, 10), (4, 29), (21, 29), (13, 20), (8, 21), (28, 9), (2, 13), (14, 8), (23, 31), (28, 12), (19, 17), (17, 15), (10, 20), (0, 27), (30, 17), (29, 8), (21, 19), (14, 9), (18, 0), (30, 26), (22, 8), (27, 10), (26, 29), (30, 28), (30, 31), (15, 8), (1, 26), (19, 18), (32, 12), (22, 19), (31, 29), (26, 2), (11, 27), (9, 27), (4, 4), (7, 18), (25, 21), (13, 9), (13, 11), (20, 23), (13, 5), (27, 22), (10, 30), (3, 17), (1, 16), (18, 28), (31, 0), (18, 11), (24, 7), (4, 11), (21, 13), (21, 11), (2, 30), (27, 30), (4, 15), (3, 10), (20, 3), (10, 24), (25, 28), (26, 9), (27, 15), (29, 21), (16, 26), (33, 23), (8, 2), (11, 11), (33, 3), (4, 28), (32, 24), (12, 23), (26, 7), (25, 12), (10, 4), (1, 31), (28, 11), (14, 19), (6, 21), (18, 19), (1, 18), (32, 6), (6, 3), (23, 21), (14, 13), (28, 23), (9, 9), (24, 27), (1, 19), (16, 16), (18, 18), (15, 27), (24, 9), (16, 27), (10, 9), (15, 13), (6, 29), (1, 6), (18, 1), (3, 18), (27, 12), (9, 6), (7, 12), (16, 1), (24, 26), (24, 12), (14, 22), (24, 20), (13, 6), (25, 7), (3, 7), (20, 28), (22, 31), (14, 10), (6, 10), (25, 26), (29, 3), (33, 2), (23, 16), (9, 23), (16, 7), (2, 26), (33, 13), (28, 3), (10, 29), (19, 22), (4, 19), (18, 7), (21, 17), (8, 11), (31, 15), (29, 18), (1, 7), (3, 11), (6, 13), (8, 18), (15, 28), (2, 1), (4, 0), (30, 19), (10, 31), (17, 0), (28, 30), (27, 7), (24, 30), (32, 13), (22, 18), (6, 24), (32, 0), (31, 4), (6, 1), (25, 22), (13, 23), (23, 20), (26, 11), (17, 28), (16, 23), (8, 26), (33, 18), (16, 2), (24, 18), (17, 4), (23, 4), (24, 22), (7, 11), (28, 8), (20, 4), (18, 27), (3, 13), (29, 27), (8, 5), (31, 27), (23, 19), (14, 2), (5, 12), (2, 20), (17, 19), (31, 9), (1, 3), (25, 20), (14, 17), (20, 26), (22, 15), (19, 14), (28, 4), (20, 19), (8, 23), (22, 21), (28, 27), (2, 17), (25, 0), (1, 17), (13, 1), (25, 3), (11, 12), (31, 13), (27, 26), (12, 24), (23, 2), (26, 17), (28, 26), (13, 29), (2, 3), (2, 23), (5, 28), (1, 1), (26, 4), (2, 18), (29, 22), (24, 4), (30, 13), (0, 29), (21, 0), (28, 29), (18, 3), (21, 18), (14, 7), (9, 12), (2, 9), (18, 5), (14, 18), (24, 5), (12, 12), (14, 0), (1, 15), (26, 20), (5, 8), (8, 14), (30, 2), (3, 16), (21, 3), (32, 19), (12, 29), (4, 17), (28, 20), (6, 25), (19, 15), (20, 13), (4, 8), (7, 10), (12, 31), (11, 14), (0, 5), (20, 21), (22, 13), (0, 22), (7, 15), (30, 25), (29, 11), (32, 31), (31, 5), (30, 8), (18, 9), (32, 1), (27, 1), (32, 28), (17, 23), (8, 19), (33, 10), (23, 1), (33, 12), (23, 24), (5, 21), (6, 23), (20, 6), (21, 7), (30, 6), (15, 2), (9, 4), (23, 27), (15, 9), (17, 2), (7, 2), (5, 16), (7, 30), (23, 15), (14, 6), (16, 0), (18, 20), (16, 19), (16, 12), (19, 3), (32, 22), (32, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48480", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (37, 24), (13, 13), (29, 13), (12, 12), (32, 26), (28, 29), (16, 10), (3, 13), (37, 29), (28, 30), (30, 28), (13, 7), (13, 11), (23, 0), (10, 28), (21, 21), (37, 17), (15, 17), (10, 7), (20, 7), (1, 6), (28, 31), (23, 28), (32, 12), (0, 25), (29, 29), (0, 26), (30, 1), (21, 6), (3, 28), (12, 1), (7, 14), (29, 8), (15, 27), (8, 8), (15, 0), (14, 2), (14, 13), (3, 0), (16, 1), (9, 30), (3, 27), (6, 8), (1, 11), (24, 11), (24, 25), (17, 10), (0, 30), (31, 24), (24, 29), (28, 3), (33, 14), (26, 25), (15, 18), (7, 10), (1, 9), (35, 2), (33, 19), (7, 5), (30, 32), (36, 24), (28, 7), (20, 6), (17, 7), (34, 28), (27, 23), (4, 0), (5, 28), (30, 13), (7, 28), (9, 2), (9, 15), (24, 10), (1, 30), (4, 9), (17, 23), (33, 17), (5, 16), (33, 0), (32, 21), (33, 11), (13, 15), (17, 30), (2, 13), (4, 14), (35, 31), (34, 3), (7, 25), (15, 20), (3, 9), (34, 0), (13, 31), (12, 30), (17, 21), (14, 31), (34, 9), (1, 25), (30, 4), (9, 7), (28, 5), (13, 9), (12, 4), (34, 26), (33, 26), (26, 0), (23, 10), (29, 32), (3, 17), (2, 21), (19, 13), (30, 10), (2, 11), (24, 23), (15, 22), (18, 16), (3, 30), (17, 15), (6, 24), (18, 8), (23, 12), (11, 23), (27, 15), (37, 14), (28, 12), (15, 2), (12, 9), (30, 6), (15, 16), (8, 32), (4, 12), (9, 16), (8, 5), (17, 0), (0, 8), (24, 2), (28, 28), (25, 1), (22, 31), (35, 12), (10, 3), (6, 3), (0, 12), (11, 19), (27, 4), (27, 9), (8, 13), (31, 25), (9, 11), (21, 12), (14, 9), (14, 8), (18, 10), (9, 0), (6, 29), (20, 24), (3, 1), (29, 25), (3, 26), (20, 8), (37, 30), (35, 26), (32, 16), (15, 11), (8, 20), (37, 9), (29, 5), (2, 19), (14, 1), (25, 22), (5, 18), (19, 16), (20, 22), (21, 17), (19, 4), (2, 5), (8, 18), (19, 10), (11, 31), (6, 15), (37, 7), (14, 16), (35, 29), (18, 23), (15, 1), (35, 13), (31, 26), (30, 14), (31, 2), (16, 17), (17, 20), (37, 10), (4, 10), (30, 19), (26, 29), (32, 31), (29, 27), (26, 6), (1, 8), (5, 17), (5, 9), (18, 14), (28, 17), (11, 17), (11, 10), (12, 6), (28, 0), (2, 30), (3, 10), (26, 32), (36, 22), (21, 16), (36, 14), (23, 30), (6, 23), (18, 27), (21, 24), (19, 21), (21, 27), (1, 7), (6, 11), (22, 19), (31, 23), (20, 11), (5, 24), (11, 11), (23, 25), (19, 7), (16, 13), (0, 23), (27, 11), (12, 23), (16, 28), (25, 5), (13, 22), (22, 28), (21, 31), (9, 26), (15, 5), (20, 18), (1, 21), (35, 9), (34, 10), (31, 11), (9, 24), (0, 18), (36, 12), (34, 12), (6, 26), (16, 25), (31, 6), (35, 11), (8, 26), (30, 17), (30, 16), (19, 20), (26, 16), (34, 25), (33, 10), (19, 1), (6, 1), (30, 25), (12, 7), (8, 12), (13, 28), (24, 15), (32, 3), (4, 21), (23, 24), (13, 6), (27, 31), (12, 21), (37, 12), (4, 17), (7, 24), (22, 11), (32, 4), (35, 24), (22, 8), (3, 22), (17, 9), (27, 0), (19, 18), (11, 13), (0, 21), (15, 13), (5, 5), (28, 32), (17, 2), (36, 30), (24, 16), (7, 29), (24, 3), (34, 27), (23, 17), (6, 5), (36, 10), (13, 12), (4, 11), (3, 16), (19, 11), (23, 14), (29, 30), (0, 22), (9, 3), (27, 12), (7, 12), (20, 3), (33, 21), (15, 19), (34, 23), (30, 22), (10, 27), (16, 32), (34, 5), (1, 10), (5, 20), (36, 11), (4, 8), (8, 11), (1, 29), (20, 15), (29, 22), (2, 25), (20, 0), (6, 0), (10, 0), (2, 6), (22, 29), (12, 5), (3, 29), (5, 6), (11, 21), (27, 6), (19, 5), (9, 10), (32, 24), (21, 32), (11, 28), (23, 27), (32, 2), (31, 32), (18, 29), (26, 26), (26, 14), (28, 23), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946080", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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), (19, 9), (18, 18), (13, 2), (33, 3), (29, 6), (33, 9), (3, 17), (11, 19), (17, 3), (14, 15), (2, 17), (24, 22), (26, 20), (3, 12), (2, 10), (4, 4), (19, 26), (34, 8), (4, 23), (28, 3), (13, 6), (19, 5), (33, 23), (12, 17), (3, 15), (1, 12), (19, 10), (2, 25), (28, 29), (6, 15), (11, 22), (4, 8), (22, 15), (28, 30), (11, 5), (10, 9), (17, 11), (6, 16), (13, 30), (7, 21), (27, 26), (30, 18), (15, 16), (9, 22), (22, 25), (17, 9), (11, 13), (22, 16), (23, 14), (6, 25), (21, 16), (26, 11), (32, 7), (8, 13), (12, 27), (7, 28), (20, 2), (19, 22), (7, 3), (25, 26), (23, 1), (9, 21), (23, 15), (11, 28), (27, 28), (9, 31), (10, 7), (3, 8), (5, 28), (2, 2), (27, 4), (2, 1), (8, 2), (23, 13), (33, 12), (16, 5), (33, 30), (5, 14), (5, 19), (32, 23), (9, 5), (31, 15), (0, 23), (20, 31), (11, 1), (31, 21), (7, 5), (28, 25), (14, 24), (4, 25), (27, 3), (16, 7), (3, 19), (20, 22), (21, 29), (15, 6), (6, 19), (11, 15), (13, 17), (3, 9), (8, 16), (14, 20), (32, 3), (8, 19), (24, 6), (3, 4), (22, 18), (2, 8), (28, 4), (31, 16), (19, 13), (9, 29), (1, 5), (18, 29), (2, 4), (11, 31), (4, 21), (34, 9), (32, 18), (5, 29), (14, 18), (15, 22), (3, 22), (27, 25), (30, 4), (24, 2), (7, 12), (34, 10), (20, 29), (16, 15), (13, 27), (32, 24), (13, 0), (32, 9), (24, 26), (10, 13), (7, 20), (30, 13), (21, 23), (25, 21), (22, 31), (14, 12), (31, 26), (8, 27), (20, 19), (22, 20), (33, 10), (31, 17), (31, 3), (1, 8), (1, 22), (29, 1), (20, 4), (14, 8), (27, 2), (6, 10), (33, 27), (10, 22), (30, 5), (19, 16), (25, 29), (25, 5), (26, 16), (12, 13), (33, 5), (24, 13), (29, 16), (14, 11), (12, 8), (15, 17), (22, 3), (4, 26), (5, 17), (26, 5), (9, 11), (13, 20), (5, 8), (34, 14), (3, 20), (11, 16), (27, 14), (20, 15), (17, 22), (10, 26), (4, 15), (2, 27), (17, 26), (2, 15), (27, 23), (17, 1), (21, 31), (27, 31), (8, 28), (7, 19), (15, 20), (15, 12), (16, 17), (18, 11), (11, 27), (15, 26), (7, 31), (34, 21), (5, 20), (29, 18), (26, 2), (20, 17), (16, 28), (20, 28), (18, 19), (12, 19), (31, 8), (12, 29), (33, 7), (33, 4), (3, 21), (34, 17), (5, 12), (0, 16), (15, 10), (30, 22), (5, 15), (32, 26), (9, 6), (6, 1), (1, 15), (1, 24), (7, 26), (3, 0), (27, 17), (28, 8), (1, 27), (34, 6), (31, 11), (18, 5), (15, 24), (32, 16), (17, 4), (31, 13), (15, 15), (25, 19), (13, 10), (1, 6), (18, 13), (2, 29), (29, 17), (12, 12), (7, 0), (29, 26), (23, 0), (28, 9), (24, 8), (25, 20), (24, 24), (11, 26), (24, 5), (28, 17), (10, 20), (1, 14), (31, 4), (6, 12), (9, 13), (8, 26), (13, 7), (31, 7), (29, 24), (26, 28), (18, 4), (6, 20), (16, 4), (6, 26), (31, 19), (1, 10), (25, 14), (9, 8), (4, 7), (17, 18), (0, 30), (19, 17), (15, 9), (27, 16), (9, 27), (19, 24), (14, 31), (12, 16), (19, 31), (25, 0), (29, 4), (21, 24), (8, 0), (1, 25), (4, 19), (33, 8), (30, 31), (17, 20), (29, 2), (13, 11), (22, 28), (21, 8), (0, 28), (12, 23), (30, 24), (24, 18), (32, 17), (26, 3), (31, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947640", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (19, 26), (8, 24), (17, 15), (4, 11), (32, 24), (8, 22), (6, 7), (17, 27), (28, 17), (13, 21), (12, 21), (32, 0), (19, 18), (14, 9), (13, 2), (18, 9), (9, 9), (8, 10), (29, 23), (9, 22), (19, 11), (28, 3), (25, 29), (25, 8), (4, 20), (5, 4), (23, 26), (13, 1), (28, 5), (13, 23), (14, 0), (13, 28), (20, 18), (16, 27), (9, 2), (26, 1), (10, 23), (11, 9), (22, 11), (19, 27), (21, 15), (31, 14), (17, 3), (7, 28), (8, 15), (21, 21), (10, 3), (4, 25), (14, 3), (17, 14), (12, 10), (6, 15), (24, 27), (12, 25), (30, 21), (2, 26), (13, 12), (8, 28), (1, 27), (8, 12), (29, 10), (32, 2), (32, 3), (29, 29), (1, 6), (17, 30), (29, 6), (18, 24), (31, 0), (26, 4), (16, 12), (28, 0), (14, 19), (18, 13), (10, 2), (26, 20), (29, 1), (22, 21), (18, 7), (22, 4), (23, 18), (13, 7), (12, 27), (2, 12), (11, 11), (17, 7), (21, 5), (28, 14), (20, 17), (7, 27), (30, 2), (10, 0), (0, 3), (16, 26), (13, 19), (15, 17), (7, 7), (11, 30), (28, 8), (31, 20), (7, 0), (21, 22), (12, 28), (6, 13), (15, 11), (0, 24), (20, 29), (31, 18), (0, 10), (27, 23), (1, 0), (24, 2), (9, 21), (10, 12), (15, 20), (18, 12), (13, 5), (26, 13), (3, 11), (30, 20), (12, 29), (3, 13), (6, 29), (10, 14), (3, 7), (16, 30), (0, 9), (16, 20), (16, 14), (6, 11), (4, 30), (6, 1), (1, 15), (12, 12), (20, 0), (25, 2), (16, 13), (18, 20), (31, 26), (9, 29), (23, 20), (16, 9), (30, 28), (27, 10), (24, 26), (1, 17), (16, 15), (28, 21), (29, 26), (12, 16), (20, 30), (21, 7), (22, 19), (16, 25), (0, 27), (31, 28), (4, 22), (4, 24), (19, 23), (3, 12), (3, 27), (14, 4), (0, 26), (26, 23), (27, 24), (12, 18), (3, 28), (28, 12), (23, 16), (25, 30), (23, 15), (0, 16), (4, 15), (6, 25), (4, 13), (9, 1), (26, 11), (25, 27), (10, 19), (8, 1), (13, 25), (22, 27), (19, 10), (29, 14), (27, 3), (20, 20), (24, 24), (4, 29), (15, 4), (18, 14), (32, 26), (8, 20), (14, 14), (31, 27), (21, 24), (10, 27), (31, 1), (6, 30), (24, 10), (21, 1), (13, 4), (18, 22), (13, 8), (31, 10), (32, 21), (23, 7), (6, 4), (13, 6), (27, 6), (11, 4), (27, 14), (5, 6), (19, 29), (31, 13), (9, 16), (15, 24), (1, 12), (0, 14), (9, 26), (14, 12), (23, 0), (16, 18), (14, 28), (17, 21), (11, 26), (10, 5), (30, 16), (19, 21), (14, 15), (21, 2), (11, 23), (27, 26), (14, 25), (26, 10), (22, 14), (2, 30), (7, 8), (14, 18), (4, 10), (26, 18), (16, 19), (15, 22), (9, 25), (16, 11), (22, 22), (2, 18), (32, 29), (7, 29), (26, 19), (10, 11), (21, 11), (23, 14), (2, 19), (21, 23), (12, 23), (4, 0), (26, 8), (11, 25), (19, 8), (26, 27), (26, 17), (13, 16), (6, 2), (13, 10), (32, 9), (1, 13), (22, 7), (17, 29), (26, 7), (28, 25), (14, 20), (2, 20), (4, 19), (28, 26), (23, 4), (27, 28), (31, 7), (4, 14), (2, 7), (2, 3), (26, 5), (7, 26), (21, 3), (3, 26), (0, 30), (12, 1), (21, 4), (12, 20), (10, 25), (1, 19), (9, 3), (4, 16), (10, 10), (3, 15), (3, 9), (21, 13), (11, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766584", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 33), (27, 5), (30, 16), (9, 23), (12, 16), (23, 3), (25, 22), (9, 18), (36, 19), (31, 22), (2, 9), (10, 6), (14, 18), (30, 8), (9, 27), (30, 20), (34, 4), (8, 18), (9, 26), (0, 21), (2, 25), (24, 8), (5, 33), (10, 24), (15, 25), (13, 14), (23, 31), (20, 21), (9, 35), (16, 35), (20, 24), (22, 5), (11, 22), (12, 36), (18, 22), (18, 5), (34, 32), (22, 35), (20, 31), (29, 3), (25, 31), (17, 15), (16, 38), (15, 35), (3, 12), (15, 26), (27, 30), (8, 0), (8, 5), (13, 11), (22, 16), (31, 18), (32, 25), (34, 24), (27, 7), (16, 37), (5, 17), (5, 31), (30, 2), (6, 29), (26, 5), (29, 0), (1, 12), (9, 5), (16, 13), (14, 14), (35, 31), (0, 38), (19, 6), (35, 20), (24, 18), (23, 4), (34, 20), (22, 38), (29, 28), (8, 25), (21, 20), (12, 7), (32, 27), (28, 29), (9, 2), (16, 27), (12, 24), (6, 2), (24, 19), (23, 21), (35, 15), (5, 8), (3, 36), (9, 36), (8, 1), (27, 16), (21, 2), (20, 30), (6, 30), (31, 36), (0, 22), (7, 34), (30, 11), (34, 13), (16, 0), (31, 10), (21, 11), (18, 13), (21, 30), (13, 30), (27, 1), (9, 30), (23, 14), (35, 33), (11, 16), (1, 18), (0, 18), (5, 24), (11, 6), (21, 18), (6, 4), (17, 10), (0, 20), (16, 22), (24, 12), (16, 30), (1, 38), (12, 25), (0, 7), (4, 26), (5, 9), (34, 8), (20, 38), (5, 6), (35, 5), (12, 33), (6, 37), (3, 35), (22, 19), (8, 13), (3, 31), (36, 26), (11, 36), (10, 19), (28, 28), (16, 9), (15, 12), (7, 20), (17, 1), (23, 17), (6, 25), (15, 27), (19, 31), (22, 29), (22, 13), (31, 3), (0, 4), (12, 4), (14, 12), (22, 25), (34, 31), (13, 18), (34, 9), (32, 16), (8, 27), (24, 36), (29, 15), (15, 36), (13, 20), (22, 8), (11, 26), (4, 3), (7, 0), (15, 13), (4, 7), (12, 1), (7, 33), (19, 15), (16, 2), (8, 34), (14, 11), (30, 33), (19, 24), (24, 29), (22, 28), (15, 23), (14, 29), (34, 6), (21, 0), (33, 11), (20, 0), (30, 32), (4, 9), (31, 38), (23, 2), (7, 21), (8, 12), (17, 24), (14, 34), (15, 29), (19, 4), (15, 10), (7, 23), (35, 24), (29, 14), (7, 4), (8, 16), (8, 29), (11, 15), (4, 16), (28, 24), (22, 33), (30, 30), (5, 12), (9, 7), (31, 17), (21, 33), (11, 31), (22, 31), (30, 7), (18, 33), (31, 11), (17, 14), (13, 32), (22, 10), (20, 12), (8, 11), (34, 15), (1, 24), (6, 11), (14, 21), (17, 20), (2, 6), (2, 27), (27, 36), (24, 25), (18, 0), (22, 37), (26, 29), (20, 16), (20, 7), (20, 29), (32, 4), (36, 32), (6, 9), (20, 15), (19, 10), (2, 7), (19, 29), (30, 21), (21, 27), (17, 7), (34, 25), (11, 2), (26, 25), (35, 10), (24, 11), (23, 0), (16, 16), (21, 26), (7, 18), (30, 5), (2, 30), (17, 19), (10, 2), (35, 14), (0, 28), (28, 25), (35, 35), (1, 25), (25, 6), (19, 5), (34, 3), (36, 18), (12, 22), (3, 23), (2, 1), (27, 37), (31, 6), (10, 36), (4, 13), (31, 9), (32, 24), (26, 14), (11, 32), (13, 21), (26, 4), (34, 37), (9, 10), (14, 4), (23, 37), (20, 34), (33, 34), (27, 34), (19, 3), (2, 16), (11, 12), (0, 19), (0, 13), (25, 15), (31, 12), (23, 5), (32, 2), (8, 10), (4, 34), (31, 34), (23, 32), (33, 23), (30, 36), (9, 19), (25, 25), (11, 11), (17, 30), (36, 6), (12, 29), (6, 38), (7, 2), (6, 31), (24, 22), (16, 14), (3, 5), (23, 7), (18, 24), (2, 15), (18, 12), (28, 12), (12, 20), (2, 32), (19, 25), (25, 32), (19, 7), (0, 33), (25, 38), (32, 32), (26, 26), (28, 8), (11, 33), (16, 18), (13, 38), (36, 1), (29, 25), (22, 12), (11, 17), (28, 33), (23, 15), (34, 26), (35, 18), (28, 35), (12, 9), (35, 2), (27, 0), (8, 38), (31, 27), (0, 2), (28, 19), (7, 8), (24, 33), (20, 25), (30, 22), (19, 19), (11, 0), (7, 22), (5, 1), (33, 32), (13, 6), (24, 17), (15, 38), (32, 18), (25, 2), (8, 30), (7, 12), (32, 8), (27, 31), (33, 7), (2, 20), (18, 11), (35, 0), (5, 32), (10, 4), (35, 6), (27, 15), (2, 22), (15, 8), (30, 23), (36, 0), (34, 17), (17, 31), (29, 1), (29, 5), (36, 25), (30, 18), (4, 0), (11, 19), (4, 25), (16, 24), (25, 11), (35, 3), (9, 14), (6, 3), (14, 28), (18, 4), (0, 26), (24, 23), (17, 38), (0, 12), (12, 37), (18, 23), (6, 14), (12, 15), (0, 29), (26, 38), (3, 7), (27, 23), (5, 4), (20, 22), (18, 9), (30, 1), (27, 19), (22, 36), (32, 20), (14, 25), (2, 35), (21, 36), (1, 37), (35, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "812700", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 25), (8, 5), (6, 15), (9, 25), (28, 26), (1, 19), (24, 7), (19, 29), (15, 1), (27, 35), (8, 33), (21, 12), (29, 19), (32, 1), (5, 35), (33, 22), (29, 29), (7, 19), (24, 26), (1, 5), (16, 32), (21, 13), (21, 15), (3, 35), (11, 35), (26, 5), (7, 13), (31, 15), (21, 29), (27, 30), (7, 21), (23, 10), (4, 2), (4, 7), (22, 20), (31, 31), (27, 26), (34, 10), (3, 12), (30, 20), (27, 34), (13, 28), (6, 20), (0, 11), (8, 17), (7, 0), (19, 15), (14, 21), (22, 6), (3, 4), (28, 28), (1, 14), (3, 15), (12, 14), (24, 0), (32, 19), (25, 7), (5, 28), (10, 14), (13, 30), (17, 13), (30, 6), (5, 7), (17, 21), (1, 17), (26, 28), (7, 10), (19, 4), (30, 25), (10, 15), (21, 5), (30, 32), (27, 22), (18, 30), (2, 22), (25, 30), (15, 12), (8, 10), (25, 19), (12, 7), (0, 24), (7, 17), (2, 0), (0, 15), (14, 34), (20, 31), (22, 17), (2, 7), (21, 4), (20, 14), (24, 21), (4, 16), (9, 26), (26, 1), (15, 30), (21, 3), (17, 34), (33, 25), (19, 12), (13, 8), (20, 30), (20, 10), (18, 5), (32, 17), (34, 15), (34, 34), (34, 5), (27, 14), (18, 31), (8, 25), (25, 15), (2, 13), (21, 33), (7, 26), (31, 30), (34, 8), (30, 34), (12, 11), (23, 35), (2, 6), (25, 6), (0, 7), (29, 32), (26, 34), (13, 6), (9, 8), (30, 21), (15, 0), (3, 30), (23, 14), (18, 17), (30, 15), (5, 33), (8, 8), (30, 19), (6, 31), (16, 3), (9, 11), (34, 18), (0, 9), (10, 22), (33, 4), (4, 3), (25, 34), (31, 14), (19, 20), (19, 23), (13, 34), (11, 8), (0, 17), (27, 4), (12, 19), (20, 18), (20, 26), (33, 0), (24, 22), (19, 31), (8, 21), (5, 10), (7, 5), (18, 34), (15, 14), (5, 13), (10, 10), (6, 9), (34, 21), (28, 25), (7, 35), (16, 6), (0, 33), (33, 29), (1, 9), (26, 29), (3, 21), (9, 2), (10, 28), (2, 9), (2, 28), (23, 21), (28, 24), (32, 23), (31, 34), (14, 28), (27, 10), (30, 5), (2, 8), (34, 32), (32, 30), (31, 23), (0, 19), (5, 32), (2, 21), (20, 9), (2, 26), (14, 10), (0, 5), (7, 27), (5, 9), (31, 29), (11, 3), (19, 28), (12, 33), (11, 27), (31, 17), (11, 15), (15, 32), (8, 23), (18, 21), (8, 27), (26, 8), (7, 23), (22, 25), (7, 34), (11, 7), (27, 23), (9, 29), (16, 20), (13, 32), (17, 3), (26, 33), (21, 27), (2, 31), (4, 31), (23, 25), (21, 1), (29, 28), (17, 5), (23, 6), (1, 23), (34, 12), (19, 34), (2, 33), (22, 27), (2, 4), (32, 4), (14, 22), (20, 21), (4, 27), (12, 17), (34, 7), (33, 2), (7, 6), (30, 26), (6, 16), (1, 35), (6, 25), (9, 35), (13, 17), (29, 8), (19, 6), (5, 20), (12, 28), (29, 15), (0, 10), (28, 32), (10, 13), (17, 25), (26, 13), (3, 24), (3, 34), (25, 10), (22, 29), (6, 24), (11, 9), (21, 31), (32, 29), (16, 26), (12, 10), (14, 20), (23, 24), (6, 11), (8, 15), (10, 27), (20, 19), (12, 15), (11, 32), (17, 1), (22, 30), (0, 34), (15, 3), (16, 16), (1, 4), (33, 12), (4, 22), (23, 22), (34, 0), (7, 25), (23, 30), (34, 1), (9, 13), (34, 9), (17, 6), (32, 21), (29, 30), (1, 33), (29, 22), (22, 31), (29, 4), (28, 7), (20, 22), (10, 12), (26, 9), (20, 3), (16, 5), (2, 17), (24, 27), (8, 24), (13, 29), (23, 33), (15, 35), (32, 14), (26, 23), (14, 16), (30, 30), (19, 5), (15, 28), (4, 33), (30, 27), (18, 3), (27, 9), (23, 34), (15, 33), (6, 23), (33, 8), (18, 15), (27, 5), (24, 23), (5, 4), (14, 1), (30, 35), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "609984", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (38, 14), (28, 20), (27, 20), (2, 26), (27, 13), (19, 34), (30, 30), (8, 15), (12, 14), (23, 18), (20, 5), (23, 11), (0, 11), (5, 12), (18, 5), (33, 25), (23, 30), (28, 22), (5, 16), (6, 9), (11, 33), (36, 18), (7, 6), (0, 31), (27, 4), (34, 2), (9, 24), (20, 7), (23, 34), (34, 31), (23, 28), (10, 0), (30, 17), (11, 24), (13, 7), (22, 33), (30, 19), (16, 34), (36, 3), (20, 19), (26, 15), (37, 8), (29, 0), (17, 7), (4, 18), (9, 14), (6, 1), (1, 21), (5, 32), (1, 13), (14, 20), (35, 9), (9, 32), (8, 22), (19, 18), (25, 26), (21, 20), (19, 1), (25, 14), (30, 11), (2, 0), (35, 28), (4, 14), (24, 8), (35, 15), (31, 22), (16, 3), (16, 4), (1, 15), (26, 29), (4, 3), (19, 33), (6, 2), (27, 9), (19, 15), (30, 21), (32, 25), (12, 4), (35, 7), (13, 32), (38, 7), (1, 31), (4, 0), (13, 17), (11, 15), (27, 8), (15, 19), (5, 9), (6, 11), (34, 23), (13, 31), (30, 23), (14, 15), (7, 14), (14, 16), (12, 24), (14, 4), (1, 29), (0, 17), (17, 14), (10, 3), (19, 21), (29, 21), (30, 8), (34, 27), (8, 12), (26, 8), (9, 26), (33, 28), (33, 5), (1, 11), (15, 3), (26, 22), (2, 12), (27, 22), (21, 32), (32, 29), (12, 29), (18, 28), (7, 1), (22, 25), (35, 32), (16, 23), (38, 1), (24, 28), (19, 25), (29, 31), (20, 32), (34, 17), (26, 17), (27, 3), (19, 4), (30, 2), (27, 34), (2, 30), (26, 5), (12, 0), (17, 17), (33, 34), (32, 11), (32, 34), (15, 23), (22, 5), (31, 29), (18, 6), (5, 23), (26, 28), (4, 20), (15, 6), (12, 21), (2, 17), (12, 34), (38, 22), (28, 19), (15, 2), (8, 9), (12, 13), (17, 33), (19, 8), (8, 4), (25, 28), (8, 21), (33, 27), (4, 12), (21, 19), (20, 15), (34, 15), (5, 28), (3, 33), (7, 15), (0, 1), (37, 17), (24, 24), (13, 23), (13, 20), (24, 30), (0, 15), (1, 16), (17, 30), (10, 26), (14, 2), (2, 23), (3, 31), (7, 33), (26, 23), (18, 9), (1, 32), (26, 9), (13, 12), (23, 21), (21, 27), (33, 7), (34, 24), (38, 15), (13, 24), (21, 1), (31, 20), (20, 16), (34, 30), (32, 5), (16, 11), (14, 23), (38, 25), (18, 22), (29, 25), (28, 9), (29, 12), (10, 29), (10, 33), (12, 32), (16, 6), (7, 28), (29, 30), (33, 23), (24, 20), (28, 0), (5, 2), (17, 25), (21, 15), (15, 27), (4, 17), (9, 23), (30, 9), (4, 26), (5, 8), (20, 33), (8, 19), (1, 5), (22, 23), (25, 1), (16, 29), (29, 33), (14, 13), (11, 17), (10, 24), (0, 27), (32, 8), (33, 14), (34, 29), (18, 20), (21, 25), (33, 9), (19, 31), (32, 3), (1, 20), (9, 33), (19, 19), (15, 0), (2, 24), (30, 18), (8, 7), (30, 20), (0, 9), (29, 2), (34, 7), (24, 0), (38, 10), (17, 22), (36, 11), (36, 19), (24, 6), (0, 30), (32, 16), (37, 20), (15, 20), (13, 0), (16, 9), (10, 2), (25, 25), (22, 4), (2, 2), (0, 19), (15, 15), (28, 15), (37, 15), (35, 18), (36, 9), (4, 8), (28, 27), (3, 26), (25, 31), (19, 10), (24, 34), (18, 23), (22, 24), (37, 29), (1, 23), (14, 29), (13, 27), (26, 14), (2, 16), (15, 1), (20, 9), (28, 14), (9, 28), (35, 19), (2, 14), (16, 14), (2, 25), (15, 30), (31, 25), (6, 7), (32, 32), (16, 15), (31, 13), (15, 10), (33, 2), (16, 28), (32, 4), (22, 10), (22, 8), (29, 24), (5, 14), (18, 30), (18, 24), (11, 3), (32, 21), (7, 21), (6, 29), (23, 20), (26, 11), (22, 34), (13, 18), (20, 31), (28, 30), (7, 18), (28, 34), (21, 16), (18, 2), (2, 31), (28, 32), (24, 19), (14, 14), (28, 11), (20, 25), (5, 6), (32, 23), (33, 10), (3, 12), (36, 13), (7, 0), (8, 31), (14, 5), (2, 27), (34, 28), (26, 3), (36, 24), (21, 26), (37, 10), (33, 1), (23, 14), (21, 0), (13, 29), (3, 21), (0, 23), (32, 31), (37, 22), (23, 13), (13, 34), (28, 29), (3, 7), (10, 14), (27, 28), (6, 27), (14, 9), (15, 11), (11, 7), (14, 24), (34, 5), (18, 16), (28, 3), (35, 30), (37, 7), (38, 31), (13, 6), (27, 33), (25, 8), (38, 2), (38, 30), (8, 8), (25, 22), (18, 8), (12, 10), (24, 13), (16, 25), (4, 34), (34, 13), (36, 0), (21, 31), (32, 20), (1, 2), (29, 8), (3, 34), (16, 7), (8, 6), (5, 3), (34, 21), (27, 10), (37, 5), (37, 6), (14, 11), (22, 0), (30, 26), (28, 4), (32, 9), (27, 29), (26, 2), (30, 16), (16, 12), (12, 12), (6, 19), (16, 32), (15, 5), (11, 9), (0, 18), (37, 26), (10, 4), (20, 2), (14, 10), (27, 5), (19, 13), (38, 11), (3, 6), (10, 1), (11, 16), (19, 0), (34, 16), (0, 20), (33, 0), (23, 8), (24, 15), (2, 28), (32, 33), (23, 4), (26, 1), (25, 27), (17, 0), (0, 22), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842688", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 27), (16, 5), (23, 1), (8, 31), (12, 17), (1, 21), (2, 18), (17, 4), (8, 9), (5, 3), (25, 8), (27, 31), (16, 1), (25, 14), (10, 20), (22, 0), (32, 19), (4, 28), (29, 24), (6, 32), (27, 9), (16, 17), (13, 9), (12, 14), (6, 23), (24, 0), (1, 25), (14, 29), (6, 24), (6, 8), (20, 11), (34, 7), (31, 30), (27, 27), (22, 19), (23, 16), (6, 0), (7, 20), (13, 1), (31, 16), (16, 4), (3, 18), (11, 0), (1, 4), (12, 29), (11, 4), (11, 3), (18, 13), (28, 1), (33, 12), (25, 28), (26, 3), (12, 21), (12, 19), (11, 7), (3, 9), (32, 30), (17, 5), (11, 20), (4, 13), (31, 24), (10, 5), (34, 2), (34, 18), (18, 22), (25, 27), (1, 8), (7, 9), (21, 15), (3, 16), (12, 2), (7, 0), (0, 22), (16, 27), (11, 8), (7, 11), (32, 32), (10, 30), (23, 28), (26, 1), (12, 3), (17, 25), (24, 6), (1, 13), (9, 18), (26, 24), (32, 24), (15, 4), (13, 27), (9, 9), (32, 12), (24, 8), (30, 12), (19, 2), (5, 5), (27, 25), (12, 12), (23, 21), (24, 5), (4, 14), (21, 25), (9, 28), (7, 13), (14, 5), (5, 27), (15, 23), (13, 12), (7, 26), (29, 18), (16, 20), (24, 4), (31, 6), (21, 0), (1, 3), (12, 8), (9, 29), (19, 30), (0, 16), (10, 8), (11, 22), (15, 18), (18, 16), (33, 9), (25, 24), (24, 7), (25, 21), (31, 5), (23, 6), (10, 28), (8, 24), (14, 18), (3, 12), (8, 27), (29, 0), (15, 11), (7, 19), (15, 12), (8, 0), (0, 14), (9, 10), (12, 25), (25, 30), (4, 21), (22, 12), (21, 21), (31, 1), (33, 15), (0, 7), (7, 23), (31, 15), (32, 10), (23, 13), (2, 23), (27, 26), (33, 26), (16, 24), (4, 32), (15, 29), (28, 4), (26, 30), (10, 12), (21, 23), (9, 32), (5, 17), (19, 22), (30, 21), (8, 16), (24, 14), (7, 6), (13, 16), (16, 10), (30, 31), (23, 27), (21, 24), (12, 28), (18, 18), (17, 15), (28, 21), (16, 3), (27, 21), (20, 12), (12, 30), (26, 17), (26, 15), (26, 10), (15, 3), (21, 30), (10, 19), (3, 20), (20, 19), (17, 11), (29, 10), (27, 15), (32, 21), (26, 9), (29, 23), (23, 19), (5, 10), (9, 23), (21, 12), (14, 22), (9, 20), (21, 31), (2, 22), (18, 26), (32, 22), (30, 16), (19, 24), (2, 8), (16, 31), (19, 15), (25, 5), (22, 17), (0, 32), (3, 27), (12, 4), (4, 29), (29, 3), (20, 10), (5, 14), (20, 6), (9, 11), (31, 27), (25, 12), (31, 0), (30, 25), (1, 2), (22, 9), (25, 17), (6, 4), (7, 30), (18, 1), (27, 3), (28, 16), (28, 29), (0, 28), (33, 28), (5, 8), (27, 11), (25, 1), (11, 9), (31, 18), (6, 16), (16, 9), (28, 15), (0, 8), (19, 12), (17, 30), (33, 8), (0, 24), (8, 14), (20, 15), (7, 25), (2, 24), (11, 11), (16, 13), (18, 11), (20, 5), (23, 25), (2, 12), (32, 27), (4, 2), (33, 27), (32, 15), (19, 14), (32, 13), (9, 3), (13, 17), (23, 10), (15, 6), (21, 28), (23, 5), (17, 9), (9, 22), (10, 4), (12, 13), (4, 7), (7, 7), (29, 20), (4, 15), (15, 15), (3, 6), (24, 15), (27, 32), (11, 10), (19, 13), (6, 17), (5, 1), (2, 21), (32, 2), (16, 19), (24, 19), (22, 10), (14, 14), (27, 4), (29, 9), (8, 26), (16, 15), (21, 27), (23, 2), (25, 20), (28, 24), (5, 26), (34, 19), (8, 28), (29, 32), (25, 13), (22, 1), (25, 3), (1, 5), (34, 10), (3, 3), (11, 5), (7, 1), (3, 26), (32, 0), (3, 23), (1, 32), (5, 22), (16, 12), (7, 14), (32, 9), (29, 15), (11, 29), (28, 0), (31, 8), (10, 13), (30, 11), (22, 23), (30, 5), (22, 20), (33, 31), (11, 19), (4, 5), (6, 13), (29, 19), (15, 28), (17, 3), (18, 10), (33, 10), (27, 16), (17, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508500", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 36), (36, 13), (35, 34), (6, 29), (17, 1), (34, 4), (28, 6), (13, 24), (31, 8), (25, 25), (31, 32), (27, 16), (3, 20), (6, 2), (34, 1), (1, 12), (29, 35), (37, 17), (14, 35), (0, 27), (26, 6), (9, 23), (22, 25), (4, 31), (24, 21), (19, 37), (32, 7), (11, 32), (20, 20), (9, 22), (20, 3), (21, 36), (37, 31), (25, 18), (31, 12), (30, 13), (35, 24), (35, 10), (15, 16), (34, 10), (1, 31), (31, 26), (1, 16), (19, 21), (10, 3), (3, 16), (8, 21), (37, 27), (26, 37), (18, 0), (36, 37), (8, 35), (15, 11), (30, 4), (15, 14), (16, 24), (12, 11), (38, 23), (17, 6), (16, 22), (8, 32), (13, 2), (18, 18), (0, 2), (5, 10), (9, 34), (19, 4), (1, 3), (24, 5), (0, 34), (17, 16), (2, 35), (32, 25), (11, 10), (34, 31), (0, 25), (37, 20), (28, 20), (18, 21), (22, 20), (24, 2), (10, 28), (0, 21), (10, 15), (0, 30), (25, 13), (14, 8), (37, 23), (34, 16), (19, 19), (2, 18), (29, 13), (30, 31), (11, 11), (25, 11), (37, 18), (35, 31), (14, 24), (30, 25), (14, 36), (12, 31), (9, 37), (21, 12), (8, 27), (24, 16), (23, 24), (0, 28), (16, 8), (28, 10), (1, 25), (12, 5), (3, 7), (29, 27), (14, 10), (28, 34), (20, 33), (13, 23), (15, 33), (13, 10), (8, 25), (15, 18), (24, 24), (27, 20), (6, 33), (9, 19), (11, 23), (38, 22), (9, 15), (3, 9), (36, 8), (37, 22), (5, 5), (33, 30), (23, 23), (14, 30), (3, 17), (38, 5), (12, 7), (35, 33), (18, 12), (2, 31), (9, 32), (25, 19), (1, 33), (34, 30), (16, 5), (18, 1), (5, 6), (1, 30), (15, 19), (13, 6), (14, 19), (1, 0), (5, 1), (0, 26), (5, 11), (35, 22), (27, 34), (27, 15), (30, 35), (25, 30), (17, 7), (23, 31), (22, 23), (38, 35), (30, 22), (4, 11), (34, 12), (6, 7), (29, 25), (30, 27), (28, 24), (35, 37), (31, 11), (12, 26), (36, 16), (21, 10), (28, 18), (27, 35), (37, 2), (5, 19), (1, 27), (16, 29), (10, 0), (26, 10), (29, 17), (33, 13), (17, 27), (30, 15), (31, 7), (2, 8), (22, 8), (35, 2), (32, 22), (32, 23), (8, 33), (14, 3), (31, 31), (24, 27), (33, 9), (15, 5), (32, 12), (17, 21), (11, 26), (14, 5), (34, 26), (6, 25), (36, 34), (7, 20), (11, 34), (22, 3), (33, 3), (33, 4), (28, 14), (4, 33), (0, 37), (17, 37), (24, 26), (7, 2), (2, 33), (35, 14), (0, 20), (24, 28), (25, 10), (27, 26), (33, 19), (14, 18), (36, 33), (10, 8), (38, 29), (38, 10), (27, 14), (20, 13), (18, 22), (20, 5), (23, 27), (11, 19), (22, 29), (33, 8), (2, 32), (22, 13), (5, 24), (38, 31), (11, 4), (37, 34), (24, 11), (26, 4), (4, 9), (20, 32), (13, 36), (3, 0), (13, 9), (2, 23), (1, 2), (36, 20), (7, 14), (15, 25), (4, 19), (25, 16), (10, 9), (16, 33), (27, 7), (24, 25), (27, 31), (10, 2), (11, 29), (34, 33), (32, 1), (1, 14), (14, 13), (32, 34), (28, 2), (28, 12), (37, 35), (33, 17), (8, 5), (17, 31), (19, 30), (17, 33), (19, 16), (7, 10), (2, 37), (31, 18), (9, 35), (0, 15), (25, 20), (26, 33), (0, 35), (37, 24), (38, 34), (14, 29), (7, 31), (1, 7), (1, 32), (0, 16), (13, 17), (33, 7), (38, 11), (33, 26), (10, 26), (10, 23), (37, 4), (24, 31), (2, 30), (27, 29), (28, 30), (5, 34), (37, 14), (11, 28), (16, 23), (25, 17), (7, 27), (30, 9), (13, 20), (21, 6), (32, 6), (9, 9), (5, 32), (27, 10), (6, 13), (36, 0), (3, 23), (26, 21), (30, 8), (28, 1), (36, 10), (38, 1), (21, 27), (32, 13), (35, 28), (12, 16), (15, 1), (17, 0), (2, 19), (28, 29), (32, 19), (5, 9), (5, 21), (15, 7), (0, 6), (17, 13), (13, 7), (9, 8), (18, 5), (36, 27), (31, 0), (30, 16), (15, 6), (30, 14), (23, 0), (29, 12), (20, 31), (17, 25), (3, 29), (13, 3), (36, 5), (9, 5), (34, 25), (14, 16), (28, 36), (14, 17), (14, 0), (12, 20), (32, 10), (22, 19), (35, 4), (19, 23), (29, 3), (20, 34), (8, 10), (11, 25), (6, 22), (25, 1), (13, 16), (25, 2), (21, 14), (10, 16), (29, 30), (0, 7), (9, 28), (16, 7), (28, 21), (20, 16), (1, 21), (31, 35), (36, 12), (13, 30), (38, 27), (18, 10), (4, 22), (38, 0), (23, 2), (34, 34), (32, 11), (17, 11), (23, 36), (30, 30), (36, 22), (12, 36), (3, 24), (12, 25), (30, 10), (27, 3), (27, 21), (30, 32), (19, 26), (33, 14), (6, 26), (20, 6), (13, 28), (29, 7), (25, 26), (8, 17), (36, 35), (17, 9), (8, 12), (15, 21), (29, 15), (15, 26), (14, 32), (0, 8), (5, 14), (7, 0), (0, 31), (9, 30), (4, 25), (32, 20), (4, 20), (12, 33), (31, 29), (35, 29), (27, 8), (21, 8), (4, 2), (7, 18), (16, 19), (25, 3), (3, 3), (13, 14), (36, 29), (1, 28), (26, 25), (30, 20), (19, 33), (21, 30), (30, 19), (8, 13), (12, 2), (19, 32), (0, 18), (1, 24), (21, 18), (14, 6), (25, 4), (8, 34), (22, 18), (4, 26), (35, 30), (9, 31), (30, 36), (33, 2), (24, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28512", "dataset": "MATH"}
{"messages": [{"content": "In a 31x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 2), (12, 6), (19, 18), (15, 16), (28, 11), (3, 15), (30, 11), (12, 1), (14, 15), (3, 13), (27, 2), (13, 21), (6, 4), (18, 3), (7, 14), (20, 10), (23, 23), (0, 24), (30, 2), (11, 24), (16, 5), (14, 11), (17, 17), (13, 29), (30, 9), (21, 29), (10, 7), (16, 21), (21, 9), (26, 27), (16, 24), (12, 17), (12, 13), (5, 17), (12, 3), (16, 6), (8, 0), (20, 22), (25, 9), (9, 17), (11, 6), (28, 5), (8, 7), (7, 1), (22, 14), (25, 14), (17, 3), (11, 17), (14, 1), (19, 10), (12, 24), (12, 10), (7, 15), (15, 2), (14, 2), (1, 15), (21, 11), (4, 10), (14, 26), (19, 13), (18, 1), (27, 20), (4, 12), (5, 21), (19, 25), (8, 25), (7, 28), (28, 24), (29, 5), (12, 20), (10, 2), (24, 17), (1, 7), (13, 10), (23, 15), (20, 2), (30, 18), (22, 20), (17, 27), (22, 18), (20, 16), (8, 4), (15, 24), (24, 3), (18, 25), (13, 22), (15, 15), (0, 7), (28, 27), (30, 5), (8, 17), (11, 13), (21, 24), (11, 29), (4, 5), (0, 26), (15, 27), (13, 14), (19, 8), (5, 19), (28, 2), (8, 12), (29, 6), (20, 1), (14, 6), (26, 12), (28, 21), (27, 8), (19, 4), (17, 16), (16, 16), (0, 12), (25, 27), (20, 11), (9, 0), (1, 16), (21, 23), (23, 26), (7, 23), (29, 24), (9, 1), (17, 8), (8, 13), (21, 26), (20, 28), (23, 0), (7, 24), (5, 14), (24, 1), (1, 3), (8, 23), (28, 22), (9, 25), (18, 4), (19, 24), (18, 10), (2, 19), (27, 9), (27, 12), (24, 4), (9, 13), (2, 16), (21, 0), (11, 27), (11, 0), (22, 9), (25, 4), (20, 24), (8, 21), (1, 21), (0, 4), (8, 1), (3, 12), (0, 29), (30, 8), (4, 2), (18, 17), (7, 8), (16, 23), (3, 16), (19, 7), (14, 17), (22, 16), (5, 25), (22, 12), (24, 21), (17, 11), (30, 15), (13, 17), (30, 14), (29, 4), (26, 24), (8, 11), (3, 29), (0, 8), (1, 25), (23, 10), (29, 26), (29, 28), (11, 9), (20, 17), (8, 2), (5, 15), (10, 1), (13, 12), (0, 25), (27, 18), (24, 26), (1, 6), (21, 17), (2, 27), (18, 22), (27, 29), (11, 25), (17, 20), (7, 10), (4, 17), (5, 13), (24, 28), (24, 23), (21, 8), (18, 13), (23, 29), (16, 13), (6, 25), (21, 13), (1, 14), (9, 24), (18, 7), (27, 25), (5, 16), (14, 7), (16, 3), (9, 11), (0, 15), (0, 27), (9, 6), (10, 18), (25, 10), (11, 2), (5, 5), (2, 15), (9, 14), (8, 18), (27, 22), (17, 2), (4, 1), (10, 10), (6, 24), (19, 21), (8, 8), (24, 25), (20, 27), (7, 12), (20, 15), (24, 2), (19, 9), (1, 29), (17, 13), (5, 0), (24, 10), (21, 27), (14, 4), (3, 27), (1, 8), (4, 27), (24, 7), (25, 12), (2, 18), (2, 21), (16, 29), (24, 5), (30, 4), (2, 10), (14, 9), (30, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "647088", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), 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), (13, 19), (5, 3), (17, 16), (32, 23), (9, 20), (22, 11), (26, 20), (31, 6), (2, 10), (37, 18), (33, 17), (21, 4), (6, 7), (26, 27), (17, 8), (23, 27), (38, 26), (24, 2), (23, 17), (6, 24), (31, 20), (16, 11), (32, 15), (10, 14), (7, 10), (3, 16), (13, 30), (9, 3), (13, 17), (15, 3), (18, 3), (13, 13), (5, 29), (14, 19), (27, 19), (13, 24), (20, 28), (7, 28), (2, 18), (26, 25), (30, 18), (29, 28), (8, 15), (13, 25), (37, 22), (14, 16), (3, 5), (28, 19), (27, 25), (28, 30), (6, 23), (19, 24), (1, 10), (20, 29), (14, 24), (20, 13), (17, 13), (8, 30), (35, 10), (28, 8), (20, 27), (35, 5), (18, 14), (13, 16), (35, 6), (3, 4), (20, 10), (3, 30), (1, 18), (16, 8), (23, 0), (15, 20), (2, 3), (8, 13), (17, 12), (34, 12), (6, 26), (10, 13), (16, 3), (5, 30), (15, 11), (38, 0), (9, 23), (31, 10), (36, 9), (38, 1), (31, 15), (24, 3), (1, 4), (7, 4), (17, 0), (37, 12), (23, 24), (31, 1), (34, 21), (15, 8), (36, 16), (7, 7), (36, 20), (9, 9), (13, 10), (8, 14), (0, 30), (11, 3), (2, 16), (3, 1), (19, 30), (4, 1), (0, 20), (5, 16), (15, 30), (36, 7), (18, 26), (14, 29), (0, 7), (3, 29), (21, 27), (34, 20), (2, 1), (30, 4), (5, 9), (25, 9), (16, 28), (24, 29), (34, 23), (14, 6), (38, 3), (29, 11), (22, 6), (34, 10), (13, 5), (10, 1), (1, 1), (35, 12), (2, 27), (4, 23), (24, 11), (22, 13), (32, 19), (31, 21), (33, 9), (12, 25), (29, 22), (28, 23), (14, 22), (11, 2), (1, 12), (0, 4), (15, 0), (22, 22), (4, 9), (34, 18), (17, 10), (14, 21), (28, 24), (0, 11), (32, 26), (32, 25), (11, 13), (22, 17), (24, 30), (33, 19), (0, 26), (0, 27), (30, 24), (24, 7), (35, 2), (17, 21), (16, 14), (37, 9), (6, 15), (29, 23), (2, 23), (19, 3), (15, 14), (18, 0), (3, 20), (23, 26), (3, 7), (19, 11), (38, 15), (29, 14), (7, 29), (19, 26), (35, 14), (18, 23), (10, 26), (2, 19), (27, 27), (31, 5), (27, 5), (10, 28), (10, 6), (37, 26), (19, 28), (31, 13), (2, 11), (26, 30), (6, 16), (20, 23), (14, 13), (28, 6), (15, 27), (3, 28), (32, 20), (7, 0), (11, 4), (24, 15), (31, 28), (4, 17), (21, 20), (18, 25), (20, 14), (8, 0), (6, 5), (28, 27), (19, 14), (25, 21), (33, 22), (23, 21), (12, 18), (13, 15), (13, 22), (14, 3), (25, 14), (24, 18), (10, 22), (11, 25), (6, 6), (9, 28), (23, 1), (20, 9), (12, 16), (38, 12), (31, 27), (0, 12), (21, 12), (11, 12), (12, 2), (11, 24), (29, 2), (5, 17), (2, 25), (7, 17), (20, 24), (30, 7), (29, 12), (8, 25), (34, 19), (25, 16), (12, 14), (30, 30), (36, 27), (12, 22), (34, 7), (1, 11), (27, 10), (8, 8), (19, 0), (38, 19), (36, 26), (9, 5), (27, 28), (26, 16), (9, 15), (30, 1), (21, 28), (17, 11), (22, 0), (25, 30), (10, 12), (5, 13), (2, 2), (18, 6), (3, 24), (35, 9), (27, 26), (20, 4), (28, 14), (4, 25), (13, 26), (36, 28), (9, 30), (8, 17), (19, 16), (15, 22), (19, 6), (37, 8), (24, 26), (11, 18), (10, 17), (12, 19), (7, 9), (33, 6), (37, 24), (17, 9), (38, 23), (27, 15), (36, 5), (9, 4), (28, 26), (38, 22), (28, 4), (33, 10), (18, 5), (15, 21), (28, 18), (38, 21), (33, 4), (38, 24), (16, 16), (2, 28), (35, 7), (12, 10), (11, 11), (33, 16), (1, 6), (19, 10), (18, 11), (10, 4), (32, 1), (5, 15), (38, 9), (9, 10), (17, 23), (13, 12), (9, 22), (20, 6), (6, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320400", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 24), (17, 29), (11, 4), (4, 0), (3, 25), (0, 27), (5, 27), (18, 8), (27, 23), (21, 1), (0, 5), (14, 6), (6, 12), (23, 2), (6, 3), (18, 1), (11, 8), (17, 20), (17, 12), (27, 4), (18, 13), (27, 2), (24, 7), (20, 24), (18, 10), (11, 9), (12, 18), (19, 6), (23, 24), (29, 8), (1, 8), (30, 1), (25, 2), (32, 6), (7, 21), (23, 0), (21, 20), (5, 9), (21, 27), (23, 16), (15, 1), (32, 2), (15, 14), (20, 12), (22, 11), (4, 25), (25, 25), (11, 6), (20, 29), (22, 14), (9, 10), (23, 28), (19, 24), (0, 19), (19, 29), (25, 5), (11, 18), (25, 18), (30, 11), (15, 8), (31, 3), (7, 14), (31, 28), (2, 0), (29, 21), (32, 29), (31, 19), (10, 2), (28, 12), (30, 26), (6, 14), (27, 5), (14, 27), (10, 30), (19, 7), (15, 12), (4, 6), (26, 14), (13, 13), (10, 9), (8, 22), (9, 29), (31, 24), (1, 12), (24, 21), (21, 28), (9, 1), (26, 3), (16, 13), (10, 6), (32, 4), (28, 5), (8, 26), (32, 26), (13, 2), (24, 25), (17, 7), (19, 13), (18, 29), (1, 9), (19, 9), (7, 17), (13, 30), (9, 24), (30, 8), (28, 19), (4, 26), (28, 28), (17, 5), (10, 4), (18, 23), (17, 22), (28, 29), (10, 26), (28, 18), (19, 0), (25, 1), (20, 3), (14, 5), (15, 20), (2, 20), (12, 30), (19, 1), (31, 0), (1, 19), (16, 6), (23, 1), (2, 16), (25, 29), (12, 20), (11, 2), (6, 27), (14, 25), (6, 17), (1, 26), (22, 28), (5, 21), (27, 11), (17, 8), (4, 7), (18, 27), (27, 18), (1, 14), (0, 4), (14, 30), (25, 4), (9, 16), (2, 5), (10, 23), (7, 9), (20, 11), (32, 9), (2, 13), (1, 30), (5, 18), (5, 7), (21, 6), (20, 27), (28, 0), (18, 15), (28, 11), (29, 20), (15, 7), (21, 26), (18, 22), (23, 3), (27, 1), (15, 6), (13, 24), (28, 4), (32, 0), (3, 15), (16, 4), (25, 30), (0, 14), (12, 14), (8, 25), (27, 7), (20, 19), (3, 14), (25, 11), (25, 21), (3, 3), (0, 16), (19, 21), (0, 10), (13, 28), (27, 21), (22, 4), (17, 17), (16, 22), (18, 5), (27, 22), (16, 17), (25, 13), (12, 22), (23, 29), (3, 29), (3, 1), (31, 20), (26, 1), (0, 21), (24, 4), (15, 4), (10, 24), (19, 22), (5, 23), (20, 25), (4, 12), (12, 2), (6, 23), (0, 18), (18, 6), (16, 27), (31, 2), (20, 20), (22, 0), (29, 17), (6, 4), (9, 9), (27, 10), (25, 17), (27, 30), (24, 1), (10, 10), (30, 14), (16, 9), (16, 19), (8, 8), (0, 11), (17, 1), (30, 2), (4, 9), (6, 29), (8, 15), (1, 0), (17, 28), (1, 11), (7, 19), (29, 1), (18, 3), (12, 16), (5, 4), (28, 27), (12, 11), (1, 7), (20, 7), (13, 23), (23, 15), (24, 17), (22, 29), (6, 10), (8, 12), (12, 10), (20, 30), (21, 16), (23, 14), (2, 8), (9, 11), (27, 3), (1, 3), (8, 2), (23, 22), (10, 12), (21, 2), (6, 6), (16, 8), (27, 6), (3, 8), (31, 10), (1, 6), (4, 8), (16, 29), (3, 28), (24, 15), (18, 2), (5, 8), (21, 17), (29, 19), (2, 17), (22, 25), (20, 5), (15, 2), (28, 13), (2, 14), (16, 21), (4, 15), (17, 23), (15, 16), (0, 22), (31, 22), (29, 0), (19, 15), (8, 21), (3, 19), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13860", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 18), (11, 2), (10, 4), (35, 10), (22, 28), (29, 30), (37, 21), (22, 11), (21, 1), (14, 28), (10, 17), (18, 13), (12, 30), (16, 23), (20, 11), (26, 16), (20, 18), (37, 29), (36, 2), (20, 24), (8, 23), (34, 26), (11, 4), (17, 7), (18, 0), (20, 30), (33, 28), (32, 20), (11, 22), (6, 30), (1, 24), (8, 18), (24, 25), (33, 6), (32, 12), (25, 26), (14, 8), (6, 22), (19, 21), (4, 9), (0, 20), (18, 9), (18, 15), (12, 26), (1, 23), (17, 9), (5, 9), (3, 17), (33, 20), (6, 12), (35, 2), (36, 20), (20, 28), (29, 13), (37, 10), (16, 14), (33, 0), (7, 11), (18, 21), (19, 11), (12, 8), (23, 1), (31, 28), (6, 3), (1, 14), (14, 21), (24, 12), (16, 5), (32, 21), (15, 19), (25, 8), (4, 22), (22, 26), (24, 2), (17, 4), (31, 9), (2, 23), (26, 25), (20, 5), (9, 2), (33, 26), (9, 15), (16, 0), (28, 20), (0, 6), (12, 16), (11, 5), (18, 5), (15, 13), (7, 25), (28, 4), (30, 27), (20, 16), (17, 23), (6, 0), (20, 12), (8, 26), (21, 18), (19, 2), (22, 3), (0, 18), (22, 2), (11, 15), (32, 10), (1, 0), (33, 12), (16, 17), (37, 15), (26, 11), (32, 22), (22, 23), (27, 1), (21, 8), (6, 1), (31, 26), (23, 28), (18, 27), (22, 19), (16, 11), (7, 17), (20, 15), (34, 25), (6, 4), (8, 30), (14, 9), (4, 16), (2, 13), (20, 23), (0, 25), (10, 5), (4, 18), (8, 12), (5, 0), (11, 19), (17, 11), (29, 26), (8, 20), (8, 29), (10, 29), (12, 18), (23, 22), (27, 27), (18, 3), (18, 16), (21, 6), (20, 27), (14, 5), (16, 4), (30, 24), (5, 6), (8, 16), (19, 17), (26, 24), (13, 26), (25, 20), (32, 4), (31, 19), (17, 30), (16, 27), (17, 27), (37, 18), (31, 27), (15, 22), (34, 7), (11, 25), (27, 26), (33, 3), (36, 11), (14, 30), (0, 10), (3, 6), (34, 30), (29, 28), (18, 2), (30, 21), (8, 1), (17, 14), (12, 10), (22, 20), (32, 7), (3, 22), (36, 26), (32, 2), (2, 0), (37, 7), (4, 0), (4, 26), (1, 30), (1, 15), (19, 15), (14, 15), (9, 0), (18, 6), (27, 28), (5, 16), (34, 0), (11, 7), (1, 28), (26, 4), (18, 26), (32, 9), (8, 15), (10, 28), (16, 7), (26, 5), (37, 25), (29, 7), (11, 30), (28, 19), (1, 22), (24, 1), (9, 22), (22, 9), (13, 7), (11, 17), (28, 10), (8, 14), (28, 13), (13, 17), (24, 30), (13, 28), (31, 13), (31, 18), (12, 12), (19, 24), (2, 4), (4, 17), (5, 3), (22, 15), (23, 23), (23, 8), (34, 6), (35, 18), (34, 15), (2, 19), (20, 19), (16, 8), (24, 4), (3, 23), (37, 5), (35, 14), (37, 2), (0, 30), (3, 30), (0, 14), (34, 14), (7, 30), (14, 22), (22, 8), (7, 27), (36, 4), (2, 8), (34, 28), (14, 6), (18, 1), (12, 29), (13, 16), (6, 9), (30, 5), (36, 17), (3, 7), (35, 20), (8, 8), (28, 29), (27, 25), (15, 5), (6, 5), (25, 18), (10, 7), (2, 27), (16, 29), (6, 7), (23, 24), (6, 2), (30, 3), (26, 19), (18, 23), (9, 3), (25, 27), (8, 24), (20, 9), (24, 0), (5, 21), (18, 4), (19, 29), (21, 20), (18, 14), (24, 6), (23, 16), (33, 13), (10, 13), (33, 29), (21, 16), (23, 29), (22, 12), (27, 14), (37, 24), (30, 8), (14, 25), (9, 21), (11, 13), (10, 0), (3, 27), (34, 22), (15, 3), (4, 19), (12, 9), (18, 24), (29, 19), (4, 10), (16, 30), (12, 7), (32, 17), (8, 9), (5, 5), (4, 27), (26, 7), (22, 13), (30, 30), (23, 11), (6, 29), (0, 5), (16, 13), (35, 12), (5, 17), (17, 10), (20, 14), (5, 25), (21, 5), (13, 13), (0, 19), (10, 25), (9, 1), (13, 19), (31, 3), (3, 5), (22, 10), (2, 30), (14, 24), (25, 25), (15, 26), (30, 1), (19, 18), (24, 15), (3, 10), (17, 16), (32, 8), (5, 30), (5, 13), (17, 22), (13, 3), (23, 20), (29, 8), (28, 6), (13, 8), (33, 1), (36, 14), (12, 17), (1, 17), (12, 22), (8, 11), (23, 6), (15, 12), (12, 3), (24, 20), (16, 16), (16, 25), (13, 6), (17, 21), (22, 18), (30, 20), (19, 7), (27, 10), (34, 19), (30, 28), (7, 6), (28, 9), (12, 19), (0, 2), (30, 6), (7, 7), (6, 17), (18, 18), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "525280", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 4), (6, 16), (5, 12), (34, 21), (22, 12), (11, 12), (11, 36), (12, 22), (6, 15), (5, 29), (33, 18), (24, 3), (15, 4), (7, 30), (16, 4), (30, 25), (17, 19), (32, 14), (11, 14), (31, 23), (16, 8), (21, 8), (35, 20), (11, 27), (33, 1), (15, 6), (28, 11), (13, 2), (21, 14), (12, 17), (33, 14), (10, 19), (18, 18), (32, 26), (24, 30), (29, 23), (26, 31), (2, 36), (15, 25), (33, 13), (15, 3), (23, 22), (8, 25), (17, 21), (33, 17), (22, 22), (35, 11), (0, 20), (28, 9), (23, 14), (17, 1), (21, 0), (4, 33), (6, 26), (12, 8), (0, 22), (34, 3), (27, 28), (3, 17), (22, 28), (10, 34), (18, 12), (3, 32), (9, 33), (33, 6), (31, 10), (27, 21), (30, 10), (19, 34), (17, 34), (23, 5), (8, 2), (7, 22), (28, 18), (13, 10), (33, 35), (25, 32), (35, 23), (11, 22), (9, 14), (17, 8), (35, 29), (7, 6), (22, 9), (35, 35), (2, 4), (4, 7), (13, 17), (24, 27), (9, 32), (13, 21), (16, 20), (17, 13), (33, 20), (25, 26), (29, 14), (2, 1), (10, 30), (23, 19), (15, 21), (10, 22), (30, 26), (29, 8), (7, 5), (25, 7), (24, 1), (22, 33), (6, 30), (23, 15), (35, 33), (24, 6), (1, 24), (30, 13), (19, 21), (4, 36), (3, 33), (7, 24), (8, 20), (20, 8), (1, 34), (2, 15), (30, 16), (26, 10), (28, 1), (31, 31), (25, 15), (18, 34), (14, 8), (24, 32), (20, 3), (33, 2), (23, 29), (34, 18), (8, 5), (4, 31), (16, 35), (6, 8), (23, 34), (18, 0), (11, 9), (17, 4), (9, 7), (26, 26), (2, 30), (16, 16), (27, 10), (18, 23), (10, 21), (17, 16), (14, 6), (2, 20), (26, 14), (10, 0), (10, 33), (26, 34), (22, 23), (4, 18), (3, 15), (15, 11), (31, 24), (3, 30), (26, 13), (15, 20), (0, 34), (31, 12), (30, 6), (23, 26), (33, 12), (22, 11), (1, 7), (31, 7), (7, 14), (19, 10), (35, 27), (12, 7), (8, 6), (18, 10), (1, 29), (29, 20), (1, 25), (30, 34), (30, 19), (16, 14), (13, 30), (31, 30), (9, 1), (33, 10), (34, 20), (19, 23), (23, 2), (30, 28), (7, 17), (14, 27), (21, 28), (25, 19), (3, 13), (14, 2), (35, 26), (23, 24), (11, 8), (24, 18), (30, 8), (26, 16), (5, 32), (6, 5), (6, 35), (32, 18), (18, 16), (16, 5), (1, 12), (19, 27), (21, 25), (9, 35), (18, 2), (18, 32), (27, 27), (27, 36), (1, 19), (17, 3), (0, 6), (4, 25), (8, 3), (1, 13), (24, 9), (12, 11), (30, 36), (9, 16), (7, 18), (1, 8), (2, 12), (20, 31), (32, 30), (20, 4), (9, 11), (6, 36), (16, 29), (29, 18), (4, 16), (26, 5), (32, 2), (19, 30), (35, 12), (12, 0), (5, 8), (3, 10), (0, 18), (14, 29), (27, 3), (15, 17), (7, 9), (22, 30), (22, 2), (20, 12), (8, 34), (10, 24), (14, 18), (8, 28), (33, 25), (33, 21), (32, 9), (4, 1), (33, 8), (27, 30), (19, 16), (32, 35), (11, 1), (27, 26), (30, 9), (33, 19), (17, 32), (30, 22), (5, 27), (23, 1), (31, 2), (8, 11), (23, 16), (29, 7), (19, 6), (34, 17), (8, 15), (4, 10), (9, 26), (4, 32), (26, 36), (7, 10), (6, 17), (10, 1), (13, 4), (0, 27), (32, 6), (30, 23), (27, 25), (21, 29), (3, 23), (5, 3), (28, 30), (26, 9), (1, 16), (2, 22), (12, 6), (11, 2), (27, 7), (6, 34), (14, 9), (35, 7), (11, 31), (19, 35), (25, 13), (34, 24), (3, 18), (22, 17), (26, 22), (23, 7), (34, 12), (2, 7), (7, 0), (6, 20), (7, 23), (12, 4), (13, 24), (15, 36), (5, 22), (0, 25), (7, 11), (7, 15), (30, 17), (0, 36), (11, 28), (9, 5), (31, 14), (3, 36), (11, 10), (20, 25), (31, 25), (23, 6), (26, 1), (26, 3), (35, 1), (1, 26), (20, 21), (11, 17), (3, 8), (9, 30), (9, 18), (22, 25), (35, 22), (24, 21), (14, 26), (29, 6), (5, 23), (25, 5), (28, 19), (27, 33), (27, 8), (7, 3), (28, 34), (16, 13), (17, 17), (29, 30), (32, 8), (18, 28), (30, 2), (5, 21), (15, 29), (26, 24), (1, 35), (3, 22), (1, 27), (5, 1), (22, 3), (2, 21), (3, 0), (9, 23), (16, 15), (18, 27), (11, 4), (10, 11), (32, 3), (18, 11), (25, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "518592", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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), (13, 29), (33, 8), (7, 7), (16, 17), (18, 7), (15, 0), (21, 1), (25, 21), (21, 20), (20, 10), (10, 24), (24, 27), (6, 17), (24, 6), (4, 9), (10, 25), (2, 3), (18, 5), (20, 13), (25, 16), (1, 5), (6, 3), (12, 5), (30, 27), (6, 14), (24, 19), (17, 10), (30, 18), (22, 9), (23, 5), (1, 28), (12, 4), (1, 23), (2, 25), (28, 15), (2, 30), (25, 28), (21, 9), (4, 17), (22, 28), (17, 22), (20, 3), (22, 15), (32, 13), (31, 5), (11, 8), (32, 19), (28, 29), (20, 20), (7, 6), (0, 5), (20, 8), (29, 13), (7, 14), (19, 14), (4, 21), (3, 10), (7, 0), (25, 2), (30, 12), (10, 21), (27, 18), (19, 5), (24, 11), (15, 3), (5, 5), (8, 29), (9, 3), (8, 20), (4, 12), (16, 1), (7, 16), (18, 24), (21, 2), (3, 28), (31, 10), (28, 9), (29, 8), (6, 9), (26, 27), (20, 19), (20, 24), (18, 26), (21, 17), (3, 21), (27, 5), (31, 6), (18, 8), (27, 25), (32, 6), (24, 30), (9, 0), (17, 27), (9, 16), (21, 14), (12, 0), (19, 0), (19, 29), (17, 19), (24, 25), (16, 21), (25, 30), (23, 23), (23, 4), (6, 5), (15, 19), (28, 1), (27, 29), (11, 28), (28, 11), (25, 14), (33, 12), (3, 15), (28, 17), (30, 16), (17, 29), (22, 12), (22, 11), (13, 30), (18, 16), (13, 7), (2, 9), (21, 28), (19, 11), (19, 12), (15, 18), (27, 19), (24, 21), (1, 21), (33, 21), (32, 11), (23, 0), (30, 23), (15, 27), (17, 20), (9, 24), (9, 7), (13, 18), (30, 30), (12, 22), (31, 4), (8, 9), (30, 19), (19, 2), (28, 24), (22, 25), (24, 17), (27, 6), (28, 3), (6, 30), (30, 22), (26, 3), (19, 23), (33, 25), (28, 10), (23, 26), (24, 3), (20, 22), (6, 2), (6, 11), (32, 8), (13, 22), (15, 30), (12, 6), (31, 1), (23, 13), (12, 19), (23, 12), (26, 7), (18, 1), (5, 20), (13, 21), (11, 13), (17, 18), (24, 26), (11, 24), (18, 9), (28, 14), (16, 24), (22, 17), (30, 25), (12, 13), (29, 0), (32, 20), (14, 22), (6, 15), (11, 1), (12, 16), (15, 12), (16, 15), (10, 27), (31, 26), (0, 21), (15, 14), (12, 11), (8, 8), (33, 3), (32, 9), (12, 9), (17, 13), (4, 24), (28, 7), (8, 6), (14, 29), (15, 5), (18, 25), (13, 8), (12, 23), (8, 2), (7, 18), (1, 10), (30, 3), (22, 20), (30, 4), (5, 28), (32, 10), (28, 20), (7, 20), (29, 27), (6, 4), (29, 5), (2, 0), (19, 10), (13, 17), (13, 28), (21, 23), (5, 27), (23, 21), (17, 26), (21, 19), (5, 14), (6, 13), (28, 27), (1, 9), (20, 23), (21, 10), (9, 1), (6, 16), (8, 12), (29, 22), (7, 12), (14, 16), (32, 12), (25, 27), (2, 15), (2, 2), (3, 30), (4, 30), (12, 29), (26, 23), (20, 30), (6, 8), (10, 9), (25, 26), (26, 21), (13, 6), (14, 2), (24, 13), (0, 11), (1, 22), (4, 18), (11, 5), (32, 3), (20, 9), (20, 26), (0, 26), (1, 2), (8, 26), (28, 26), (1, 26), (2, 28), (21, 4), (13, 19), (33, 10), (13, 16), (26, 30), (5, 6), (16, 22), (6, 12), (20, 4), (16, 5), (32, 27), (8, 1), (11, 26), (32, 16), (11, 0), (14, 19), (33, 5), (26, 18), (20, 28), (17, 0), (3, 18), (11, 22), (33, 28), (1, 24), (25, 20), (24, 9), (13, 11), (2, 16), (2, 10), (18, 2), (25, 23), (26, 10), (13, 12), (33, 24), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "999680", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 16), (8, 0), (22, 5), (23, 1), (27, 4), (25, 23), (23, 26), (3, 5), (7, 22), (22, 16), (5, 33), (29, 4), (18, 26), (3, 31), (16, 25), (18, 25), (19, 2), (20, 12), (9, 3), (19, 10), (8, 4), (2, 3), (22, 29), (1, 17), (14, 10), (15, 5), (14, 19), (10, 6), (13, 29), (14, 1), (12, 30), (25, 24), (16, 23), (12, 10), (14, 22), (15, 21), (27, 23), (20, 16), (9, 5), (5, 30), (4, 13), (29, 10), (11, 11), (31, 21), (31, 6), (29, 21), (14, 30), (0, 33), (22, 2), (28, 30), (19, 13), (1, 10), (6, 23), (22, 11), (8, 2), (13, 1), (23, 6), (1, 28), (24, 17), (22, 9), (7, 6), (18, 16), (22, 20), (9, 0), (24, 21), (7, 32), (21, 23), (23, 33), (25, 19), (21, 20), (9, 12), (13, 13), (9, 9), (16, 28), (28, 25), (31, 24), (21, 9), (25, 21), (18, 3), (23, 4), (8, 9), (27, 9), (11, 17), (6, 25), (10, 32), (4, 8), (6, 6), (24, 31), (16, 31), (23, 11), (25, 6), (14, 8), (21, 7), (18, 32), (20, 11), (2, 27), (19, 11), (6, 26), (19, 5), (6, 14), (7, 12), (15, 28), (12, 2), (13, 22), (0, 1), (21, 35), (28, 19), (13, 19), (5, 27), (8, 12), (27, 28), (28, 32), (5, 12), (21, 34), (24, 12), (3, 25), (0, 16), (17, 0), (5, 29), (21, 19), (30, 29), (6, 2), (10, 4), (8, 14), (25, 29), (26, 11), (18, 21), (21, 4), (7, 21), (13, 32), (19, 26), (30, 32), (3, 15), (28, 26), (2, 25), (26, 16), (27, 8), (26, 33), (15, 22), (5, 16), (1, 11), (25, 8), (19, 21), (26, 13), (4, 11), (2, 32), (13, 24), (1, 21), (12, 34), (22, 32), (28, 16), (12, 26), (10, 13), (8, 22), (4, 29), (20, 24), (31, 8), (24, 9), (8, 24), (4, 32), (24, 15), (18, 12), (10, 34), (4, 31), (30, 22), (16, 26), (13, 27), (14, 20), (2, 22), (29, 13), (2, 18), (13, 9), (0, 3), (6, 13), (10, 16), (11, 1), (10, 12), (5, 11), (3, 33), (17, 26), (20, 31), (6, 9), (8, 34), (4, 6), (15, 34), (25, 28), (14, 4), (8, 19), (31, 23), (30, 23), (3, 18), (11, 0), (22, 33), (31, 19), (3, 3), (4, 19), (12, 27), (22, 7), (30, 3), (24, 29), (15, 2), (9, 1), (18, 4), (24, 32), (7, 23), (4, 0), (19, 14), (11, 6), (16, 35), (26, 12), (11, 13), (27, 19), (8, 20), (26, 19), (3, 2), (3, 35), (7, 0), (20, 29), (28, 31), (26, 7), (16, 9), (29, 32), (29, 6), (0, 15), (22, 21), (31, 16), (12, 9), (12, 23), (18, 11), (19, 4), (30, 11), (28, 12), (9, 26), (2, 33), (2, 29), (1, 15), (29, 12), (1, 32), (26, 1), (16, 3), (24, 25), (21, 14), (11, 12), (6, 18), (27, 10), (18, 22), (12, 31), (25, 7), (6, 4), (23, 23), (18, 19), (17, 32), (6, 35), (4, 9), (9, 22), (15, 16), (0, 4), (29, 9), (2, 31), (12, 20), (20, 22), (10, 25), (14, 24), (0, 30), (15, 4), (30, 1), (14, 17), (30, 34), (11, 25), (23, 3), (18, 34), (22, 26), (23, 35), (4, 20), (21, 8), (27, 34), (27, 11), (16, 14), (1, 8), (14, 28), (7, 24), (23, 29), (1, 27), (19, 30), (14, 34), (13, 10), (31, 5), (18, 33), (27, 27), (4, 5), (6, 10), (24, 3), (15, 35), (25, 1), (7, 30), (4, 3), (27, 0), (11, 23), (2, 6), (0, 11), (9, 13), (8, 1), (6, 15), (5, 18), (26, 30), (5, 19), (2, 13), (15, 17), (23, 28), (16, 12), (18, 6), (0, 27), (4, 2), (10, 11), (19, 23), (23, 15), (18, 14), (28, 2), (2, 20), (13, 26), (10, 5), (16, 8), (18, 28), (11, 30), (16, 32), (31, 2), (3, 30), (10, 27), (3, 7), (31, 11), (9, 4), (15, 19), (21, 27), (1, 12), (26, 17), (15, 11), (24, 7), (3, 21), (16, 2), (10, 28), (30, 21), (21, 2), (10, 0), (3, 4), (2, 26), (23, 0), (3, 20), (22, 15), (20, 28), (20, 2), (1, 9), (29, 7), (15, 27), (28, 34), (18, 17), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "957600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 36), (14, 14), (13, 0), (12, 6), (18, 16), (8, 31), (6, 21), (13, 26), (13, 28), (28, 32), (13, 17), (11, 25), (25, 10), (26, 32), (7, 7), (12, 26), (27, 32), (14, 37), (23, 6), (27, 8), (1, 27), (12, 25), (8, 10), (9, 23), (15, 25), (10, 8), (27, 34), (24, 38), (5, 19), (11, 34), (19, 17), (19, 7), (16, 3), (6, 5), (0, 4), (25, 7), (27, 3), (29, 25), (17, 6), (23, 28), (7, 34), (6, 4), (24, 15), (30, 24), (9, 22), (27, 35), (28, 15), (10, 21), (20, 21), (3, 3), (27, 1), (7, 6), (5, 34), (28, 12), (5, 9), (24, 6), (24, 7), (23, 2), (15, 4), (17, 16), (13, 32), (3, 31), (25, 11), (11, 4), (3, 15), (11, 17), (18, 29), (1, 32), (12, 22), (26, 19), (20, 4), (5, 11), (11, 19), (17, 21), (9, 34), (17, 19), (22, 30), (0, 22), (22, 1), (20, 14), (15, 31), (0, 13), (2, 25), (16, 0), (21, 23), (23, 20), (19, 15), (23, 1), (30, 26), (18, 9), (22, 16), (7, 38), (14, 0), (13, 34), (16, 11), (2, 3), (25, 18), (7, 8), (15, 5), (23, 33), (5, 4), (11, 23), (27, 26), (16, 16), (7, 4), (23, 16), (3, 2), (12, 37), (15, 11), (17, 34), (26, 35), (19, 16), (26, 14), (12, 5), (10, 35), (19, 3), (17, 29), (14, 2), (25, 1), (12, 19), (30, 28), (22, 7), (20, 3), (18, 17), (16, 10), (13, 24), (28, 20), (18, 38), (16, 29), (6, 30), (16, 36), (4, 22), (21, 5), (14, 38), (8, 28), (23, 14), (9, 18), (15, 9), (23, 36), (29, 2), (8, 13), (9, 24), (30, 23), (21, 21), (22, 8), (26, 27), (5, 35), (6, 37), (7, 26), (21, 11), (20, 2), (0, 15), (7, 27), (8, 0), (2, 12), (28, 1), (26, 28), (17, 17), (17, 37), (16, 35), (3, 29), (14, 1), (24, 22), (12, 23), (19, 10), (22, 23), (0, 32), (27, 9), (8, 1), (27, 20), (15, 6), (18, 12), (19, 35), (26, 2), (2, 15), (19, 5), (22, 12), (14, 16), (29, 16), (28, 0), (21, 16), (4, 25), (30, 1), (24, 33), (30, 30), (24, 25), (17, 10), (14, 17), (13, 14), (8, 15), (29, 5), (22, 32), (3, 20), (16, 38), (22, 36), (16, 24), (8, 29), (1, 23), (5, 8), (14, 34), (30, 12), (17, 32), (25, 34), (26, 31), (29, 1), (6, 38), (8, 2), (0, 29), (13, 4), (2, 27), (4, 0), (7, 21), (21, 32), (18, 19), (10, 17), (5, 18), (23, 13), (4, 19), (0, 21), (12, 7), (8, 22), (18, 22), (18, 36), (26, 29), (13, 27), (6, 31), (22, 25), (1, 25), (10, 10), (27, 0), (15, 29), (5, 14), (15, 24), (10, 37), (19, 38), (22, 38), (27, 37), (6, 13), (3, 35), (22, 11), (3, 18), (5, 32), (3, 10), (11, 3), (2, 34), (7, 24), (24, 31), (9, 27), (29, 21), (28, 35), (29, 13), (20, 24), (10, 30), (23, 22), (13, 16), (20, 20), (14, 26), (18, 33), (9, 21), (14, 18), (6, 36), (24, 1), (20, 30), (23, 24), (6, 8), (8, 34), (14, 32), (1, 37), (26, 12), (24, 26), (17, 38), (14, 12), (15, 0), (23, 3), (20, 22), (7, 30), (11, 36), (19, 19), (6, 26), (5, 6), (14, 10), (30, 22), (28, 30), (2, 20), (3, 32), (18, 25), (13, 33), (4, 21), (11, 35), (21, 34), (27, 10), (21, 26), (28, 8), (17, 1), (23, 15), (17, 3), (22, 9), (5, 7), (18, 23), (12, 18), (22, 10), (11, 2), (7, 18), (22, 5), (29, 20), (28, 28), (0, 11), (20, 25), (6, 35), (20, 23), (3, 38), (10, 28), (17, 28), (26, 22), (25, 5), (7, 31), (2, 0), (13, 11), (18, 34), (9, 10), (15, 37), (17, 31), (1, 35), (13, 30), (17, 13), (19, 31), (28, 5), (18, 10), (11, 26), (8, 5), (13, 20), (17, 24), (0, 27), (3, 37), (30, 20), (3, 4), (24, 34), (7, 36), (30, 31), (18, 35), (20, 28), (15, 36), (25, 26), (27, 11), (13, 12), (10, 5), (24, 29), (25, 28), (22, 0), (4, 13), (23, 9), (9, 28), (0, 35), (14, 27), (28, 38), (11, 30), (21, 3), (12, 4), (1, 11), (1, 13), (5, 10), (3, 28), (7, 2), (14, 3), (18, 11), (4, 36), (30, 33), (4, 10), (27, 2), (30, 7), (28, 11), (27, 17), (30, 18), (14, 24), (8, 14), (17, 4), (17, 20), (29, 11), (22, 2), (1, 9), (16, 4), (17, 9), (29, 36), (9, 37), (12, 1), (20, 34), (25, 37), (15, 3), (1, 28), (19, 9), (22, 22), (28, 7), (6, 14), (7, 10), (19, 25), (10, 2), (30, 11), (24, 19), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "532800", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), 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), (9, 3), (11, 3), (28, 23), (10, 2), (25, 13), (0, 28), (16, 23), (25, 9), (34, 21), (29, 11), (20, 21), (7, 19), (2, 19), (3, 20), (8, 11), (12, 17), (25, 29), (3, 5), (15, 14), (16, 28), (15, 10), (30, 11), (18, 3), (30, 16), (5, 10), (7, 25), (29, 30), (25, 0), (5, 12), (2, 16), (2, 5), (18, 2), (22, 6), (15, 18), (2, 24), (14, 13), (30, 27), (17, 24), (14, 6), (20, 29), (26, 9), (7, 16), (30, 22), (12, 9), (30, 2), (12, 3), (12, 28), (34, 24), (27, 30), (12, 4), (4, 30), (17, 26), (4, 27), (13, 30), (16, 17), (11, 20), (1, 25), (29, 9), (25, 19), (10, 27), (8, 17), (13, 5), (26, 10), (24, 28), (3, 10), (31, 12), (6, 6), (24, 2), (0, 21), (12, 21), (0, 9), (9, 30), (7, 4), (30, 24), (3, 29), (20, 30), (21, 30), (26, 11), (25, 26), (6, 16), (3, 26), (24, 1), (32, 2), (22, 20), (3, 16), (34, 4), (4, 5), (10, 16), (34, 9), (2, 1), (12, 12), (9, 2), (18, 5), (9, 7), (16, 3), (10, 12), (10, 20), (28, 5), (32, 18), (5, 11), (19, 9), (8, 6), (6, 7), (26, 12), (3, 2), (22, 19), (20, 15), (11, 2), (4, 28), (27, 18), (32, 4), (8, 10), (11, 1), (26, 25), (8, 3), (18, 0), (4, 4), (30, 25), (0, 15), (3, 12), (33, 21), (16, 26), (29, 21), (15, 12), (22, 28), (24, 18), (9, 29), (11, 16), (16, 6), (32, 10), (32, 12), (26, 23), (14, 7), (29, 5), (23, 24), (5, 23), (15, 29), (2, 29), (34, 27), (1, 2), (22, 30), (24, 22), (21, 0), (29, 10), (7, 6), (30, 12), (26, 15), (25, 1), (3, 1), (23, 4), (29, 16), (1, 21), (10, 9), (1, 12), (5, 24), (11, 24), (14, 21), (13, 7), (28, 19), (29, 29), (20, 0), (21, 13), (23, 15), (32, 14), (2, 22), (30, 0), (9, 18), (7, 8), (7, 2), (30, 6), (26, 21), (32, 7), (8, 21), (17, 4), (19, 30), (23, 10), (2, 17), (2, 25), (13, 28), (15, 0), (1, 22), (8, 26), (12, 26), (28, 0), (32, 29), (2, 23), (4, 18), (22, 18), (5, 2), (11, 28), (11, 0), (17, 17), (8, 13), (23, 29), (29, 8), (22, 23), (33, 13), (10, 11), (2, 8), (28, 6), (1, 9), (23, 12), (8, 9), (31, 1), (13, 1), (15, 24), (31, 17), (14, 30), (12, 2), (24, 29), (6, 3), (34, 19), (27, 25), (7, 23), (24, 24), (29, 15), (28, 18), (23, 28), (4, 9), (17, 5), (22, 16), (4, 13), (19, 27), (33, 26), (5, 1), (21, 3), (9, 21), (0, 18), (11, 10), (19, 7), (17, 20), (15, 13), (33, 17), (8, 12), (7, 1), (0, 29), (6, 21), (12, 18), (25, 3), (34, 17), (20, 9), (6, 13), (31, 14), (33, 14), (8, 22), (12, 11), (25, 20), (33, 27), (18, 19), (2, 10), (4, 11), (31, 6), (4, 25), (29, 19), (20, 23), (27, 6), (4, 1), (18, 29), (16, 30), (19, 23), (28, 12), (7, 20), (13, 24), (27, 26), (5, 27), (9, 12), (4, 14), (21, 15), (1, 28), (31, 16), (20, 11), (10, 15), (15, 15), (2, 15), (21, 20), (17, 6), (19, 8), (24, 6), (13, 9), (24, 9), (22, 27), (7, 29), (17, 27), (11, 6), (24, 20), (10, 25), (26, 6), (21, 5), (19, 13), (7, 24), (22, 21), (32, 27), (2, 12), (30, 17), (7, 7), (32, 23), (17, 21), (13, 15), (28, 3), (30, 5), (30, 9), (25, 6), (27, 29), (8, 29), (6, 10), (34, 0), (13, 27), (33, 9), (21, 21), (0, 5), (6, 5), (31, 5), (33, 8), (33, 18), (17, 12), (29, 4), (29, 13), (24, 16), (32, 9), (8, 4), (19, 18), (27, 27), (5, 30), (12, 15), (24, 8), (27, 15), (24, 30), (1, 24), (25, 14), (19, 19), (29, 7), (17, 3), (28, 2), (21, 17), (31, 8), (6, 1), (4, 16), (21, 4), (9, 11), (4, 26), (2, 14), (33, 6), (17, 9), (12, 6), (6, 11), (10, 13), (30, 7), (24, 17), (22, 10), (10, 26), (5, 22), (15, 22), (22, 4), (33, 28), (23, 0), (34, 26), (1, 17), (10, 0), (25, 7), (23, 9), (6, 4), (1, 14), (28, 13), (29, 12), (31, 3), (9, 28), (18, 26), (5, 17), (24, 12), (18, 10), (21, 8), (15, 21), (27, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 33), (15, 24), (29, 26), (13, 26), (12, 32), (29, 30), (16, 34), (6, 19), (5, 27), (21, 13), (10, 36), (22, 20), (21, 34), (8, 29), (23, 4), (18, 8), (28, 21), (20, 17), (16, 13), (15, 10), (11, 36), (19, 18), (7, 33), (1, 24), (14, 1), (4, 11), (12, 29), (23, 13), (20, 11), (24, 30), (19, 20), (14, 22), (0, 3), (19, 36), (8, 25), (11, 29), (13, 18), (14, 26), (4, 14), (3, 21), (19, 26), (20, 6), (24, 33), (4, 32), (25, 6), (24, 26), (10, 34), (3, 31), (16, 18), (20, 16), (12, 36), (15, 6), (4, 5), (20, 4), (15, 3), (7, 20), (8, 17), (2, 35), (25, 0), (29, 24), (28, 19), (25, 11), (22, 21), (14, 33), (7, 21), (3, 27), (23, 20), (12, 3), (4, 19), (7, 11), (19, 19), (7, 30), (13, 20), (2, 5), (7, 7), (7, 36), (13, 16), (10, 1), (28, 35), (28, 13), (3, 26), (26, 5), (13, 29), (25, 19), (16, 25), (20, 30), (19, 13), (4, 9), (19, 23), (10, 20), (25, 12), (24, 16), (10, 35), (5, 21), (18, 22), (7, 29), (9, 11), (2, 24), (20, 33), (11, 19), (8, 16), (29, 22), (17, 3), (23, 21), (16, 6), (29, 4), (2, 32), (4, 18), (27, 6), (16, 32), (23, 14), (25, 31), (7, 9), (5, 0), (15, 18), (11, 21), (22, 4), (10, 16), (25, 5), (7, 34), (13, 3), (3, 19), (0, 28), (27, 28), (23, 2), (3, 13), (4, 6), (25, 22), (26, 27), (1, 0), (6, 11), (19, 4), (28, 29), (13, 25), (0, 30), (11, 24), (26, 32), (27, 30), (24, 5), (9, 25), (6, 9), (24, 18), (20, 5), (29, 15), (18, 0), (6, 13), (24, 27), (14, 8), (15, 20), (3, 23), (20, 28), (14, 32), (1, 11), (3, 15), (8, 34), (15, 15), (16, 36), (13, 6), (12, 2), (17, 26), (19, 21), (6, 32), (26, 14), (5, 18), (25, 26), (10, 6), (10, 11), (15, 4), (22, 28), (6, 10), (29, 10), (17, 18), (12, 34), (25, 10), (6, 8), (16, 0), (8, 22), (17, 14), (12, 0), (21, 1), (12, 22), (14, 18), (27, 29), (27, 27), (0, 20), (28, 3), (29, 32), (17, 31), (21, 3), (22, 29), (23, 1), (14, 0), (20, 0), (20, 21), (0, 10), (2, 28), (28, 12), (29, 11), (9, 23), (20, 9), (29, 2), (13, 4), (24, 6), (6, 36), (9, 6), (15, 2), (17, 28), (16, 26), (14, 2), (2, 36), (5, 20), (11, 10), (10, 30), (12, 30), (26, 16), (14, 36), (4, 17), (14, 31), (12, 15), (10, 8), (25, 34), (26, 21), (23, 9), (20, 27), (16, 20), (16, 30), (12, 6), (27, 18), (17, 0), (28, 15), (17, 12), (3, 30), (23, 10), (10, 27), (3, 32), (22, 19), (22, 16), (9, 15), (29, 9), (5, 33), (25, 14), (2, 15), (19, 25), (11, 14), (19, 27), (10, 24), (24, 34), (6, 22), (23, 36), (24, 24), (11, 20), (14, 3), (13, 31), (25, 1), (6, 7), (26, 23), (13, 28), (19, 28), (27, 3), (9, 36), (1, 7), (11, 4), (0, 17), (23, 17), (18, 32), (6, 18), (7, 13), (2, 33), (18, 14), (24, 12), (24, 17), (25, 32), (10, 14), (13, 17), (18, 2), (18, 27), (23, 7), (14, 30), (21, 26), (3, 16), (8, 6), (0, 32), (29, 17), (8, 28), (23, 30), (6, 31), (17, 15), (28, 30), (18, 6), (12, 25), (17, 10), (27, 34), (8, 10), (28, 0), (13, 0), (8, 0), (12, 27), (1, 19), (25, 8), (29, 18), (27, 19), (5, 2), (5, 9), (28, 23), (26, 13), (24, 15), (0, 25), (0, 34), (21, 36), (25, 30), (9, 33), (11, 33), (5, 11), (5, 34), (24, 19), (20, 31), (1, 10), (24, 3), (10, 28), (18, 35), (23, 19), (9, 5), (0, 29), (17, 35), (18, 19), (15, 17), (4, 26), (5, 10), (13, 13), (16, 4), (14, 12), (15, 26), (6, 2), (18, 33), (9, 18), (3, 4), (18, 5), (14, 29), (4, 33), (2, 17), (27, 35), (28, 17), (21, 7), (24, 7), (12, 4), (18, 12), (28, 5), (21, 2), (12, 20), (14, 35), (16, 29), (14, 19), (28, 2), (17, 2), (13, 1), (24, 14), (27, 24), (24, 8), (20, 25), (24, 23), (9, 30), (22, 25), (9, 22), (29, 12), (28, 32), (24, 9), (1, 32), (25, 23), (18, 28), (5, 31), (3, 25), (16, 14), (5, 26), (14, 20), (13, 36), (3, 36), (16, 1), (18, 15), (24, 2), (27, 25), (4, 12), (25, 20), (16, 19), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943488", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), 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), (12, 22), (13, 19), (8, 14), (12, 31), (20, 6), (3, 5), (16, 13), (15, 19), (1, 27), (24, 31), (2, 14), (20, 17), (20, 35), (9, 8), (3, 0), (27, 0), (19, 6), (6, 4), (28, 19), (25, 12), (30, 8), (27, 10), (10, 34), (30, 9), (29, 8), (8, 12), (28, 22), (9, 17), (28, 3), (7, 17), (32, 9), (12, 32), (7, 32), (19, 31), (28, 4), (14, 3), (3, 7), (24, 10), (30, 27), (28, 35), (12, 14), (25, 13), (27, 2), (25, 4), (27, 11), (1, 23), (21, 21), (23, 17), (31, 23), (18, 28), (32, 29), (17, 28), (26, 1), (18, 22), (19, 15), (29, 32), (2, 16), (8, 7), (29, 31), (14, 0), (12, 10), (0, 34), (10, 25), (13, 23), (0, 19), (23, 3), (15, 38), (26, 29), (20, 4), (12, 20), (19, 24), (28, 33), (20, 30), (21, 33), (4, 7), (28, 12), (5, 8), (0, 11), (12, 6), (30, 11), (19, 3), (4, 16), (7, 30), (6, 0), (0, 30), (20, 18), (21, 32), (20, 24), (18, 0), (20, 21), (0, 35), (1, 30), (0, 5), (24, 21), (27, 33), (27, 12), (24, 29), (32, 19), (27, 28), (32, 37), (14, 25), (13, 21), (19, 10), (3, 31), (25, 11), (28, 13), (1, 35), (0, 6), (14, 10), (18, 7), (13, 35), (5, 35), (32, 8), (6, 14), (30, 37), (26, 23), (18, 32), (12, 11), (2, 17), (10, 9), (5, 34), (24, 26), (2, 4), (11, 18), (19, 14), (9, 15), (24, 12), (4, 5), (14, 36), (16, 19), (8, 22), (15, 35), (23, 15), (26, 32), (1, 32), (24, 19), (17, 18), (5, 20), (24, 37), (9, 35), (23, 30), (19, 29), (15, 6), (15, 8), (32, 5), (30, 32), (9, 1), (10, 35), (32, 15), (8, 26), (25, 6), (0, 28), (26, 37), (25, 3), (19, 13), (7, 38), (7, 22), (31, 24), (14, 22), (3, 24), (11, 14), (10, 17), (21, 17), (0, 18), (4, 18), (23, 34), (24, 14), (2, 0), (6, 19), (15, 26), (21, 15), (27, 35), (11, 15), (9, 27), (1, 18), (9, 38), (11, 0), (24, 2), (22, 5), (5, 31), (25, 8), (24, 11), (32, 2), (19, 17), (0, 29), (31, 34), (25, 20), (24, 27), (12, 25), (17, 4), (5, 38), (32, 35), (14, 34), (12, 16), (18, 31), (11, 22), (2, 26), (11, 29), (25, 17), (29, 4), (22, 11), (11, 10), (32, 17), (24, 34), (17, 25), (24, 4), (22, 19), (12, 13), (4, 21), (32, 18), (16, 10), (19, 30), (28, 0), (8, 21), (21, 22), (25, 26), (31, 3), (2, 22), (32, 6), (26, 14), (8, 27), (20, 10), (31, 35), (29, 7), (22, 12), (4, 31), (3, 20), (10, 19), (21, 0), (0, 33), (18, 2), (29, 25), (16, 24), (31, 10), (14, 30), (15, 32), (9, 19), (4, 20), (28, 2), (19, 21), (27, 23), (31, 29), (17, 21), (32, 3), (27, 22), (1, 8), (20, 1), (3, 14), (5, 32), (3, 15), (12, 18), (26, 27), (13, 38), (21, 24), (2, 11), (14, 7), (20, 22), (29, 19), (32, 4), (15, 13), (5, 13), (26, 15), (25, 1), (13, 10), (18, 37), (4, 8), (5, 5), (30, 30), (22, 13), (18, 36), (27, 25), (28, 25), (6, 2), (26, 13), (30, 2), (7, 35), (22, 4), (10, 22), (5, 21), (3, 10), (8, 18), (7, 3), (6, 11), (14, 11), (9, 10), (25, 15), (28, 8), (13, 6), (15, 23), (31, 21), (26, 25), (2, 5), (30, 23), (28, 37), (21, 10), (9, 21), (29, 22), (24, 22), (13, 29), (21, 35), (4, 11), (29, 24), (22, 23), (3, 38), (16, 9), (16, 4), (9, 20), (4, 25), (1, 16), (31, 9), (13, 11), (17, 37), (5, 3), (10, 27), (32, 31), (9, 12), (3, 29), (16, 12), (4, 23), (8, 17), (31, 27), (12, 37), (22, 31), (26, 20), (25, 0), (11, 23), (28, 16), (24, 18), (10, 30), (14, 33), (18, 25), (7, 9), (28, 18), (17, 19), (25, 34), (30, 3), (24, 24), (10, 11), (26, 30), (0, 27), (24, 9), (20, 15), (7, 10), (14, 16), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919191", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 8), (17, 22), (19, 28), (5, 22), (10, 3), (29, 7), (16, 21), (2, 12), (8, 27), (11, 18), (26, 16), (28, 30), (6, 18), (17, 26), (24, 19), (13, 19), (9, 15), (2, 19), (25, 27), (9, 19), (20, 16), (10, 11), (8, 33), (13, 22), (9, 2), (15, 17), (2, 26), (9, 23), (22, 33), (2, 16), (16, 23), (26, 31), (29, 2), (19, 20), (6, 22), (6, 3), (27, 16), (20, 2), (27, 1), (2, 30), (28, 23), (9, 24), (0, 22), (15, 12), (2, 22), (21, 30), (6, 24), (20, 22), (3, 12), (5, 26), (13, 10), (22, 26), (18, 22), (22, 5), (24, 3), (21, 19), (29, 14), (16, 16), (12, 32), (19, 7), (29, 21), (11, 15), (7, 23), (14, 14), (20, 8), (21, 7), (6, 13), (11, 26), (12, 28), (3, 16), (18, 0), (29, 29), (0, 17), (24, 12), (14, 31), (4, 6), (21, 17), (24, 27), (12, 14), (1, 23), (26, 15), (3, 30), (19, 31), (15, 9), (20, 24), (18, 14), (15, 29), (2, 21), (8, 5), (28, 0), (7, 5), (27, 19), (26, 14), (17, 25), (29, 3), (27, 17), (19, 29), (13, 0), (4, 29), (6, 10), (19, 33), (29, 9), (26, 13), (19, 24), (10, 24), (0, 10), (9, 25), (8, 8), (24, 13), (20, 28), (12, 27), (18, 2), (11, 19), (4, 24), (21, 1), (17, 15), (24, 5), (17, 30), (0, 6), (5, 33), (15, 33), (22, 2), (9, 20), (21, 8), (4, 2), (13, 30), (5, 30), (23, 32), (26, 1), (24, 0), (20, 21), (26, 27), (23, 5), (4, 21), (1, 30), (25, 25), (18, 10), (23, 18), (29, 17), (28, 24), (22, 23), (18, 29), (21, 5), (22, 30), (22, 14), (2, 29), (6, 7), (10, 10), (24, 7), (10, 23), (24, 24), (9, 7), (12, 17), (24, 10), (10, 2), (22, 10), (3, 18), (14, 21), (29, 5), (8, 10), (0, 29), (25, 20), (12, 21), (0, 21), (12, 2), (20, 19), (10, 17), (7, 20), (27, 31), (0, 1), (18, 33), (8, 17), (14, 5), (1, 8), (6, 9), (9, 21), (14, 6), (1, 21), (7, 7), (11, 8), (10, 21), (3, 8), (1, 15), (9, 1), (0, 11), (27, 21), (19, 2), (20, 27), (26, 12), (14, 24), (22, 9), (15, 26), (20, 23), (23, 4), (29, 20), (22, 11), (13, 14), (6, 28), (6, 1), (28, 9), (26, 5), (0, 25), (2, 3), (17, 1), (11, 21), (25, 26), (11, 14), (4, 26), (27, 12), (29, 31), (9, 4), (8, 7), (25, 31), (5, 21), (3, 4), (25, 8), (11, 11), (5, 28), (15, 2), (27, 14), (20, 1), (3, 32), (8, 29), (4, 16), (10, 7), (18, 25), (20, 29), (6, 5), (28, 4), (8, 12), (28, 17), (21, 6), (19, 5), (3, 0), (19, 17), (0, 9), (14, 18), (1, 10), (22, 13), (7, 11), (15, 32), (19, 10), (5, 32), (17, 28), (3, 28), (18, 20), (4, 12), (6, 6), (23, 3), (4, 10), (18, 16), (27, 0), (3, 2), (26, 25), (26, 26), (7, 33), (3, 27), (19, 6), (7, 2), (19, 27), (17, 20), (22, 29), (2, 15), (28, 18), (25, 28), (19, 8), (12, 12), (28, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382720", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 4), (5, 34), (24, 13), (23, 5), (23, 33), (24, 18), (28, 10), (5, 25), (22, 22), (14, 21), (0, 9), (5, 7), (1, 8), (17, 34), (27, 3), (28, 28), (22, 24), (21, 12), (5, 10), (7, 8), (22, 9), (11, 18), (16, 3), (29, 0), (17, 5), (25, 30), (3, 16), (25, 33), (6, 13), (15, 9), (12, 21), (20, 34), (23, 34), (2, 27), (12, 9), (14, 9), (14, 7), (8, 4), (15, 8), (3, 19), (9, 10), (1, 12), (21, 10), (16, 14), (0, 11), (27, 17), (15, 25), (8, 0), (5, 33), (29, 22), (19, 18), (14, 6), (10, 12), (27, 8), (26, 9), (25, 15), (5, 19), (10, 17), (18, 31), (4, 14), (17, 35), (25, 28), (0, 14), (28, 19), (25, 25), (23, 2), (29, 10), (19, 11), (3, 22), (1, 29), (19, 9), (5, 27), (23, 10), (11, 5), (27, 9), (28, 11), (15, 31), (19, 26), (24, 35), (26, 14), (1, 23), (0, 2), (27, 13), (12, 34), (15, 1), (21, 0), (22, 14), (10, 29), (29, 30), (13, 8), (16, 18), (28, 20), (5, 31), (19, 12), (1, 7), (3, 17), (11, 0), (4, 4), (22, 25), (13, 24), (29, 21), (18, 15), (20, 35), (0, 13), (24, 28), (25, 22), (23, 13), (16, 16), (11, 11), (3, 0), (19, 19), (16, 26), (22, 32), (16, 17), (11, 7), (19, 3), (28, 29), (18, 22), (4, 12), (6, 4), (6, 15), (1, 22), (24, 9), (19, 4), (27, 11), (23, 14), (12, 15), (27, 33), (18, 30), (14, 35), (3, 28), (26, 6), (21, 27), (6, 12), (17, 2), (17, 17), (23, 6), (12, 22), (22, 0), (12, 5), (6, 3), (3, 13), (25, 26), (11, 30), (20, 18), (0, 4), (18, 4), (7, 19), (3, 35), (8, 1), (1, 17), (7, 6), (3, 5), (7, 7), (11, 34), (12, 18), (12, 24), (0, 1), (26, 7), (10, 11), (0, 20), (27, 29), (9, 19), (5, 13), (20, 19), (0, 24), (29, 29), (21, 6), (18, 13), (7, 0), (17, 0), (8, 2), (23, 35), (15, 5), (0, 3), (12, 33), (17, 29), (19, 17), (13, 12), (22, 29), (13, 9), (16, 25), (26, 21), (11, 28), (23, 21), (4, 11), (15, 16), (2, 30), (12, 19), (25, 4), (29, 8), (3, 30), (7, 28), (18, 8), (19, 33), (14, 28), (19, 14), (5, 21), (28, 27), (24, 34), (9, 23), (20, 5), (29, 34), (14, 3), (28, 23), (22, 27), (10, 21), (25, 9), (14, 22), (28, 21), (15, 2), (4, 15), (9, 24), (15, 21), (16, 27), (21, 14), (17, 7), (16, 24), (9, 34), (27, 21), (5, 1), (10, 5), (20, 32), (1, 11), (19, 35), (24, 4), (9, 25), (14, 29), (21, 7), (19, 20), (10, 8), (9, 5), (20, 21), (24, 25), (21, 32), (19, 29), (10, 30), (22, 21), (22, 23), (26, 11), (23, 3), (13, 32), (9, 15), (10, 23), (11, 10), (23, 27), (19, 5), (27, 24), (6, 14), (23, 32), (0, 26), (19, 7), (18, 34), (13, 18), (29, 23), (24, 16), (9, 22), (7, 27), (9, 30), (21, 17), (6, 20), (2, 25), (17, 14), (1, 24), (23, 7), (10, 24), (23, 1), (11, 19), (25, 13), (4, 24), (21, 30), (17, 4), (27, 16), (26, 16), (23, 15), (18, 2), (26, 26), (26, 34), (12, 25), (13, 33), (5, 23), (26, 29), (9, 17), (5, 2), (12, 23), (3, 25), (25, 6), (16, 9), (8, 22), (19, 24), (10, 35), (29, 13), (29, 2), (11, 14), (25, 29), (25, 24), (1, 16), (18, 10), (6, 26), (13, 1), (22, 7), (19, 31), (13, 7), (15, 28), (7, 13), (12, 26), (21, 26), (27, 0), (5, 15), (22, 34), (28, 2), (26, 31), (26, 22), (2, 32), (6, 8), (0, 34), (22, 17), (11, 6), (24, 20), (28, 6), (12, 1), (12, 29), (7, 29), (0, 6), (15, 30), (23, 9), (28, 14), (16, 33), (7, 11), (24, 5), (14, 1), (25, 35), (5, 32), (20, 31), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8904", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), 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), (37, 8), (37, 28), (28, 13), (1, 30), (20, 18), (6, 2), (38, 29), (14, 2), (3, 28), (3, 14), (6, 10), (37, 22), (19, 21), (22, 17), (25, 8), (13, 24), (28, 22), (32, 12), (38, 30), (26, 19), (21, 31), (38, 22), (6, 13), (20, 2), (24, 32), (34, 1), (6, 27), (3, 11), (1, 22), (20, 26), (15, 31), (37, 15), (1, 8), (38, 1), (1, 15), (14, 15), (16, 6), (15, 26), (30, 5), (37, 17), (28, 29), (36, 28), (9, 24), (34, 12), (8, 5), (33, 9), (13, 21), (11, 6), (14, 9), (0, 32), (15, 8), (10, 31), (15, 4), (9, 5), (13, 16), (10, 30), (1, 31), (0, 5), (26, 29), (5, 4), (17, 1), (16, 14), (26, 16), (6, 1), (13, 32), (7, 20), (11, 28), (36, 2), (18, 24), (6, 22), (21, 13), (36, 21), (21, 24), (35, 14), (25, 20), (35, 23), (38, 18), (23, 17), (6, 23), (15, 20), (37, 6), (21, 0), (34, 23), (31, 6), (19, 24), (3, 23), (28, 14), (21, 12), (2, 9), (18, 32), (23, 18), (13, 1), (23, 1), (32, 20), (15, 1), (34, 9), (12, 14), (29, 1), (22, 15), (36, 11), (31, 32), (9, 8), (7, 14), (10, 18), (6, 30), (34, 13), (9, 19), (6, 14), (28, 9), (1, 32), (28, 4), (8, 25), (35, 27), (12, 26), (38, 2), (4, 27), (23, 8), (33, 20), (4, 16), (13, 7), (21, 9), (1, 9), (38, 9), (29, 30), (28, 7), (9, 15), (14, 29), (18, 29), (18, 26), (31, 23), (16, 30), (15, 23), (20, 11), (16, 12), (10, 27), (27, 1), (37, 24), (30, 7), (14, 0), (18, 27), (8, 18), (35, 15), (18, 16), (5, 29), (38, 24), (0, 22), (38, 20), (7, 3), (16, 17), (32, 4), (17, 16), (29, 32), (3, 12), (25, 27), (34, 28), (27, 13), (22, 31), (11, 11), (33, 24), (35, 4), (34, 20), (26, 28), (6, 25), (31, 28), (0, 20), (13, 17), (22, 0), (3, 4), (10, 23), (4, 24), (34, 14), (35, 19), (23, 0), (19, 8), (33, 18), (16, 31), (38, 0), (38, 31), (8, 21), (28, 19), (0, 12), (21, 5), (30, 26), (28, 31), (34, 15), (37, 13), (24, 8), (17, 5), (19, 4), (1, 6), (14, 19), (19, 10), (26, 11), (11, 25), (6, 32), (13, 0), (11, 5), (20, 15), (9, 14), (24, 14), (9, 28), (4, 14), (25, 23), (22, 25), (38, 25), (15, 17), (31, 5), (36, 25), (33, 2), (33, 32), (4, 5), (12, 32), (29, 13), (17, 22), (24, 29), (4, 18), (22, 32), (8, 6), (0, 23), (2, 22), (20, 28), (29, 0), (35, 25), (2, 3), (0, 14), (15, 7), (1, 10), (8, 32), (5, 13), (1, 11), (17, 2), (27, 17), (14, 21), (9, 9), (20, 29), (3, 9), (5, 18), (3, 32), (29, 22), (14, 30), (10, 16), (23, 9), (6, 18), (22, 22), (24, 11), (21, 32), (15, 16), (29, 26), (37, 30), (18, 7), (36, 0), (11, 12), (11, 23), (31, 24), (8, 4), (15, 12), (36, 32), (3, 16), (28, 2), (4, 13), (31, 11), (35, 11), (9, 3), (22, 19), (4, 25), (16, 8), (4, 6), (19, 32), (22, 16), (34, 29), (35, 22), (24, 13), (16, 27), (17, 26), (1, 28), (17, 23), (30, 28), (9, 21), (28, 15), (25, 12), (27, 21), (13, 20), (16, 7), (36, 29), (35, 20), (38, 8), (21, 19), (13, 18), (31, 0), (10, 2), (20, 19), (18, 14), (8, 27), (31, 20), (37, 12), (21, 30), (4, 11), (5, 19), (26, 22), (17, 10), (14, 6), (33, 5), (10, 19), (24, 25), (23, 13), (1, 29), (13, 3), (24, 21), (11, 9), (9, 2), (30, 8), (8, 9), (8, 11), (13, 15), (30, 3), (15, 21), (9, 0), (30, 19), (4, 10), (5, 31), (17, 17), (14, 7), (13, 28), (21, 29), (23, 12), (13, 25), (21, 16), (15, 10), (4, 15), (24, 17), (35, 28), (10, 9), (23, 14), (20, 22), (6, 5), (7, 26), (16, 5), (33, 25), (24, 3), (37, 19), (32, 3), (12, 7), (7, 24), (0, 11), (24, 15), (10, 32), (2, 30), (23, 2), (17, 24), (3, 30), (34, 11), (29, 10), (18, 12), (29, 29), (14, 10), (35, 8), (30, 20), (12, 8), (26, 1), (5, 20), (24, 18), (7, 17), (27, 22), (25, 30), (11, 29), (7, 27), (37, 5), (25, 6), (11, 27), (12, 28), (23, 11), (2, 24), (21, 21), (2, 19), (9, 26), (23, 15), (3, 26), (30, 23), (12, 23), (8, 15), (16, 20), (21, 18), (4, 26), (37, 7), (15, 19), (27, 31), (1, 20), (25, 14), (6, 26), (8, 1), (13, 27), (22, 7), (12, 27), (33, 23), (28, 0), (11, 3), (30, 25), (1, 4), (25, 5), (11, 16), (6, 9), (31, 25), (27, 28), (12, 24), (37, 29), (6, 21), (11, 15), (3, 8), (4, 0), (24, 28), (30, 0), (5, 1), (6, 17), (5, 16), (5, 24), (2, 32), (12, 5), (9, 16), (12, 16), (35, 10), (28, 6), (1, 5), (8, 7), (14, 25), (5, 26), (25, 9), (37, 11), (9, 25), (32, 8), (1, 17), (27, 5), (38, 4), (0, 19), (26, 18), (32, 1), (3, 31), (27, 6), (3, 10), (23, 20), (24, 22), (19, 0), (36, 15), (8, 20), (23, 31), (11, 13), (10, 26), (16, 1), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641240", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 30), (7, 17), (19, 28), (21, 18), (0, 35), (2, 10), (11, 14), (6, 21), (26, 30), (1, 35), (23, 28), (24, 7), (8, 21), (26, 0), (27, 7), (8, 20), (23, 29), (7, 6), (16, 14), (3, 14), (24, 11), (5, 27), (28, 24), (16, 25), (18, 12), (27, 29), (10, 6), (20, 29), (12, 18), (15, 0), (24, 26), (10, 9), (19, 9), (21, 34), (6, 32), (26, 11), (4, 3), (3, 15), (5, 23), (3, 29), (6, 28), (29, 34), (23, 25), (4, 11), (28, 20), (10, 1), (29, 5), (26, 31), (3, 33), (13, 1), (23, 12), (21, 12), (1, 7), (18, 18), (27, 31), (25, 35), (4, 5), (10, 23), (25, 15), (15, 35), (9, 10), (10, 19), (20, 2), (0, 3), (23, 17), (16, 13), (2, 23), (12, 16), (16, 34), (5, 12), (15, 9), (16, 5), (2, 24), (3, 28), (1, 32), (12, 25), (9, 29), (3, 4), (13, 24), (9, 28), (23, 34), (6, 19), (27, 4), (29, 8), (16, 10), (19, 35), (10, 4), (2, 20), (25, 8), (6, 23), (29, 35), (0, 21), (17, 36), (28, 16), (4, 13), (24, 14), (5, 2), (18, 33), (16, 35), (6, 14), (28, 21), (19, 0), (14, 11), (21, 20), (11, 29), (13, 25), (29, 6), (21, 36), (1, 31), (5, 30), (14, 21), (19, 22), (9, 17), (12, 27), (11, 21), (19, 10), (15, 7), (1, 34), (11, 11), (21, 2), (18, 9), (9, 9), (26, 9), (4, 22), (6, 17), (13, 16), (10, 13), (1, 13), (3, 6), (1, 18), (19, 14), (3, 9), (22, 30), (12, 33), (18, 24), (17, 19), (11, 18), (25, 14), (15, 6), (2, 22), (5, 18), (6, 29), (14, 12), (9, 3), (23, 4), (12, 20), (19, 4), (14, 36), (21, 31), (27, 14), (0, 4), (25, 6), (16, 11), (22, 25), (14, 28), (0, 28), (22, 26), (12, 15), (15, 4), (15, 22), (1, 1), (2, 18), (16, 22), (22, 15), (24, 20), (23, 27), (22, 7), (10, 5), (10, 34), (15, 12), (1, 22), (28, 2), (3, 0), (13, 29), (14, 20), (17, 26), (20, 21), (10, 26), (18, 28), (25, 17), (3, 34), (8, 19), (3, 36), (16, 7), (16, 21), (23, 35), (11, 26), (20, 23), (0, 26), (9, 35), (5, 9), (22, 28), (17, 18), (5, 19), (27, 1), (2, 4), (8, 17), (10, 7), (27, 11), (10, 32), (18, 26), (27, 30), (24, 13), (24, 27), (9, 1), (18, 30), (29, 2), (4, 29), (18, 20), (1, 3), (1, 24), (4, 12), (18, 16), (8, 30), (29, 23), (21, 35), (28, 1), (13, 19), (14, 32), (4, 28), (15, 29), (1, 11), (3, 18), (29, 32), (9, 33), (3, 8), (8, 27), (9, 23), (2, 6), (15, 10), (14, 18), (7, 2), (7, 36), (10, 33), (25, 23), (22, 20), (9, 0), (14, 9), (21, 6), (11, 28), (9, 7), (8, 10), (28, 28), (5, 14), (18, 25), (12, 29), (13, 23), (12, 21), (7, 28), (4, 17), (12, 31), (6, 12), (16, 2), (12, 26), (1, 12), (23, 13), (10, 20), (0, 13), (28, 19), (22, 32), (21, 1), (8, 29), (14, 23), (2, 14), (7, 0), (0, 20), (3, 31), (4, 36), (8, 3), (6, 9), (25, 9), (20, 34), (12, 0), (6, 30), (4, 19), (14, 19), (26, 19), (19, 29), (20, 9), (1, 25), (7, 32), (20, 14), (8, 35), (8, 0), (25, 4), (5, 34), (3, 25), (25, 10), (17, 8), (1, 6), (1, 15), (0, 30), (3, 16), (21, 27), (20, 12), (13, 2), (14, 17), (3, 3), (21, 9), (0, 11), (22, 6), (23, 33), (11, 8), (9, 5), (10, 25), (5, 3), (17, 32), (11, 31), (28, 15), (16, 6), (27, 19), (4, 23), (22, 33), (26, 2), (18, 15), (2, 29), (28, 27), (4, 8), (20, 22), (9, 18), (21, 22), (7, 27), (8, 7), (10, 21), (6, 13), (17, 28), (23, 8), (24, 35), (25, 22), (1, 27), (28, 4), (6, 16), (1, 17), (3, 27), (14, 34), (23, 31), (4, 6), (7, 16), (29, 20), (9, 32), (29, 31), (25, 36), (27, 5), (20, 25), (15, 18), (0, 29), (13, 27), (8, 18), (21, 15), (13, 13), (3, 24), (26, 10), (17, 5), (27, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432458", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 24), (0, 16), (15, 32), (17, 18), (7, 7), (30, 27), (27, 15), (11, 10), (23, 3), (25, 34), (7, 18), (26, 27), (18, 15), (28, 36), (29, 19), (17, 19), (1, 23), (29, 7), (9, 24), (21, 6), (30, 18), (14, 14), (7, 2), (1, 27), (29, 20), (6, 34), (6, 13), (8, 31), (23, 19), (28, 5), (30, 30), (5, 34), (10, 34), (11, 14), (23, 28), (16, 14), (20, 2), (2, 22), (19, 6), (10, 21), (11, 5), (26, 20), (14, 9), (7, 5), (22, 22), (29, 4), (25, 28), (10, 24), (12, 32), (1, 30), (17, 23), (6, 14), (23, 18), (1, 32), (24, 19), (28, 23), (18, 14), (27, 27), (1, 13), (26, 35), (14, 13), (2, 34), (5, 8), (30, 8), (17, 12), (2, 0), (6, 27), (2, 33), (7, 13), (5, 25), (8, 19), (26, 33), (20, 12), (16, 26), (10, 17), (26, 1), (30, 12), (12, 23), (11, 17), (7, 23), (15, 9), (27, 36), (9, 34), (28, 2), (24, 0), (2, 27), (8, 0), (23, 4), (1, 36), (11, 19), (22, 16), (11, 21), (19, 4), (19, 34), (16, 17), (20, 15), (5, 29), (6, 26), (12, 14), (19, 16), (4, 2), (7, 1), (13, 35), (22, 5), (29, 28), (8, 11), (16, 1), (16, 7), (8, 29), (2, 30), (19, 11), (18, 24), (5, 5), (28, 20), (27, 0), (25, 19), (19, 25), (15, 5), (21, 0), (23, 21), (9, 36), (18, 5), (8, 18), (20, 9), (20, 3), (22, 32), (25, 22), (26, 26), (6, 30), (24, 37), (21, 5), (24, 24), (4, 21), (28, 16), (28, 22), (29, 23), (6, 19), (16, 4), (22, 25), (10, 13), (14, 16), (12, 22), (4, 24), (23, 34), (29, 8), (18, 8), (2, 12), (29, 15), (3, 35), (3, 31), (15, 8), (9, 37), (13, 30), (20, 18), (28, 33), (14, 2), (29, 13), (0, 37), (16, 24), (29, 5), (8, 6), (15, 26), (26, 4), (22, 6), (13, 5), (17, 16), (2, 4), (21, 27), (20, 24), (16, 23), (7, 31), (5, 4), (27, 26), (27, 13), (29, 30), (21, 9), (11, 11), (11, 16), (6, 29), (29, 10), (23, 29), (0, 36), (6, 31), (21, 36), (0, 9), (28, 13), (19, 19), (28, 11), (11, 6), (21, 37), (16, 13), (21, 21), (13, 37), (7, 25), (25, 20), (26, 18), (3, 33), (11, 8), (24, 11), (3, 28), (25, 2), (28, 31), (4, 0), (6, 0), (15, 16), (15, 3), (28, 30), (18, 11), (2, 37), (8, 12), (25, 7), (6, 28), (17, 0), (18, 32), (4, 4), (7, 32), (27, 30), (24, 23), (2, 2), (3, 2), (12, 5), (6, 6), (11, 23), (23, 26), (1, 25), (16, 8), (12, 13), (30, 9), (2, 24), (18, 13), (27, 18), (9, 12), (11, 13), (21, 29), (22, 36), (30, 3), (1, 16), (10, 22), (15, 28), (1, 8), (17, 26), (16, 35), (7, 6), (27, 3), (17, 2), (10, 29), (0, 19), (19, 15), (16, 34), (29, 35), (20, 31), (0, 12), (21, 17), (5, 26), (12, 10), (1, 18), (25, 5), (5, 15), (22, 0), (17, 5), (24, 13), (5, 14), (24, 22), (10, 7), (4, 5), (4, 23), (20, 29), (20, 33), (7, 20), (29, 34), (2, 32), (21, 3), (0, 20), (14, 27), (17, 36), (3, 21), (3, 37), (3, 19), (11, 20), (12, 33), (18, 28), (16, 22), (14, 3), (1, 26), (14, 8), (18, 25), (20, 37), (12, 19), (15, 30), (16, 21), (23, 20), (2, 13), (22, 33), (12, 28), (3, 7), (28, 17), (16, 31), (2, 28), (9, 32), (6, 20), (13, 22), (5, 11), (29, 3), (16, 32), (28, 14), (4, 17), (8, 14), (4, 1), (23, 11), (19, 30), (11, 37), (17, 28), (11, 24), (14, 5), (17, 3), (11, 36), (7, 19), (23, 33), (27, 14), (5, 7), (9, 29), (11, 1), (0, 15), (12, 16), (25, 37), (20, 25), (17, 20), (16, 2), (18, 36), (14, 17), (8, 35), (2, 25), (6, 4), (7, 4), (15, 36), (5, 28), (16, 37), (23, 15), (13, 19), (1, 21), (14, 11), (20, 22), (18, 9), (9, 33), (3, 13), (20, 11), (2, 16), (29, 2), (0, 22), (16, 5), (1, 7), (25, 16), (24, 12), (15, 19), (1, 15), (8, 33), (15, 21), (24, 15), (3, 32), (17, 9), (18, 4), (17, 21), (3, 16), (9, 19), (18, 23), (22, 11), (2, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "412320", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), 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), (26, 17), (34, 19), (13, 19), (12, 3), (0, 25), (23, 26), (6, 22), (2, 29), (7, 5), (26, 15), (19, 11), (6, 29), (24, 10), (16, 19), (9, 13), (33, 15), (15, 1), (24, 1), (14, 19), (27, 8), (16, 25), (31, 5), (32, 6), (30, 6), (23, 4), (33, 6), (10, 4), (14, 10), (28, 29), (3, 1), (3, 5), (11, 17), (13, 11), (18, 12), (25, 15), (6, 26), (5, 4), (25, 1), (18, 10), (30, 5), (14, 5), (29, 2), (29, 10), (0, 28), (17, 20), (11, 26), (8, 16), (2, 21), (7, 18), (19, 16), (10, 9), (1, 20), (19, 5), (26, 20), (14, 9), (21, 24), (33, 20), (22, 28), (19, 13), (12, 13), (5, 2), (35, 0), (25, 26), (20, 6), (6, 9), (19, 28), (5, 0), (15, 28), (4, 29), (34, 15), (33, 25), (11, 25), (29, 6), (23, 6), (9, 5), (26, 3), (31, 9), (35, 2), (22, 9), (10, 29), (12, 4), (6, 21), (13, 20), (9, 12), (19, 29), (6, 2), (7, 17), (26, 10), (27, 19), (28, 12), (11, 16), (22, 18), (25, 14), (22, 4), (18, 4), (14, 13), (35, 16), (4, 1), (33, 28), (19, 12), (28, 2), (13, 12), (29, 22), (3, 4), (14, 28), (30, 4), (5, 26), (35, 10), (17, 4), (34, 26), (11, 11), (27, 18), (5, 28), (29, 9), (26, 12), (29, 0), (5, 19), (32, 28), (3, 22), (24, 5), (1, 14), (21, 0), (30, 15), (16, 3), (1, 27), (35, 13), (16, 28), (14, 29), (4, 8), (21, 16), (8, 9), (19, 1), (35, 7), (32, 20), (0, 16), (20, 20), (11, 14), (8, 6), (14, 6), (16, 1), (21, 4), (3, 3), (21, 7), (30, 1), (2, 2), (5, 8), (1, 11), (11, 2), (34, 17), (0, 24), (23, 8), (25, 0), (1, 4), (21, 25), (12, 5), (11, 22), (15, 4), (16, 14), (11, 9), (17, 5), (35, 11), (1, 5), (10, 22), (4, 6), (25, 20), (28, 1), (20, 27), (18, 14), (31, 28), (2, 25), (20, 19), (12, 19), (10, 24), (2, 23), (8, 17), (26, 14), (31, 22), (15, 19), (28, 23), (25, 2), (8, 19), (23, 23), (23, 2), (10, 6), (10, 1), (25, 10), (9, 23), (17, 11), (29, 7), (25, 17), (11, 20), (27, 21), (33, 11), (1, 18), (0, 7), (5, 11), (31, 2), (26, 1), (22, 24), (5, 15), (32, 8), (20, 14), (28, 28), (14, 27), (32, 0), (28, 15), (35, 25), (30, 19), (27, 24), (2, 0), (2, 9), (10, 19), (10, 7), (28, 7), (18, 21), (15, 25), (3, 24), (14, 24), (17, 2), (30, 22), (10, 16), (34, 21), (10, 21), (10, 11), (7, 24), (27, 16), (0, 21), (18, 6), (20, 29), (17, 22), (16, 29), (34, 22), (6, 20), (29, 23), (12, 25), (7, 20), (24, 17), (28, 21), (9, 19), (21, 19), (23, 19), (33, 19), (17, 10), (13, 6), (35, 6), (2, 11), (20, 25), (19, 10), (20, 13), (6, 23), (11, 5), (27, 9), (6, 24), (14, 22), (16, 26), (21, 10), (26, 5), (35, 26), (23, 11), (27, 7), (8, 27), (33, 8), (3, 11), (33, 12), (28, 26), (28, 25), (29, 20), (8, 7), (18, 17), (25, 21), (1, 22), (33, 3), (23, 5), (19, 23), (19, 2), (28, 19), (5, 9), (4, 13), (23, 28), (35, 4), (18, 23), (6, 16), (12, 6), (4, 19), (10, 27), (23, 12), (32, 2), (19, 8), (27, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60720", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), 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), (21, 6), (25, 20), (23, 19), (15, 28), (5, 24), (0, 11), (12, 13), (1, 20), (20, 4), (10, 26), (6, 10), (11, 21), (25, 3), (24, 24), (14, 13), (21, 26), (34, 17), (28, 2), (16, 12), (5, 18), (26, 20), (29, 3), (4, 19), (19, 26), (33, 17), (18, 23), (2, 23), (1, 11), (10, 9), (1, 21), (6, 18), (11, 29), (20, 1), (12, 6), (19, 8), (27, 20), (33, 6), (7, 8), (25, 0), (32, 17), (5, 15), (4, 6), (1, 4), (21, 0), (19, 23), (33, 8), (21, 16), (2, 6), (22, 27), (14, 7), (17, 4), (27, 6), (1, 14), (6, 19), (15, 24), (5, 28), (25, 29), (15, 0), (25, 5), (10, 25), (26, 25), (26, 19), (2, 7), (28, 0), (11, 15), (29, 11), (21, 25), (4, 20), (5, 10), (25, 11), (19, 18), (16, 26), (6, 8), (3, 14), (3, 1), (16, 7), (29, 2), (7, 15), (10, 18), (26, 13), (15, 12), (26, 28), (0, 9), (11, 2), (10, 15), (20, 12), (19, 6), (15, 5), (22, 5), (21, 20), (14, 25), (23, 9), (17, 27), (31, 7), (20, 9), (30, 19), (29, 29), (20, 0), (12, 2), (19, 22), (31, 16), (12, 16), (13, 9), (15, 13), (11, 26), (3, 7), (17, 6), (7, 21), (15, 6), (23, 3), (7, 22), (10, 21), (33, 4), (33, 11), (25, 18), (11, 11), (16, 2), (31, 29), (9, 14), (20, 13), (17, 26), (33, 5), (1, 15), (14, 6), (2, 10), (23, 16), (1, 24), (17, 14), (29, 27), (18, 1), (24, 2), (24, 19), (6, 3), (13, 16), (21, 21), (12, 20), (23, 24), (12, 10), (2, 0), (14, 23), (29, 10), (21, 8), (32, 15), (9, 29), (32, 18), (8, 24), (29, 22), (20, 11), (9, 18), (6, 29), (22, 11), (30, 7), (13, 20), (6, 4), (15, 3), (27, 23), (26, 8), (17, 24), (23, 15), (8, 3), (7, 4), (12, 8), (28, 20), (5, 22), (15, 10), (6, 0), (0, 25), (32, 1), (12, 29), (29, 19), (22, 18), (24, 29), (14, 14), (28, 25), (24, 18), (17, 0), (20, 22), (13, 19), (27, 24), (3, 16), (11, 7), (18, 29), (24, 16), (13, 4), (16, 21), (23, 0), (32, 25), (20, 23), (6, 9), (10, 17), (24, 27), (28, 15), (4, 3), (18, 11), (18, 8), (31, 17), (7, 14), (9, 0), (25, 25), (5, 23), (25, 23), (7, 23), (4, 24), (24, 5), (31, 28), (0, 3), (33, 26), (9, 15), (27, 22), (14, 5), (20, 20), (22, 12), (6, 6), (34, 0), (30, 10), (5, 5), (26, 14), (12, 26), (31, 20), (0, 12), (7, 18), (25, 12), (13, 6), (27, 13), (9, 9), (30, 0), (13, 0), (27, 5), (20, 26), (24, 23), (8, 27), (8, 23), (4, 0), (1, 13), (31, 5), (20, 18), (4, 8), (18, 26), (8, 14), (9, 10), (18, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907470", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 33), (20, 0), (27, 29), (24, 25), (29, 28), (33, 8), (15, 4), (32, 12), (33, 1), (25, 35), (8, 28), (10, 9), (26, 12), (18, 4), (19, 27), (13, 21), (6, 22), (16, 7), (18, 11), (3, 6), (9, 29), (28, 34), (1, 17), (28, 6), (18, 0), (2, 34), (2, 20), (26, 23), (3, 22), (9, 21), (32, 3), (4, 0), (21, 15), (15, 6), (34, 12), (24, 13), (30, 2), (2, 7), (15, 31), (19, 6), (7, 6), (10, 3), (16, 24), (22, 34), (1, 21), (0, 1), (7, 15), (25, 14), (31, 1), (17, 33), (5, 35), (13, 19), (30, 16), (6, 19), (2, 35), (10, 34), (1, 25), (18, 31), (6, 1), (25, 1), (28, 18), (27, 12), (15, 22), (29, 32), (29, 6), (8, 11), (28, 31), (16, 16), (1, 14), (11, 27), (18, 27), (9, 23), (24, 4), (22, 27), (9, 32), (21, 2), (21, 23), (31, 12), (27, 24), (15, 35), (22, 24), (29, 8), (29, 3), (13, 25), (31, 34), (34, 26), (32, 19), (19, 17), (3, 8), (8, 0), (16, 18), (19, 22), (6, 33), (12, 18), (18, 7), (6, 2), (2, 29), (10, 19), (2, 4), (14, 15), (29, 20), (12, 32), (19, 3), (23, 17), (19, 24), (28, 2), (25, 20), (29, 35), (34, 5), (34, 23), (30, 14), (25, 2), (34, 9), (9, 18), (6, 32), (16, 28), (19, 28), (11, 12), (1, 23), (31, 10), (20, 11), (7, 32), (9, 11), (21, 7), (14, 26), (2, 21), (16, 22), (5, 18), (17, 31), (5, 26), (26, 27), (11, 10), (32, 24), (14, 24), (13, 10), (24, 24), (28, 14), (17, 0), (11, 7), (14, 1), (7, 27), (14, 27), (16, 9), (11, 31), (30, 10), (10, 1), (11, 18), (32, 2), (22, 5), (20, 23), (8, 7), (16, 3), (29, 13), (6, 6), (23, 18), (11, 20), (3, 28), (1, 12), (34, 14), (29, 7), (26, 31), (17, 25), (3, 4), (11, 22), (31, 26), (30, 26), (30, 4), (26, 0), (16, 0), (15, 25), (13, 28), (32, 25), (23, 29), (20, 1), (4, 23), (7, 0), (17, 35), (25, 32), (16, 11), (15, 18), (30, 22), (24, 18), (5, 25), (27, 27), (4, 31), (34, 27), (8, 10), (17, 32), (16, 31), (28, 9), (12, 9), (29, 1), (5, 12), (12, 10), (34, 19), (10, 21), (32, 18), (2, 22), (18, 35), (17, 8), (28, 16), (32, 32), (33, 35), (17, 6), (10, 4), (29, 16), (9, 20), (11, 21), (11, 2), (32, 20), (18, 23), (1, 5), (16, 10), (15, 2), (27, 11), (27, 18), (18, 1), (17, 15), (28, 21), (14, 6), (1, 13), (9, 26), (10, 33), (3, 10), (4, 20), (11, 32), (3, 21), (22, 8), (31, 29), (7, 21), (16, 26), (9, 34), (31, 22), (4, 11), (29, 18), (21, 25), (3, 26), (16, 17), (33, 4), (16, 19), (20, 34), (14, 0), (6, 3), (16, 1), (25, 25), (28, 11), (19, 25), (21, 21), (34, 11), (25, 9), (23, 12), (26, 20), (20, 4), (29, 22), (0, 9), (8, 27), (26, 16), (15, 20), (33, 28), (3, 35), (20, 14), (17, 7), (21, 6), (21, 29), (6, 18), (18, 5), (0, 19), (5, 31), (16, 5), (20, 29), (21, 16), (33, 31), (6, 12), (31, 9), (10, 31), (22, 31), (26, 15), (20, 2), (26, 14), (28, 10), (22, 14), (14, 34), (24, 26), (25, 12), (12, 4), (11, 28), (23, 3), (18, 15), (30, 1), (24, 9), (13, 35), (27, 7), (16, 15), (32, 5), (12, 14), (32, 16), (30, 24), (16, 33), (22, 23), (10, 24), (23, 19), (11, 5), (34, 17), (23, 11), (12, 30), (20, 8), (24, 12), (4, 24), (20, 25), (19, 34), (0, 33), (1, 33), (30, 21), (29, 30), (12, 31), (24, 17), (30, 29), (33, 30), (10, 8), (2, 8), (17, 22), (28, 24), (0, 5), (13, 26), (12, 3), (15, 34), (19, 32), (6, 20), (3, 33), (22, 33), (18, 10), (0, 2), (27, 19), (26, 8), (25, 23), (14, 9), (7, 20), (17, 23), (8, 22), (33, 18), (9, 14), (19, 5), (21, 18), (13, 20), (20, 17), (0, 8), (5, 34), (15, 28), (5, 16), (7, 34), (34, 4), (15, 15), (14, 3), (23, 15), (19, 20), (5, 0), (6, 29), (13, 0), (2, 3), (5, 4), (18, 3), (31, 5), (9, 0), (19, 13), (32, 17), (20, 6), (9, 2), (28, 15), (2, 27), (15, 0), (31, 0), (5, 23), (20, 24), (15, 19), (8, 9), (9, 13), (8, 2), (33, 29), (1, 24), (20, 15), (5, 8), (9, 1), (31, 18), (8, 29), (33, 11), (10, 25), (22, 20), (24, 15), (13, 17), (17, 5), (10, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840960", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), 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), (27, 10), (29, 11), (8, 21), (2, 25), (29, 32), (15, 5), (4, 19), (24, 22), (12, 9), (1, 17), (3, 12), (5, 30), (7, 12), (12, 24), (6, 5), (22, 20), (20, 7), (13, 12), (0, 25), (24, 20), (24, 7), (14, 17), (9, 32), (28, 6), (25, 20), (6, 7), (7, 7), (15, 17), (10, 18), (22, 9), (1, 32), (11, 31), (20, 13), (22, 4), (8, 27), (8, 20), (5, 29), (6, 18), (3, 26), (9, 23), (2, 5), (15, 1), (1, 23), (24, 4), (16, 31), (22, 0), (27, 4), (26, 23), (23, 18), (4, 26), (5, 19), (27, 6), (26, 27), (13, 22), (17, 12), (25, 2), (17, 21), (14, 28), (28, 31), (23, 5), (0, 22), (17, 33), (11, 21), (29, 1), (0, 9), (12, 15), (16, 32), (20, 20), (2, 31), (0, 32), (10, 29), (5, 10), (25, 14), (8, 35), (5, 17), (26, 8), (2, 14), (1, 22), (15, 37), (10, 20), (29, 22), (1, 36), (29, 33), (27, 24), (16, 24), (14, 2), (28, 7), (26, 25), (5, 27), (25, 24), (20, 29), (4, 28), (5, 25), (6, 27), (6, 1), (28, 19), (13, 19), (25, 32), (29, 21), (0, 17), (14, 34), (12, 23), (18, 27), (3, 2), (0, 33), (24, 18), (19, 29), (7, 37), (24, 33), (28, 1), (23, 3), (18, 25), (17, 23), (16, 16), (27, 34), (12, 31), (7, 13), (9, 14), (16, 26), (16, 22), (20, 9), (13, 28), (10, 21), (21, 7), (7, 34), (29, 29), (29, 8), (27, 18), (19, 37), (15, 10), (11, 11), (8, 16), (20, 19), (18, 5), (26, 32), (7, 5), (4, 5), (9, 1), (10, 24), (15, 14), (5, 36), (22, 22), (24, 16), (11, 8), (1, 20), (14, 35), (11, 27), (24, 25), (10, 12), (29, 27), (18, 34), (0, 23), (16, 29), (9, 10), (25, 13), (29, 7), (6, 25), (28, 3), (11, 22), (28, 13), (9, 5), (15, 9), (25, 6), (2, 17), (28, 2), (12, 4), (25, 0), (9, 11), (12, 11), (6, 6), (21, 14), (11, 30), (14, 30), (6, 4), (28, 17), (11, 35), (4, 10), (8, 34), (13, 4), (18, 0), (11, 9), (20, 36), (19, 19), (7, 8), (5, 14), (9, 12), (8, 25), (11, 34), (3, 30), (20, 2), (0, 20), (17, 25), (17, 31), (16, 12), (8, 2), (29, 3), (3, 16), (3, 23), (6, 24), (26, 26), (25, 1), (10, 19), (2, 0), (3, 21), (6, 13), (25, 18), (4, 16), (14, 32), (3, 31), (18, 3), (25, 4), (8, 7), (8, 3), (29, 2), (27, 3), (10, 22), (11, 12), (21, 0), (7, 28), (6, 17), (9, 22), (21, 36), (11, 25), (7, 27), (3, 8), (7, 9), (2, 28), (16, 37), (10, 33), (7, 35), (9, 13), (2, 23), (18, 10), (26, 35), (17, 17), (27, 37), (12, 12), (6, 21), (14, 5), (13, 10), (24, 37), (26, 13), (0, 36), (8, 31), (14, 3), (16, 10), (28, 26), (28, 25), (25, 22), (19, 20), (13, 27), (13, 6), (17, 30), (6, 10), (15, 7), (7, 32), (26, 24), (5, 33), (24, 6), (18, 15), (17, 6), (20, 12), (18, 35), (5, 16), (19, 3), (11, 5), (4, 23), (21, 4), (25, 35), (26, 18), (28, 14), (14, 18), (11, 32), (1, 34), (5, 20), (8, 29), (22, 17), (15, 29), (15, 13), (2, 29), (20, 27), (15, 31), (10, 15), (22, 26), (3, 19), (21, 27), (7, 29), (9, 7), (13, 9), (17, 20), (24, 2), (25, 16), (19, 14), (7, 31), (5, 35), (19, 10), (3, 9), (23, 2), (12, 6), (29, 25), (21, 1), (12, 26), (19, 2), (19, 5), (5, 3), (29, 28), (26, 4), (28, 10), (10, 4), (8, 33), (24, 17), (9, 24), (19, 21), (2, 35), (14, 13), (16, 33), (10, 16), (6, 33), (12, 18), (3, 32), (2, 24), (8, 5), (23, 7), (16, 1), (15, 22), (6, 16), (14, 15), (12, 27), (12, 13), (21, 24), (7, 10), (7, 22), (11, 10), (19, 26), (20, 33), (29, 19), (16, 9), (21, 10), (7, 14), (10, 32), (12, 0), (10, 2), (25, 7), (18, 36), (4, 33), (21, 16), (22, 34), (20, 34), (26, 1), (1, 29), (9, 34), (0, 31), (17, 10), (12, 17), (12, 14), (20, 32), (20, 4), (19, 15), (11, 4), (4, 13), (17, 11), (28, 20), (20, 21), (22, 31), (12, 25), (0, 18), (2, 37), (9, 4), (25, 36), (24, 35), (6, 19), (14, 20), (27, 17), (12, 8), (5, 0), (0, 30), (4, 15), (27, 2), (18, 22), (4, 37), (13, 24), (17, 18), (16, 36), (18, 16), (13, 1), (6, 2), (24, 36), (10, 7), (6, 28), (26, 29), (16, 28), (22, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "699360", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (37, 6), (8, 2), (22, 36), (7, 23), (30, 3), (25, 6), (38, 5), (17, 5), (25, 5), (6, 13), (26, 17), (28, 33), (11, 28), (11, 1), (21, 27), (1, 32), (22, 11), (24, 14), (1, 6), (11, 17), (6, 31), (31, 38), (2, 22), (17, 24), (1, 14), (26, 23), (7, 16), (22, 5), (8, 10), (13, 24), (35, 20), (21, 33), (31, 28), (4, 19), (8, 35), (10, 0), (23, 38), (29, 23), (29, 12), (14, 31), (12, 3), (16, 12), (1, 20), (0, 24), (3, 19), (37, 21), (2, 31), (9, 31), (7, 30), (13, 3), (13, 31), (26, 20), (38, 19), (3, 9), (37, 28), (22, 8), (36, 14), (13, 34), (38, 2), (22, 13), (24, 20), (21, 19), (23, 6), (1, 18), (10, 19), (3, 37), (30, 7), (7, 37), (19, 3), (14, 0), (34, 30), (1, 36), (26, 19), (24, 27), (21, 9), (35, 26), (34, 26), (15, 16), (22, 22), (22, 17), (15, 28), (6, 14), (0, 22), (29, 24), (31, 16), (7, 10), (12, 14), (0, 6), (21, 29), (35, 6), (36, 2), (14, 1), (20, 29), (28, 19), (27, 0), (18, 35), (29, 19), (17, 3), (13, 21), (10, 2), (23, 11), (35, 9), (34, 14), (2, 18), (14, 27), (29, 26), (20, 1), (9, 10), (16, 15), (9, 34), (10, 11), (3, 20), (10, 9), (5, 14), (26, 13), (19, 8), (19, 4), (3, 10), (36, 28), (36, 34), (32, 6), (20, 20), (25, 8), (1, 30), (22, 25), (38, 35), (32, 0), (27, 35), (26, 36), (33, 31), (19, 17), (10, 7), (34, 7), (0, 1), (15, 3), (28, 21), (34, 15), (26, 1), (38, 14), (17, 22), (23, 32), (36, 36), (33, 38), (21, 2), (3, 18), (25, 35), (20, 23), (8, 9), (12, 8), (8, 6), (27, 16), (21, 17), (11, 30), (34, 3), (34, 38), (5, 33), (30, 31), (38, 33), (13, 29), (37, 12), (8, 24), (8, 7), (17, 37), (2, 3), (3, 33), (23, 34), (11, 14), (18, 36), (7, 8), (29, 22), (33, 25), (6, 38), (10, 18), (6, 16), (21, 8), (4, 23), (26, 16), (31, 6), (22, 31), (6, 24), (25, 26), (35, 23), (37, 17), (21, 26), (38, 21), (21, 37), (27, 2), (18, 26), (4, 29), (16, 16), (16, 20), (36, 12), (27, 32), (28, 2), (6, 7), (14, 17), (0, 37), (29, 2), (36, 18), (26, 24), (28, 31), (24, 16), (1, 5), (10, 27), (2, 11), (8, 17), (11, 5), (32, 10), (9, 22), (11, 4), (17, 14), (11, 26), (38, 28), (34, 27), (26, 33), (26, 30), (22, 4), (0, 38), (5, 26), (17, 15), (13, 5), (9, 11), (2, 21), (31, 12), (23, 30), (24, 5), (29, 16), (12, 32), (19, 11), (20, 37), (32, 34), (13, 18), (7, 6), (8, 38), (23, 1), (13, 4), (21, 3), (12, 7), (3, 3), (26, 21), (11, 2), (38, 8), (27, 14), (14, 2), (14, 19), (3, 8), (33, 9), (34, 32), (31, 36), (38, 10), (8, 37), (6, 3), (16, 11), (9, 14), (7, 26), (20, 33), (31, 20), (6, 34), (10, 23), (16, 33), (35, 35), (33, 20), (19, 7), (18, 27), (34, 19), (25, 10), (14, 33), (36, 29), (24, 13), (20, 27), (26, 35), (4, 37), (22, 34), (16, 0), (19, 27), (10, 31), (13, 33), (10, 21), (11, 6), (20, 3), (34, 31), (7, 28), (2, 28), (17, 23), (18, 38), (6, 21), (15, 24), (17, 0), (9, 38), (15, 36), (9, 32), (33, 28), (11, 25), (14, 16), (22, 12), (33, 34), (13, 11), (24, 22), (2, 27), (7, 36), (4, 16), (30, 38), (35, 14), (38, 7), (9, 30), (10, 36), (34, 1), (1, 24), (34, 35), (12, 29), (18, 31), (16, 13), (32, 30), (16, 14), (36, 33), (16, 23), (24, 28), (17, 34), (20, 6), (12, 13), (10, 38), (24, 8), (27, 33), (28, 32), (17, 18), (2, 2), (17, 33), (13, 32), (18, 14), (12, 24), (5, 8), (24, 24), (31, 13), (1, 10), (1, 16), (15, 20), (9, 33), (25, 25), (3, 32), (4, 17), (26, 0), (4, 28), (30, 8), (32, 5), (38, 12), (30, 5), (8, 26), (2, 4), (29, 1), (12, 11), (31, 29), (29, 6), (29, 35), (2, 0), (16, 26), (6, 17), (28, 38), (17, 35), (7, 25), (12, 21), (28, 15), (15, 18), (32, 13), (29, 36), (35, 12), (35, 4), (22, 16), (1, 7), (21, 12), (6, 32), (37, 5), (16, 31), (23, 29), (13, 27), (34, 17), (15, 25), (12, 4), (1, 27), (17, 20), (16, 34), (2, 26), (34, 34), (0, 12), (33, 11), (2, 34), (9, 17), (33, 17), (2, 20), (33, 35), (25, 21), (37, 0), (0, 16), (27, 17), (21, 7), (12, 19), (37, 36), (37, 24), (11, 10), (36, 26), (30, 13), (8, 16), (4, 5), (0, 5), (24, 30), (15, 15), (21, 20), (22, 38), (28, 0), (37, 35), (8, 36), (4, 32), (22, 15), (26, 32), (3, 21), (23, 37), (27, 22), (2, 9), (33, 1), (2, 6), (7, 15), (26, 25), (23, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "753984", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 33), (26, 31), (29, 25), (1, 5), (14, 3), (2, 8), (30, 19), (29, 34), (24, 3), (5, 10), (1, 18), (33, 11), (14, 13), (27, 14), (28, 0), (3, 14), (10, 17), (4, 19), (30, 34), (24, 25), (34, 13), (20, 28), (1, 33), (33, 15), (28, 30), (24, 13), (9, 20), (4, 12), (18, 21), (4, 16), (34, 6), (24, 35), (20, 35), (29, 4), (11, 5), (29, 1), (16, 33), (19, 26), (3, 29), (3, 3), (19, 21), (3, 15), (6, 15), (32, 28), (1, 25), (31, 30), (10, 26), (6, 30), (25, 32), (12, 0), (25, 33), (3, 13), (19, 14), (34, 23), (27, 11), (9, 17), (7, 25), (32, 32), (6, 1), (22, 3), (19, 7), (11, 0), (20, 2), (21, 13), (8, 10), (11, 31), (12, 11), (13, 21), (14, 20), (3, 0), (29, 17), (8, 25), (26, 34), (17, 20), (26, 30), (7, 14), (24, 16), (24, 7), (10, 35), (1, 10), (25, 17), (27, 10), (14, 6), (0, 6), (33, 16), (9, 9), (1, 16), (31, 9), (22, 9), (25, 34), (9, 10), (16, 16), (13, 36), (12, 33), (2, 14), (31, 19), (13, 24), (23, 29), (21, 12), (11, 23), (24, 26), (7, 11), (15, 26), (7, 0), (33, 19), (24, 22), (16, 13), (12, 31), (32, 29), (16, 22), (14, 30), (33, 18), (4, 10), (19, 1), (28, 22), (3, 8), (7, 1), (33, 33), (18, 26), (26, 3), (0, 30), (5, 7), (2, 24), (31, 22), (31, 12), (9, 36), (19, 9), (10, 31), (30, 25), (14, 18), (1, 14), (32, 30), (29, 11), (6, 8), (24, 20), (30, 26), (20, 29), (11, 35), (25, 20), (3, 22), (14, 19), (10, 3), (27, 17), (2, 18), (5, 13), (25, 26), (3, 6), (34, 15), (29, 22), (11, 28), (32, 35), (2, 11), (1, 11), (4, 32), (8, 2), (0, 13), (17, 12), (12, 21), (2, 0), (16, 29), (34, 9), (21, 25), (6, 20), (18, 32), (14, 26), (12, 22), (9, 5), (16, 36), (26, 24), (0, 1), (30, 31), (30, 6), (13, 8), (2, 34), (30, 21), (21, 9), (5, 17), (27, 26), (16, 34), (19, 11), (1, 8), (13, 7), (1, 23), (26, 5), (30, 16), (19, 2), (15, 19), (27, 3), (21, 1), (25, 7), (16, 17), (23, 12), (8, 1), (9, 16), (26, 7), (0, 5), (1, 9), (7, 27), (14, 2), (11, 9), (10, 5), (23, 1), (2, 6), (21, 27), (23, 31), (0, 15), (25, 30), (3, 12), (17, 34), (27, 8), (30, 15), (3, 10), (23, 3), (33, 28), (26, 27), (21, 31), (4, 18), (15, 31), (15, 30), (17, 23), (1, 30), (25, 15), (16, 21), (10, 13), (19, 22), (9, 30), (18, 27), (10, 18), (6, 21), (27, 0), (33, 20), (13, 20), (15, 22), (29, 2), (21, 24), (18, 13), (4, 11), (32, 17), (23, 23), (11, 6), (17, 4), (11, 36), (2, 12), (17, 10), (10, 24), (5, 0), (28, 2), (24, 11), (7, 2), (33, 6), (31, 26), (0, 24), (24, 9), (15, 29), (16, 5), (19, 34), (24, 15), (30, 3), (12, 36), (34, 18), (8, 27), (25, 19), (8, 36), (9, 14), (27, 34), (8, 35), (14, 1), (3, 16), (7, 20), (18, 29), (27, 7), (31, 24), (6, 26), (5, 11), (4, 3), (11, 25), (13, 0), (28, 18), (10, 0), (22, 32), (5, 6), (21, 7), (26, 22), (22, 29), (11, 17), (28, 25), (14, 27), (13, 2), (15, 14), (5, 29), (1, 15), (28, 1), (11, 10), (23, 5), (29, 9), (2, 32), (12, 4), (1, 6), (29, 0), (3, 25), (8, 18), (2, 16), (9, 18), (13, 22), (25, 0), (27, 4), (31, 2), (13, 4), (12, 10), (19, 6), (28, 34), (4, 4), (22, 25), (29, 35), (6, 36), (6, 35), (6, 19), (21, 6), (16, 35), (24, 34), (25, 10), (11, 8), (8, 5), (26, 13), (31, 13), (2, 5), (32, 31), (17, 16), (4, 24), (29, 29), (31, 21), (31, 0), (24, 17), (26, 36), (17, 15), (15, 3), (16, 20), (32, 27), (4, 34), (7, 17), (19, 33), (32, 36), (15, 23), (17, 3), (8, 22), (2, 36), (27, 35), (0, 12), (32, 6), (11, 27), (13, 25), (22, 33), (5, 35), (15, 12), (32, 2), (17, 25), (4, 20), (17, 8), (34, 25), (16, 19), (18, 9), (32, 8), (8, 14), (30, 11), (18, 35), (6, 4), (9, 35), (29, 31), (29, 32), (3, 23), (0, 14), (9, 28), (29, 33), (30, 28), (34, 10), (17, 7), (13, 10), (28, 23), (10, 27), (12, 8), (17, 6), (23, 11), (7, 16), (3, 32), (8, 6), (33, 27), (18, 1), (6, 34), (20, 21), (31, 33), (24, 27), (7, 22), (33, 9), (6, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "954912", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 24), (15, 21), (1, 18), (21, 18), (13, 10), (5, 7), (12, 6), (6, 6), (22, 18), (27, 5), (4, 13), (13, 1), (5, 15), (24, 9), (29, 29), (12, 2), (28, 6), (8, 8), (3, 25), (21, 23), (5, 3), (20, 17), (16, 7), (11, 5), (16, 29), (3, 23), (25, 24), (7, 12), (7, 15), (3, 21), (13, 23), (27, 19), (26, 23), (16, 15), (18, 15), (8, 21), (21, 3), (8, 11), (19, 8), (6, 24), (18, 20), (3, 12), (15, 12), (6, 21), (29, 6), (9, 8), (25, 11), (0, 23), (26, 20), (22, 4), (0, 30), (23, 10), (2, 8), (16, 27), (18, 26), (17, 23), (12, 23), (26, 26), (16, 25), (4, 12), (23, 3), (24, 17), (21, 6), (29, 8), (6, 17), (3, 6), (13, 6), (18, 17), (15, 15), (12, 21), (15, 9), (8, 20), (22, 27), (26, 30), (7, 13), (2, 7), (22, 28), (21, 12), (27, 3), (13, 8), (1, 0), (6, 27), (7, 10), (22, 1), (3, 30), (3, 3), (10, 3), (22, 12), (6, 5), (22, 21), (5, 6), (10, 21), (22, 6), (1, 6), (7, 14), (24, 25), (27, 25), (0, 12), (17, 27), (18, 6), (17, 10), (10, 4), (4, 20), (3, 26), (3, 1), (1, 17), (5, 23), (2, 5), (29, 28), (0, 25), (23, 21), (23, 4), (22, 8), (10, 30), (12, 30), (6, 15), (0, 27), (3, 9), (15, 16), (24, 22), (14, 14), (12, 13), (16, 30), (13, 27), (13, 11), (11, 0), (6, 19), (8, 3), (3, 28), (14, 9), (5, 30), (29, 10), (26, 16), (22, 22), (9, 15), (9, 28), (20, 20), (25, 2), (26, 15), (24, 18), (27, 20), (9, 9), (25, 14), (6, 10), (14, 12), (19, 26), (11, 29), (13, 14), (7, 2), (3, 19), (17, 25), (7, 11), (2, 6), (26, 17), (28, 7), (7, 16), (23, 22), (0, 11), (1, 15), (15, 13), (17, 20), (27, 18), (1, 29), (13, 5), (16, 16), (16, 2), (16, 24), (21, 0), (17, 26), (5, 12), (21, 25), (1, 30), (4, 17), (22, 13), (9, 26), (19, 18), (20, 9), (27, 15), (9, 21), (16, 14), (23, 0), (3, 15), (3, 4), (12, 16), (27, 0), (17, 4), (22, 20), (26, 10), (14, 18), (5, 20), (19, 27), (1, 28), (9, 27), (24, 13), (21, 27), (4, 9), (3, 16), (17, 5), (18, 19), (21, 15), (9, 6), (16, 22), (25, 27), (10, 20), (14, 27), (12, 15), (7, 19), (5, 4), (27, 10), (12, 1), (2, 12), (23, 8), (2, 3), (24, 23), (27, 28), (0, 28), (8, 2), (23, 28), (2, 13), (5, 5), (8, 24), (16, 0), (7, 20), (17, 12), (1, 4), (25, 7), (27, 21), (8, 18), (2, 24), (19, 25), (6, 0), (14, 20), (29, 25), (6, 8), (28, 16), (10, 14), (7, 26), (18, 18), (20, 5), (0, 19), (28, 28), (25, 28), (27, 30), (25, 20), (29, 4), (19, 17), (14, 25), (28, 24), (22, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732102", "dataset": "MATH"}
{"messages": [{"content": "In a 37x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 6), (0, 33), (30, 15), (28, 20), (18, 16), (28, 23), (3, 34), (16, 16), (2, 6), (17, 21), (10, 35), (22, 14), (32, 8), (5, 12), (32, 7), (7, 13), (0, 27), (32, 16), (9, 3), (9, 15), (21, 18), (0, 17), (30, 35), (23, 21), (30, 23), (10, 18), (33, 21), (14, 1), (31, 8), (2, 13), (6, 27), (15, 33), (21, 32), (6, 10), (32, 1), (29, 34), (17, 27), (13, 28), (26, 24), (30, 11), (36, 7), (11, 33), (9, 5), (3, 32), (33, 24), (28, 29), (22, 8), (21, 20), (29, 0), (14, 13), (21, 34), (22, 6), (26, 4), (1, 13), (35, 9), (34, 25), (19, 36), (32, 31), (0, 26), (18, 14), (19, 32), (31, 22), (16, 28), (36, 29), (4, 9), (1, 29), (28, 36), (6, 4), (0, 16), (4, 25), (12, 30), (2, 5), (19, 11), (23, 0), (31, 26), (20, 12), (19, 9), (22, 22), (24, 34), (30, 12), (31, 13), (9, 0), (24, 13), (23, 20), (25, 1), (17, 33), (20, 31), (16, 2), (20, 11), (19, 26), (15, 31), (4, 17), (18, 24), (1, 27), (20, 24), (23, 6), (17, 24), (5, 27), (25, 5), (23, 28), (19, 3), (17, 22), (32, 19), (14, 19), (24, 1), (9, 19), (8, 36), (22, 35), (0, 19), (35, 15), (11, 5), (1, 15), (18, 4), (21, 14), (31, 33), (23, 36), (5, 3), (29, 23), (21, 27), (34, 12), (36, 23), (14, 10), (30, 17), (11, 8), (16, 5), (27, 23), (34, 21), (14, 18), (35, 20), (28, 17), (2, 7), (21, 15), (32, 3), (5, 23), (26, 7), (33, 3), (32, 14), (25, 31), (9, 35), (18, 30), (0, 12), (15, 35), (26, 33), (12, 32), (0, 9), (23, 3), (14, 0), (29, 18), (30, 16), (2, 1), (2, 10), (11, 27), (3, 8), (4, 31), (10, 13), (35, 34), (6, 18), (16, 25), (0, 35), (0, 25), (11, 18), (31, 16), (28, 8), (34, 30), (17, 14), (24, 31), (18, 9), (26, 1), (16, 7), (31, 4), (16, 12), (10, 20), (19, 19), (21, 13), (15, 28), (26, 26), (32, 24), (20, 28), (9, 25), (13, 5), (28, 13), (11, 31), (16, 33), (19, 16), (28, 32), (27, 36), (6, 36), (23, 12), (1, 10), (14, 35), (22, 1), (21, 10), (17, 31), (29, 30), (35, 33), (4, 30), (8, 22), (7, 12), (1, 16), (18, 22), (25, 29), (12, 9), (27, 30), (7, 24), (33, 14), (26, 13), (34, 20), (16, 14), (35, 19), (35, 27), (30, 13), (13, 33), (24, 0), (35, 24), (21, 0), (31, 34), (27, 15), (11, 1), (30, 14), (12, 20), (20, 21), (24, 15), (22, 10), (2, 8), (21, 8), (33, 11), (31, 0), (18, 18), (31, 6), (2, 23), (0, 2), (13, 35), (17, 5), (29, 14), (0, 14), (22, 20), (9, 16), (12, 21), (34, 10), (24, 14), (13, 4), (26, 0), (28, 25), (21, 25), (28, 28), (5, 5), (20, 5), (36, 1), (21, 16), (33, 6), (26, 20), (9, 18), (12, 35), (20, 0), (4, 18), (31, 35), (35, 8), (13, 30), (32, 18), (23, 25), (31, 5), (6, 19), (10, 28), (13, 25), (3, 2), (13, 18), (27, 24), (9, 29), (12, 5), (7, 11), (33, 1), (19, 24), (4, 1), (19, 6), (28, 31), (24, 17), (30, 33), (26, 36), (33, 27), (6, 13), (2, 11), (33, 15), (23, 16), (25, 8), (30, 24), (14, 7), (29, 35), (29, 31), (4, 4), (17, 20), (9, 28), (4, 7), (8, 15), (30, 2), (11, 7), (30, 28), (12, 3), (5, 25), (3, 7), (29, 25), (5, 7), (22, 27), (1, 26), (30, 32), (22, 30), (3, 30), (13, 29), (36, 4), (12, 1), (27, 12), (36, 35), (17, 19), (2, 0), (3, 23), (5, 30), (30, 21), (16, 4), (3, 20), (18, 13), (23, 31), (8, 34), (11, 29), (2, 29), (3, 0), (5, 17), (4, 36), (22, 9), (5, 0), (13, 23), (33, 8), (28, 33), (10, 7), (34, 27), (23, 30), (20, 15), (21, 24), (27, 3), (34, 34), (27, 0), (2, 34), (34, 28), (5, 21), (0, 5), (5, 29), (13, 34), (7, 33), (1, 14), (25, 18), (15, 16), (19, 35), (9, 33), (36, 26), (6, 20), (3, 25), (2, 24), (10, 1), (13, 17), (10, 4), (33, 22), (6, 2), (0, 32), (24, 33), (5, 32), (4, 12), (2, 3), (9, 11), (3, 22), (5, 14), (32, 9), (34, 5), (26, 29), (17, 16), (19, 20), (26, 32), (29, 21), (15, 5), (2, 32), (31, 25), (23, 14), (17, 4), (36, 8), (8, 9), (11, 19), (36, 18), (25, 15), (10, 16), (29, 8), (31, 30), (10, 34), (26, 25), (13, 21), (9, 24), (26, 22), (2, 15), (20, 17), (2, 19), (31, 21), (5, 22), (8, 30), (32, 15), (34, 23), (10, 32), (8, 28), (19, 5), (5, 36), (34, 11), (10, 19), (8, 31), (13, 32), (9, 36), (19, 25), (11, 25), (9, 13), (3, 35), (6, 17), (29, 13), (1, 11), (36, 9), (17, 2), (12, 7), (14, 17), (0, 29), (14, 24), (5, 4), (19, 17), (20, 6), (26, 18), (9, 10), (0, 15), (22, 28), (0, 6), (1, 12), (9, 2), (31, 20), (22, 18), (15, 12), (3, 29), (35, 22), (33, 5), (24, 25), (36, 10), (10, 30), (12, 25), (4, 5), (0, 31), (33, 7), (21, 28), (25, 19), (29, 16), (5, 26), (11, 16), (21, 21), (26, 2), (31, 12), (1, 19), (1, 34), (13, 26), (15, 14), (11, 20), (11, 21), (8, 23), (32, 36), (30, 7), (34, 4), (25, 12), (8, 26), (9, 9), (20, 22), (27, 25), (23, 32), (15, 26), (23, 35), (0, 4), (13, 15), (7, 7), (20, 3), (19, 4), (14, 6), (35, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822416", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 5), (36, 1), (8, 1), (35, 33), (32, 0), (37, 26), (17, 21), (5, 16), (9, 18), (37, 16), (23, 26), (28, 23), (3, 33), (36, 18), (23, 18), (9, 7), (33, 13), (34, 14), (9, 5), (11, 2), (3, 29), (3, 18), (22, 24), (4, 13), (14, 21), (29, 3), (20, 7), (19, 20), (14, 11), (18, 33), (9, 17), (27, 8), (10, 3), (8, 24), (21, 6), (34, 30), (14, 4), (29, 7), (9, 16), (17, 9), (16, 1), (37, 11), (18, 22), (29, 10), (21, 16), (13, 21), (23, 20), (5, 2), (26, 33), (26, 17), (28, 31), (19, 26), (19, 22), (28, 11), (35, 3), (20, 9), (16, 31), (32, 21), (36, 29), (1, 8), (20, 10), (7, 13), (18, 31), (30, 20), (5, 4), (26, 5), (1, 22), (7, 4), (11, 12), (34, 23), (17, 5), (27, 2), (10, 29), (26, 19), (30, 31), (1, 24), (3, 3), (11, 21), (17, 27), (22, 33), (11, 10), (34, 11), (11, 4), (6, 28), (10, 9), (31, 24), (4, 29), (17, 26), (13, 9), (36, 20), (0, 6), (26, 3), (26, 25), (16, 5), (29, 31), (21, 17), (14, 29), (10, 30), (31, 27), (29, 30), (36, 23), (8, 20), (19, 17), (18, 13), (21, 7), (0, 17), (14, 30), (13, 7), (25, 12), (24, 4), (35, 27), (30, 10), (34, 26), (0, 23), (34, 25), (0, 29), (7, 29), (4, 16), (10, 31), (34, 7), (31, 15), (13, 16), (21, 20), (8, 30), (37, 24), (24, 12), (33, 15), (11, 33), (10, 22), (5, 24), (34, 24), (31, 31), (8, 31), (17, 23), (2, 8), (16, 26), (9, 12), (37, 14), (10, 15), (33, 28), (18, 7), (3, 12), (37, 19), (33, 14), (8, 7), (21, 0), (37, 18), (20, 32), (17, 11), (12, 22), (25, 29), (18, 32), (26, 2), (35, 20), (1, 29), (7, 27), (17, 2), (10, 6), (31, 21), (9, 1), (21, 26), (22, 32), (27, 3), (13, 10), (13, 32), (28, 17), (2, 9), (24, 30), (31, 33), (1, 30), (3, 19), (34, 1), (31, 19), (32, 25), (35, 22), (25, 33), (7, 20), (10, 11), (32, 26), (7, 19), (17, 20), (7, 25), (2, 31), (26, 1), (34, 13), (5, 27), (31, 2), (24, 24), (33, 0), (13, 26), (6, 3), (21, 14), (17, 17), (21, 32), (20, 28), (0, 14), (28, 13), (23, 9), (16, 21), (14, 0), (16, 24), (32, 8), (15, 33), (30, 33), (32, 10), (23, 8), (4, 4), (0, 27), (7, 24), (4, 6), (34, 20), (22, 19), (10, 4), (9, 26), (5, 12), (19, 24), (0, 5), (14, 23), (8, 5), (23, 27), (1, 12), (16, 22), (33, 11), (26, 20), (1, 14), (9, 31), (10, 24), (7, 2), (5, 9), (3, 15), (30, 32), (18, 28), (22, 9), (30, 13), (24, 10), (32, 13), (27, 11), (24, 31), (20, 20), (13, 14), (19, 23), (24, 27), (14, 1), (25, 13), (8, 22), (4, 23), (34, 19), (25, 3), (8, 0), (13, 22), (23, 0), (3, 27), (30, 8), (33, 9), (36, 3), (6, 6), (35, 11), (25, 10), (2, 25), (4, 11), (4, 2), (35, 21), (33, 30), (37, 3), (4, 14), (33, 4), (35, 0), (21, 27), (33, 26), (9, 25), (4, 19), (28, 24), (13, 20), (8, 14), (36, 12), (1, 0), (24, 18), (20, 6), (13, 19), (34, 27), (35, 1), (36, 15), (11, 3), (21, 28), (37, 15), (21, 30), (17, 7), (18, 15), (26, 0), (8, 13), (14, 9), (26, 16), (36, 32), (23, 30), (19, 28), (14, 7), (14, 10), (27, 25), (0, 24), (6, 22), (10, 21), (0, 26), (28, 8), (24, 3), (18, 20), (8, 21), (9, 13), (5, 20), (12, 11), (4, 20), (17, 30), (29, 8), (33, 12), (15, 13), (27, 32), (24, 21), (23, 15), (11, 13), (32, 6), (16, 25), (35, 23), (27, 7), (35, 8), (21, 2), (1, 20), (29, 9), (11, 15), (27, 12), (34, 8), (26, 27), (7, 18), (16, 10), (21, 3), (25, 8), (16, 29), (25, 5), (22, 6), (0, 2), (4, 9), (14, 6), (20, 27), (30, 5), (1, 15), (0, 8), (18, 30), (14, 12), (34, 10), (8, 3), (6, 29), (18, 21), (3, 2), (26, 14), (15, 18), (18, 26), (18, 11), (32, 30), (10, 16), (28, 26), (12, 26), (34, 32), (32, 17), (20, 0), (9, 24), (15, 23), (25, 27), (22, 25), (21, 23), (28, 28), (23, 31), (29, 14), (1, 26), (5, 11), (37, 6), (36, 0), (3, 1), (16, 27), (13, 18), (33, 17), (8, 18), (31, 4), (24, 17), (7, 0), (36, 16), (4, 30), (18, 1), (26, 31), (21, 12), (22, 27), (30, 15), (11, 24), (3, 11), (18, 18), (32, 1), (8, 11), (2, 23), (2, 17), (32, 23), (20, 21), (32, 27), (1, 23), (12, 3), (12, 17), (7, 14), (0, 15), (32, 14), (32, 22), (8, 15), (34, 18), (31, 5), (9, 27), (2, 6), (9, 33), (25, 15), (36, 7), (25, 19), (2, 3), (37, 30), (22, 15), (23, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600960", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 16), (0, 8), (31, 9), (22, 22), (27, 32), (7, 7), (34, 0), (35, 30), (5, 20), (19, 17), (26, 28), (12, 12), (27, 20), (10, 19), (29, 11), (6, 24), (9, 8), (32, 27), (12, 7), (25, 12), (37, 9), (35, 0), (28, 17), (13, 2), (6, 28), (25, 5), (20, 11), (23, 3), (17, 9), (11, 27), (33, 3), (32, 16), (3, 10), (17, 0), (31, 27), (15, 13), (19, 19), (35, 10), (12, 3), (31, 29), (15, 1), (32, 30), (4, 22), (4, 15), (11, 24), (24, 19), (21, 25), (13, 24), (17, 3), (10, 3), (16, 17), (20, 17), (16, 23), (33, 2), (22, 19), (11, 5), (1, 8), (24, 21), (35, 23), (10, 32), (28, 16), (14, 21), (30, 10), (0, 18), (9, 10), (15, 0), (23, 20), (30, 15), (37, 21), (21, 4), (13, 13), (7, 13), (11, 23), (6, 12), (34, 14), (18, 32), (28, 30), (16, 4), (14, 13), (0, 14), (23, 31), (2, 16), (32, 1), (1, 5), (6, 25), (17, 29), (9, 11), (13, 6), (20, 30), (31, 15), (4, 6), (27, 21), (18, 17), (33, 32), (22, 23), (0, 11), (32, 18), (16, 3), (14, 9), (3, 24), (13, 1), (31, 28), (7, 1), (38, 6), (26, 31), (7, 12), (13, 4), (23, 8), (15, 9), (11, 13), (38, 0), (2, 19), (12, 0), (5, 31), (1, 32), (7, 25), (16, 11), (26, 23), (24, 9), (0, 3), (37, 20), (19, 14), (34, 24), (24, 14), (6, 10), (16, 0), (25, 19), (30, 31), (2, 28), (23, 17), (4, 5), (4, 27), (27, 8), (23, 2), (27, 7), (0, 21), (15, 30), (34, 9), (28, 15), (4, 21), (19, 27), (5, 30), (35, 2), (36, 26), (36, 10), (30, 11), (21, 30), (18, 24), (36, 15), (34, 28), (26, 22), (14, 32), (30, 4), (7, 8), (22, 18), (36, 13), (8, 10), (29, 17), (19, 24), (18, 14), (32, 10), (22, 30), (11, 17), (6, 7), (18, 3), (35, 18), (27, 30), (10, 27), (26, 19), (17, 25), (1, 16), (27, 15), (15, 8), (27, 10), (28, 5), (21, 2), (1, 19), (9, 28), (36, 23), (35, 13), (32, 31), (23, 7), (18, 25), (34, 18), (4, 8), (34, 13), (4, 25), (10, 11), (23, 10), (2, 22), (37, 17), (19, 12), (5, 17), (27, 27), (28, 22), (8, 8), (28, 21), (2, 13), (9, 12), (35, 16), (17, 17), (27, 4), (10, 24), (12, 4), (7, 2), (36, 17), (10, 22), (3, 31), (18, 26), (12, 25), (30, 17), (32, 5), (33, 1), (33, 26), (32, 29), (19, 0), (3, 19), (11, 0), (32, 21), (36, 8), (22, 27), (21, 31), (24, 10), (15, 7), (6, 2), (8, 3), (23, 26), (11, 4), (10, 14), (1, 26), (0, 27), (15, 23), (8, 23), (9, 23), (9, 20), (16, 5), (8, 1), (1, 7), (38, 28), (1, 22), (20, 1), (18, 13), (14, 20), (38, 15), (30, 18), (0, 28), (26, 14), (18, 0), (0, 1), (9, 25), (21, 23), (14, 7), (21, 20), (19, 18), (23, 21), (14, 22), (34, 6), (34, 31), (33, 17), (15, 22), (21, 11), (0, 22), (38, 8), (7, 3), (35, 24), (18, 5), (12, 1), (23, 29), (32, 14), (5, 24), (14, 10), (34, 30), (3, 18), (2, 9), (19, 32), (33, 12), (31, 11), (31, 32), (23, 15), (1, 3), (34, 8), (37, 14), (30, 0), (38, 24), (23, 16), (26, 11), (18, 18), (3, 12), (16, 24), (15, 14), (12, 22), (23, 25), (22, 0), (10, 13), (16, 29), (25, 29), (30, 30), (34, 2), (9, 30), (5, 25), (29, 6), (18, 11), (38, 21), (12, 28), (0, 30), (7, 21), (2, 6), (36, 9), (22, 25), (23, 18), (17, 2), (35, 12), (32, 3), (19, 31), (17, 8), (15, 17), (38, 17), (0, 7), (25, 6), (13, 18), (35, 14), (10, 20), (16, 13), (33, 18), (0, 31), (0, 24), (27, 11), (20, 10), (4, 18), (10, 18), (14, 8), (20, 6), (36, 20), (21, 16), (38, 16), (11, 6), (6, 17), (15, 18), (27, 19), (4, 20), (25, 1), (16, 30), (28, 8), (1, 17), (35, 28), (38, 19), (16, 12), (5, 12), (29, 0), (2, 20), (9, 27), (8, 6), (33, 11), (19, 30), (24, 7), (5, 26), (34, 11), (22, 10), (24, 23), (12, 26), (18, 19), (1, 30), (25, 13), (11, 16), (23, 12), (27, 31), (17, 32), (37, 31), (35, 20), (2, 1), (31, 25), (19, 2), (13, 20), (22, 1), (21, 14), (28, 28), (34, 10), (14, 29), (21, 0), (34, 22), (38, 9), (10, 29), (26, 18), (0, 13), (27, 23), (26, 25), (15, 24), (38, 25), (34, 27), (34, 29), (30, 19), (7, 29), (16, 10), (3, 29), (18, 15), (6, 22), (16, 20), (38, 18), (27, 6), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "599760", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 30), (22, 16), (6, 6), (11, 0), (5, 34), (11, 23), (1, 35), (10, 26), (30, 12), (10, 12), (0, 15), (1, 22), (12, 24), (0, 30), (27, 35), (29, 26), (21, 8), (21, 5), (23, 27), (2, 15), (5, 24), (21, 25), (23, 24), (16, 25), (12, 1), (20, 9), (23, 26), (29, 15), (2, 22), (6, 33), (22, 26), (8, 0), (27, 24), (25, 20), (22, 9), (10, 22), (30, 32), (9, 29), (12, 28), (8, 2), (1, 18), (11, 9), (17, 25), (24, 27), (19, 12), (2, 3), (14, 25), (19, 19), (4, 20), (16, 1), (16, 29), (16, 32), (1, 2), (3, 10), (27, 4), (0, 23), (30, 10), (12, 22), (26, 26), (2, 0), (22, 1), (20, 32), (27, 17), (17, 12), (29, 23), (26, 32), (0, 17), (27, 26), (24, 8), (25, 27), (9, 8), (20, 30), (4, 16), (14, 20), (5, 30), (14, 19), (1, 21), (26, 8), (3, 27), (25, 30), (10, 33), (8, 31), (3, 18), (6, 28), (18, 35), (26, 24), (18, 16), (16, 16), (3, 34), (14, 8), (17, 17), (28, 18), (0, 26), (12, 15), (4, 19), (9, 5), (19, 24), (9, 35), (0, 6), (27, 16), (18, 34), (9, 14), (13, 5), (12, 29), (11, 21), (17, 29), (21, 12), (12, 14), (28, 2), (18, 19), (5, 35), (24, 16), (28, 13), (19, 26), (0, 33), (14, 3), (19, 21), (14, 10), (27, 20), (26, 34), (30, 9), (10, 30), (15, 35), (30, 20), (6, 31), (13, 24), (17, 5), (9, 32), (15, 27), (9, 13), (30, 16), (26, 16), (29, 17), (30, 7), (15, 3), (5, 3), (16, 23), (24, 35), (8, 16), (21, 15), (12, 17), (12, 16), (2, 24), (1, 1), (24, 6), (14, 14), (19, 4), (17, 32), (23, 30), (22, 15), (1, 30), (23, 35), (4, 22), (11, 18), (18, 6), (27, 12), (13, 1), (7, 1), (2, 8), (17, 2), (19, 5), (11, 29), (11, 24), (19, 7), (18, 7), (4, 12), (10, 13), (20, 14), (7, 7), (8, 4), (18, 8), (3, 15), (9, 24), (22, 35), (15, 7), (18, 25), (11, 34), (24, 15), (30, 33), (2, 6), (22, 23), (4, 15), (18, 33), (3, 16), (11, 4), (3, 3), (20, 4), (20, 16), (25, 31), (28, 21), (29, 20), (13, 35), (1, 27), (25, 35), (28, 5), (29, 25), (6, 19), (21, 7), (22, 18), (17, 33), (19, 31), (7, 25), (28, 14), (16, 31), (23, 0), (15, 28), (21, 27), (12, 6), (14, 27), (25, 12), (24, 13), (3, 20), (9, 18), (9, 27), (30, 2), (20, 1), (21, 19), (26, 14), (2, 2), (4, 0), (29, 18), (7, 21), (8, 12), (23, 28), (9, 19), (16, 26), (19, 33), (13, 31), (13, 2), (25, 13), (23, 25), (25, 19), (7, 4), (7, 34), (1, 33), (3, 19), (10, 24), (28, 25), (0, 20), (3, 35), (9, 28), (5, 12), (18, 27), (7, 31), (25, 9), (20, 12), (26, 15), (2, 17), (2, 20), (3, 24), (29, 4), (26, 13), (24, 10), (2, 21), (30, 29), (20, 5), (29, 12), (21, 18), (28, 11), (11, 35), (25, 11), (27, 15), (16, 35), (28, 23), (23, 19), (17, 9), (13, 29), (2, 25), (17, 1), (22, 31), (6, 10), (0, 9), (7, 26), (23, 5), (30, 26), (13, 18), (29, 27), (30, 21), (4, 10), (23, 15), (25, 21), (12, 13), (15, 33), (27, 30), (8, 29), (8, 35), (17, 8), (12, 32), (15, 22), (16, 11), (19, 0), (15, 18), (20, 22), (23, 33), (27, 7), (24, 19), (13, 25), (4, 5), (4, 4), (8, 32), (26, 12), (30, 11), (9, 16), (6, 8), (10, 4), (8, 6), (19, 27), (15, 34), (22, 20), (4, 17), (9, 21), (30, 15), (9, 10), (7, 6), (11, 31), (9, 25), (2, 1), (7, 2), (15, 20), (15, 11), (26, 7), (1, 24), (27, 27), (10, 2), (3, 26), (30, 30), (4, 18), (25, 0), (26, 17), (3, 21), (22, 28), (30, 13), (2, 9), (1, 15), (11, 28), (28, 32), (4, 8), (16, 27), (2, 11), (5, 25), (11, 1), (2, 14), (13, 6), (21, 9), (7, 8), (6, 35), (25, 18), (12, 9), (19, 11), (0, 31), (28, 1), (5, 16), (13, 26), (8, 3), (2, 4), (16, 4), (28, 24), (27, 33), (13, 0), (22, 19), (5, 23), (10, 9), (11, 7), (22, 34), (16, 30), (12, 18), (27, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "535968", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 25), (0, 18), (13, 20), (19, 35), (17, 31), (3, 27), (4, 16), (23, 16), (13, 3), (20, 20), (17, 3), (22, 8), (20, 3), (10, 32), (30, 24), (25, 35), (18, 18), (9, 12), (6, 10), (16, 15), (34, 22), (37, 7), (9, 29), (13, 10), (12, 15), (18, 9), (1, 24), (27, 21), (16, 23), (23, 8), (29, 23), (7, 14), (9, 23), (18, 7), (14, 36), (0, 27), (30, 20), (9, 10), (2, 9), (36, 6), (9, 5), (8, 29), (19, 23), (14, 13), (10, 33), (35, 30), (3, 20), (13, 0), (6, 21), (16, 31), (18, 1), (24, 12), (29, 25), (22, 17), (9, 24), (13, 21), (36, 13), (11, 25), (21, 34), (26, 6), (18, 33), (0, 13), (31, 28), (8, 24), (32, 0), (0, 24), (35, 9), (10, 4), (0, 26), (3, 4), (7, 22), (36, 22), (13, 15), (34, 12), (9, 32), (33, 26), (4, 25), (30, 10), (27, 7), (30, 19), (38, 12), (27, 29), (3, 26), (0, 31), (23, 30), (21, 18), (28, 32), (17, 20), (29, 5), (14, 8), (4, 4), (32, 31), (12, 28), (9, 6), (32, 19), (20, 21), (24, 15), (9, 25), (29, 27), (3, 1), (9, 27), (12, 9), (27, 25), (3, 16), (33, 27), (28, 24), (27, 22), (36, 21), (37, 23), (20, 11), (38, 7), (13, 4), (4, 26), (23, 20), (4, 36), (17, 21), (5, 25), (9, 18), (6, 29), (17, 35), (22, 24), (20, 16), (28, 10), (32, 11), (33, 33), (19, 20), (21, 33), (0, 36), (16, 25), (5, 3), (1, 31), (31, 32), (36, 19), (20, 28), (33, 30), (13, 9), (27, 12), (5, 13), (2, 17), (27, 36), (26, 9), (3, 33), (3, 13), (19, 7), (16, 26), (16, 8), (38, 34), (36, 10), (9, 9), (26, 24), (25, 0), (25, 14), (0, 5), (33, 24), (1, 27), (31, 9), (28, 33), (33, 34), (2, 28), (8, 12), (5, 0), (2, 1), (11, 0), (20, 4), (32, 13), (22, 14), (34, 21), (1, 5), (2, 11), (27, 3), (14, 6), (21, 28), (25, 9), (37, 35), (29, 4), (20, 19), (38, 25), (11, 9), (10, 9), (14, 27), (23, 1), (9, 15), (2, 12), (33, 8), (3, 36), (8, 22), (35, 36), (1, 30), (8, 23), (36, 14), (4, 0), (26, 36), (29, 3), (37, 26), (6, 17), (7, 27), (28, 18), (38, 2), (28, 5), (28, 29), (4, 31), (5, 12), (0, 25), (36, 17), (11, 7), (30, 33), (24, 4), (10, 35), (31, 7), (2, 35), (9, 8), (18, 35), (27, 20), (36, 7), (10, 5), (2, 4), (27, 18), (11, 19), (34, 31), (13, 22), (26, 11), (4, 5), (33, 31), (4, 23), (37, 22), (5, 8), (25, 7), (16, 24), (13, 16), (35, 26), (24, 3), (33, 14), (6, 35), (20, 24), (20, 14), (21, 29), (9, 33), (15, 21), (2, 10), (33, 10), (32, 10), (21, 21), (12, 35), (8, 32), (27, 8), (35, 17), (22, 32), (24, 22), (10, 1), (19, 34), (24, 21), (20, 18), (16, 1), (15, 14), (32, 28), (15, 25), (22, 5), (15, 15), (3, 29), (19, 14), (20, 13), (15, 31), (25, 17), (6, 16), (15, 30), (37, 10), (11, 10), (11, 8), (15, 23), (28, 0), (5, 20), (28, 22), (35, 1), (6, 22), (23, 24), (12, 27), (10, 17), (31, 5), (18, 29), (14, 35), (30, 16), (23, 14), (18, 19), (30, 1), (29, 18), (22, 34), (27, 9), (14, 15), (33, 35), (26, 13), (27, 15), (30, 32), (1, 11), (34, 32), (2, 26), (1, 33), (0, 15), (37, 2), (13, 24), (5, 36), (12, 5), (9, 22), (30, 9), (6, 8), (10, 30), (18, 21), (29, 12), (0, 1), (2, 21), (38, 10), (24, 1), (0, 34), (1, 9), (23, 0), (17, 15), (21, 35), (4, 33), (0, 14), (21, 25), (2, 3), (6, 1), (12, 3), (4, 32), (33, 20), (8, 0), (34, 35), (6, 6), (32, 14), (23, 21), (29, 26), (19, 29), (13, 6), (33, 4), (30, 7), (16, 0), (5, 32), (35, 6), (10, 12), (17, 6), (2, 32), (0, 12), (25, 3), (3, 18), (20, 7), (0, 10), (13, 28), (24, 24), (1, 26), (18, 11), (10, 6), (35, 29), (25, 11), (31, 8), (34, 34), (36, 27), (2, 27), (33, 9), (1, 3), (21, 36), (29, 32), (6, 36), (33, 15), (19, 33), (4, 3), (20, 0), (6, 24), (33, 36), (37, 8), (6, 0), (22, 12), (29, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "672960", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 38), (6, 31), (15, 12), (12, 2), (12, 27), (6, 38), (16, 23), (11, 26), (14, 25), (17, 29), (19, 24), (12, 4), (3, 18), (16, 37), (24, 13), (9, 34), (24, 7), (26, 4), (27, 18), (25, 24), (20, 5), (29, 8), (14, 8), (3, 19), (8, 28), (19, 27), (1, 0), (19, 20), (26, 2), (10, 35), (5, 7), (3, 3), (11, 3), (24, 0), (0, 24), (2, 11), (10, 29), (15, 13), (15, 20), (2, 0), (5, 38), (7, 15), (27, 33), (29, 1), (25, 7), (22, 32), (26, 3), (25, 13), (3, 35), (3, 24), (17, 4), (0, 28), (22, 20), (22, 36), (26, 7), (28, 18), (11, 18), (15, 11), (23, 34), (30, 11), (31, 26), (30, 15), (9, 5), (21, 8), (1, 14), (3, 30), (3, 20), (4, 9), (14, 17), (26, 22), (18, 29), (5, 29), (14, 14), (4, 26), (21, 12), (11, 8), (5, 15), (20, 15), (28, 22), (22, 17), (7, 27), (7, 13), (9, 36), (31, 25), (6, 27), (15, 19), (10, 34), (3, 22), (25, 11), (5, 31), (4, 18), (18, 18), (23, 22), (14, 0), (26, 32), (2, 17), (27, 7), (16, 30), (31, 1), (14, 33), (15, 3), (15, 36), (13, 34), (19, 3), (14, 12), (27, 4), (5, 23), (24, 18), (1, 11), (11, 33), (5, 18), (31, 14), (13, 13), (23, 24), (7, 31), (7, 25), (1, 10), (3, 7), (26, 13), (10, 17), (3, 15), (12, 8), (22, 9), (5, 0), (25, 26), (5, 28), (28, 4), (24, 35), (17, 16), (16, 32), (30, 3), (27, 10), (2, 30), (15, 18), (8, 7), (25, 27), (1, 32), (14, 19), (1, 13), (27, 28), (5, 13), (7, 1), (24, 1), (22, 26), (12, 21), (15, 15), (16, 35), (28, 23), (31, 7), (6, 32), (18, 21), (30, 37), (14, 11), (4, 11), (9, 31), (30, 23), (9, 14), (11, 14), (14, 18), (8, 11), (10, 6), (13, 4), (9, 12), (16, 4), (15, 7), (0, 16), (15, 14), (16, 22), (3, 37), (17, 10), (7, 4), (28, 35), (2, 12), (23, 3), (13, 6), (22, 1), (12, 37), (1, 21), (21, 38), (7, 2), (9, 22), (10, 15), (0, 10), (9, 23), (31, 0), (1, 20), (16, 26), (21, 16), (13, 20), (24, 15), (29, 22), (11, 38), (23, 2), (22, 5), (22, 28), (18, 31), (30, 22), (17, 24), (7, 32), (16, 0), (11, 29), (30, 31), (31, 33), (29, 34), (1, 15), (12, 1), (0, 27), (19, 28), (11, 25), (30, 19), (3, 1), (10, 26), (16, 28), (17, 17), (22, 38), (17, 18), (28, 9), (18, 16), (5, 27), (3, 29), (21, 14), (10, 10), (14, 24), (3, 34), (19, 25), (21, 7), (12, 7), (29, 28), (20, 26), (24, 5), (3, 38), (24, 31), (20, 2), (7, 6), (5, 11), (29, 36), (24, 17), (1, 22), (24, 36), (8, 22), (26, 20), (0, 11), (11, 32), (11, 15), (27, 11), (1, 2), (6, 18), (28, 26), (14, 15), (24, 16), (2, 18), (11, 7), (29, 21), (4, 36), (13, 25), (13, 17), (3, 33), (13, 7), (13, 2), (25, 19), (31, 31), (9, 27), (15, 30), (9, 2), (7, 30), (30, 4), (9, 19), (20, 17), (2, 6), (16, 2), (31, 30), (16, 20), (7, 38), (26, 10), (27, 15), (18, 28), (13, 33), (18, 22), (24, 34), (26, 34), (6, 7), (15, 38), (23, 21), (11, 9), (8, 33), (26, 35), (24, 8), (28, 38), (8, 32), (2, 10), (27, 5), (24, 20), (31, 19), (11, 4), (6, 33), (23, 0), (13, 12), (15, 10), (17, 13), (10, 27), (10, 20), (29, 20), (15, 17), (22, 4), (8, 35), (8, 23), (24, 37), (25, 10), (28, 33), (31, 16), (0, 15), (23, 29), (29, 7), (26, 31), (29, 29), (20, 21), (17, 36), (16, 27), (13, 18), (30, 14), (4, 28), (1, 37), (17, 7), (5, 34), (22, 16), (25, 31), (21, 36), (11, 16), (3, 12), (18, 12), (6, 36), (12, 13), (23, 28), (27, 9), (6, 16), (24, 29), (23, 5), (14, 6), (19, 18), (5, 19), (9, 29), (19, 16), (7, 23), (2, 28), (18, 6), (28, 6), (5, 2), (0, 21), (30, 8), (19, 1), (26, 17), (20, 31), (0, 7), (5, 21), (6, 28), (11, 1), (0, 18), (29, 26), (20, 35), (29, 31), (9, 38), (17, 30), (28, 34), (9, 24), (11, 27), (2, 33), (7, 29), (26, 16), (26, 27), (25, 20), (12, 12), (20, 8), (9, 21), (1, 25), (1, 24), (31, 21), (22, 29), (31, 5), (30, 24), (10, 1), (14, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488856", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 10), (8, 33), (8, 11), (9, 4), (14, 35), (9, 5), (20, 31), (25, 17), (23, 30), (17, 31), (28, 13), (27, 11), (18, 16), (12, 26), (29, 3), (13, 4), (30, 1), (8, 23), (23, 27), (7, 20), (5, 25), (28, 16), (9, 26), (10, 12), (10, 34), (21, 28), (0, 19), (9, 10), (11, 31), (21, 26), (1, 17), (11, 4), (8, 10), (20, 34), (19, 25), (28, 14), (2, 8), (22, 32), (5, 0), (16, 33), (28, 22), (22, 16), (10, 5), (15, 27), (1, 2), (4, 18), (5, 10), (1, 11), (22, 1), (18, 30), (11, 26), (29, 18), (11, 32), (31, 30), (11, 34), (20, 2), (12, 1), (8, 27), (30, 35), (26, 9), (26, 34), (9, 11), (22, 30), (25, 2), (4, 26), (4, 20), (23, 2), (20, 22), (3, 28), (20, 35), (4, 36), (20, 23), (27, 34), (9, 1), (21, 22), (5, 29), (1, 31), (21, 1), (18, 25), (4, 13), (11, 36), (27, 5), (7, 25), (13, 13), (26, 20), (10, 13), (7, 0), (24, 14), (23, 3), (23, 1), (21, 25), (29, 21), (2, 7), (7, 1), (27, 20), (22, 24), (3, 31), (27, 36), (25, 19), (2, 20), (12, 19), (0, 5), (17, 16), (3, 35), (26, 6), (1, 28), (5, 9), (17, 35), (30, 11), (11, 24), (23, 0), (2, 14), (18, 27), (29, 33), (27, 22), (1, 16), (13, 25), (18, 36), (0, 4), (15, 36), (6, 9), (14, 1), (15, 35), (14, 3), (0, 29), (26, 19), (14, 23), (6, 13), (19, 26), (2, 17), (8, 8), (23, 25), (27, 13), (17, 30), (10, 36), (25, 14), (16, 27), (3, 22), (15, 20), (16, 34), (16, 1), (24, 16), (1, 8), (28, 19), (16, 30), (14, 9), (25, 24), (20, 27), (4, 8), (24, 9), (8, 2), (19, 27), (2, 4), (31, 9), (20, 3), (9, 12), (25, 27), (1, 22), (6, 32), (29, 34), (2, 37), (13, 12), (20, 24), (16, 22), (16, 9), (12, 11), (26, 14), (11, 6), (30, 12), (25, 9), (8, 20), (17, 24), (20, 12), (1, 36), (10, 2), (22, 5), (0, 32), (5, 14), (11, 16), (0, 21), (21, 32), (30, 18), (10, 27), (0, 20), (28, 34), (7, 30), (4, 2), (0, 33), (17, 28), (30, 0), (13, 35), (0, 22), (13, 20), (19, 22), (28, 8), (16, 13), (27, 16), (15, 19), (12, 14), (26, 0), (9, 16), (13, 16), (16, 20), (9, 8), (7, 31), (0, 27), (5, 7), (4, 4), (22, 34), (16, 23), (3, 23), (0, 26), (2, 35), (0, 1), (8, 19), (27, 33), (6, 20), (2, 15), (29, 26), (31, 3), (12, 32), (31, 17), (23, 18), (7, 23), (30, 25), (27, 19), (30, 14), (28, 30), (15, 30), (3, 17), (28, 32), (15, 21), (23, 15), (11, 9), (29, 6), (20, 17), (30, 33), (9, 7), (12, 30), (6, 15), (20, 29), (29, 28), (12, 25), (7, 21), (13, 10), (22, 0), (1, 33), (4, 15), (24, 2), (3, 29), (22, 15), (30, 20), (5, 6), (22, 23), (16, 15), (21, 7), (13, 11), (31, 16), (18, 18), (30, 37), (19, 19), (0, 11), (0, 25), (16, 29), (25, 23), (25, 31), (10, 20), (1, 6), (5, 23), (31, 10), (7, 3), (17, 6), (28, 28), (23, 33), (15, 18), (21, 16), (25, 22), (8, 25), (22, 3), (11, 22), (25, 4), (4, 31), (6, 22), (31, 1), (3, 34), (18, 8), (16, 5), (27, 7), (6, 16), (23, 16), (30, 31), (19, 1), (15, 31), (18, 23), (31, 0), (11, 11), (8, 31), (10, 25), (31, 22), (25, 20), (3, 30), (8, 13), (16, 7), (22, 20), (15, 7), (28, 37), (1, 3), (27, 3), (23, 23), (3, 10), (27, 27), (21, 21), (23, 37), (26, 23), (1, 12), (9, 0), (12, 13), (2, 2), (10, 14), (22, 22), (20, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614304", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 28), (19, 13), (20, 28), (14, 1), (14, 31), (7, 23), (13, 19), (20, 31), (24, 35), (15, 22), (20, 22), (11, 20), (20, 4), (16, 30), (6, 27), (12, 14), (26, 12), (21, 18), (27, 24), (4, 20), (0, 3), (15, 12), (33, 13), (15, 31), (32, 18), (8, 32), (15, 6), (6, 8), (16, 33), (25, 13), (14, 20), (27, 13), (32, 1), (11, 11), (17, 22), (34, 9), (3, 5), (25, 5), (29, 18), (6, 23), (33, 3), (7, 5), (32, 14), (9, 31), (29, 31), (29, 21), (16, 22), (16, 25), (18, 31), (5, 18), (35, 7), (25, 30), (6, 18), (1, 15), (15, 25), (5, 15), (34, 28), (8, 7), (10, 15), (5, 30), (5, 14), (24, 6), (29, 2), (24, 19), (8, 4), (14, 30), (20, 21), (33, 1), (31, 26), (6, 30), (28, 33), (18, 8), (4, 30), (20, 27), (7, 32), (26, 9), (20, 34), (10, 16), (15, 13), (13, 33), (30, 18), (14, 5), (11, 14), (14, 14), (6, 9), (11, 1), (26, 6), (30, 24), (15, 0), (11, 5), (3, 7), (30, 3), (26, 16), (27, 11), (34, 17), (13, 12), (8, 30), (30, 35), (34, 12), (17, 19), (14, 32), (9, 5), (22, 13), (6, 5), (6, 20), (27, 0), (21, 24), (1, 14), (2, 22), (0, 11), (3, 29), (23, 4), (33, 8), (33, 35), (18, 24), (1, 18), (29, 23), (18, 18), (5, 20), (0, 18), (31, 18), (19, 6), (24, 1), (30, 1), (5, 11), (8, 29), (17, 23), (7, 19), (13, 13), (9, 11), (10, 35), (19, 11), (8, 12), (20, 19), (18, 29), (5, 7), (12, 32), (30, 4), (0, 4), (4, 15), (5, 3), (15, 8), (31, 17), (6, 28), (20, 11), (10, 22), (30, 8), (29, 3), (31, 32), (23, 29), (0, 23), (6, 25), (5, 2), (24, 34), (17, 35), (21, 2), (5, 5), (15, 14), (10, 24), (13, 9), (11, 33), (7, 0), (5, 0), (2, 16), (32, 11), (6, 24), (5, 26), (23, 33), (22, 26), (31, 4), (23, 20), (6, 0), (27, 8), (26, 34), (28, 12), (32, 30), (3, 30), (2, 7), (10, 26), (0, 28), (26, 30), (0, 31), (33, 33), (27, 34), (0, 24), (13, 11), (10, 10), (33, 7), (17, 7), (14, 4), (25, 3), (34, 15), (29, 12), (19, 8), (35, 6), (17, 29), (12, 20), (0, 15), (19, 24), (32, 33), (34, 31), (21, 11), (35, 16), (23, 0), (19, 2), (17, 1), (16, 12), (19, 10), (4, 4), (13, 26), (23, 35), (20, 17), (24, 16), (2, 32), (2, 18), (10, 2), (34, 27), (31, 23), (3, 9), (27, 20), (26, 27), (25, 9), (26, 3), (11, 0), (26, 7), (5, 31), (16, 9), (22, 11), (33, 4), (22, 3), (29, 6), (3, 12), (4, 0), (34, 30), (24, 2), (6, 7), (9, 24), (32, 12), (0, 27), (16, 5), (0, 20), (14, 13), (11, 31), (23, 11), (29, 26), (16, 10), (20, 1), (0, 26), (34, 18), (23, 26), (18, 19), (2, 35), (7, 33), (35, 18), (27, 4), (6, 33), (18, 23), (7, 31), (9, 8), (17, 15), (8, 0), (16, 18), (8, 18), (33, 16), (30, 29), (26, 32), (1, 20), (13, 8), (34, 4), (34, 3), (27, 30), (8, 16), (31, 34), (4, 35), (22, 23), (22, 34), (21, 12), (4, 2), (1, 33), (26, 1), (11, 12), (13, 2), (33, 34), (0, 21), (35, 13), (21, 31), (11, 3), (25, 28), (24, 7), (28, 26), (24, 21), (18, 30), (26, 19), (7, 24), (17, 20), (31, 29), (28, 17), (18, 3), (15, 24), (32, 22), (35, 26), (29, 0), (13, 7), (9, 7), (19, 18), (21, 16), (33, 25), (3, 1), (33, 20), (30, 22), (7, 28), (6, 32), (30, 6), (4, 27), (31, 2), (14, 6), (9, 13), (24, 20), (0, 12), (16, 11), (18, 7), (27, 29), (23, 34), (22, 15), (22, 8), (24, 29), (20, 26), (32, 20), (1, 19), (3, 24), (19, 17), (13, 31), (12, 13), (2, 27), (5, 24), (22, 12), (15, 27), (22, 33), (2, 0), (18, 16), (10, 4), (8, 5), (22, 17), (5, 28), (16, 3), (5, 9), (12, 2), (17, 18), (8, 35), (0, 5), (34, 24), (25, 18), (27, 18), (22, 24), (33, 9), (2, 24), (9, 17), (17, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "947646", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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), (1, 7), (26, 21), (25, 3), (17, 0), (13, 10), (29, 31), (23, 9), (20, 17), (6, 25), (21, 23), (11, 18), (27, 4), (20, 31), (11, 3), (2, 4), (18, 12), (29, 1), (1, 19), (27, 0), (8, 5), (28, 16), (23, 15), (8, 11), (15, 19), (27, 18), (21, 27), (20, 21), (0, 25), (21, 21), (11, 23), (9, 15), (12, 21), (9, 16), (28, 12), (6, 15), (0, 29), (21, 28), (16, 9), (15, 10), (26, 32), (3, 8), (21, 6), (25, 28), (28, 0), (13, 28), (25, 27), (29, 17), (25, 21), (10, 10), (2, 9), (20, 13), (13, 13), (20, 10), (21, 32), (18, 31), (2, 18), (27, 6), (26, 14), (4, 20), (21, 20), (2, 15), (21, 3), (21, 10), (20, 29), (11, 0), (5, 28), (11, 8), (24, 24), (5, 31), (16, 10), (11, 25), (6, 2), (20, 9), (22, 21), (21, 5), (18, 27), (13, 23), (23, 20), (16, 26), (19, 29), (18, 30), (3, 15), (26, 19), (26, 7), (25, 4), (9, 1), (19, 8), (11, 28), (14, 30), (21, 7), (21, 25), (0, 32), (22, 24), (11, 7), (6, 31), (17, 2), (0, 15), (2, 29), (21, 26), (16, 7), (20, 16), (19, 26), (24, 18), (28, 24), (15, 25), (2, 26), (19, 30), (17, 8), (20, 28), (27, 10), (0, 11), (11, 15), (21, 0), (1, 11), (22, 14), (23, 1), (22, 13), (2, 0), (0, 9), (4, 25), (12, 24), (4, 7), (19, 5), (8, 9), (0, 5), (7, 18), (9, 23), (10, 11), (12, 15), (11, 14), (5, 18), (7, 6), (17, 9), (3, 26), (0, 17), (1, 18), (23, 25), (6, 29), (15, 20), (16, 28), (25, 18), (14, 1), (14, 7), (6, 12), (6, 16), (13, 0), (17, 29), (7, 17), (13, 30), (27, 21), (29, 22), (20, 18), (7, 0), (8, 13), (15, 18), (28, 7), (24, 8), (4, 5), (20, 0), (17, 17), (12, 29), (29, 20), (22, 15), (15, 28), (28, 26), (2, 27), (29, 15), (8, 25), (11, 19), (4, 11), (10, 15), (2, 11), (9, 8), (18, 17), (2, 2), (5, 3), (13, 18), (9, 29), (18, 7), (11, 24), (27, 25), (23, 24), (1, 6), (9, 17), (12, 5), (24, 29), (24, 32), (6, 4), (7, 19), (12, 16), (25, 9), (8, 18), (19, 19), (16, 21), (24, 31), (23, 2), (0, 14), (23, 7), (12, 25), (28, 25), (17, 26), (19, 15), (22, 11), (16, 23), (5, 9), (25, 8), (6, 24), (3, 20), (4, 30), (14, 14), (18, 20), (20, 26), (6, 28), (14, 25), (11, 6), (14, 2), (0, 12), (4, 14), (5, 12), (20, 25), (3, 23), (22, 16), (1, 27), (29, 12), (14, 12), (27, 3), (28, 20), (22, 30), (3, 0), (24, 0), (1, 12), (20, 14), (7, 1), (22, 25), (12, 26), (27, 22), (3, 12), (18, 21), (19, 21), (15, 7), (11, 2), (7, 7), (16, 11), (12, 12), (22, 19), (19, 7), (23, 22), (19, 25), (19, 31), (16, 24), (24, 14), (3, 7), (17, 7), (18, 15), (15, 5), (22, 20), (4, 26), (10, 4), (4, 23), (14, 13), (22, 6), (20, 4), (17, 25), (7, 31), (5, 8), (7, 26), (2, 23), (14, 10), (12, 19), (10, 21), (7, 30), (7, 5), (23, 14), (16, 6), (26, 9), (21, 1), (16, 12), (13, 32), (9, 26), (15, 26), (12, 2), (6, 13), (7, 27), (25, 6), (26, 17), (16, 15), (8, 15), (1, 5), (10, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742560", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), 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), (15, 13), (8, 23), (24, 27), (26, 19), (9, 0), (6, 8), (9, 13), (11, 24), (6, 16), (29, 3), (10, 22), (17, 26), (37, 7), (3, 16), (8, 22), (24, 2), (34, 0), (6, 9), (5, 15), (22, 15), (32, 0), (35, 3), (12, 15), (10, 4), (11, 25), (37, 26), (35, 5), (2, 12), (34, 22), (22, 16), (25, 8), (21, 7), (17, 23), (8, 4), (26, 7), (2, 29), (24, 20), (8, 27), (13, 16), (14, 14), (23, 7), (7, 30), (0, 27), (14, 15), (19, 13), (31, 14), (1, 24), (4, 1), (35, 16), (18, 28), (21, 1), (23, 3), (25, 26), (36, 1), (7, 0), (36, 5), (15, 5), (33, 6), (16, 29), (19, 27), (26, 3), (17, 8), (27, 19), (28, 13), (25, 5), (27, 17), (3, 23), (37, 22), (33, 13), (7, 25), (26, 13), (2, 8), (9, 28), (5, 21), (7, 21), (28, 10), (37, 3), (23, 18), (26, 27), (30, 5), (20, 13), (16, 26), (33, 26), (3, 19), (20, 22), (25, 6), (19, 28), (16, 17), (2, 17), (21, 5), (31, 3), (31, 11), (25, 24), (9, 25), (10, 23), (1, 9), (35, 2), (33, 14), (37, 24), (9, 18), (29, 15), (26, 11), (26, 25), (11, 0), (11, 9), (21, 9), (4, 0), (17, 21), (0, 7), (20, 2), (12, 23), (21, 30), (37, 28), (34, 12), (32, 7), (19, 21), (31, 21), (35, 18), (9, 15), (29, 18), (20, 25), (11, 12), (6, 12), (32, 12), (0, 6), (22, 11), (5, 28), (32, 16), (0, 18), (33, 1), (28, 1), (22, 27), (1, 19), (29, 23), (2, 10), (14, 3), (23, 12), (20, 9), (26, 20), (29, 8), (27, 5), (15, 9), (16, 10), (20, 30), (8, 20), (29, 16), (35, 9), (27, 6), (33, 22), (32, 17), (8, 15), (9, 29), (4, 30), (32, 24), (0, 12), (19, 16), (20, 16), (32, 23), (10, 17), (21, 6), (31, 10), (10, 1), (29, 12), (23, 9), (33, 28), (32, 1), (23, 20), (1, 8), (24, 7), (29, 17), (31, 15), (29, 1), (20, 5), (25, 4), (34, 18), (4, 18), (26, 14), (23, 29), (1, 14), (17, 9), (17, 14), (26, 23), (1, 25), (18, 18), (19, 3), (22, 20), (1, 30), (32, 8), (20, 20), (18, 9), (22, 8), (24, 25), (21, 11), (17, 29), (25, 25), (10, 27), (28, 3), (12, 5), (23, 11), (18, 3), (30, 13), (16, 19), (3, 12), (34, 13), (7, 19), (3, 9), (30, 21), (11, 10), (25, 9), (10, 19), (12, 17), (27, 3), (33, 25), (0, 5), (9, 8), (25, 14), (2, 27), (35, 27), (20, 1), (6, 3), (1, 27), (1, 6), (35, 20), (11, 15), (32, 19), (2, 30), (25, 1), (25, 11), (15, 29), (8, 30), (8, 11), (19, 25), (34, 6), (11, 17), (30, 7), (36, 11), (9, 10), (36, 12), (37, 16), (31, 19), (29, 10), (31, 24), (10, 7), (20, 24), (2, 1), (16, 8), (11, 13), (7, 12), (0, 1), (7, 1), (30, 15), (24, 15), (35, 7), (12, 9), (14, 19), (29, 29), (33, 20), (12, 12), (26, 28), (2, 26), (15, 0), (17, 22), (4, 23), (34, 4), (32, 3), (12, 6), (16, 11), (32, 15), (12, 20), (31, 7), (9, 26), (8, 17), (12, 29), (7, 8), (5, 12), (19, 22), (15, 18), (19, 5), (5, 19), (26, 21), (29, 20), (36, 17), (15, 21), (6, 26), (35, 23), (4, 15), (26, 22), (32, 4), (36, 2), (9, 22), (22, 13), (6, 24), (5, 17), (18, 15), (25, 20), (27, 20), (18, 27), (13, 20), (4, 21), (10, 14), (27, 1), (16, 24), (17, 12), (29, 30), (26, 16), (0, 29), (27, 2), (20, 4), (4, 4), (20, 15), (16, 16), (22, 17), (29, 24), (11, 19), (31, 22), (19, 6), (16, 13), (33, 8), (3, 17), (28, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "282240", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 1), (13, 14), (33, 24), (10, 4), (32, 2), (32, 23), (22, 26), (0, 26), (18, 26), (32, 13), (3, 0), (18, 0), (4, 3), (34, 30), (15, 32), (24, 27), (29, 5), (10, 13), (1, 17), (26, 10), (12, 0), (0, 17), (5, 6), (17, 2), (29, 21), (4, 30), (32, 19), (18, 23), (15, 31), (3, 8), (17, 0), (23, 19), (33, 6), (8, 7), (12, 16), (0, 31), (2, 25), (11, 24), (4, 11), (16, 23), (23, 17), (18, 30), (10, 6), (24, 6), (0, 11), (9, 20), (13, 16), (25, 13), (20, 19), (8, 29), (26, 12), (29, 11), (33, 2), (29, 6), (22, 28), (13, 0), (23, 22), (17, 7), (18, 9), (19, 15), (2, 7), (29, 19), (18, 6), (25, 26), (12, 32), (30, 29), (5, 0), (16, 18), (31, 11), (19, 3), (13, 32), (29, 13), (29, 25), (32, 24), (23, 14), (7, 7), (8, 25), (13, 25), (23, 5), (12, 1), (11, 4), (28, 0), (24, 8), (12, 21), (17, 12), (31, 26), (22, 1), (7, 6), (5, 1), (14, 32), (6, 26), (10, 3), (11, 19), (1, 20), (28, 7), (12, 31), (31, 0), (19, 7), (7, 14), (24, 5), (19, 20), (19, 8), (14, 7), (8, 6), (26, 29), (26, 18), (31, 16), (32, 32), (33, 18), (21, 27), (23, 26), (9, 7), (9, 14), (24, 7), (3, 21), (13, 6), (3, 5), (0, 19), (11, 28), (30, 2), (30, 4), (5, 7), (25, 11), (10, 26), (26, 11), (28, 14), (6, 24), (32, 21), (18, 25), (12, 8), (16, 10), (16, 25), (18, 14), (26, 9), (16, 2), (5, 26), (14, 1), (17, 20), (5, 21), (21, 31), (28, 31), (26, 8), (7, 21), (29, 30), (20, 26), (5, 32), (0, 13), (3, 24), (0, 32), (16, 26), (4, 17), (5, 24), (34, 18), (1, 1), (29, 8), (22, 32), (13, 8), (12, 23), (4, 26), (20, 2), (20, 32), (16, 11), (23, 21), (32, 29), (5, 20), (15, 2), (20, 25), (3, 25), (1, 30), (31, 6), (3, 23), (0, 3), (5, 22), (6, 27), (21, 13), (25, 3), (13, 15), (17, 1), (9, 12), (14, 21), (2, 10), (22, 25), (4, 15), (3, 7), (7, 8), (30, 16), (4, 27), (1, 14), (2, 14), (7, 30), (17, 29), (2, 23), (5, 30), (11, 16), (22, 20), (29, 26), (27, 4), (26, 31), (13, 1), (27, 2), (15, 23), (10, 19), (19, 10), (12, 2), (22, 23), (28, 29), (1, 9), (8, 14), (7, 31), (17, 22), (1, 5), (19, 26), (4, 16), (17, 25), (2, 16), (19, 22), (23, 10), (25, 1), (19, 18), (33, 32), (8, 11), (20, 31), (23, 0), (24, 29), (7, 16), (13, 24), (21, 6), (33, 11), (2, 27), (11, 9), (30, 20), (23, 27), (11, 8), (25, 32), (9, 5), (23, 30), (17, 21), (20, 5), (3, 17), (32, 8), (17, 11), (27, 15), (34, 16), (32, 26), (33, 8), (32, 28), (31, 1), (9, 25), (29, 24), (34, 21), (33, 29), (18, 22), (10, 27), (13, 28), (28, 3), (1, 16), (9, 19), (4, 21), (19, 19), (9, 9), (10, 7), (16, 24), (23, 6), (20, 30), (25, 17), (20, 29), (19, 6), (15, 30), (25, 24), (3, 12), (21, 11), (28, 20), (31, 24), (16, 19), (27, 29), (18, 5), (22, 11), (3, 28), (10, 22), (33, 16), (28, 5), (17, 24), (19, 4), (29, 3), (19, 5), (27, 3), (0, 24), (12, 5), (34, 7), (22, 27), (13, 30), (9, 10), (25, 15), (28, 28), (14, 30), (34, 3), (6, 29), (24, 10), (24, 1), (14, 18), (30, 12), (13, 2), (25, 31), (6, 2), (24, 20), (32, 15), (8, 21), (10, 32), (10, 31), (0, 8), (15, 4), (26, 30), (27, 17), (12, 28), (13, 10), (13, 20), (14, 28), (0, 10), (7, 1), (27, 28), (23, 18), (6, 4), (9, 22), (22, 5), (29, 20), (1, 24), (13, 19), (28, 21), (34, 10), (15, 29), (13, 31), (30, 32), (28, 22), (4, 2), (33, 27), (19, 2), (6, 21), (1, 27), (24, 11), (20, 24), (26, 14), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "810216", "dataset": "MATH"}
{"messages": [{"content": "In a 37x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 36), 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), (21, 12), (20, 9), (14, 22), (1, 12), (8, 25), (29, 25), (17, 11), (1, 25), (25, 14), (32, 24), (14, 9), (16, 15), (6, 17), (9, 26), (23, 29), (23, 21), (15, 7), (14, 24), (35, 24), (2, 16), (14, 20), (0, 7), (15, 5), (16, 31), (12, 26), (6, 16), (34, 25), (19, 30), (6, 31), (6, 29), (27, 27), (6, 6), (31, 35), (36, 18), (3, 16), (34, 9), (0, 3), (10, 10), (15, 17), (0, 9), (34, 11), (20, 27), (32, 25), (20, 19), (18, 19), (34, 31), (33, 9), (30, 2), (3, 4), (5, 23), (27, 2), (29, 30), (32, 35), (26, 12), (17, 21), (27, 21), (8, 7), (33, 10), (11, 12), (2, 34), (22, 24), (11, 33), (27, 30), (22, 20), (28, 27), (8, 1), (21, 24), (35, 27), (4, 34), (27, 32), (15, 3), (18, 22), (12, 16), (21, 18), (7, 15), (18, 13), (16, 20), (15, 23), (13, 0), (15, 21), (29, 19), (4, 11), (4, 23), (0, 36), (17, 9), (35, 33), (2, 8), (10, 14), (0, 19), (25, 23), (35, 29), (10, 28), (4, 4), (31, 11), (36, 16), (19, 14), (22, 2), (26, 17), (2, 11), (29, 24), (33, 26), (22, 27), (9, 17), (24, 36), (12, 7), (0, 6), (11, 34), (24, 0), (22, 15), (5, 14), (4, 33), (11, 17), (7, 23), (27, 11), (24, 4), (31, 33), (7, 3), (18, 36), (28, 21), (19, 28), (19, 11), (28, 8), (28, 2), (9, 11), (17, 29), (12, 15), (22, 21), (17, 26), (5, 24), (1, 15), (34, 0), (15, 9), (12, 17), (34, 16), (27, 20), (3, 6), (14, 31), (26, 15), (29, 18), (25, 2), (5, 15), (30, 29), (27, 17), (30, 28), (2, 10), (26, 24), (29, 22), (6, 22), (11, 4), (27, 19), (36, 7), (27, 13), (2, 1), (19, 35), (13, 18), (4, 18), (20, 17), (22, 6), (18, 8), (7, 17), (1, 13), (31, 31), (7, 30), (17, 2), (13, 21), (24, 3), (23, 31), (11, 32), (7, 9), (12, 25), (31, 13), (9, 18), (15, 29), (22, 32), (32, 31), (10, 23), (30, 7), (12, 4), (14, 32), (28, 18), (18, 30), (16, 11), (7, 25), (28, 23), (5, 7), (21, 7), (10, 22), (12, 14), (4, 9), (16, 21), (35, 35), (22, 35), (7, 10), (17, 31), (8, 18), (17, 15), (0, 4), (10, 30), (9, 21), (14, 13), (15, 33), (15, 6), (3, 31), (35, 11), (11, 6), (6, 5), (24, 28), (28, 36), (11, 5), (7, 32), (9, 35), (10, 36), (35, 22), (21, 31), (16, 12), (33, 24), (8, 10), (23, 32), (22, 7), (18, 32), (30, 9), (20, 24), (2, 17), (13, 13), (32, 16), (25, 3), (7, 24), (33, 6), (25, 7), (19, 12), (13, 9), (12, 22), (23, 5), (16, 29), (28, 3), (2, 35), (4, 16), (27, 0), (8, 26), (22, 13), (0, 14), (31, 18), (2, 5), (29, 12), (20, 35), (7, 7), (32, 5), (27, 18), (20, 20), (15, 34), (6, 30), (20, 12), (29, 15), (30, 20), (32, 21), (28, 14), (1, 32), (8, 17), (26, 13), (32, 36), (14, 35), (6, 34), (22, 33), (2, 27), (35, 28), (0, 11), (3, 29), (3, 11), (33, 19), (19, 34), (27, 31), (0, 28), (26, 14), (7, 28), (19, 21), (20, 25), (23, 27), (18, 5), (3, 5), (4, 17), (5, 19), (11, 30), (28, 22), (34, 6), (18, 3), (29, 9), (9, 14), (4, 0), (17, 18), (4, 15), (30, 30), (35, 12), (11, 14), (21, 9), (22, 23), (3, 21), (0, 24), (36, 24), (15, 13), (24, 5), (26, 8), (3, 3), (1, 28), (28, 28), (30, 21), (34, 29), (29, 36), (0, 30), (7, 34), (31, 15), (3, 17), (12, 31), (33, 0), (36, 30), (15, 28), (7, 22), (36, 33), (10, 21), (8, 8), (5, 32), (23, 9), (11, 29), (31, 21), (31, 10), (14, 29), (29, 27), (23, 18), (12, 24), (10, 4), (2, 33), (8, 28), (0, 8), (0, 26), (11, 8), (28, 33), (22, 25), (19, 7), (26, 20), (2, 23), (21, 4), (24, 17), (18, 14), (27, 29), (20, 22), (23, 28), (2, 12), (3, 1), (8, 21), (1, 7), (6, 3), (26, 31), (9, 6), (27, 16), (33, 2), (26, 22), (4, 5), (0, 32), (26, 19), (20, 8), (12, 23), (11, 9), (9, 34), (4, 36), (4, 32), (30, 13), (32, 14), (13, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "329184", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 6), (37, 19), (17, 27), (2, 2), (5, 11), (23, 30), (12, 11), (22, 14), (0, 19), (24, 19), (0, 1), (35, 25), (23, 19), (11, 7), (38, 19), (15, 7), (29, 12), (31, 14), (28, 23), (5, 19), (6, 21), (35, 28), (36, 26), (37, 23), (35, 22), (22, 31), (32, 29), (27, 20), (31, 2), (1, 16), (21, 16), (0, 16), (11, 26), (26, 27), (0, 2), (9, 19), (7, 6), (21, 8), (17, 16), (17, 29), (14, 20), (2, 20), (24, 27), (29, 5), (28, 24), (34, 2), (32, 27), (5, 23), (16, 25), (7, 17), (36, 16), (31, 16), (29, 16), (0, 8), (20, 7), (36, 17), (17, 7), (12, 8), (19, 1), (38, 0), (7, 22), (28, 10), (31, 22), (38, 29), (36, 14), (24, 7), (10, 10), (33, 28), (0, 17), (4, 16), (29, 19), (9, 32), (34, 10), (17, 9), (28, 20), (23, 25), (19, 28), (28, 7), (32, 13), (30, 6), (24, 20), (37, 32), (29, 31), (8, 0), (2, 16), (29, 17), (29, 0), (32, 18), (13, 9), (29, 18), (2, 15), (11, 10), (17, 30), (31, 3), (21, 0), (20, 15), (27, 4), (37, 28), (36, 32), (4, 3), (23, 3), (10, 30), (32, 30), (28, 15), (31, 6), (12, 13), (13, 3), (16, 4), (36, 13), (2, 1), (6, 7), (13, 14), (21, 4), (34, 28), (14, 22), (32, 4), (1, 18), (15, 0), (24, 23), (5, 14), (31, 29), (21, 2), (25, 18), (12, 9), (30, 3), (25, 28), (20, 2), (26, 23), (15, 10), (3, 14), (16, 32), (33, 24), (31, 9), (4, 23), (35, 6), (36, 30), (14, 27), (33, 2), (12, 24), (38, 5), (10, 4), (33, 1), (22, 0), (18, 32), (14, 3), (31, 17), (9, 5), (2, 27), (5, 32), (3, 26), (7, 8), (29, 24), (22, 10), (7, 9), (2, 32), (14, 2), (12, 1), (26, 30), (33, 18), (31, 32), (32, 14), (4, 17), (19, 8), (32, 31), (2, 17), (21, 9), (0, 14), (1, 30), (28, 2), (1, 20), (32, 6), (32, 32), (32, 23), (26, 7), (1, 15), (10, 14), (4, 24), (4, 14), (18, 17), (7, 12), (31, 7), (7, 4), (7, 0), (9, 30), (37, 0), (4, 8), (37, 27), (27, 24), (22, 13), (19, 0), (28, 16), (37, 20), (5, 16), (5, 27), (6, 28), (10, 21), (36, 4), (12, 14), (22, 18), (33, 11), (36, 31), (25, 3), (30, 18), (37, 4), (38, 10), (38, 20), (32, 11), (14, 14), (1, 28), (14, 8), (1, 24), (3, 18), (7, 5), (15, 24), (23, 20), (5, 20), (24, 32), (35, 12), (24, 14), (36, 21), (20, 10), (15, 11), (24, 3), (6, 10), (7, 15), (32, 12), (1, 3), (27, 0), (17, 13), (24, 30), (38, 27), (35, 31), (30, 4), (16, 30), (4, 2), (6, 4), (34, 0), (13, 6), (30, 21), (6, 19), (23, 12), (3, 13), (1, 8), (0, 31), (7, 13), (26, 6), (27, 14), (27, 27), (35, 10), (13, 19), (23, 9), (8, 28), (15, 6), (8, 5), (34, 30), (24, 31), (30, 17), (12, 18), (38, 15), (16, 10), (25, 4), (7, 16), (22, 6), (25, 21), (19, 26), (29, 9), (15, 26), (17, 3), (19, 9), (18, 2), (33, 5), (15, 12), (34, 15), (13, 26), (36, 7), (3, 23), (15, 17), (31, 18), (2, 9), (0, 25), (0, 11), (8, 20), (3, 30), (38, 17), (17, 11), (7, 10), (20, 6), (13, 2), (0, 26), (21, 30), (1, 21), (28, 26), (16, 22), (11, 14), (22, 7), (7, 26), (29, 29), (16, 8), (30, 1), (14, 26), (21, 11), (34, 22), (17, 22), (7, 32), (20, 17), (14, 11), (36, 15), (27, 2), (19, 18), (33, 8), (5, 3), (19, 27), (11, 17), (23, 13), (33, 3), (26, 12), (16, 19), (17, 10), (35, 32), (19, 15), (14, 10), (37, 12), (30, 13), (11, 32), (14, 12), (36, 11), (30, 20), (30, 19), (5, 29), (5, 1), (4, 1), (2, 10), (18, 22), (1, 7), (35, 13), (21, 19), (37, 26), (23, 31), (37, 25), (18, 9), (36, 0), (37, 6), (11, 19), (32, 3), (36, 25), (30, 10), (11, 6), (23, 4), (15, 1), (28, 17), (23, 11), (38, 21), (6, 6), (5, 30), (27, 16), (24, 29), (4, 19), (26, 3), (19, 11), (3, 11), (26, 14), (31, 24), (2, 11), (28, 21), (26, 16), (5, 12), (32, 10), (3, 32), (19, 30), (25, 30), (36, 12), (22, 16), (19, 2), (11, 12), (1, 13), (36, 19), (25, 6), (24, 16), (22, 30), (38, 13), (35, 4), (13, 4), (21, 21), (28, 27), (9, 13), (23, 32), (21, 28), (7, 31), (11, 9), (7, 25), (6, 0), (29, 32), (10, 12), (12, 27), (17, 24), (13, 31), (20, 16), (17, 12), (17, 20), (19, 16), (0, 9), (24, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904208", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 31), (14, 9), (20, 31), (5, 2), (11, 35), (8, 29), (10, 27), (0, 6), (7, 15), (14, 18), (25, 25), (11, 2), (12, 34), (21, 0), (33, 15), (24, 33), (30, 27), (15, 2), (26, 23), (4, 20), (8, 21), (21, 10), (6, 33), (13, 5), (20, 34), (17, 15), (1, 25), (27, 21), (10, 4), (5, 25), (16, 4), (30, 32), (4, 19), (28, 32), (30, 35), (25, 7), (1, 10), (29, 18), (23, 0), (31, 22), (23, 10), (32, 31), (1, 18), (29, 29), (9, 17), (30, 24), (22, 21), (23, 7), (5, 21), (24, 14), (7, 26), (4, 22), (8, 10), (29, 12), (25, 1), (10, 20), (28, 31), (32, 20), (8, 17), (20, 16), (25, 6), (22, 8), (15, 20), (1, 32), (27, 15), (29, 23), (3, 32), (26, 12), (31, 19), (20, 23), (14, 24), (9, 22), (8, 11), (9, 19), (21, 19), (21, 1), (4, 18), (13, 29), (10, 7), (16, 7), (7, 11), (29, 26), (24, 6), (1, 28), (20, 24), (18, 18), (27, 16), (33, 34), (4, 25), (16, 12), (14, 32), (1, 11), (30, 21), (5, 26), (2, 35), (5, 8), (6, 16), (0, 10), (3, 21), (13, 13), (2, 13), (1, 16), (18, 3), (26, 19), (26, 9), (19, 21), (12, 5), (19, 2), (9, 28), (22, 32), (20, 29), (14, 33), (1, 3), (12, 27), (33, 23), (15, 6), (7, 32), (24, 1), (31, 31), (0, 26), (25, 8), (11, 16), (27, 17), (26, 29), (34, 9), (16, 11), (30, 5), (19, 23), (13, 4), (24, 22), (1, 5), (16, 15), (8, 0), (26, 4), (0, 34), (11, 3), (34, 8), (9, 5), (12, 4), (9, 4), (13, 17), (21, 22), (2, 25), (17, 28), (29, 15), (14, 17), (10, 3), (25, 19), (33, 7), (10, 12), (21, 26), (4, 30), (10, 33), (22, 14), (20, 33), (34, 31), (12, 0), (22, 24), (23, 1), (12, 22), (25, 18), (22, 17), (21, 27), (7, 1), (8, 7), (24, 27), (18, 16), (6, 7), (4, 13), (11, 12), (30, 4), (12, 18), (33, 24), (23, 16), (2, 7), (26, 21), (3, 1), (13, 16), (0, 3), (20, 6), (23, 30), (30, 31), (0, 35), (19, 10), (32, 29), (18, 29), (17, 25), (26, 30), (17, 24), (15, 24), (32, 19), (32, 17), (32, 9), (0, 12), (3, 31), (15, 4), (16, 25), (13, 18), (18, 23), (4, 16), (13, 2), (6, 14), (33, 20), (15, 11), (3, 12), (29, 4), (14, 22), (0, 24), (29, 2), (15, 15), (28, 23), (30, 7), (7, 20), (34, 5), (24, 28), (4, 0), (1, 1), (23, 14), (33, 9), (0, 30), (31, 23), (15, 8), (11, 18), (29, 17), (1, 34), (27, 32), (4, 34), (19, 19), (32, 35), (3, 15), (28, 26), (6, 13), (4, 28), (23, 24), (25, 34), (1, 4), (30, 0), (4, 17), (31, 20), (34, 20), (17, 1), (29, 3), (17, 29), (28, 21), (0, 22), (25, 0), (32, 6), (9, 11), (27, 4), (6, 2), (11, 8), (23, 13), (10, 11), (16, 9), (5, 10), (28, 1), (16, 24), (11, 11), (33, 12), (13, 26), (22, 22), (33, 26), (1, 19), (16, 35), (9, 3), (18, 28), (29, 6), (23, 12), (32, 23), (6, 20), (2, 4), (30, 22), (17, 32), (33, 30), (21, 35), (14, 26), (0, 8), (14, 6), (29, 34), (8, 8), (15, 16), (24, 11), (27, 1), (31, 29), (31, 35), (31, 6), (10, 19), (16, 6), (4, 1), (26, 16), (22, 11), (15, 30), (13, 24), (5, 28), (28, 0), (22, 1), (31, 14), (20, 1), (32, 32), (7, 14), (5, 9), (22, 35), (25, 28), (25, 30), (20, 11), (30, 10), (21, 33), (6, 9), (19, 31), (1, 33), (3, 14), (33, 10), (18, 34), (16, 16), (2, 1), (25, 10), (18, 33), (29, 24), (21, 24), (31, 5), (27, 7), (16, 17), (34, 32), (23, 28), (10, 6), (15, 33), (6, 34), (25, 24), (14, 16), (20, 8), (18, 1), (9, 9), (1, 0), (17, 4), (12, 15), (33, 19), (14, 27), (32, 26), (24, 24), (19, 7), (26, 6), (18, 2), (2, 8), (12, 20), (27, 9), (14, 23), (22, 15), (20, 21), (28, 30), (2, 12), (7, 34), (18, 10), (31, 21), (7, 3), (12, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86184", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (14, 13), (17, 19), (14, 4), (2, 26), (22, 21), (27, 2), (3, 18), (25, 8), (18, 5), (30, 30), (27, 16), (5, 17), (32, 28), (25, 6), (23, 13), (11, 32), (15, 12), (18, 21), (12, 9), (11, 27), (12, 5), (28, 21), (18, 17), (16, 11), (6, 18), (16, 19), (31, 3), (16, 13), (5, 4), (24, 6), (14, 29), (30, 2), (22, 2), (25, 5), (23, 20), (18, 29), (27, 24), (0, 14), (0, 10), (16, 18), (23, 0), (29, 14), (13, 11), (21, 5), (0, 19), (23, 17), (30, 23), (22, 5), (27, 1), (32, 22), (11, 22), (12, 12), (32, 23), (32, 14), (23, 1), (20, 10), (1, 3), (3, 32), (30, 24), (8, 17), (30, 4), (7, 4), (17, 22), (24, 26), (4, 26), (9, 30), (6, 13), (33, 3), (8, 23), (23, 28), (6, 30), (29, 2), (26, 30), (9, 9), (17, 29), (31, 1), (2, 6), (11, 13), (2, 14), (7, 28), (0, 17), (29, 11), (20, 6), (21, 28), (3, 10), (34, 31), (13, 16), (11, 23), (7, 30), (2, 32), (19, 16), (11, 29), (5, 0), (32, 30), (15, 1), (23, 11), (10, 12), (34, 2), (1, 14), (18, 2), (15, 2), (23, 9), (34, 23), (8, 19), (28, 11), (5, 22), (31, 27), (26, 1), (19, 4), (22, 16), (6, 27), (28, 12), (14, 18), (6, 19), (8, 6), (32, 7), (22, 20), (0, 20), (33, 28), (0, 21), (6, 1), (10, 27), (10, 23), (26, 14), (19, 10), (12, 18), (26, 20), (28, 16), (5, 20), (25, 30), (25, 31), (21, 0), (30, 12), (29, 22), (15, 11), (13, 12), (28, 7), (8, 2), (11, 28), (31, 13), (28, 18), (13, 13), (19, 25), (3, 21), (11, 15), (12, 26), (30, 14), (25, 22), (21, 25), (15, 30), (20, 2), (13, 0), (23, 26), (13, 23), (23, 27), (32, 9), (10, 4), (17, 1), (27, 32), (25, 3), (19, 13), (11, 5), (16, 14), (19, 6), (6, 29), (17, 0), (3, 31), (18, 4), (3, 25), (19, 5), (2, 31), (26, 23), (27, 9), (31, 11), (22, 13), (24, 28), (34, 18), (32, 6), (20, 32), (20, 11), (4, 16), (21, 1), (18, 3), (9, 17), (15, 29), (32, 5), (30, 26), (24, 9), (13, 31), (17, 18), (27, 13), (29, 7), (17, 8), (29, 1), (5, 28), (21, 13), (0, 11), (19, 18), (32, 18), (15, 0), (34, 29), (0, 23), (19, 31), (1, 21), (12, 22), (5, 25), (30, 18), (4, 0), (10, 10), (9, 25), (13, 18), (7, 11), (7, 6), (20, 18), (21, 18), (24, 31), (17, 15), (11, 26), (12, 11), (29, 17), (4, 13), (34, 27), (5, 13), (0, 29), (14, 7), (15, 3), (29, 18), (31, 29), (18, 1), (7, 8), (16, 0), (8, 11), (4, 32), (3, 7), (16, 32), (2, 0), (23, 19), (3, 12), (17, 28), (28, 20), (21, 12), (5, 8), (33, 1), (19, 19), (25, 14), (12, 8), (0, 28), (31, 26), (8, 28), (22, 23), (19, 32), (4, 2), (5, 1), (25, 18), (18, 9), (4, 19), (34, 25), (31, 9), (12, 4), (33, 0), (14, 14), (4, 7), (29, 4), (7, 2), (25, 1), (29, 12), (32, 27), (3, 13), (1, 18), (3, 17), (13, 28), (26, 28), (6, 6), (34, 10), (9, 6), (17, 16), (26, 9), (17, 21), (22, 9), (8, 14), (16, 31), (23, 5), (21, 6), (3, 0), (16, 10), (5, 26), (18, 6), (8, 32), (26, 4), (27, 30), (4, 28), (31, 21), (3, 19), (34, 20), (18, 11), (16, 4), (20, 25), (2, 5), (25, 32), (34, 7), (19, 24), (28, 22), (20, 4), (10, 22), (4, 25), (20, 28), (27, 6), (26, 25), (7, 13), (24, 1), (3, 6), (29, 30), (11, 4), (30, 10), (18, 28), (30, 21), (21, 17), (5, 10), (5, 5), (32, 13), (8, 13), (3, 24), (9, 12), (27, 21), (29, 3), (15, 5), (20, 29), (23, 2), (12, 3), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781488", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 28), (26, 13), (10, 15), (8, 26), (5, 15), (28, 18), (20, 22), (29, 16), (13, 10), (31, 26), (20, 31), (28, 12), (21, 2), (29, 27), (15, 9), (30, 1), (20, 32), (17, 5), (14, 23), (33, 8), (10, 12), (3, 22), (25, 14), (1, 32), (16, 12), (14, 22), (8, 4), (13, 27), (2, 31), (23, 18), (19, 26), (5, 8), (8, 31), (3, 11), (9, 14), (32, 6), (31, 20), (31, 4), (14, 7), (9, 4), (10, 3), (5, 21), (14, 18), (27, 6), (30, 31), (22, 23), (31, 6), (1, 3), (1, 28), (9, 27), (34, 18), (33, 19), (34, 12), (0, 8), (17, 23), (12, 16), (22, 20), (18, 12), (31, 19), (33, 27), (15, 32), (22, 30), (9, 19), (16, 26), (31, 0), (0, 29), (18, 28), (23, 9), (14, 0), (18, 31), (29, 30), (31, 1), (13, 30), (31, 27), (26, 8), (6, 8), (17, 24), (26, 19), (16, 28), (4, 8), (6, 18), (1, 27), (0, 30), (22, 15), (5, 28), (23, 26), (18, 6), (0, 6), (31, 22), (17, 2), (31, 21), (23, 23), (31, 31), (28, 6), (15, 18), (26, 25), (19, 8), (31, 3), (3, 14), (33, 6), (21, 31), (14, 32), (26, 1), (30, 18), (31, 23), (9, 23), (15, 3), (18, 14), (29, 22), (27, 20), (9, 10), (12, 1), (11, 9), (19, 30), (8, 20), (22, 14), (23, 5), (5, 7), (1, 30), (6, 15), (14, 8), (2, 18), (14, 6), (23, 10), (17, 29), (23, 20), (6, 25), (9, 11), (11, 14), (5, 1), (33, 20), (21, 32), (7, 12), (10, 27), (12, 30), (28, 14), (28, 20), (12, 11), (27, 19), (26, 32), (10, 26), (2, 24), (22, 21), (4, 9), (7, 30), (5, 29), (5, 14), (26, 15), (33, 9), (23, 19), (2, 19), (13, 12), (15, 21), (25, 15), (28, 21), (24, 24), (22, 32), (32, 4), (19, 29), (33, 4), (18, 8), (3, 32), (21, 10), (29, 20), (32, 18), (6, 4), (22, 1), (7, 16), (17, 21), (16, 5), (34, 0), (15, 26), (6, 20), (21, 12), (26, 14), (16, 1), (26, 29), (14, 16), (24, 10), (7, 6), (30, 2), (4, 25), (24, 15), (16, 7), (15, 4), (16, 8), (3, 3), (20, 1), (23, 28), (28, 29), (3, 12), (27, 23), (14, 20), (15, 17), (29, 32), (12, 7), (33, 10), (25, 13), (25, 19), (32, 30), (26, 5), (29, 24), (12, 13), (2, 5), (20, 15), (21, 27), (17, 0), (15, 13), (27, 32), (33, 25), (28, 28), (30, 21), (17, 32), (23, 30), (11, 4), (33, 31), (12, 18), (30, 23), (12, 24), (33, 12), (10, 16), (18, 0), (8, 23), (26, 9), (0, 13), (1, 31), (14, 26), (14, 10), (0, 24), (24, 9), (9, 8), (14, 1), (1, 24), (32, 16), (8, 15), (32, 12), (4, 18), (9, 21), (17, 10), (14, 9), (34, 16), (28, 13), (24, 22), (15, 15), (9, 20), (31, 24), (23, 6), (33, 3), (17, 4), (26, 3), (28, 17), (16, 10), (6, 30), (3, 9), (1, 18), (15, 30), (33, 1), (14, 30), (23, 11), (12, 3), (9, 7), (13, 17), (26, 18), (7, 23), (5, 11), (26, 17), (1, 26), (12, 4), (1, 14), (32, 22), (24, 0), (8, 19), (14, 21), (13, 26), (3, 15), (11, 13), (23, 32), (12, 22), (7, 29), (22, 8), (24, 27), (30, 28), (26, 12), (1, 5), (20, 0), (5, 5), (14, 17), (6, 32), (4, 21), (26, 23), (3, 21), (1, 29), (3, 2), (8, 3), (30, 15), (20, 28), (29, 19), (5, 4), (4, 2), (0, 12), (23, 31), (30, 11), (32, 24), (26, 0), (19, 12), (25, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913152", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 26), (21, 26), (23, 11), (13, 26), (14, 27), (27, 21), (11, 21), (20, 29), (6, 24), (24, 29), (16, 23), (0, 19), (29, 33), (10, 3), (19, 12), (14, 16), (27, 4), (7, 20), (28, 10), (31, 6), (15, 26), (10, 21), (8, 18), (17, 16), (6, 4), (30, 10), (24, 31), (14, 33), (4, 18), (31, 11), (31, 14), (14, 22), (16, 2), (13, 1), (6, 27), (0, 25), (10, 12), (9, 26), (8, 26), (31, 29), (18, 28), (0, 11), (26, 8), (8, 28), (14, 17), (23, 2), (9, 19), (3, 8), (30, 21), (19, 20), (15, 21), (22, 25), (10, 23), (25, 17), (3, 3), (6, 18), (0, 33), (3, 29), (1, 12), (12, 23), (18, 2), (11, 11), (22, 11), (14, 6), (24, 19), (17, 0), (23, 31), (16, 28), (30, 20), (7, 12), (20, 30), (11, 28), (10, 4), (0, 27), (15, 33), (7, 5), (6, 10), (21, 11), (31, 18), (7, 10), (6, 12), (22, 13), (29, 23), (22, 20), (8, 32), (5, 23), (17, 14), (29, 22), (0, 20), (4, 15), (6, 16), (2, 4), (10, 17), (16, 11), (30, 9), (18, 23), (27, 6), (15, 31), (10, 31), (1, 10), (8, 14), (30, 3), (15, 24), (19, 5), (6, 0), (27, 24), (31, 20), (1, 29), (7, 8), (29, 8), (6, 7), (24, 14), (12, 13), (16, 25), (27, 27), (20, 33), (25, 22), (9, 4), (8, 4), (29, 12), (18, 18), (23, 30), (19, 16), (21, 21), (27, 3), (10, 10), (23, 9), (4, 29), (22, 30), (11, 27), (20, 2), (19, 33), (3, 1), (19, 27), (28, 30), (21, 28), (26, 11), (10, 5), (26, 6), (25, 14), (22, 18), (25, 11), (2, 28), (15, 10), (15, 0), (1, 33), (14, 25), (4, 1), (8, 12), (16, 20), (11, 4), (20, 24), (29, 25), (2, 13), (27, 14), (22, 14), (2, 22), (8, 31), (5, 17), (24, 5), (27, 1), (26, 21), (3, 13), (25, 30), (2, 20), (7, 21), (12, 17), (21, 12), (24, 10), (5, 21), (27, 5), (3, 6), (16, 0), (9, 3), (26, 17), (9, 9), (1, 23), (21, 5), (24, 22), (23, 3), (16, 31), (26, 30), (14, 8), (11, 15), (25, 0), (28, 0), (8, 19), (24, 16), (26, 29), (22, 0), (13, 20), (7, 2), (0, 23), (19, 3), (2, 2), (21, 19), (23, 6), (9, 30), (19, 29), (13, 19), (19, 23), (1, 8), (24, 4), (3, 10), (25, 33), (3, 19), (15, 27), (24, 8), (10, 1), (31, 28), (26, 31), (6, 14), (20, 22), (15, 14), (0, 3), (28, 12), (9, 17), (13, 13), (18, 11), (0, 2), (28, 24), (19, 18), (2, 25), (16, 16), (8, 0), (21, 13), (7, 17), (24, 6), (22, 3), (20, 7), (27, 23), (22, 31), (22, 2), (0, 28), (12, 28), (4, 11), (0, 32), (24, 32), (1, 1), (6, 2), (18, 4), (5, 22), (1, 20), (13, 2), (3, 21), (20, 15), (27, 28), (6, 6), (17, 10), (25, 15), (29, 14), (24, 24), (6, 31), (4, 10), (15, 12), (31, 0), (12, 18), (16, 29), (8, 29), (18, 25), (7, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124416", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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), (4, 14), (16, 0), (16, 21), (11, 34), (4, 3), (2, 32), (19, 24), (24, 32), (22, 24), (29, 0), (0, 32), (12, 17), (20, 25), (14, 31), (21, 10), (15, 13), (13, 13), (14, 2), (25, 19), (16, 32), (24, 16), (9, 18), (2, 7), (27, 17), (21, 7), (5, 25), (6, 21), (17, 27), (11, 3), (13, 9), (3, 13), (29, 24), (5, 22), (10, 8), (3, 21), (24, 12), (14, 12), (23, 13), (19, 2), (21, 23), (23, 8), (10, 2), (2, 0), (11, 14), (9, 0), (4, 33), (21, 15), (22, 32), (28, 15), (15, 30), (13, 19), (6, 13), (3, 6), (14, 24), (21, 29), (19, 34), (27, 9), (0, 31), (25, 24), (7, 0), (14, 22), (25, 21), (11, 28), (7, 17), (24, 26), (24, 7), (17, 32), (23, 31), (2, 16), (10, 7), (9, 24), (17, 34), (2, 5), (17, 19), (20, 16), (16, 29), (8, 28), (11, 23), (5, 15), (15, 7), (9, 2), (3, 20), (3, 33), (23, 11), (6, 18), (1, 14), (4, 24), (15, 27), (27, 15), (12, 22), (3, 22), (21, 25), (28, 24), (21, 26), (15, 9), (23, 19), (17, 6), (19, 19), (24, 5), (1, 13), (10, 5), (21, 4), (13, 15), (24, 6), (29, 5), (16, 10), (28, 19), (18, 17), (18, 13), (11, 31), (3, 18), (3, 7), (26, 6), (15, 17), (3, 34), (3, 11), (23, 16), (11, 2), (26, 7), (18, 24), (13, 7), (9, 19), (15, 24), (10, 23), (8, 33), (28, 29), (6, 3), (6, 14), (21, 1), (13, 25), (1, 11), (20, 23), (9, 5), (16, 11), (23, 28), (14, 27), (0, 10), (16, 19), (2, 22), (15, 6), (13, 32), (25, 4), (7, 6), (13, 2), (28, 18), (4, 22), (12, 32), (9, 20), (16, 12), (23, 32), (12, 31), (17, 28), (7, 2), (19, 25), (18, 33), (23, 21), (2, 2), (12, 6), (1, 32), (24, 18), (3, 23), (4, 17), (6, 12), (15, 8), (1, 25), (16, 24), (20, 17), (9, 31), (4, 32), (15, 1), (15, 20), (6, 8), (2, 14), (10, 32), (4, 13), (0, 18), (24, 34), (0, 16), (19, 16), (13, 3), (9, 27), (12, 21), (20, 27), (23, 0), (0, 13), (0, 22), (20, 4), (0, 2), (8, 13), (6, 7), (15, 5), (23, 27), (8, 27), (12, 3), (2, 20), (25, 8), (2, 30), (16, 23), (20, 11), (1, 19), (9, 4), (14, 17), (17, 25), (17, 23), (14, 21), (21, 34), (14, 10), (3, 4), (29, 23), (23, 10), (29, 6), (27, 8), (14, 30), (26, 10), (24, 1), (22, 26), (22, 23), (0, 11), (15, 32), (24, 4), (13, 16), (26, 11), (12, 8), (10, 26), (16, 25), (7, 31), (19, 22), (8, 21), (22, 33), (28, 3), (28, 5), (28, 21), (2, 9), (1, 9), (14, 0), (5, 6), (10, 3), (29, 10), (7, 29), (14, 4), (24, 19), (3, 3), (19, 29), (3, 16), (11, 19), (25, 6), (4, 31), (6, 34), (11, 5), (22, 14), (12, 28), (11, 17), (4, 16), (8, 20), (28, 12), (12, 10), (25, 15), (25, 2), (21, 20), (17, 7), (13, 5), (19, 17), (26, 19), (7, 5), (25, 7), (29, 3), (5, 31), (5, 29), (20, 32), (10, 16), (22, 22), (10, 1), (29, 26), (5, 2), (23, 4), (27, 2), (15, 29), (17, 20), (25, 0), (25, 5), (18, 26), (2, 28), (18, 20), (19, 32), (0, 23), (20, 22), (27, 31), (23, 14), (6, 24), (22, 9), (21, 14), (29, 11), (17, 2), (21, 12), (8, 15), (18, 12), (3, 9), (18, 7), (15, 14), (8, 2), (13, 22), (25, 1), (28, 31), (22, 15), (4, 29), (14, 3), (7, 25), (15, 16), (11, 13), (4, 15), (2, 19), (3, 28), (5, 21), (28, 25), (26, 30), (7, 7), (11, 18), (27, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "585216", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), 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), (22, 17), (8, 16), (31, 18), (10, 10), (0, 24), (22, 25), (12, 11), (0, 7), (20, 21), (20, 24), (6, 23), (5, 22), (3, 18), (17, 6), (31, 11), (15, 18), (28, 25), (27, 28), (31, 13), (9, 8), (1, 24), (8, 1), (9, 16), (29, 18), (17, 29), (27, 0), (1, 14), (22, 21), (4, 19), (24, 11), (6, 14), (14, 4), (20, 29), (7, 15), (31, 7), (17, 27), (2, 18), (2, 5), (30, 24), (18, 3), (22, 6), (11, 20), (15, 26), (15, 17), (1, 21), (11, 0), (17, 17), (8, 0), (4, 13), (12, 14), (6, 22), (7, 5), (15, 29), (14, 17), (22, 5), (1, 16), (26, 5), (4, 6), (23, 12), (1, 2), (26, 27), (15, 7), (7, 8), (7, 10), (12, 5), (26, 0), (13, 5), (7, 9), (21, 8), (14, 7), (30, 2), (13, 27), (3, 6), (20, 20), (11, 14), (27, 18), (8, 6), (16, 19), (0, 1), (25, 13), (15, 24), (17, 12), (1, 12), (11, 6), (7, 6), (26, 10), (6, 11), (22, 1), (14, 21), (10, 9), (24, 25), (12, 20), (8, 28), (15, 8), (21, 0), (20, 22), (17, 0), (28, 2), (19, 2), (12, 13), (5, 29), (2, 8), (14, 24), (3, 28), (6, 29), (13, 0), (26, 1), (5, 30), (27, 9), (9, 15), (28, 0), (12, 17), (10, 20), (0, 12), (29, 29), (29, 23), (27, 22), (24, 8), (3, 19), (8, 22), (28, 21), (4, 29), (3, 22), (18, 2), (22, 9), (28, 16), (24, 19), (8, 11), (18, 17), (26, 12), (17, 19), (30, 21), (8, 15), (25, 2), (28, 22), (3, 1), (22, 15), (27, 4), (30, 26), (9, 20), (17, 14), (14, 14), (24, 18), (1, 29), (2, 2), (28, 30), (28, 1), (21, 15), (4, 16), (17, 8), (25, 6), (17, 1), (4, 3), (4, 20), (12, 12), (17, 21), (9, 4), (30, 5), (31, 20), (7, 18), (9, 9), (16, 22), (16, 0), (6, 3), (17, 7), (12, 24), (14, 5), (19, 1), (26, 7), (10, 7), (8, 5), (22, 19), (25, 25), (7, 11), (31, 4), (18, 9), (26, 28), (12, 22), (20, 7), (18, 16), (20, 5), (11, 22), (12, 19), (25, 16), (26, 20), (27, 5), (12, 2), (21, 24), (9, 18), (25, 12), (31, 29), (28, 4), (13, 28), (15, 10), (23, 16), (4, 25), (24, 26), (13, 19), (11, 17), (23, 20), (26, 4), (1, 28), (24, 10), (9, 23), (19, 11), (15, 20), (31, 21), (17, 23), (15, 23), (0, 22), (31, 25), (31, 2), (25, 28), (11, 18), (26, 3), (29, 17), (8, 18), (6, 28), (23, 7), (29, 12), (29, 30), (19, 8), (5, 15), (9, 25), (7, 1), (4, 30), (30, 7), (7, 14), (14, 27), (5, 0), (25, 24), (0, 6), (15, 15), (25, 19), (1, 4), (17, 13), (22, 10), (1, 8), (7, 7), (21, 3), (19, 14), (22, 3), (4, 27), (26, 21), (28, 29), (3, 2), (27, 24), (22, 13), (1, 18), (13, 7), (5, 23), (4, 11), (7, 0), (10, 8), (26, 2), (20, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "345600", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 25), (10, 28), (29, 3), (11, 2), (25, 28), (13, 20), (1, 12), (5, 10), (18, 25), (2, 18), (10, 35), (9, 26), (5, 3), (17, 30), (0, 32), (17, 16), (19, 19), (25, 10), (3, 29), (27, 13), (20, 35), (29, 25), (17, 23), (20, 17), (4, 19), (4, 27), (30, 16), (34, 27), (14, 17), (20, 5), (25, 7), (21, 28), (23, 25), (2, 9), (35, 17), (3, 31), (23, 32), (22, 26), (31, 5), (29, 32), (20, 25), (35, 24), (13, 17), (35, 2), (18, 14), (12, 17), (7, 13), (23, 35), (17, 34), (15, 23), (28, 1), (3, 12), (4, 20), (23, 0), (0, 28), (30, 30), (9, 4), (10, 4), (11, 34), (6, 10), (23, 4), (29, 4), (30, 6), (0, 14), (10, 3), (18, 7), (11, 29), (16, 22), (5, 18), (28, 15), (1, 6), (26, 4), (15, 33), (4, 0), (12, 11), (28, 20), (25, 5), (21, 7), (21, 32), (11, 24), (25, 8), (28, 25), (10, 16), (34, 1), (7, 18), (16, 14), (3, 13), (27, 34), (18, 21), (6, 19), (34, 0), (33, 1), (26, 3), (23, 1), (8, 8), (11, 10), (6, 16), (10, 26), (33, 14), (32, 4), (0, 23), (31, 21), (30, 15), (25, 27), (12, 27), (7, 14), (14, 4), (14, 34), (32, 22), (3, 33), (19, 17), (26, 6), (15, 10), (14, 7), (24, 6), (4, 16), (31, 6), (32, 35), (17, 8), (2, 2), (5, 8), (26, 25), (0, 29), (24, 8), (6, 0), (27, 10), (9, 5), (4, 15), (17, 24), (11, 0), (21, 30), (25, 25), (33, 24), (6, 2), (16, 4), (3, 30), (16, 24), (33, 6), (10, 23), (0, 5), (21, 18), (28, 5), (23, 13), (35, 10), (0, 13), (20, 22), (24, 28), (26, 20), (29, 30), (16, 12), (1, 25), (19, 0), (23, 28), (10, 17), (6, 11), (1, 21), (13, 6), (13, 23), (30, 14), (24, 7), (34, 17), (24, 16), (20, 30), (14, 32), (18, 4), (33, 28), (30, 23), (26, 10), (9, 22), (18, 1), (16, 21), (16, 6), (20, 0), (5, 22), (30, 25), (23, 9), (28, 11), (20, 9), (6, 13), (16, 33), (7, 24), (18, 28), (24, 2), (20, 11), (34, 11), (33, 27), (20, 13), (8, 33), (13, 28), (18, 11), (14, 18), (28, 13), (21, 35), (8, 1), (33, 18), (22, 6), (5, 4), (22, 31), (33, 11), (7, 9), (18, 22), (13, 10), (23, 17), (23, 3), (34, 34), (29, 35), (16, 17), (22, 0), (18, 31), (10, 27), (19, 11), (26, 9), (25, 4), (22, 1), (29, 5), (8, 18), (11, 30), (20, 14), (14, 5), (0, 6), (27, 20), (23, 12), (22, 14), (13, 0), (12, 15), (28, 8), (11, 15), (27, 14), (9, 27), (5, 16), (24, 21), (14, 3), (3, 19), (33, 0), (15, 6), (18, 23), (27, 31), (31, 29), (2, 17), (24, 14), (30, 17), (21, 19), (14, 26), (23, 26), (2, 14), (8, 4), (14, 24), (29, 15), (10, 25), (1, 30), (33, 33), (11, 5), (7, 32), (4, 25), (26, 0), (27, 7), (9, 0), (32, 29), (18, 30), (20, 32), (28, 24), (23, 21), (32, 14), (5, 17), (16, 9), (2, 13), (35, 16), (13, 18), (8, 2), (8, 7), (29, 33), (9, 8), (23, 16), (18, 26), (9, 28), (5, 9), (23, 20), (5, 0), (7, 28), (16, 30), (33, 2), (29, 12), (16, 5), (23, 11), (4, 26), (24, 12), (34, 12), (5, 27), (32, 6), (28, 22), (8, 30), (3, 15), (11, 12), (32, 18), (4, 3), (3, 3), (19, 15), (7, 21), (14, 22), (27, 16), (0, 35), (17, 27), (27, 11), (24, 5), (2, 4), (6, 28), (32, 27), (26, 22), (34, 16), (4, 7), (14, 29), (12, 2), (1, 8), (7, 35), (13, 3), (35, 25), (24, 1), (24, 32), (13, 5), (12, 21), (24, 29), (10, 9), (25, 20), (22, 25), (13, 30), (30, 7), (1, 18), (16, 13), (30, 8), (5, 5), (21, 20), (28, 9), (34, 26), (16, 15), (12, 20), (35, 34), (31, 20), (12, 8), (14, 27), (31, 11), (30, 3), (3, 20), (31, 15), (22, 19), (34, 2), (29, 16), (25, 26), (26, 18), (27, 35), (16, 26), (19, 6), (8, 22), (32, 0), (26, 28), (34, 30), (19, 10), (26, 13), (2, 19), (8, 9), (16, 25), (8, 5), (15, 34), (31, 10), (35, 29), (11, 25), (32, 19), (2, 5), (23, 15), (31, 0), (18, 8), (11, 18), (26, 31), (26, 12), (29, 2), (33, 5), (15, 27), (26, 11), (16, 0), (5, 32), (32, 20), (11, 19), (18, 27), (1, 17), (17, 17), (6, 21), (20, 29), (21, 6), (14, 12), (20, 26), (11, 17), (6, 31), (35, 23), (30, 11), (34, 10), (0, 24), (7, 19), (21, 10), (12, 30), (20, 27), (29, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371696", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 8), (31, 15), (19, 7), (0, 4), (23, 0), (31, 28), (35, 13), (0, 19), (34, 23), (4, 24), (33, 14), (30, 11), (1, 23), (4, 7), (30, 12), (36, 17), (36, 14), (20, 4), (32, 0), (4, 20), (1, 6), (35, 22), (6, 26), (32, 5), (22, 12), (18, 25), (12, 32), (21, 0), (25, 23), (17, 2), (21, 5), (35, 10), (6, 17), (21, 2), (30, 27), (20, 5), (23, 1), (37, 1), (15, 16), (29, 1), (25, 32), (1, 15), (7, 5), (29, 27), (17, 23), (36, 21), (6, 21), (16, 26), (36, 8), (33, 27), (0, 22), (9, 2), (16, 24), (22, 24), (32, 9), (33, 8), (19, 22), (25, 5), (13, 31), (24, 23), (16, 0), (7, 28), (17, 25), (16, 6), (33, 10), (6, 0), (32, 15), (18, 1), (34, 28), (13, 6), (27, 15), (20, 29), (8, 14), (28, 9), (28, 5), (2, 17), (24, 26), (33, 12), (21, 10), (21, 30), (35, 21), (3, 2), (14, 28), (9, 5), (7, 29), (33, 0), (33, 2), (12, 13), (23, 8), (10, 11), (12, 10), (36, 3), (28, 6), (21, 28), (32, 25), (10, 26), (12, 0), (0, 27), (10, 0), (6, 32), (36, 27), (9, 30), (23, 25), (14, 1), (35, 9), (31, 14), (14, 21), (1, 22), (30, 28), (24, 3), (15, 25), (15, 11), (5, 28), (28, 7), (31, 11), (33, 3), (18, 13), (19, 30), (26, 3), (30, 5), (7, 6), (32, 18), (20, 13), (34, 12), (18, 6), (37, 9), (15, 1), (3, 0), (19, 32), (18, 24), (38, 19), (38, 12), (16, 31), (7, 19), (30, 0), (24, 7), (10, 10), (5, 29), (5, 0), (1, 21), (28, 29), (18, 15), (3, 8), (25, 24), (30, 7), (15, 8), (33, 17), (22, 6), (13, 25), (13, 10), (25, 28), (26, 10), (21, 29), (0, 21), (38, 2), (29, 16), (5, 5), (23, 3), (3, 23), (37, 0), (18, 21), (34, 4), (32, 16), (8, 7), (8, 12), (13, 3), (20, 18), (3, 31), (2, 15), (11, 4), (18, 19), (3, 16), (37, 29), (14, 13), (38, 9), (30, 30), (21, 4), (26, 17), (19, 5), (7, 18), (5, 25), (21, 16), (21, 20), (11, 0), (15, 15), (14, 9), (7, 14), (35, 20), (28, 21), (29, 24), (35, 26), (16, 12), (9, 6), (22, 19), (4, 18), (6, 5), (7, 7), (5, 12), (3, 10), (30, 20), (12, 18), (2, 24), (25, 14), (34, 2), (30, 1), (36, 22), (20, 10), (14, 20), (27, 23), (7, 15), (1, 7), (2, 22), (11, 25), (16, 29), (4, 9), (4, 15), (19, 4), (9, 27), (30, 16), (25, 31), (16, 13), (28, 24), (28, 32), (26, 16), (20, 15), (15, 10), (32, 12), (14, 0), (23, 29), (12, 6), (1, 10), (37, 8), (24, 22), (1, 9), (32, 17), (0, 16), (35, 12), (36, 19), (37, 13), (6, 11), (17, 3), (10, 20), (37, 4), (33, 22), (2, 6), (34, 8), (23, 16), (14, 3), (24, 29), (22, 11), (5, 23), (36, 20), (11, 29), (7, 0), (8, 32), (19, 11), (32, 30), (31, 2), (31, 6), (0, 30), (2, 1), (17, 30), (11, 10), (27, 20), (36, 23), (32, 3), (25, 27), (10, 2), (19, 8), (5, 24), (19, 17), (8, 10), (14, 27), (11, 19), (16, 11), (38, 6), (37, 12), (7, 23), (30, 23), (27, 30), (2, 11), (4, 29), (33, 25), (29, 14), (13, 9), (38, 16), (4, 5), (8, 6), (38, 3), (12, 28), (30, 4), (0, 11), (0, 26), (35, 11), (31, 16), (14, 5), (16, 23), (37, 25), (31, 19), (28, 30), (15, 27), (23, 18), (21, 12), (31, 1), (0, 14), (5, 17), (7, 32), (13, 19), (18, 12), (33, 11), (37, 19), (24, 28), (38, 25), (3, 30), (32, 11), (9, 28), (12, 11), (22, 10), (11, 7), (3, 15), (22, 20), (17, 6), (25, 30), (38, 26), (15, 2), (35, 15), (1, 28), (17, 29), (17, 14), (24, 1), (37, 28), (26, 14), (28, 11), (33, 28), (9, 11), (10, 28), (22, 32), (37, 32), (30, 17), (18, 29), (30, 29), (8, 16), (38, 5), (32, 14), (6, 13), (0, 17), (34, 0), (33, 23), (19, 23), (33, 9), (31, 29), (9, 18), (31, 3), (33, 15), (27, 24), (34, 18), (18, 31), (37, 31), (38, 20), (6, 19), (37, 5), (12, 15), (10, 29), (22, 29), (17, 16), (8, 26), (9, 24), (16, 15), (34, 13), (27, 11), (13, 8), (19, 14), (34, 27), (27, 26), (12, 31), (5, 20), (37, 24), (15, 26), (16, 18), (18, 32), (24, 18), (35, 6), (31, 7), (26, 29), (31, 12), (36, 29), (12, 20), (32, 1), (36, 28), (29, 30), (30, 2), (36, 11), (29, 3), (22, 21), (28, 20), (21, 1), (23, 10), (17, 21), (24, 17), (36, 6), (22, 30), (24, 14), (14, 6), (13, 0), (16, 28), (23, 15), (36, 31), (34, 26), (25, 10), (37, 23), (30, 18), (20, 2), (33, 7), (23, 5), (18, 9), (14, 19), (11, 27), (7, 31), (32, 13), (20, 28), (33, 31), (10, 23), (22, 27), (12, 12), (5, 14), (28, 12), (5, 32), (21, 23), (20, 3), (1, 0), (13, 7), (1, 16), (20, 16), (31, 0), (12, 16), (0, 13), (4, 14), (20, 20), (6, 9), (12, 24), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497664", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), 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), (33, 11), (2, 29), (18, 4), (24, 1), (8, 17), (4, 13), (25, 32), (0, 26), (20, 10), (28, 1), (13, 4), (34, 29), (20, 28), (21, 25), (33, 1), (24, 25), (21, 12), (33, 21), (34, 3), (12, 31), (27, 28), (32, 1), (16, 1), (24, 30), (30, 30), (25, 0), (17, 3), (24, 17), (13, 32), (8, 31), (3, 6), (2, 15), (4, 14), (19, 6), (21, 1), (20, 24), (31, 34), (26, 20), (7, 2), (12, 29), (4, 22), (0, 7), (14, 24), (5, 7), (26, 6), (22, 1), (22, 21), (14, 4), (20, 21), (1, 22), (14, 15), (8, 7), (16, 23), (19, 16), (30, 32), (18, 10), (7, 15), (13, 15), (19, 28), (32, 33), (34, 22), (17, 11), (14, 34), (33, 24), (6, 16), (1, 4), (34, 16), (21, 14), (12, 14), (5, 29), (29, 3), (7, 11), (32, 32), (26, 32), (6, 10), (23, 3), (3, 5), (34, 24), (6, 33), (6, 34), (3, 29), (14, 21), (15, 27), (17, 1), (32, 6), (5, 9), (13, 13), (9, 12), (29, 27), (21, 26), (27, 26), (32, 25), (12, 30), (5, 21), (2, 26), (29, 4), (26, 23), (26, 29), (22, 11), (18, 2), (21, 8), (33, 9), (27, 15), (4, 16), (20, 11), (27, 20), (21, 0), (20, 4), (1, 3), (28, 24), (10, 0), (32, 13), (31, 16), (32, 27), (8, 5), (17, 20), (10, 8), (1, 33), (24, 2), (13, 19), (16, 25), (0, 28), (0, 15), (11, 19), (3, 9), (24, 23), (23, 1), (16, 13), (23, 11), (4, 26), (26, 28), (20, 25), (19, 27), (1, 13), (5, 23), (26, 4), (9, 1), (1, 18), (32, 15), (20, 2), (6, 11), (21, 6), (6, 2), (12, 23), (20, 6), (28, 6), (18, 5), (25, 12), (11, 30), (26, 27), (26, 0), (0, 24), (10, 32), (4, 25), (25, 20), (6, 21), (1, 14), (32, 26), (2, 8), (31, 32), (16, 22), (23, 30), (32, 18), (15, 2), (13, 21), (8, 10), (2, 7), (19, 1), (8, 4), (4, 31), (20, 12), (26, 19), (32, 11), (28, 11), (21, 33), (24, 13), (6, 13), (7, 9), (25, 8), (27, 25), (12, 27), (25, 13), (12, 12), (26, 9), (16, 24), (33, 4), (8, 8), (30, 21), (22, 15), (25, 29), (1, 0), (1, 20), (9, 27), (29, 11), (4, 3), (18, 3), (15, 16), (10, 10), (14, 9), (2, 3), (31, 6), (8, 20), (32, 23), (21, 22), (6, 32), (4, 10), (10, 11), (21, 21), (18, 15), (13, 1), (15, 32), (24, 5), (19, 18), (15, 11), (28, 29), (32, 10), (10, 16), (5, 34), (24, 6), (0, 4), (32, 20), (29, 22), (28, 17), (3, 33), (31, 9), (32, 8), (17, 9), (19, 21), (31, 25), (5, 4), (8, 13), (1, 19), (15, 30), (3, 0), (34, 9), (25, 28), (2, 13), (25, 15), (24, 19), (2, 16), (6, 9), (11, 10), (31, 21), (11, 14), (18, 31), (31, 1), (2, 12), (10, 21), (25, 33), (16, 0), (18, 17), (20, 0), (21, 29), (31, 29), (25, 27), (23, 18), (3, 16), (12, 5), (14, 13), (12, 21), (14, 14), (18, 27), (10, 28), (6, 12), (32, 24), (27, 6), (5, 27), (11, 28), (1, 23), (0, 3), (5, 24), (8, 28), (13, 9), (22, 34), (11, 33), (1, 26), (16, 15), (12, 10), (33, 34), (15, 20), (1, 25), (33, 2), (22, 6), (0, 31), (19, 17), (22, 18), (13, 29), (11, 34), (17, 26), (25, 34), (18, 6), (31, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799872", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), 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), (15, 9), (30, 20), (18, 29), (31, 19), (20, 31), (31, 15), (28, 19), (18, 35), (26, 11), (30, 21), (4, 12), (35, 18), (25, 29), (20, 30), (8, 1), (25, 6), (10, 37), (24, 36), (23, 19), (3, 4), (24, 28), (26, 37), (22, 2), (34, 11), (9, 31), (7, 19), (12, 38), (15, 17), (27, 29), (8, 8), (24, 15), (2, 4), (14, 25), (13, 27), (23, 7), (31, 27), (25, 11), (30, 37), (11, 12), (19, 9), (31, 31), (30, 13), (18, 34), (4, 10), (23, 23), (26, 34), (6, 16), (24, 5), (6, 36), (21, 17), (16, 10), (26, 33), (5, 5), (18, 18), (28, 3), (9, 14), (2, 18), (34, 37), (34, 2), (32, 7), (32, 1), (22, 29), (6, 6), (13, 4), (16, 6), (8, 0), (7, 2), (30, 32), (29, 32), (25, 31), (20, 34), (32, 8), (24, 27), (32, 20), (21, 38), (8, 29), (20, 7), (22, 36), (29, 26), (31, 8), (8, 17), (1, 3), (3, 1), (20, 22), (14, 36), (3, 10), (20, 19), (8, 31), (13, 38), (28, 27), (26, 18), (18, 20), (27, 2), (21, 28), (16, 34), (7, 11), (17, 29), (10, 17), (20, 32), (2, 3), (16, 32), (24, 25), (6, 29), (22, 3), (26, 21), (34, 3), (34, 34), (32, 16), (12, 24), (1, 16), (31, 30), (17, 31), (18, 2), (4, 11), (0, 33), (14, 7), (34, 1), (25, 23), (22, 19), (22, 28), (2, 15), (10, 15), (0, 30), (0, 3), (21, 29), (33, 23), (11, 33), (31, 38), (7, 7), (15, 3), (14, 38), (31, 32), (28, 24), (29, 21), (15, 13), (25, 12), (18, 25), (6, 4), (28, 36), (4, 31), (32, 22), (10, 18), (10, 16), (34, 27), (19, 16), (18, 23), (21, 2), (9, 3), (2, 22), (14, 20), (16, 37), (9, 4), (0, 36), (21, 32), (20, 17), (29, 30), (3, 13), (18, 32), (14, 23), (1, 10), (14, 10), (24, 35), (5, 25), (16, 3), (10, 34), (24, 9), (32, 4), (18, 7), (22, 9), (9, 0), (8, 28), (3, 37), (9, 35), (33, 16), (24, 33), (35, 3), (33, 15), (23, 32), (21, 35), (30, 27), (10, 33), (32, 5), (15, 4), (9, 12), (14, 11), (5, 2), (20, 16), (9, 16), (28, 37), (24, 23), (26, 4), (23, 8), (31, 6), (28, 0), (30, 12), (34, 32), (29, 27), (16, 13), (27, 23), (4, 2), (11, 37), (8, 2), (23, 11), (4, 28), (1, 13), (23, 35), (32, 36), (30, 17), (4, 27), (13, 22), (20, 38), (8, 30), (9, 11), (23, 28), (29, 36), (18, 30), (27, 7), (19, 5), (33, 36), (32, 31), (15, 23), (23, 24), (17, 18), (20, 14), (29, 23), (27, 15), (28, 16), (29, 20), (18, 31), (23, 27), (14, 33), (1, 14), (2, 31), (13, 17), (6, 34), (13, 12), (11, 9), (17, 17), (2, 2), (1, 28), (5, 23), (5, 1), (11, 27), (10, 23), (21, 9), (6, 35), (2, 36), (20, 6), (16, 19), (30, 22), (33, 1), (12, 26), (31, 29), (1, 32), (22, 17), (27, 0), (32, 0), (23, 4), (7, 33), (15, 26), (35, 1), (0, 37), (2, 34), (34, 21), (21, 0), (8, 14), (30, 5), (6, 26), (29, 34), (25, 0), (20, 36), (28, 4), (12, 5), (20, 20), (24, 29), (19, 7), (30, 18), (26, 27), (17, 14), (15, 22), (14, 27), (1, 9), (24, 26), (11, 29), (2, 20), (20, 12), (7, 4), (32, 11), (23, 0), (23, 5), (27, 20), (4, 36), (0, 16), (6, 7), (15, 8), (17, 3), (17, 13), (4, 7), (15, 14), (31, 36), (31, 10), (24, 31), (5, 37), (9, 24), (16, 16), (1, 29), (35, 33), (9, 7), (2, 30), (33, 30), (12, 19), (17, 35), (16, 17), (5, 6), (10, 5), (28, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402120", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 29), (31, 15), (10, 10), (36, 19), (1, 18), (34, 24), (18, 12), (33, 11), (14, 26), (17, 12), (5, 18), (23, 28), (10, 3), (6, 14), (32, 24), (12, 29), (2, 9), (14, 12), (7, 12), (5, 19), (1, 9), (19, 23), (11, 5), (28, 14), (36, 24), (17, 23), (19, 16), (8, 19), (15, 7), (5, 12), (17, 27), (1, 26), (7, 21), (14, 21), (4, 27), (8, 6), (9, 27), (2, 7), (20, 9), (12, 23), (36, 9), (32, 4), (30, 27), (33, 14), (7, 24), (35, 6), (30, 25), (12, 15), (6, 19), (13, 4), (31, 28), (19, 10), (22, 21), (20, 26), (18, 4), (10, 16), (24, 8), (19, 9), (25, 25), (16, 20), (13, 5), (25, 27), (29, 1), (7, 10), (12, 5), (5, 14), (23, 9), (3, 7), (12, 28), (9, 21), (34, 18), (11, 14), (21, 18), (6, 15), (20, 17), (2, 11), (14, 7), (29, 0), (23, 3), (9, 24), (36, 0), (27, 1), (8, 13), (0, 23), (31, 10), (26, 26), (36, 29), (16, 17), (38, 27), (34, 1), (5, 23), (29, 15), (14, 8), (21, 9), (35, 27), (3, 23), (3, 18), (11, 16), (34, 26), (9, 5), (3, 4), (2, 19), (8, 0), (24, 15), (37, 19), (16, 14), (18, 2), (24, 16), (11, 11), (12, 25), (28, 27), (2, 8), (14, 18), (1, 22), (4, 26), (35, 20), (29, 29), (14, 29), (7, 20), (19, 12), (6, 23), (27, 7), (16, 21), (7, 14), (21, 2), (0, 21), (21, 20), (23, 23), (36, 27), (23, 22), (16, 1), (10, 29), (12, 12), (38, 13), (19, 22), (23, 6), (16, 9), (24, 10), (24, 19), (0, 24), (20, 6), (28, 25), (13, 8), (24, 13), (33, 18), (30, 20), (15, 28), (35, 13), (8, 26), (18, 16), (31, 9), (23, 13), (31, 16), (19, 2), (17, 4), (33, 12), (18, 19), (23, 14), (3, 15), (20, 18), (7, 13), (20, 28), (25, 13), (1, 29), (34, 0), (27, 28), (34, 16), (24, 0), (26, 10), (31, 19), (22, 26), (31, 24), (35, 17), (11, 8), (22, 9), (24, 1), (32, 28), (31, 13), (12, 16), (26, 16), (0, 26), (29, 19), (36, 5), (29, 17), (3, 5), (2, 17), (36, 1), (11, 9), (8, 8), (13, 13), (3, 25), (20, 11), (16, 3), (26, 3), (3, 14), (25, 2), (19, 17), (27, 12), (12, 17), (17, 20), (5, 29), (0, 20), (37, 12), (3, 9), (37, 10), (26, 18), (24, 29), (25, 1), (9, 10), (38, 0), (17, 13), (20, 4), (2, 27), (25, 0), (28, 10), (14, 6), (14, 9), (33, 23), (36, 6), (12, 21), (32, 12), (29, 5), (26, 23), (28, 12), (18, 17), (23, 24), (36, 16), (31, 27), (0, 15), (5, 8), (18, 22), (5, 1), (36, 22), (30, 13), (25, 3), (18, 14), (34, 6), (1, 21), (3, 17), (29, 18), (19, 19), (26, 15), (19, 15), (8, 10), (14, 20), (10, 11), (27, 4), (12, 22), (1, 23), (1, 17), (8, 27), (24, 11), (15, 2), (22, 3), (2, 25), (10, 1), (35, 14), (36, 28), (27, 13), (12, 26), (15, 8), (28, 28), (20, 10), (36, 26), (2, 23), (34, 22), (21, 14), (20, 5), (15, 24), (9, 3), (29, 24), (26, 13), (14, 5), (4, 1), (0, 3), (30, 12), (16, 12), (25, 21), (17, 2), (37, 14), (9, 0), (20, 24), (0, 18), (6, 3), (27, 16), (25, 22), (12, 18), (17, 0), (33, 15), (24, 28), (31, 22), (24, 17), (37, 20), (30, 1), (18, 23), (5, 27), (3, 0), (31, 4), (21, 22), (36, 25), (33, 1), (15, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622080", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 34), (1, 32), (12, 13), (17, 10), (10, 19), (2, 36), (31, 11), (23, 28), (16, 2), (21, 10), (16, 32), (7, 28), (13, 17), (20, 2), (0, 26), (0, 37), (30, 26), (15, 1), (32, 0), (17, 4), (6, 27), (23, 24), (2, 11), (13, 18), (13, 32), (22, 24), (3, 11), (2, 7), (22, 27), (32, 28), (0, 34), (12, 35), (11, 21), (6, 11), (1, 33), (6, 8), (4, 36), (22, 30), (27, 9), (4, 9), (29, 12), (26, 6), (18, 14), (14, 8), (12, 20), (9, 14), (20, 36), (31, 21), (31, 9), (15, 37), (15, 10), (5, 26), (21, 35), (10, 33), (30, 16), (19, 25), (18, 34), (27, 15), (5, 38), (3, 7), (15, 16), (20, 29), (9, 31), (1, 31), (31, 26), (19, 36), (14, 24), (27, 5), (7, 32), (0, 6), (9, 25), (16, 3), (30, 15), (19, 5), (1, 5), (30, 12), (32, 6), (12, 37), (8, 5), (19, 1), (17, 19), (8, 37), (18, 26), (29, 28), (17, 3), (13, 6), (18, 3), (22, 25), (27, 35), (11, 32), (19, 2), (13, 28), (0, 4), (7, 29), (11, 20), (10, 0), (31, 38), (13, 7), (6, 12), (21, 14), (28, 2), (14, 10), (18, 13), (0, 35), (1, 13), (12, 19), (23, 37), (13, 34), (15, 19), (8, 10), (32, 36), (24, 31), (14, 21), (15, 13), (1, 29), (2, 34), (32, 4), (18, 1), (5, 24), (14, 4), (17, 21), (28, 31), (28, 14), (23, 23), (23, 18), (30, 17), (27, 20), (18, 35), (27, 32), (17, 2), (12, 1), (4, 4), (31, 4), (22, 1), (29, 16), (21, 27), (24, 16), (0, 22), (19, 12), (3, 27), (28, 32), (23, 31), (25, 9), (24, 17), (2, 8), (32, 1), (13, 25), (31, 31), (2, 20), (22, 6), (28, 22), (16, 34), (12, 38), (19, 21), (31, 7), (25, 3), (32, 16), (32, 25), (19, 0), (31, 24), (25, 33), (23, 15), (31, 12), (29, 37), (7, 27), (21, 1), (12, 18), (8, 21), (27, 38), (14, 11), (30, 22), (4, 0), (31, 6), (6, 31), (9, 35), (28, 36), (20, 5), (28, 1), (8, 33), (23, 1), (23, 26), (7, 35), (15, 3), (18, 23), (0, 31), (11, 3), (6, 23), (18, 10), (7, 0), (19, 10), (2, 37), (25, 24), (11, 31), (12, 6), (7, 25), (13, 3), (17, 7), (4, 24), (29, 27), (23, 32), (5, 27), (16, 10), (20, 30), (15, 20), (1, 7), (19, 31), (24, 10), (6, 20), (28, 15), (21, 13), (22, 26), (25, 18), (26, 38), (10, 4), (22, 32), (25, 15), (14, 20), (19, 9), (14, 22), (12, 28), (1, 8), (4, 27), (22, 31), (7, 21), (13, 33), (30, 36), (16, 38), (3, 29), (16, 5), (5, 13), (14, 36), (11, 6), (24, 8), (1, 14), (18, 20), (10, 16), (26, 20), (5, 6), (28, 12), (32, 35), (10, 9), (16, 25), (7, 11), (16, 0), (19, 7), (7, 7), (29, 26), (0, 16), (18, 0), (25, 6), (9, 16), (21, 36), (6, 29), (31, 10), (2, 5), (30, 21), (7, 34), (1, 9), (21, 19), (10, 14), (7, 23), (27, 18), (4, 19), (2, 26), (26, 3), (27, 19), (15, 33), (17, 34), (1, 17), (19, 32), (26, 9), (9, 19), (28, 34), (4, 2), (25, 21), (12, 17), (18, 22), (4, 22), (18, 8), (13, 24), (14, 9), (26, 29), (32, 33), (21, 22), (8, 38), (0, 27), (6, 21), (27, 16), (7, 4), (16, 15), (20, 14), (29, 8), (29, 24), (0, 8), (25, 32), (10, 35), (2, 32), (28, 30), (27, 13), (9, 23), (3, 1), (4, 16), (25, 35), (25, 13), (26, 0), (6, 13), (31, 17), (16, 18), (7, 8), (31, 5), (8, 31), (20, 4), (27, 1), (10, 7), (16, 7), (27, 8), (26, 26), (24, 19), (5, 35), (18, 25), (11, 26), (8, 34), (20, 9), (27, 14), (0, 11), (31, 23), (26, 16), (18, 7), (24, 1), (19, 17), (11, 11), (2, 31), (11, 36), (31, 22), (9, 12), (7, 30), (24, 9), (10, 13), (2, 25), (24, 30), (24, 20), (23, 10), (26, 8), (25, 31), (18, 19), (31, 1), (25, 5), (21, 3), (20, 0), (25, 25), (20, 3), (20, 15), (21, 30), (24, 18), (18, 30), (30, 34), (15, 8), (31, 0), (29, 21), (2, 28), (12, 29), (13, 2), (32, 7), (9, 7), (28, 35), (21, 5), (16, 20), (32, 14), (6, 15), (27, 25), (17, 9), (8, 28), (7, 38), (15, 30), (14, 17), (24, 23), (15, 21), (4, 3), (26, 14), (13, 22), (8, 12), (31, 18), (28, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 12), (17, 19), (2, 19), (19, 15), (6, 32), (32, 19), (9, 4), (1, 11), (26, 7), (23, 0), (3, 24), (22, 20), (14, 16), (19, 18), (32, 9), (9, 19), (31, 22), (2, 2), (22, 32), (4, 25), (27, 5), (15, 19), (24, 14), (8, 19), (7, 29), (12, 30), (1, 17), (11, 14), (25, 13), (28, 33), (33, 15), (9, 0), (17, 21), (10, 9), (24, 8), (32, 21), (8, 7), (9, 1), (24, 22), (32, 13), (12, 12), (14, 27), (27, 6), (7, 30), (18, 9), (14, 24), (33, 4), (31, 7), (7, 24), (32, 22), (12, 31), (31, 19), (28, 22), (25, 12), (14, 4), (1, 7), (19, 2), (7, 14), (23, 9), (21, 4), (20, 22), (12, 32), (27, 8), (6, 28), (14, 2), (26, 22), (1, 14), (2, 7), (15, 15), (1, 6), (0, 8), (30, 13), (31, 28), (27, 18), (31, 14), (17, 23), (28, 10), (26, 4), (23, 16), (20, 5), (1, 30), (32, 17), (0, 28), (10, 3), (22, 33), (20, 16), (9, 32), (31, 6), (26, 24), (16, 8), (29, 8), (28, 7), (5, 29), (31, 9), (10, 28), (10, 2), (15, 4), (16, 29), (28, 14), (25, 6), (5, 19), (19, 7), (25, 32), (10, 24), (1, 19), (5, 17), (9, 15), (23, 28), (6, 1), (27, 15), (30, 20), (19, 11), (8, 0), (14, 33), (6, 0), (15, 5), (4, 8), (25, 21), (17, 5), (3, 13), (30, 18), (32, 20), (4, 19), (31, 0), (1, 12), (8, 8), (18, 17), (11, 1), (22, 16), (14, 6), (18, 28), (10, 33), (3, 21), (11, 21), (29, 26), (5, 16), (17, 29), (8, 15), (20, 21), (11, 7), (10, 13), (1, 2), (7, 17), (29, 31), (11, 16), (7, 31), (28, 28), (28, 30), (15, 12), (8, 31), (19, 23), (32, 1), (27, 25), (13, 12), (5, 0), (13, 0), (24, 12), (10, 6), (20, 32), (12, 7), (11, 23), (32, 11), (3, 26), (16, 20), (0, 9), (1, 28), (0, 19), (1, 18), (27, 13), (21, 6), (33, 28), (3, 20), (26, 11), (31, 23), (5, 3), (21, 7), (28, 2), (6, 33), (8, 10), (5, 14), (23, 4), (17, 31), (4, 5), (27, 29), (2, 24), (27, 21), (6, 14), (33, 5), (12, 8), (31, 26), (31, 13), (13, 6), (27, 20), (29, 21), (22, 2), (20, 24), (8, 28), (32, 27), (26, 2), (0, 24), (15, 33), (17, 3), (2, 8), (27, 17), (28, 0), (30, 27), (33, 3), (29, 9), (16, 23), (19, 26), (21, 11), (3, 18), (6, 8), (14, 14), (33, 16), (1, 22), (21, 23), (25, 2), (5, 20), (12, 10), (28, 6), (9, 26), (12, 26), (20, 13), (14, 20), (13, 5), (18, 14), (12, 15), (20, 29), (14, 23), (18, 7), (28, 11), (30, 26), (33, 29), (2, 12), (7, 15), (17, 33), (9, 24), (32, 8), (28, 32), (10, 8), (15, 14), (11, 19), (23, 25), (23, 21), (15, 10), (21, 1), (14, 11), (15, 3), (11, 27), (8, 17), (2, 20), (12, 0), (8, 9), (30, 30), (14, 5), (11, 6), (8, 23), (31, 32), (13, 30), (17, 32), (33, 27), (2, 26), (22, 1), (12, 18), (15, 9), (10, 16), (2, 15), (19, 22), (7, 21), (9, 17), (16, 7), (2, 23), (1, 9), (21, 2), (27, 7), (7, 2), (24, 7), (5, 30), (28, 3), (24, 5), (2, 33), (22, 28), (19, 29), (13, 18), (22, 12), (16, 11), (9, 6), (19, 21), (29, 25), (9, 29), (8, 11), (6, 15), (28, 26), (2, 31), (33, 31), (26, 3), (20, 11), (25, 24), (17, 26), (12, 11), (31, 12), (7, 4), (20, 0), (33, 1), (0, 21), (15, 22), (17, 15), (1, 33), (5, 21), (12, 23), (11, 17), (25, 28), (22, 25), (11, 33), (10, 27), (7, 27), (20, 20), (0, 20), (8, 2), (24, 2), (29, 15), (12, 16), (6, 5), (9, 25), (22, 22), (22, 31), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944640", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 33), (5, 28), (35, 0), (2, 0), (20, 6), (30, 22), (21, 10), (25, 13), (22, 0), (28, 11), (33, 20), (34, 31), (14, 1), (11, 28), (22, 33), (19, 33), (34, 7), (32, 30), (5, 13), (29, 3), (4, 3), (35, 14), (33, 26), (21, 8), (13, 6), (19, 31), (23, 29), (16, 28), (17, 27), (8, 8), (12, 6), (15, 11), (17, 23), (20, 24), (19, 13), (35, 17), (10, 0), (17, 4), (24, 26), (27, 18), (23, 14), (3, 27), (27, 11), (2, 14), (9, 16), (14, 32), (27, 4), (9, 13), (19, 18), (0, 25), (36, 11), (21, 23), (0, 20), (30, 13), (26, 18), (36, 23), (24, 8), (20, 18), (33, 2), (35, 15), (0, 6), (23, 2), (2, 27), (28, 3), (26, 19), (23, 33), (23, 5), (26, 9), (19, 9), (30, 5), (12, 27), (0, 30), (21, 11), (25, 11), (27, 19), (1, 5), (30, 24), (9, 22), (35, 5), (16, 5), (7, 1), (18, 16), (28, 29), (16, 30), (6, 18), (1, 28), (34, 6), (13, 3), (21, 2), (34, 22), (22, 18), (11, 26), (17, 14), (35, 16), (21, 4), (35, 10), (0, 23), (0, 10), (4, 32), (35, 26), (19, 14), (2, 19), (19, 30), (3, 2), (35, 2), (36, 4), (8, 24), (7, 9), (18, 17), (0, 16), (4, 18), (26, 25), (33, 1), (3, 31), (5, 18), (4, 28), (1, 9), (9, 5), (19, 29), (11, 3), (22, 7), (17, 31), (10, 31), (30, 12), (25, 14), (31, 32), (27, 29), (7, 17), (23, 31), (28, 15), (16, 29), (12, 31), (5, 2), (13, 2), (28, 7), (32, 26), (1, 10), (12, 20), (22, 23), (5, 15), (12, 14), (0, 13), (31, 6), (13, 12), (32, 8), (0, 7), (26, 13), (11, 13), (3, 7), (28, 23), (13, 27), (2, 5), (28, 6), (18, 30), (20, 5), (18, 6), (33, 5), (11, 9), (32, 17), (13, 25), (30, 0), (0, 22), (2, 21), (25, 28), (32, 6), (2, 20), (17, 22), (10, 6), (26, 7), (36, 29), (15, 20), (9, 0), (27, 10), (0, 31), (28, 0), (24, 27), (19, 17), (8, 7), (4, 15), (23, 27), (11, 6), (8, 15), (13, 29), (23, 9), (18, 1), (18, 13), (3, 10), (10, 8), (7, 32), (7, 31), (34, 32), (6, 28), (13, 21), (14, 22), (6, 4), (33, 8), (30, 4), (28, 8), (18, 14), (35, 20), (21, 24), (28, 12), (18, 12), (35, 22), (1, 24), (3, 1), (14, 33), (25, 1), (20, 14), (4, 27), (24, 20), (4, 22), (1, 0), (31, 26), (11, 4), (29, 27), (29, 2), (20, 2), (27, 17), (36, 9), (17, 18), (7, 30), (14, 23), (5, 22), (7, 29), (6, 8), (12, 12), (34, 16), (6, 24), (9, 31), (36, 32), (14, 8), (32, 5), (34, 5), (35, 27), (36, 22), (8, 22), (24, 23), (18, 21), (9, 11), (12, 29), (17, 30), (8, 20), (27, 13), (7, 13), (36, 31), (6, 7), (19, 0), (26, 30), (31, 18), (23, 1), (17, 9), (5, 8), (22, 26), (6, 15), (28, 25), (7, 16), (31, 24), (34, 28), (34, 25), (9, 2), (4, 24), (4, 23), (6, 27), (33, 33), (31, 8), (2, 1), (24, 12), (3, 30), (21, 22), (32, 25), (5, 4), (30, 20), (11, 10), (34, 14), (2, 28), (27, 8), (13, 0), (2, 7), (23, 28), (2, 8), (20, 22), (6, 3), (11, 14), (24, 10), (21, 15), (36, 19), (25, 19), (9, 17), (18, 20), (8, 12), (15, 23), (9, 9), (21, 27), (18, 24), (31, 13), (1, 30), (18, 4), (30, 32), (34, 8), (0, 2), (21, 0), (8, 26), (34, 15), (30, 31), (23, 26), (17, 16), (24, 31), (22, 12), (0, 17), (6, 13), (10, 7), (27, 23), (20, 20), (29, 14), (22, 9), (15, 2), (26, 3), (32, 1), (22, 4), (11, 25), (5, 25), (31, 20), (18, 28), (13, 16), (1, 31), (21, 26), (13, 20), (32, 15), (3, 20), (12, 8), (30, 19), (30, 25), (25, 29), (27, 0), (2, 4), (2, 9), (2, 17), (33, 27), (10, 17), (14, 7), (31, 33), (34, 17), (18, 29), (0, 33), (6, 26), (27, 31), (4, 21), (22, 32), (34, 29), (35, 12), (35, 13), (32, 21), (26, 27), (17, 15), (23, 0), (7, 4), (26, 24), (10, 12), (9, 33), (30, 23), (8, 3), (10, 15), (3, 22), (7, 19), (24, 18), (3, 8), (10, 20), (17, 12), (23, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "857088", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 23), (14, 31), (17, 29), (16, 1), (4, 25), (17, 8), (4, 13), (19, 18), (11, 28), (9, 31), (10, 30), (4, 12), (15, 4), (17, 28), (13, 4), (4, 6), (11, 1), (7, 21), (24, 4), (19, 16), (18, 12), (8, 0), (1, 28), (0, 22), (14, 3), (2, 9), (15, 13), (25, 28), (2, 18), (5, 28), (1, 6), (1, 25), (29, 26), (12, 23), (19, 31), (19, 21), (16, 7), (0, 24), (11, 19), (14, 4), (1, 17), (18, 5), (4, 17), (9, 5), (16, 9), (27, 14), (18, 1), (27, 2), (13, 12), (1, 3), (9, 6), (26, 17), (7, 9), (28, 29), (26, 13), (25, 4), (19, 19), (2, 22), (15, 21), (29, 20), (11, 10), (15, 15), (1, 19), (29, 18), (4, 10), (1, 15), (20, 16), (15, 2), (6, 18), (19, 12), (15, 6), (20, 4), (8, 4), (24, 21), (16, 10), (10, 8), (28, 31), (23, 23), (1, 5), (24, 7), (5, 4), (19, 22), (8, 10), (20, 1), (17, 15), (28, 9), (18, 31), (9, 25), (14, 26), (7, 8), (4, 7), (1, 30), (1, 7), (25, 25), (11, 2), (1, 14), (22, 15), (25, 6), (2, 16), (25, 10), (11, 18), (15, 8), (26, 27), (23, 27), (5, 14), (27, 29), (5, 12), (11, 16), (2, 12), (7, 15), (11, 21), (23, 26), (1, 13), (22, 11), (10, 3), (27, 11), (19, 11), (22, 21), (4, 21), (10, 28), (19, 5), (6, 25), (0, 10), (27, 31), (22, 28), (4, 8), (22, 8), (20, 20), (14, 9), (27, 5), (9, 12), (27, 27), (23, 13), (21, 26), (7, 5), (24, 18), (23, 25), (20, 19), (27, 9), (11, 27), (17, 24), (6, 24), (4, 19), (25, 27), (27, 3), (6, 11), (29, 12), (11, 26), (5, 1), (23, 9), (10, 15), (21, 15), (16, 16), (11, 22), (24, 29), (6, 9), (22, 19), (25, 7), (13, 5), (12, 17), (24, 27), (21, 30), (28, 20), (14, 0), (9, 23), (3, 28), (3, 23), (20, 7), (11, 9), (24, 19), (17, 18), (19, 6), (4, 0), (3, 3), (11, 5), (2, 7), (22, 2), (1, 22), (3, 0), (26, 22), (23, 14), (29, 3), (6, 8), (8, 7), (20, 5), (3, 19), (20, 11), (7, 16), (12, 12), (21, 19), (0, 8), (28, 3), (25, 30), (5, 21), (12, 14), (6, 29), (25, 8), (7, 12), (6, 15), (15, 28), (21, 17), (19, 9), (4, 18), (14, 2), (12, 19), (26, 3), (14, 16), (2, 4), (17, 11), (9, 28), (3, 17), (6, 1), (25, 9), (26, 23), (20, 22), (18, 22), (17, 9), (13, 29), (6, 10), (23, 17), (10, 22), (22, 9), (3, 2), (0, 11), (2, 13), (0, 20), (26, 2), (16, 14), (8, 1), (0, 13), (2, 3), (4, 24), (27, 0), (21, 20), (9, 29), (28, 1), (6, 7), (16, 15), (18, 19), (4, 9), (13, 21), (14, 27), (4, 15), (10, 23), (26, 11), (1, 23), (3, 30), (26, 1), (10, 2), (28, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816480", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 28), (31, 14), (20, 24), (18, 15), (4, 8), (8, 15), (23, 9), (22, 28), (1, 9), (0, 3), (9, 1), (26, 24), (0, 4), (14, 18), (28, 6), (14, 16), (20, 7), (20, 14), (5, 8), (19, 3), (27, 24), (26, 26), (21, 34), (16, 33), (22, 23), (14, 5), (13, 23), (9, 31), (18, 13), (7, 7), (9, 19), (31, 29), (31, 21), (0, 7), (10, 8), (21, 28), (27, 28), (17, 27), (5, 33), (18, 0), (23, 18), (14, 27), (26, 13), (2, 4), (0, 16), (31, 0), (9, 4), (13, 13), (7, 11), (15, 27), (27, 11), (4, 35), (2, 26), (8, 31), (1, 15), (3, 1), (24, 14), (9, 12), (23, 6), (10, 33), (14, 28), (8, 21), (1, 35), (9, 3), (18, 34), (11, 5), (21, 29), (25, 17), (28, 17), (19, 1), (10, 28), (20, 17), (11, 11), (22, 2), (17, 18), (31, 2), (3, 0), (21, 32), (17, 35), (12, 7), (1, 10), (29, 11), (4, 6), (25, 13), (23, 0), (14, 15), (7, 23), (31, 30), (5, 14), (4, 32), (26, 33), (21, 1), (16, 7), (14, 35), (21, 21), (14, 11), (18, 16), (16, 11), (3, 28), (24, 21), (17, 23), (25, 10), (1, 8), (5, 25), (30, 23), (1, 6), (23, 23), (30, 33), (22, 34), (0, 27), (15, 2), (6, 9), (23, 8), (17, 8), (24, 29), (15, 19), (16, 10), (9, 6), (16, 14), (25, 3), (31, 26), (19, 2), (6, 33), (27, 16), (31, 27), (24, 27), (32, 13), (10, 6), (25, 11), (1, 20), (26, 35), (13, 21), (3, 9), (17, 17), (0, 21), (28, 1), (13, 3), (17, 16), (6, 16), (25, 16), (4, 5), (10, 0), (32, 1), (31, 33), (8, 11), (18, 33), (28, 23), (27, 7), (32, 0), (13, 2), (5, 4), (18, 2), (26, 4), (30, 29), (30, 30), (32, 6), (13, 34), (23, 12), (20, 12), (29, 0), (5, 12), (12, 28), (17, 9), (11, 9), (32, 17), (25, 22), (28, 11), (7, 35), (25, 23), (10, 22), (25, 19), (10, 16), (19, 25), (30, 28), (33, 13), (12, 21), (11, 1), (1, 19), (22, 1), (18, 28), (15, 8), (1, 29), (8, 33), (9, 20), (28, 26), (30, 16), (25, 0), (25, 6), (7, 2), (31, 8), (7, 13), (30, 17), (33, 7), (29, 19), (6, 31), (0, 33), (21, 24), (16, 31), (18, 32), (11, 16), (33, 12), (7, 33), (14, 3), (13, 33), (33, 17), (28, 13), (18, 35), (6, 0), (9, 2), (8, 9), (25, 33), (33, 27), (15, 30), (16, 12), (2, 31), (29, 30), (16, 21), (23, 20), (16, 26), (24, 22), (23, 14), (13, 11), (26, 7), (22, 27), (2, 5), (18, 14), (15, 35), (15, 34), (9, 33), (11, 23), (28, 0), (25, 2), (5, 27), (11, 6), (5, 19), (18, 7), (13, 22), (24, 30), (15, 22), (17, 14), (5, 11), (30, 0), (5, 30), (32, 24), (14, 29), (18, 20), (26, 32), (12, 34), (18, 3), (12, 23), (26, 16), (26, 22), (13, 9), (21, 15), (24, 18), (31, 5), (24, 1), (15, 13), (2, 18), (3, 27), (7, 28), (16, 34), (24, 13), (24, 3), (29, 26), (22, 26), (6, 5), (27, 5), (13, 4), (15, 10), (12, 13), (7, 25), (28, 22), (1, 13), (2, 24), (12, 16), (21, 33), (31, 24), (30, 31), (8, 23), (12, 6), (23, 25), (15, 11), (19, 24), (25, 12), (22, 11), (1, 24), (16, 30), (8, 1), (27, 13), (17, 1), (24, 5), (26, 28), (20, 34), (18, 26), (13, 28), (32, 10), (21, 12), (20, 8), (10, 15), (11, 19), (21, 35), (29, 27), (4, 29), (20, 16), (23, 21), (9, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160320", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), 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), (31, 7), (19, 7), (3, 23), (14, 25), (29, 8), (6, 5), (31, 1), (4, 15), (7, 18), (23, 12), (8, 10), (7, 21), (26, 7), (15, 22), (21, 1), (13, 6), (28, 5), (25, 18), (0, 29), (14, 23), (18, 14), (9, 18), (5, 9), (11, 17), (22, 29), (21, 24), (3, 13), (2, 23), (30, 14), (8, 20), (24, 18), (31, 16), (29, 6), (17, 14), (0, 6), (25, 26), (4, 29), (6, 2), (24, 7), (18, 13), (13, 22), (24, 2), (25, 5), (22, 25), (6, 11), (17, 17), (18, 22), (13, 13), (14, 18), (3, 6), (8, 11), (21, 3), (4, 14), (24, 22), (17, 8), (26, 0), (14, 17), (11, 21), (16, 17), (29, 19), (1, 24), (16, 5), (4, 17), (26, 15), (25, 12), (29, 13), (18, 1), (17, 2), (11, 5), (18, 29), (3, 5), (3, 22), (2, 20), (11, 24), (1, 1), (18, 24), (15, 14), (26, 6), (23, 5), (7, 6), (3, 14), (28, 28), (8, 8), (4, 21), (29, 3), (15, 3), (16, 24), (26, 27), (11, 1), (22, 24), (1, 27), (20, 11), (4, 10), (22, 14), (21, 4), (21, 13), (26, 1), (8, 1), (22, 2), (20, 3), (24, 5), (10, 23), (17, 5), (19, 8), (20, 4), (23, 14), (0, 14), (0, 23), (12, 3), (19, 5), (30, 23), (16, 28), (27, 8), (3, 25), (22, 19), (20, 20), (21, 2), (6, 26), (25, 28), (9, 15), (31, 8), (24, 27), (10, 17), (0, 4), (5, 7), (27, 27), (15, 8), (8, 30), (17, 10), (28, 0), (1, 17), (5, 30), (7, 4), (16, 4), (5, 21), (12, 30), (3, 20), (10, 8), (31, 25), (3, 9), (9, 25), (17, 24), (28, 3), (1, 18), (15, 30), (18, 16), (16, 2), (27, 25), (5, 6), (13, 26), (23, 29), (11, 6), (9, 1), (1, 4), (8, 19), (25, 9), (23, 1), (10, 5), (22, 16), (7, 24), (2, 24), (21, 8), (18, 18), (30, 1), (2, 1), (29, 10), (13, 20), (26, 18), (24, 29), (3, 12), (9, 26), (23, 25), (21, 29), (11, 7), (27, 12), (7, 12), (1, 23), (24, 17), (25, 17), (19, 17), (26, 2), (8, 0), (13, 14), (30, 15), (6, 23), (5, 13), (7, 8), (23, 10), (15, 7), (28, 10), (25, 10), (30, 0), (19, 4), (29, 28), (7, 7), (2, 14), (3, 21), (7, 25), (9, 14), (22, 5), (23, 11), (17, 3), (18, 25), (14, 12), (19, 30), (2, 27), (0, 5), (29, 12), (4, 26), (10, 25), (0, 9), (24, 8), (25, 2), (24, 21), (0, 18), (4, 2), (1, 20), (9, 30), (15, 0), (5, 14), (8, 25), (6, 7), (21, 25), (12, 19), (1, 16), (19, 23), (23, 28), (29, 24), (27, 13), (13, 9), (2, 13), (21, 12), (26, 17), (30, 25), (29, 14), (17, 1), (11, 22), (29, 1), (2, 6), (31, 23), (27, 23), (4, 1), (31, 0), (9, 10), (11, 4), (14, 15), (8, 24), (15, 25), (24, 28), (1, 5), (18, 12), (10, 15), (25, 7), (27, 26), (15, 11), (6, 27), (12, 8), (21, 27), (3, 27), (19, 24), (4, 20), (10, 24), (24, 4), (29, 11), (16, 20), (26, 22), (20, 24), (12, 1), (19, 28), (8, 14), (1, 28), (25, 24), (27, 11), (22, 7), (17, 30), (17, 29), (2, 2), (22, 22), (20, 22), (3, 3), (22, 23), (14, 13), (27, 21), (22, 26), (10, 27), (6, 4), (25, 14), (9, 28), (23, 27), (0, 15), (29, 7), (24, 30), (0, 8), (30, 26), (6, 15), (7, 27), (27, 28), (28, 17), (24, 26), (31, 20), (31, 18), (20, 1), (19, 6), (22, 6), (5, 19), (23, 19), (15, 19), (18, 26), (19, 13), (17, 18), (12, 29), (14, 0), (15, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "662832", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 1), (29, 22), (2, 6), (20, 9), (3, 33), (30, 1), (10, 14), (7, 9), (27, 23), (34, 16), (10, 35), (22, 12), (29, 12), (27, 10), (2, 22), (18, 9), (34, 13), (17, 26), (16, 34), (13, 5), (29, 11), (9, 12), (18, 29), (14, 27), (22, 6), (1, 20), (33, 35), (31, 34), (27, 19), (35, 23), (12, 28), (22, 26), (7, 31), (28, 27), (2, 15), (34, 7), (10, 25), (21, 26), (20, 23), (16, 10), (5, 4), (2, 3), (33, 19), (26, 12), (32, 7), (0, 12), (16, 11), (21, 34), (3, 30), (0, 13), (17, 33), (21, 6), (17, 16), (9, 22), (28, 24), (5, 23), (12, 17), (35, 20), (3, 18), (33, 27), (23, 23), (0, 22), (14, 7), (4, 34), (6, 13), (0, 34), (30, 30), (16, 24), (26, 31), (16, 23), (20, 4), (12, 18), (22, 34), (18, 12), (28, 6), (2, 20), (32, 4), (24, 19), (4, 30), (9, 28), (10, 13), (6, 26), (16, 22), (34, 27), (18, 33), (2, 30), (25, 23), (10, 5), (4, 19), (3, 21), (6, 7), (24, 30), (19, 19), (5, 15), (16, 13), (7, 19), (35, 13), (5, 8), (13, 4), (15, 22), (6, 3), (25, 22), (15, 26), (23, 28), (23, 4), (11, 8), (30, 32), (6, 23), (32, 29), (9, 25), (6, 28), (36, 28), (12, 13), (4, 13), (35, 21), (22, 22), (36, 15), (4, 28), (0, 8), (31, 32), (31, 7), (19, 16), (27, 29), (30, 33), (19, 22), (16, 19), (24, 33), (5, 2), (26, 10), (34, 23), (21, 21), (4, 33), (3, 31), (28, 31), (36, 5), (21, 8), (8, 14), (5, 16), (31, 33), (26, 32), (2, 29), (15, 3), (25, 3), (1, 17), (8, 24), (29, 14), (35, 9), (17, 19), (7, 17), (19, 2), (30, 9), (19, 32), (4, 10), (12, 1), (23, 21), (12, 11), (27, 30), (8, 7), (3, 7), (17, 6), (9, 5), (11, 21), (8, 4), (26, 6), (16, 26), (36, 13), (19, 7), (28, 17), (5, 32), (10, 27), (18, 17), (10, 22), (28, 5), (15, 31), (17, 11), (10, 3), (17, 25), (35, 8), (33, 3), (25, 12), (5, 28), (12, 27), (19, 5), (32, 15), (1, 28), (32, 12), (7, 30), (5, 34), (21, 17), (8, 30), (23, 30), (1, 3), (6, 20), (8, 5), (4, 26), (30, 35), (32, 5), (34, 10), (27, 16), (21, 25), (0, 24), (9, 16), (32, 22), (6, 27), (34, 3), (27, 11), (13, 12), (1, 14), (18, 5), (15, 17), (29, 15), (35, 2), (16, 5), (17, 13), (26, 0), (33, 24), (6, 15), (30, 7), (16, 3), (29, 16), (9, 29), (7, 5), (33, 21), (4, 22), (30, 16), (27, 7), (2, 18), (28, 18), (13, 34), (9, 15), (35, 32), (29, 30), (21, 19), (29, 32), (30, 17), (10, 21), (16, 4), (17, 15), (30, 27), (17, 35), (8, 15), (31, 30), (36, 17), (9, 6), (21, 15), (15, 34), (34, 34), (5, 7), (21, 33), (23, 27), (11, 34), (4, 17), (17, 5), (2, 23), (27, 27), (20, 31), (10, 11), (10, 31), (29, 2), (32, 35), (23, 33), (35, 4), (24, 25), (24, 27), (13, 8), (22, 8), (33, 9), (18, 27), (22, 13), (20, 1), (31, 10), (4, 12), (14, 17), (22, 7), (3, 35), (3, 34), (8, 28), (29, 3), (36, 21), (28, 10), (18, 15), (24, 23), (16, 18), (25, 24), (7, 22), (29, 8), (7, 2), (26, 14), (8, 1), (30, 18), (10, 24), (34, 11), (20, 17), (19, 17), (34, 19), (26, 27), (10, 9), (15, 1), (4, 35), (28, 32), (10, 30), (25, 17), (7, 8), (3, 10), (12, 4), (15, 32), (32, 2), (14, 16), (1, 4), (29, 18), (1, 12), (2, 13), (17, 18), (5, 1), (19, 15), (24, 26), (25, 4), (3, 4), (9, 17), (32, 19), (15, 11), (12, 35), (19, 21), (8, 33), (9, 19), (34, 4), (28, 8), (10, 4), (14, 23), (31, 31), (11, 29), (24, 29), (12, 0), (30, 6), (10, 12), (1, 13), (6, 22), (18, 25), (11, 19), (25, 9), (3, 27), (22, 16), (11, 2), (33, 20), (34, 1), (6, 14), (30, 15), (24, 34), (35, 29), (23, 17), (35, 28), (36, 10), (7, 3), (28, 23), (6, 12), (25, 33), (13, 10), (36, 11), (24, 21), (8, 11), (5, 10), (13, 21), (21, 20), (34, 29), (0, 2), (0, 30), (30, 14), (34, 17), (18, 7), (7, 11), (14, 26), (35, 31), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "690768", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 30), (8, 9), (27, 18), (15, 24), (13, 26), (1, 5), (37, 5), (9, 22), (18, 28), (18, 15), (9, 27), (21, 6), (37, 6), (23, 33), (31, 15), (16, 22), (13, 33), (2, 29), (31, 30), (3, 18), (20, 21), (18, 31), (6, 4), (30, 31), (4, 9), (30, 14), (6, 2), (25, 0), (15, 8), (24, 12), (7, 31), (8, 10), (24, 24), (32, 12), (22, 29), (31, 1), (2, 12), (30, 2), (29, 16), (3, 33), (33, 4), (33, 25), (38, 28), (9, 34), (23, 21), (0, 3), (7, 11), (38, 3), (6, 19), (24, 28), (32, 22), (8, 17), (34, 16), (18, 5), (34, 2), (34, 3), (16, 31), (21, 16), (5, 21), (32, 0), (29, 11), (37, 10), (34, 4), (13, 14), (20, 34), (24, 6), (2, 31), (9, 25), (25, 25), (16, 21), (14, 15), (10, 14), (4, 20), (14, 30), (6, 1), (19, 7), (37, 9), (28, 21), (30, 11), (35, 2), (9, 17), (17, 32), (24, 5), (29, 31), (30, 23), (34, 10), (5, 31), (21, 11), (9, 9), (33, 1), (27, 29), (13, 20), (5, 3), (32, 27), (10, 18), (22, 3), (15, 34), (15, 1), (11, 29), (8, 8), (2, 4), (3, 14), (34, 6), (28, 26), (25, 9), (11, 20), (5, 14), (31, 7), (18, 21), (29, 4), (17, 20), (14, 7), (12, 5), (6, 26), (36, 22), (26, 11), (17, 17), (6, 31), (1, 18), (23, 18), (3, 16), (9, 6), (38, 16), (25, 3), (34, 8), (20, 16), (15, 12), (2, 28), (8, 4), (1, 31), (13, 5), (8, 23), (37, 21), (6, 21), (14, 27), (0, 25), (0, 18), (32, 1), (13, 0), (21, 24), (34, 23), (12, 8), (25, 12), (36, 32), (12, 33), (17, 33), (5, 2), (19, 14), (28, 34), (31, 9), (20, 2), (13, 22), (36, 24), (24, 16), (23, 20), (26, 1), (33, 32), (13, 7), (30, 19), (18, 27), (31, 24), (15, 23), (30, 25), (31, 28), (11, 6), (21, 20), (29, 7), (2, 15), (27, 28), (9, 13), (17, 12), (10, 6), (0, 12), (25, 14), (24, 32), (15, 14), (19, 4), (5, 32), (3, 32), (14, 14), (19, 25), (7, 8), (25, 4), (9, 30), (0, 29), (26, 26), (22, 16), (14, 13), (2, 11), (7, 0), (3, 24), (27, 27), (16, 33), (20, 20), (12, 3), (18, 26), (10, 34), (36, 13), (32, 11), (27, 21), (19, 23), (35, 18), (7, 23), (34, 21), (18, 0), (34, 20), (9, 29), (16, 18), (35, 26), (20, 23), (8, 34), (11, 27), (1, 16), (31, 21), (10, 2), (23, 0), (26, 4), (28, 6), (31, 14), (7, 19), (5, 28), (3, 20), (11, 31), (38, 10), (8, 25), (0, 28), (7, 28), (1, 26), (38, 13), (7, 34), (4, 32), (32, 25), (32, 19), (9, 10), (7, 26), (7, 16), (8, 2), (15, 7), (19, 3), (2, 24), (26, 12), (2, 2), (19, 18), (15, 0), (14, 34), (17, 7), (18, 24), (30, 27), (8, 13), (14, 24), (0, 11), (14, 25), (6, 27), (21, 10), (22, 9), (33, 16), (38, 29), (9, 32), (27, 33), (25, 23), (14, 29), (11, 24), (12, 25), (29, 9), (37, 0), (7, 5), (2, 26), (30, 9), (6, 32), (11, 21), (22, 23), (9, 19), (6, 10), (4, 6), (23, 27), (27, 24), (33, 22), (23, 10), (35, 19), (38, 18), (0, 1), (20, 29), (21, 4), (4, 4), (36, 11), (31, 13), (37, 19), (16, 20), (28, 32), (35, 33), (28, 1), (25, 30), (0, 31), (12, 13), (14, 3), (23, 29), (21, 27), (6, 3), (18, 4), (28, 14), (2, 3), (38, 5), (17, 1), (17, 31), (27, 23), (25, 18), (16, 0), (38, 19), (33, 20), (30, 17), (6, 33), (17, 26), (16, 15), (22, 6), (28, 23), (8, 21), (13, 34), (33, 6), (28, 20), (9, 12), (31, 3), (24, 13), (1, 2), (25, 24), (29, 29), (17, 18), (29, 26), (9, 33), (9, 24), (1, 21), (38, 8), (6, 18), (6, 24), (9, 16), (26, 13), (19, 31), (37, 24), (36, 15), (19, 15), (6, 13), (29, 34), (32, 21), (20, 4), (36, 18), (22, 21), (4, 23), (27, 11), (10, 4), (0, 7), (16, 32), (36, 0), (19, 29), (27, 15), (8, 26), (31, 34), (31, 2), (16, 25), (37, 13), (6, 34), (23, 14), (8, 5), (23, 34), (23, 8), (10, 8), (26, 32), (2, 25), (12, 27), (23, 15), (24, 30), (20, 0), (13, 16), (22, 7), (11, 28), (13, 32), (1, 14), (30, 26), (23, 30), (26, 21), (19, 6), (29, 13), (33, 9), (2, 19), (22, 32), (22, 33), (17, 13), (21, 21), (33, 17), (38, 11), (36, 9), (5, 29), (12, 16), (32, 7), (27, 0), (6, 6), (18, 29), (24, 9), (12, 0), (23, 31), (22, 0), (13, 8), (6, 14), (20, 17), (7, 25), (36, 1), (3, 12), (20, 27), (8, 32), (30, 8), (33, 27), (22, 26), (5, 8), (1, 17), (11, 18), (35, 31), (24, 15), (9, 23), (1, 28), (33, 10), (36, 8), (12, 31), (1, 9), (4, 12), (36, 14), (15, 10), (10, 30), (15, 31), (31, 25), (15, 17), (1, 7), (26, 0), (26, 17), (38, 20), (7, 33), (29, 32), (7, 2), (29, 17), (16, 34), (28, 8), (15, 2), (20, 12), (12, 4), (7, 17), (27, 26), (11, 10), (19, 12), (35, 8), (38, 32), (7, 4), (23, 5), (37, 2), (12, 29), (4, 5), (8, 18), (15, 13), (0, 23), (0, 34), (33, 30), (9, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33642", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 8), (29, 16), (19, 2), (13, 12), (7, 2), (11, 13), (28, 30), (24, 15), (28, 8), (31, 5), (7, 26), (5, 6), (8, 27), (15, 34), (24, 19), (18, 22), (13, 6), (14, 10), (25, 16), (14, 15), (9, 1), (8, 29), (26, 16), (7, 3), (14, 23), (30, 28), (7, 19), (2, 12), (17, 6), (12, 31), (27, 34), (3, 5), (28, 15), (25, 26), (3, 30), (10, 15), (15, 6), (7, 22), (20, 4), (4, 18), (29, 11), (10, 34), (17, 32), (30, 12), (0, 2), (27, 6), (17, 12), (21, 26), (23, 4), (26, 9), (6, 8), (4, 22), (8, 24), (20, 11), (3, 14), (12, 22), (23, 7), (21, 12), (1, 32), (1, 18), (4, 20), (20, 19), (31, 7), (18, 29), (27, 18), (16, 3), (29, 18), (27, 31), (20, 9), (0, 12), (28, 32), (13, 33), (13, 22), (11, 22), (10, 1), (27, 21), (10, 4), (21, 14), (21, 13), (9, 10), (15, 9), (31, 0), (8, 11), (30, 26), (11, 7), (5, 12), (17, 8), (17, 27), (24, 23), (11, 24), (22, 31), (15, 11), (0, 31), (11, 4), (24, 0), (11, 2), (13, 11), (17, 14), (11, 28), (29, 7), (18, 16), (10, 11), (14, 22), (13, 5), (1, 0), (18, 31), (10, 24), (20, 2), (21, 34), (29, 26), (19, 17), (15, 2), (18, 25), (29, 21), (26, 29), (0, 22), (22, 21), (24, 9), (17, 16), (0, 24), (8, 28), (0, 16), (16, 4), (9, 30), (8, 12), (7, 12), (24, 28), (29, 1), (23, 32), (15, 30), (15, 33), (9, 19), (15, 13), (19, 0), (26, 6), (5, 17), (5, 30), (27, 17), (20, 12), (9, 25), (2, 8), (26, 33), (7, 6), (8, 6), (8, 33), (10, 7), (9, 12), (1, 12), (11, 18), (19, 4), (29, 23), (26, 20), (20, 34), (0, 26), (1, 10), (20, 24), (18, 13), (8, 25), (21, 4), (21, 29), (10, 19), (19, 8), (24, 11), (3, 22), (19, 1), (17, 19), (6, 17), (24, 21), (15, 25), (29, 33), (3, 12), (12, 11), (31, 24), (17, 11), (6, 21), (30, 9), (12, 6), (4, 29), (0, 34), (25, 7), (21, 11), (23, 22), (16, 16), (5, 19), (27, 2), (8, 8), (26, 8), (2, 28), (13, 32), (11, 6), (0, 25), (19, 15), (12, 10), (15, 20), (31, 8), (12, 27), (22, 20), (0, 9), (22, 5), (9, 24), (21, 32), (27, 19), (5, 34), (2, 17), (3, 18), (18, 8), (19, 10), (10, 12), (14, 12), (27, 13), (2, 32), (19, 9), (5, 0), (6, 3), (2, 5), (13, 1), (22, 13), (30, 6), (24, 29), (24, 18), (29, 17), (16, 23), (19, 6), (29, 22), (2, 19), (5, 31), (30, 3), (20, 5), (9, 4), (9, 0), (7, 20), (1, 5), (23, 1), (22, 3), (4, 10), (22, 10), (28, 19), (13, 16), (18, 23), (27, 15), (4, 19), (11, 31), (12, 33), (16, 0), (0, 29), (5, 21), (1, 29), (18, 4), (30, 13), (18, 7), (15, 21), (28, 7), (14, 16), (10, 32), (18, 28), (15, 22), (18, 26), (19, 13), (8, 4), (14, 29), (30, 31), (30, 32), (3, 25), (1, 30), (11, 8), (24, 26), (18, 21), (4, 3), (14, 21), (9, 28), (23, 29), (4, 1), (27, 14), (25, 4), (18, 24), (13, 21), (28, 12), (16, 30), (27, 7), (21, 10), (20, 6), (12, 20), (26, 3), (7, 13), (8, 16), (6, 26), (15, 17), (22, 32), (31, 25), (23, 28), (25, 25), (3, 10), (21, 17), (30, 25), (30, 17), (28, 23), (21, 31), (2, 11), (23, 19), (16, 14), (19, 28), (5, 15), (29, 8), (7, 32), (12, 3), (16, 19), (11, 32), (20, 10), (26, 23), (2, 22), (25, 32), (10, 23), (14, 2), (28, 26), (18, 5), (6, 29), (24, 22), (9, 32), (29, 31), (20, 32), (24, 31), (1, 15), (16, 10), (28, 21), (24, 27), (31, 33), (10, 10), (17, 20), (11, 34), (7, 28), (1, 19), (6, 28), (6, 15), (26, 11), (13, 7), (30, 29), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "703056", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 8), (30, 35), (25, 2), (18, 4), (27, 5), (2, 0), (15, 6), (26, 11), (20, 22), (23, 11), (20, 20), (1, 20), (7, 29), (3, 1), (19, 8), (2, 8), (6, 35), (18, 37), (2, 1), (28, 14), (3, 3), (6, 21), (8, 6), (22, 32), (27, 12), (19, 24), (28, 24), (0, 21), (26, 22), (26, 13), (23, 36), (19, 17), (14, 9), (4, 16), (10, 11), (0, 36), (25, 37), (22, 23), (31, 19), (0, 25), (5, 2), (11, 31), (22, 25), (1, 31), (10, 33), (13, 36), (20, 1), (24, 11), (26, 8), (19, 36), (0, 5), (16, 26), (0, 4), (2, 7), (29, 37), (28, 3), (4, 31), (31, 11), (20, 8), (14, 2), (7, 17), (23, 28), (29, 15), (13, 2), (4, 0), (13, 32), (16, 10), (27, 19), (3, 36), (28, 6), (8, 27), (10, 25), (19, 5), (19, 27), (5, 31), (26, 25), (16, 6), (1, 19), (24, 6), (1, 37), (2, 31), (20, 6), (0, 37), (18, 10), (12, 4), (2, 2), (12, 21), (5, 10), (24, 18), (4, 13), (21, 2), (18, 16), (21, 0), (20, 11), (13, 16), (31, 0), (22, 20), (14, 25), (5, 32), (27, 1), (12, 26), (13, 3), (28, 5), (31, 25), (23, 31), (30, 9), (14, 6), (6, 8), (0, 20), (29, 1), (26, 6), (16, 21), (6, 29), (1, 15), (6, 24), (9, 17), (24, 4), (0, 8), (22, 18), (3, 12), (12, 15), (18, 32), (6, 5), (25, 28), (13, 4), (9, 7), (16, 29), (22, 22), (4, 6), (20, 17), (27, 4), (28, 2), (3, 11), (5, 12), (5, 7), (20, 35), (15, 3), (6, 16), (5, 22), (27, 13), (4, 4), (21, 21), (24, 22), (22, 17), (24, 33), (22, 13), (17, 7), (18, 1), (31, 27), (5, 28), (11, 35), (4, 23), (26, 4), (4, 1), (9, 24), (0, 35), (26, 23), (10, 1), (28, 34), (25, 0), (15, 15), (7, 16), (4, 22), (9, 33), (13, 19), (7, 22), (7, 9), (5, 15), (1, 18), (13, 18), (25, 32), (15, 19), (21, 29), (8, 19), (20, 9), (9, 21), (0, 28), (25, 15), (17, 37), (21, 20), (28, 33), (24, 16), (6, 34), (11, 36), (7, 11), (11, 29), (31, 23), (24, 7), (1, 8), (17, 8), (16, 1), (4, 5), (31, 20), (5, 21), (28, 9), (16, 7), (8, 26), (8, 36), (0, 11), (28, 31), (22, 26), (7, 13), (20, 0), (27, 27), (4, 35), (13, 31), (12, 27), (27, 0), (31, 2), (13, 6), (23, 25), (6, 6), (8, 7), (2, 18), (9, 4), (23, 19), (9, 36), (2, 20), (22, 15), (2, 9), (27, 34), (1, 23), (25, 26), (9, 1), (1, 1), (7, 21), (9, 19), (31, 30), (12, 13), (8, 18), (27, 17), (7, 5), (24, 28), (30, 11), (6, 7), (29, 31), (23, 2), (4, 32), (6, 0), (14, 0), (1, 4), (9, 12), (19, 0), (10, 10), (29, 11), (18, 12), (29, 17), (12, 8), (31, 8), (23, 30), (24, 1), (7, 36), (27, 25), (12, 23), (23, 37), (6, 14), (25, 22), (17, 13), (30, 2), (17, 25), (12, 6), (10, 16), (4, 20), (20, 27), (7, 26), (21, 26), (25, 18), (29, 14), (11, 20), (4, 8), (16, 4), (0, 23), (21, 19), (6, 36), (31, 22), (15, 32), (15, 9), (6, 17), (16, 20), (28, 35), (29, 12), (28, 21), (23, 33), (2, 36), (25, 21), (15, 14), (0, 26), (26, 34), (29, 6), (12, 9), (10, 36), (17, 9), (4, 21), (28, 18), (11, 7), (24, 26), (14, 20), (3, 30), (2, 15), (27, 7), (21, 9), (6, 10), (14, 1), (24, 3), (4, 36), (22, 9), (20, 28), (20, 36), (10, 12), (29, 29), (12, 25), (25, 14), (9, 5), (27, 2), (24, 29), (22, 7), (17, 29), (2, 33), (2, 5), (28, 29), (13, 26), (27, 16), (28, 17), (16, 14), (2, 17), (1, 27), (19, 9), (13, 29), (26, 5), (3, 2), (16, 28), (14, 30), (10, 6), (20, 30), (8, 34), (26, 1), (8, 29), (9, 37), (21, 11), (26, 9), (8, 24), (13, 22), (15, 25), (22, 6), (9, 22), (8, 4), (19, 3), (17, 11), (28, 32), (17, 26), (24, 23), (1, 12), (17, 19), (19, 35), (31, 31), (19, 33), (29, 35), (28, 27), (26, 19), (28, 8), (15, 16), (19, 15), (26, 37), (7, 25), (5, 34), (8, 9), (26, 17), (31, 7), (9, 35), (20, 23), (1, 10), (11, 30), (31, 29), (24, 27), (12, 12), (2, 11), (2, 35), (16, 3), (27, 18), (19, 25), (26, 18), (18, 33), (8, 14), (5, 26), (12, 32), (27, 29), (22, 2), (22, 14), (27, 22), (28, 20), (23, 4), (3, 15), (6, 31), (19, 6), (2, 16), (28, 15), (17, 31), (15, 27), (16, 2), (1, 11), (16, 32), (2, 6), (21, 35), (27, 11), (19, 18), (21, 34), (11, 11), (3, 24), (27, 10), (2, 24), (28, 30), (25, 1), (8, 3), (19, 2), (18, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "828000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 30), (10, 15), (15, 27), (2, 14), (12, 20), (28, 0), (32, 4), (23, 7), (24, 11), (9, 33), (1, 20), (2, 0), (0, 1), (1, 32), (38, 30), (13, 32), (10, 4), (37, 16), (1, 26), (13, 28), (38, 24), (35, 18), (33, 0), (2, 10), (34, 18), (38, 17), (29, 12), (28, 33), (34, 19), (14, 33), (5, 31), (14, 4), (10, 22), (38, 7), (7, 24), (17, 19), (5, 33), (8, 24), (20, 28), (31, 30), (22, 30), (38, 16), (3, 16), (18, 9), (30, 31), (18, 30), (31, 10), (7, 29), (33, 3), (2, 15), (9, 11), (25, 18), (36, 30), (14, 20), (18, 17), (5, 5), (23, 32), (4, 21), (29, 21), (18, 32), (12, 11), (13, 29), (5, 21), (29, 11), (29, 29), (34, 25), (17, 13), (26, 22), (8, 29), (25, 30), (23, 3), (19, 32), (26, 31), (16, 14), (11, 3), (16, 5), (12, 5), (20, 12), (6, 17), (17, 0), (8, 0), (27, 26), (37, 7), (0, 14), (22, 20), (9, 27), (34, 20), (27, 30), (24, 28), (31, 22), (29, 25), (35, 11), (10, 27), (1, 3), (22, 1), (35, 29), (37, 21), (10, 21), (26, 14), (10, 5), (24, 6), (35, 28), (36, 16), (38, 12), (33, 20), (21, 13), (11, 31), (28, 30), (35, 17), (6, 6), (38, 3), (5, 17), (36, 24), (27, 16), (24, 20), (32, 6), (21, 21), (10, 33), (16, 20), (36, 9), (32, 25), (29, 32), (23, 12), (20, 33), (33, 7), (36, 19), (5, 27), (35, 4), (22, 2), (2, 25), (35, 6), (2, 24), (3, 9), (12, 15), (5, 26), (20, 18), (8, 23), (35, 1), (16, 25), (10, 20), (34, 31), (5, 4), (14, 32), (22, 24), (8, 20), (16, 17), (23, 10), (19, 12), (25, 11), (11, 20), (4, 10), (21, 9), (0, 6), (32, 3), (15, 10), (34, 10), (18, 1), (29, 9), (32, 0), (19, 20), (29, 22), (36, 5), (12, 2), (0, 30), (22, 11), (10, 31), (31, 15), (2, 32), (36, 15), (11, 33), (11, 22), (26, 30), (1, 17), (13, 13), (18, 13), (31, 4), (33, 1), (27, 23), (37, 30), (29, 10), (1, 12), (8, 32), (20, 14), (26, 28), (38, 31), (23, 30), (28, 24), (26, 33), (9, 21), (23, 15), (27, 14), (8, 33), (21, 30), (29, 15), (25, 23), (10, 26), (2, 11), (3, 27), (38, 18), (2, 8), (15, 3), (23, 9), (4, 18), (0, 7), (22, 12), (36, 17), (20, 9), (29, 24), (0, 17), (18, 12), (7, 4), (19, 26), (8, 19), (12, 4), (12, 3), (16, 24), (11, 14), (2, 6), (3, 25), (7, 3), (35, 26), (15, 20), (24, 7), (27, 7), (17, 28), (24, 16), (4, 28), (4, 7), (12, 14), (32, 33), (33, 31), (9, 13), (24, 17), (21, 24), (38, 20), (30, 10), (32, 1), (20, 6), (3, 28), (6, 22), (0, 20), (16, 18), (29, 30), (4, 22), (33, 14), (32, 11), (30, 20), (13, 10), (19, 7), (2, 7), (29, 31), (18, 0), (18, 28), (4, 1), (37, 25), (37, 26), (3, 14), (27, 5), (8, 8), (4, 29), (20, 17), (14, 24), (2, 5), (23, 33), (10, 17), (10, 13), (33, 28), (6, 23), (14, 23), (31, 20), (30, 5), (38, 26), (0, 13), (7, 12), (18, 14), (9, 4), (26, 11), (4, 5), (21, 1), (35, 27), (19, 9), (28, 5), (32, 22), (28, 7), (17, 2), (19, 11), (34, 11), (11, 15), (2, 23), (33, 24), (21, 11), (31, 29), (2, 28), (8, 25), (32, 10), (5, 20), (7, 7), (36, 4), (27, 28), (30, 30), (20, 4), (14, 22), (10, 9), (24, 3), (16, 6), (34, 24), (16, 10), (36, 6), (16, 9), (30, 0), (9, 0), (12, 18), (15, 29), (25, 28), (36, 13), (37, 12), (23, 0), (19, 24), (4, 26), (5, 25), (25, 6), (38, 27), (6, 31), (33, 10), (11, 23), (6, 19), (3, 17), (33, 15), (2, 31), (16, 0), (7, 13), (29, 7), (20, 13), (32, 8), (21, 29), (21, 5), (3, 1), (24, 22), (14, 12), (15, 14), (14, 8), (8, 22), (19, 6), (19, 15), (22, 29), (1, 2), (26, 21), (23, 11), (11, 28), (25, 1), (0, 31), (3, 33), (36, 8), (31, 0), (5, 22), (10, 2), (23, 27), (2, 29), (24, 31), (16, 27), (28, 26), (21, 18), (33, 23), (24, 27), (0, 26), (1, 4), (38, 23), (9, 17), (27, 10), (21, 27), (31, 24), (18, 19), (18, 2), (20, 29), (12, 10), (12, 32), (15, 16), (17, 6), (6, 3), (33, 26), (38, 1), (11, 32), (10, 18), (5, 28), (26, 25), (35, 24), (20, 26), (20, 15), (25, 16), (14, 15), (29, 3), (1, 9), (17, 33), (17, 21), (32, 19), (11, 12), (34, 27), (29, 19), (22, 14), (12, 25), (26, 23), (24, 26), (7, 30), (17, 4), (13, 4), (21, 2), (35, 21), (14, 0), (9, 15), (38, 28), (13, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "89100", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), 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), (17, 9), (7, 17), (1, 3), (3, 28), (0, 1), (16, 15), (5, 12), (18, 2), (23, 26), (5, 18), (15, 21), (12, 11), (23, 28), (19, 13), (28, 11), (21, 25), (17, 8), (28, 13), (24, 6), (25, 17), (8, 14), (13, 6), (14, 7), (13, 29), (19, 29), (5, 10), (2, 9), (28, 0), (19, 3), (9, 18), (7, 20), (12, 10), (23, 12), (20, 17), (28, 8), (25, 19), (20, 25), (29, 8), (13, 1), (3, 20), (21, 16), (4, 4), (25, 21), (24, 16), (22, 29), (15, 20), (26, 15), (5, 19), (15, 2), (12, 21), (13, 14), (28, 16), (18, 7), (14, 8), (26, 0), (20, 23), (2, 23), (26, 19), (26, 28), (28, 15), (16, 12), (6, 13), (0, 6), (23, 20), (19, 17), (27, 9), (21, 19), (9, 24), (20, 18), (29, 19), (11, 18), (10, 7), (9, 7), (24, 21), (19, 27), (4, 1), (7, 27), (8, 9), (6, 29), (0, 2), (23, 13), (1, 11), (0, 22), (16, 13), (3, 9), (10, 21), (25, 25), (29, 5), (11, 17), (5, 13), (29, 14), (1, 26), (20, 4), (17, 24), (4, 15), (18, 6), (2, 13), (25, 11), (20, 11), (24, 17), (26, 25), (0, 5), (19, 0), (28, 23), (29, 1), (12, 22), (19, 10), (28, 2), (2, 4), (16, 0), (15, 24), (5, 28), (21, 23), (11, 27), (20, 19), (3, 12), (24, 11), (28, 7), (21, 26), (10, 2), (13, 20), (0, 13), (18, 27), (6, 9), (8, 19), (9, 17), (4, 28), (4, 12), (9, 0), (21, 20), (19, 23), (14, 29), (22, 3), (12, 13), (23, 7), (4, 29), (23, 29), (20, 9), (24, 13), (15, 16), (12, 26), (14, 3), (13, 16), (1, 8), (9, 2), (16, 7), (27, 18), (19, 14), (11, 14), (25, 29), (27, 24), (24, 4), (13, 24), (23, 19), (29, 2), (5, 4), (4, 5), (13, 2), (29, 12), (10, 17), (18, 9), (11, 7), (19, 2), (6, 27), (8, 13), (22, 26), (25, 15), (9, 10), (20, 10), (19, 1), (12, 27), (11, 25), (5, 29), (1, 9), (10, 27), (23, 9), (21, 22), (23, 24), (24, 26), (3, 27), (2, 12), (2, 14), (20, 27), (9, 21), (9, 11), (12, 9), (19, 20), (18, 26), (11, 4), (18, 14), (27, 6), (21, 14), (9, 5), (13, 4), (1, 17), (16, 3), (8, 25), (10, 28), (7, 8), (17, 13), (22, 21), (1, 28), (19, 11), (13, 10), (20, 24), (29, 6), (10, 13), (2, 1), (3, 26), (23, 1), (0, 14), (28, 28), (7, 6), (10, 4), (16, 1), (22, 16), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527705", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 10), (14, 3), (22, 24), (17, 19), (5, 4), (10, 27), (11, 28), (28, 1), (17, 27), (13, 13), (17, 6), (24, 18), (2, 27), (1, 1), (22, 13), (24, 4), (7, 0), (5, 7), (30, 21), (0, 16), (15, 1), (13, 20), (24, 21), (26, 14), (18, 24), (9, 8), (17, 4), (2, 21), (30, 7), (22, 20), (16, 0), (25, 22), (11, 27), (7, 9), (22, 26), (19, 12), (25, 0), (29, 22), (22, 16), (21, 0), (30, 10), (26, 15), (0, 20), (25, 2), (18, 9), (6, 18), (25, 13), (2, 18), (14, 18), (29, 2), (13, 11), (6, 19), (14, 26), (0, 8), (7, 19), (25, 27), (26, 10), (10, 6), (14, 25), (24, 22), (24, 15), (21, 25), (25, 24), (15, 12), (13, 8), (14, 2), (12, 7), (25, 7), (13, 30), (23, 13), (27, 29), (20, 2), (29, 24), (11, 5), (3, 31), (30, 30), (19, 16), (10, 19), (23, 0), (2, 0), (11, 29), (30, 22), (10, 13), (10, 16), (2, 6), (3, 13), (1, 9), (13, 14), (24, 28), (21, 30), (14, 17), (0, 21), (29, 28), (2, 30), (0, 11), (17, 24), (2, 23), (16, 17), (26, 8), (0, 29), (21, 6), (9, 4), (16, 24), (3, 18), (11, 7), (17, 16), (29, 7), (16, 16), (14, 9), (29, 25), (11, 14), (2, 31), (23, 2), (25, 16), (26, 12), (17, 17), (3, 1), (16, 6), (8, 25), (29, 4), (24, 16), (29, 20), (21, 11), (8, 29), (13, 9), (22, 8), (5, 19), (25, 6), (20, 10), (8, 4), (24, 25), (28, 24), (5, 22), (29, 13), (5, 1), (15, 0), (20, 29), (26, 22), (6, 17), (22, 4), (27, 8), (19, 23), (27, 10), (23, 12), (21, 19), (0, 5), (23, 25), (3, 3), (12, 4), (5, 11), (11, 24), (6, 3), (18, 26), (10, 23), (20, 17), (12, 14), (0, 28), (30, 18), (21, 29), (25, 4), (10, 15), (22, 7), (24, 23), (14, 14), (21, 1), (28, 6), (30, 16), (13, 31), (29, 29), (18, 0), (8, 13), (28, 9), (4, 8), (0, 6), (6, 2), (14, 21), (1, 10), (9, 25), (10, 28), (4, 29), (6, 11), (26, 19), (7, 11), (4, 6), (10, 29), (17, 11), (23, 16), (26, 3), (6, 8), (28, 7), (5, 8), (16, 8), (9, 2), (22, 10), (22, 14), (13, 21), (25, 9), (1, 19), (5, 16), (9, 19), (26, 20), (17, 2), (6, 0), (24, 14), (22, 15), (15, 30), (20, 25), (7, 14), (18, 7), (26, 28), (22, 11), (20, 3), (28, 15), (19, 20), (30, 5), (3, 21), (1, 17), (14, 23), (27, 0), (11, 3), (10, 11), (9, 17), (20, 12), (22, 3), (27, 31), (9, 1), (30, 11), (23, 23), (18, 3), (29, 16), (22, 12), (27, 16), (12, 8), (27, 20), (26, 31), (18, 30), (8, 24), (8, 26), (25, 21), (4, 1), (8, 9), (11, 18), (23, 21), (19, 6), (7, 26), (18, 20), (14, 15), (16, 12), (12, 11), (17, 0), (27, 14), (12, 5), (12, 12), (2, 1), (29, 27), (19, 30), (3, 6), (25, 11), (22, 22), (21, 20), (28, 17), (23, 24), (13, 26), (21, 15), (14, 8), (23, 19), (10, 8), (8, 1), (4, 4), (19, 29), (7, 15), (25, 5), (27, 26), (4, 5), (27, 1), (8, 18), (5, 25), (14, 27), (5, 13), (16, 4), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "614466", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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, 27), (2, 28), (3, 30), (14, 21), (25, 19), (18, 24), (12, 12), (32, 22), (1, 19), (13, 27), (31, 4), (24, 5), (35, 22), (36, 8), (4, 30), (2, 11), (18, 9), (14, 18), (24, 29), (22, 4), (24, 8), (29, 28), (1, 6), (20, 32), (0, 32), (6, 3), (15, 25), (36, 26), (13, 9), (20, 13), (3, 31), (18, 31), (5, 1), (29, 19), (34, 11), (30, 21), (5, 20), (6, 14), (33, 22), (19, 26), (27, 21), (14, 7), (19, 32), (36, 25), (35, 4), (15, 12), (37, 9), (14, 9), (26, 31), (10, 20), (24, 6), (36, 6), (8, 9), (27, 15), (9, 12), (8, 1), (17, 18), (23, 23), (23, 30), (4, 26), (32, 2), (3, 24), (23, 9), (25, 16), (12, 32), (3, 21), (9, 6), (29, 27), (37, 17), (32, 23), (9, 5), (16, 8), (34, 18), (2, 29), (13, 28), (27, 5), (33, 2), (4, 22), (10, 31), (15, 7), (11, 22), (33, 27), (23, 25), (25, 29), (35, 5), (32, 3), (32, 10), (11, 25), (9, 26), (33, 0), (3, 32), (13, 20), (15, 2), (16, 14), (25, 14), (1, 17), (26, 12), (4, 25), (35, 28), (4, 24), (20, 24), (33, 10), (17, 9), (35, 8), (19, 2), (2, 7), (15, 31), (23, 26), (10, 21), (32, 20), (11, 13), (3, 25), (32, 24), (32, 25), (36, 16), (0, 26), (27, 13), (21, 12), (26, 30), (35, 31), (22, 29), (33, 1), (21, 11), (6, 12), (29, 4), (2, 22), (7, 18), (0, 27), (3, 20), (8, 11), (24, 24), (16, 0), (31, 32), (24, 1), (23, 32), (2, 6), (1, 0), (1, 31), (25, 13), (19, 3), (8, 31), (3, 1), (7, 19), (26, 8), (10, 25), (0, 19), (36, 29), (19, 1), (30, 19), (10, 3), (22, 32), (37, 6), (1, 13), (11, 0), (20, 17), (5, 13), (13, 17), (10, 5), (0, 2), (5, 29), (30, 25), (21, 16), (35, 20), (2, 19), (8, 14), (12, 4), (31, 28), (28, 19), (36, 31), (4, 14), (2, 14), (7, 32), (24, 21), (8, 17), (1, 16), (17, 17), (17, 30), (30, 13), (32, 14), (23, 3), (29, 9), (19, 27), (28, 13), (24, 17), (14, 12), (25, 10), (29, 21), (15, 11), (21, 30), (28, 4), (12, 13), (23, 16), (22, 31), (32, 31), (16, 22), (20, 11), (24, 2), (21, 2), (25, 17), (16, 25), (26, 25), (5, 5), (1, 24), (11, 28), (7, 2), (34, 26), (14, 30), (14, 19), (32, 7), (35, 19), (22, 6), (29, 13), (19, 30), (18, 6), (5, 8), (15, 22), (16, 29), (36, 7), (37, 13), (14, 2), (8, 0), (21, 29), (23, 29), (32, 8), (36, 21), (24, 32), (28, 1), (12, 10), (16, 31), (21, 3), (27, 22), (27, 3), (11, 17), (24, 25), (32, 28), (5, 14), (27, 1), (22, 1), (28, 15), (13, 19), (3, 4), (27, 11), (16, 9), (37, 28), (4, 0), (18, 28), (31, 12), (27, 20), (6, 4), (33, 14), (23, 21), (21, 28), (12, 11), (36, 12), (9, 15), (34, 15), (25, 32), (8, 6), (30, 5), (7, 4), (35, 25), (21, 21), (0, 8), (23, 5), (14, 25), (29, 26), (35, 13), (19, 9), (16, 17), (33, 19), (9, 17), (8, 15), (21, 26), (6, 17), (24, 31), (4, 11), (15, 30), (11, 14), (21, 13), (34, 12), (37, 30), (25, 22), (33, 4), (25, 1), (16, 20), (22, 10), (11, 9), (4, 32), (7, 23), (15, 18), (16, 4), (4, 7), (29, 5), (10, 2), (7, 6), (37, 23), (3, 13), (32, 27), (15, 21), (5, 16), (2, 12), (20, 23), (3, 17), (14, 22), (3, 26), (33, 6), (13, 18), (25, 2), (27, 16), (31, 31), (17, 20), (10, 16), (33, 29), (22, 11), (18, 18), (7, 30), (22, 26), (33, 18), (5, 9), (34, 4), (16, 2), (5, 11), (28, 29), (9, 2), (5, 32), (26, 20), (8, 23), (20, 29), (22, 21), (26, 17), (20, 1), (32, 17), (4, 9), (15, 8), (20, 22), (8, 12), (19, 25), (13, 5), (28, 28), (31, 24), (3, 22), (21, 31), (1, 28), (17, 24), (37, 4), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "527040", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), 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), (17, 10), (11, 4), (25, 33), (33, 15), (30, 0), (3, 17), (35, 12), (7, 28), (21, 17), (35, 5), (7, 7), (31, 15), (11, 20), (6, 31), (35, 27), (8, 23), (34, 9), (17, 23), (1, 3), (33, 32), (17, 20), (32, 3), (26, 7), (0, 4), (7, 29), (4, 6), (15, 27), (7, 16), (10, 11), (34, 2), (34, 20), (35, 31), (15, 25), (32, 12), (22, 26), (3, 10), (14, 3), (6, 12), (26, 28), (16, 29), (29, 10), (8, 31), (3, 2), (0, 32), (23, 12), (24, 29), (28, 26), (33, 5), (17, 1), (28, 20), (5, 16), (20, 23), (35, 23), (23, 0), (24, 1), (20, 31), (0, 20), (34, 28), (17, 11), (24, 28), (12, 28), (4, 28), (26, 24), (10, 28), (8, 9), (3, 3), (23, 29), (14, 26), (23, 6), (5, 9), (12, 17), (15, 23), (33, 19), (15, 10), (21, 33), (11, 17), (17, 0), (3, 8), (35, 21), (2, 10), (14, 29), (33, 14), (1, 11), (25, 4), (3, 26), (14, 24), (0, 7), (35, 28), (26, 21), (12, 29), (7, 11), (21, 9), (5, 1), (14, 2), (11, 0), (9, 18), (9, 20), (22, 3), (14, 27), (2, 5), (34, 32), (5, 8), (32, 1), (34, 16), (11, 14), (21, 4), (0, 9), (31, 3), (9, 6), (22, 27), (33, 28), (30, 31), (26, 10), (9, 22), (20, 10), (3, 18), (27, 10), (31, 12), (7, 15), (4, 33), (14, 8), (14, 25), (7, 24), (23, 20), (7, 10), (24, 0), (35, 14), (14, 1), (12, 7), (35, 17), (19, 0), (22, 2), (2, 17), (25, 8), (8, 4), (27, 8), (19, 18), (10, 20), (8, 20), (7, 14), (21, 26), (22, 6), (26, 30), (21, 21), (16, 28), (20, 3), (19, 26), (12, 6), (1, 5), (29, 12), (20, 2), (12, 14), (25, 32), (12, 2), (17, 9), (32, 28), (14, 6), (24, 25), (26, 22), (0, 2), (29, 13), (12, 3), (27, 1), (15, 33), (2, 16), (20, 17), (1, 23), (18, 16), (30, 30), (35, 7), (5, 25), (31, 10), (35, 29), (18, 31), (10, 24), (17, 18), (9, 26), (16, 21), (9, 27), (0, 23), (16, 15), (1, 16), (31, 17), (33, 24), (34, 19), (11, 18), (25, 16), (24, 21), (4, 20), (10, 18), (6, 9), (15, 5), (28, 9), (1, 1), (34, 18), (31, 4), (10, 22), (3, 32), (25, 11), (6, 28), (19, 27), (4, 9), (15, 28), (4, 17), (10, 25), (11, 13), (1, 21), (32, 0), (30, 23), (2, 26), (16, 18), (1, 22), (31, 9), (6, 26), (3, 19), (30, 11), (25, 21), (32, 2), (28, 31), (1, 20), (15, 29), (34, 10), (19, 1), (3, 27), (0, 8), (1, 30), (13, 7), (18, 21), (20, 33), (21, 5), (17, 16), (0, 16), (4, 18), (0, 25), (34, 4), (1, 6), (32, 16), (34, 29), (6, 15), (32, 18), (26, 33), (2, 28), (0, 24), (11, 33), (11, 7), (32, 8), (9, 11), (29, 14), (13, 4), (28, 25), (25, 1), (28, 32), (0, 26), (27, 18), (20, 1), (5, 5), (11, 2), (8, 14), (5, 15), (28, 21), (2, 11), (24, 24), (22, 13), (29, 20), (17, 5), (2, 1), (5, 17), (6, 7), (1, 18), (12, 22), (2, 31), (34, 31), (24, 16), (12, 1), (26, 19), (21, 1), (6, 32), (2, 4), (30, 32), (12, 13), (15, 30), (12, 8), (3, 25), (21, 0), (18, 2), (14, 5), (23, 5), (11, 9), (24, 30), (24, 2), (15, 32), (6, 0), (1, 26), (16, 13), (25, 18), (3, 22), (16, 24), (34, 1), (27, 9), (9, 30), (3, 20), (10, 17), (28, 22), (13, 9), (23, 15), (12, 27), (22, 20), (8, 6), (6, 21), (26, 29), (7, 4), (20, 28), (14, 13), (19, 17), (20, 25), (35, 32), (35, 11), (4, 31), (13, 20), (29, 1), (12, 26), (8, 22), (16, 10), (25, 19), (33, 18), (30, 27), (18, 20), (32, 27), (33, 30), (17, 32), (17, 28), (5, 11), (16, 4), (3, 24), (10, 26), (15, 19), (27, 21), (22, 21), (1, 12), (0, 14), (5, 0), (10, 14), (23, 23), (15, 2), (26, 26), (27, 19), (33, 27), (2, 15), (11, 27), (15, 21), (12, 33), (22, 10), (29, 5), (29, 22), (26, 11), (13, 28), (33, 10), (23, 2), (25, 7), (10, 29), (35, 6), (12, 30), (11, 25), (15, 1), (28, 11), (16, 1), (22, 16), (11, 28), (24, 9), (0, 22), (27, 0), (27, 17), (24, 4), (25, 25), (32, 14), (15, 15), (34, 17), (10, 1), (30, 33), (9, 8), (22, 11), (8, 17), (5, 30), (27, 5), (12, 11), (15, 9), (1, 7), (17, 13), (4, 32), (33, 1), (20, 18), (0, 11), (30, 16), (32, 7), (4, 0), (11, 24), (30, 12), (20, 7), (14, 14), (28, 24), (32, 21), (19, 2), (30, 15), (16, 6), (14, 30), (13, 3), (19, 23), (26, 1), (10, 3), (28, 23), (24, 20), (31, 24), (24, 12), (8, 15), (27, 3), (1, 17), (9, 1), (12, 31), (14, 33), (28, 5), (19, 31), (22, 0), (10, 31), (2, 21), (4, 8), (7, 6), (9, 29), (20, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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, 7), (0, 24), (17, 17), (3, 20), (1, 35), (6, 29), (10, 13), (25, 3), (8, 34), (21, 38), (22, 30), (6, 27), (12, 25), (27, 36), (18, 26), (7, 10), (30, 10), (22, 25), (0, 8), (15, 12), (8, 31), (19, 16), (20, 31), (24, 9), (7, 16), (23, 35), (3, 9), (8, 33), (3, 10), (1, 32), (5, 8), (22, 12), (7, 31), (17, 9), (13, 37), (13, 4), (9, 19), (11, 14), (13, 19), (11, 1), (28, 12), (5, 33), (8, 6), (4, 34), (24, 37), (22, 4), (30, 13), (18, 8), (19, 6), (1, 22), (10, 16), (11, 10), (25, 1), (26, 36), (18, 28), (16, 5), (20, 18), (5, 27), (2, 8), (3, 6), (17, 31), (13, 18), (10, 0), (26, 37), (26, 12), (21, 26), (8, 13), (12, 9), (16, 14), (8, 3), (1, 21), (6, 0), (9, 23), (3, 38), (15, 6), (8, 5), (23, 3), (14, 24), (28, 23), (24, 23), (21, 25), (26, 22), (30, 7), (18, 15), (7, 38), (18, 5), (4, 19), (12, 38), (19, 12), (7, 5), (6, 11), (17, 26), (23, 22), (23, 5), (8, 1), (19, 5), (1, 29), (10, 27), (22, 26), (6, 17), (19, 13), (23, 27), (20, 11), (15, 14), (29, 14), (20, 7), (6, 24), (13, 38), (9, 5), (2, 25), (10, 5), (13, 26), (1, 33), (11, 38), (22, 6), (24, 29), (9, 4), (11, 8), (2, 10), (26, 32), (30, 37), (19, 29), (20, 34), (10, 7), (24, 27), (1, 23), (14, 28), (9, 3), (18, 4), (5, 36), (6, 7), (10, 30), (4, 4), (28, 29), (19, 3), (30, 11), (3, 36), (5, 14), (1, 0), (25, 26), (16, 29), (17, 35), (23, 33), (13, 17), (13, 25), (13, 36), (0, 19), (3, 28), (24, 4), (3, 26), (1, 12), (23, 15), (28, 32), (13, 6), (30, 22), (12, 0), (11, 3), (5, 18), (15, 7), (23, 12), (8, 14), (8, 11), (9, 13), (0, 37), (3, 1), (1, 11), (19, 9), (0, 36), (4, 13), (14, 29), (30, 29), (19, 36), (19, 11), (28, 17), (22, 24), (18, 21), (29, 26), (13, 21), (6, 6), (1, 14), (3, 24), (22, 16), (10, 36), (22, 21), (13, 11), (3, 16), (23, 30), (6, 25), (2, 27), (3, 15), (26, 10), (2, 24), (27, 23), (11, 29), (5, 25), (15, 25), (5, 7), (23, 17), (6, 26), (20, 13), (21, 30), (3, 5), (17, 37), (10, 26), (5, 29), (10, 3), (0, 28), (16, 15), (15, 34), (29, 19), (27, 6), (18, 1), (15, 18), (15, 15), (12, 27), (3, 7), (21, 0), (30, 34), (6, 8), (24, 33), (24, 28), (17, 10), (20, 38), (2, 34), (4, 11), (19, 34), (29, 32), (24, 20), (14, 34), (22, 0), (12, 15), (18, 31), (20, 23), (25, 35), (19, 2), (29, 37), (6, 16), (9, 22), (4, 3), (12, 24), (23, 4), (16, 7), (24, 35), (17, 7), (9, 21), (16, 30), (29, 16), (11, 28), (7, 32), (13, 30), (16, 31), (5, 24), (16, 36), (30, 23), (30, 19), (11, 7), (22, 19), (17, 20), (5, 28), (0, 2), (4, 38), (20, 35), (28, 37)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117392", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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, 20), (19, 19), (10, 30), (25, 10), (2, 4), (1, 3), (23, 24), (14, 4), (17, 25), (22, 8), (26, 11), (24, 33), (20, 30), (22, 19), (24, 27), (19, 4), (28, 12), (18, 27), (27, 34), (8, 20), (10, 34), (13, 25), (11, 14), (24, 20), (27, 2), (23, 0), (18, 22), (2, 1), (14, 26), (16, 28), (28, 25), (18, 26), (4, 20), (21, 29), (28, 8), (16, 27), (10, 23), (28, 26), (22, 13), (19, 14), (14, 18), (22, 11), (21, 21), (14, 25), (15, 22), (24, 26), (12, 19), (26, 31), (10, 0), (10, 24), (11, 1), (23, 25), (20, 11), (13, 33), (15, 28), (5, 26), (24, 29), (28, 0), (8, 24), (0, 31), (4, 0), (10, 3), (29, 3), (25, 32), (24, 30), (3, 5), (11, 3), (17, 20), (21, 33), (10, 16), (16, 33), (24, 24), (16, 34), (12, 15), (3, 4), (5, 28), (28, 4), (3, 8), (9, 10), (5, 8), (4, 9), (8, 6), (26, 9), (13, 7), (29, 24), (17, 23), (8, 21), (14, 0), (16, 30), (23, 22), (29, 26), (1, 34), (0, 12), (9, 12), (21, 13), (28, 9), (23, 33), (3, 34), (2, 0), (4, 32), (8, 13), (22, 20), (16, 24), (20, 7), (15, 10), (8, 29), (13, 1), (29, 16), (8, 9), (23, 17), (4, 16), (26, 26), (21, 1), (6, 20), (13, 9), (2, 23), (0, 32), (25, 27), (19, 13), (16, 7), (26, 25), (10, 29), (0, 4), (5, 13), (11, 32), (26, 28), (17, 8), (27, 6), (7, 4), (21, 32), (0, 15), (24, 19), (11, 12), (15, 31), (15, 8), (24, 28), (18, 11), (5, 1), (11, 24), (12, 23), (21, 4), (13, 3), (27, 17), (5, 7), (15, 16), (18, 25), (6, 24), (6, 7), (19, 30), (20, 10), (0, 24), (15, 17), (18, 1), (11, 28), (22, 32), (0, 18), (12, 9), (8, 7), (11, 20), (18, 4), (21, 25), (19, 34), (25, 13), (18, 28), (20, 18), (21, 27), (2, 7), (4, 34), (15, 5), (4, 33), (27, 11), (4, 5), (13, 12), (21, 24), (4, 22), (9, 8), (14, 31), (4, 8), (12, 7), (27, 13), (8, 26), (20, 21), (8, 2), (16, 31), (19, 18), (25, 33), (7, 30), (19, 17), (14, 9), (23, 31), (26, 27), (6, 15), (12, 14), (23, 18), (24, 6), (16, 21), (3, 16), (14, 6), (4, 31), (28, 23), (18, 5), (3, 25), (16, 3), (21, 31), (29, 23), (27, 16), (7, 12), (10, 14), (25, 7), (3, 24), (5, 5), (21, 34), (28, 28), (7, 18), (10, 19), (14, 23), (19, 23), (2, 11), (13, 27), (8, 0), (23, 16), (3, 6), (17, 13), (18, 21), (12, 28), (26, 1), (9, 18), (15, 19), (12, 29), (29, 29), (10, 33), (8, 28), (20, 12), (17, 22), (5, 32), (18, 16), (22, 16), (2, 30), (18, 14), (25, 6), (2, 9), (19, 6), (4, 30), (2, 16), (16, 15), (14, 21), (21, 12), (4, 6), (6, 10), (5, 31), (7, 3), (20, 29), (25, 2), (27, 3), (29, 8), (13, 10), (0, 23), (15, 24), (29, 9), (21, 2), (22, 31), (2, 6), (29, 1), (16, 10), (0, 3), (13, 30), (9, 1), (16, 9), (23, 9), (24, 10), (26, 5), (2, 22), (13, 32), (12, 25), (3, 22), (23, 19), (0, 19), (9, 28), (11, 9), (26, 34), (28, 20), (15, 11), (9, 27), (5, 23), (25, 29), (26, 3), (10, 4), (8, 17), (29, 6), (17, 18), (7, 5), (7, 33), (24, 7), (12, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891936", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (35, 15), (14, 6), (31, 19), (8, 19), (27, 24), (1, 13), (5, 15), (17, 3), (28, 14), (10, 0), (22, 30), (5, 12), (24, 13), (30, 7), (3, 13), (28, 6), (20, 22), (21, 4), (4, 22), (27, 29), (35, 28), (24, 0), (21, 10), (21, 7), (8, 14), (20, 13), (3, 16), (10, 15), (32, 6), (32, 8), (22, 5), (26, 24), (13, 0), (0, 26), (33, 21), (35, 10), (34, 19), (1, 10), (28, 17), (1, 22), (22, 6), (29, 17), (31, 29), (11, 23), (14, 5), (14, 11), (33, 6), (4, 1), (3, 3), (28, 27), (10, 2), (1, 23), (26, 13), (33, 11), (30, 4), (18, 5), (18, 6), (12, 22), (20, 1), (24, 3), (4, 2), (26, 0), (9, 23), (0, 14), (0, 7), (21, 13), (27, 16), (5, 3), (30, 22), (27, 31), (1, 11), (23, 1), (13, 25), (31, 22), (13, 27), (1, 25), (22, 14), (1, 15), (27, 0), (30, 26), (21, 3), (34, 4), (16, 17), (0, 4), (10, 23), (24, 28), (2, 4), (27, 1), (31, 23), (23, 9), (29, 19), (6, 13), (24, 29), (27, 15), (18, 14), (35, 24), (1, 0), (19, 29), (26, 16), (14, 24), (5, 4), (28, 24), (9, 16), (20, 0), (28, 25), (32, 19), (25, 30), (19, 13), (20, 6), (10, 8), (31, 0), (15, 23), (4, 13), (10, 18), (15, 13), (13, 3), (6, 28), (13, 11), (14, 23), (35, 12), (14, 4), (15, 19), (11, 20), (14, 12), (31, 15), (34, 27), (14, 17), (32, 25), (2, 14), (35, 4), (16, 8), (3, 4), (25, 15), (16, 25), (32, 17), (29, 8), (18, 26), (18, 2), (3, 27), (34, 5), (7, 4), (5, 23), (19, 16), (25, 3), (28, 10), (8, 7), (25, 9), (4, 17), (31, 20), (13, 14), (27, 17), (17, 30), (7, 9), (22, 13), (3, 0), (22, 21), (5, 29), (7, 7), (29, 29), (16, 23), (1, 19), (22, 19), (12, 7), (15, 28), (35, 23), (31, 8), (13, 29), (26, 1), (33, 17), (19, 5), (30, 21), (35, 11), (31, 18), (33, 9), (0, 8), (15, 24), (18, 9), (4, 10), (12, 26), (17, 20), (3, 2), (17, 13), (31, 2), (27, 27), (7, 18), (26, 31), (16, 15), (0, 5), (26, 14), (4, 12), (33, 20), (31, 26), (30, 11), (8, 25), (17, 24), (15, 10), (11, 16), (11, 2), (3, 7), (30, 6), (12, 16), (2, 3), (8, 1), (20, 26), (22, 23), (32, 0), (25, 23), (1, 30), (31, 28), (26, 23), (29, 28), (14, 10), (19, 8), (12, 1), (33, 29), (2, 5), (5, 13), (31, 10), (5, 9), (11, 13), (17, 10), (24, 2), (32, 23), (21, 25), (19, 31), (23, 20), (9, 3), (16, 20), (28, 5), (12, 4), (28, 30), (9, 12), (34, 2), (34, 23), (26, 28), (17, 23), (20, 9), (11, 26), (23, 19), (0, 30), (4, 24), (12, 25), (28, 0), (18, 27), (31, 27), (25, 13), (32, 10), (13, 6), (24, 1), (4, 19), (11, 11), (30, 29), (28, 12), (10, 6), (34, 3), (10, 16), (35, 13), (23, 3), (8, 5), (12, 29), (2, 22), (29, 16), (12, 21), (27, 10), (7, 30), (8, 0), (4, 0), (16, 11), (3, 28), (32, 16), (14, 16), (8, 29), (16, 4), (27, 19), (10, 26), (30, 31), (2, 23), (12, 12), (6, 9), (9, 11), (0, 24), (16, 5), (1, 12), (14, 20), (21, 17), (5, 26), (11, 21), (1, 29), (35, 27), (0, 11), (0, 6), (22, 10), (35, 29), (31, 21), (0, 13), (22, 4), (29, 7), (16, 13), (28, 11), (25, 0), (0, 25), (13, 7), (2, 16), (10, 3), (23, 18), (33, 1), (33, 3), (12, 13), (13, 30), (2, 17), (12, 27), (20, 24), (27, 9), (20, 5), (25, 1), (8, 10), (33, 15), (14, 3), (19, 0), (34, 13), (8, 16), (29, 9), (21, 30), (1, 27), (16, 31), (32, 3), (7, 22), (18, 30), (6, 2), (6, 22), (27, 23), (8, 9), (13, 20), (1, 17), (31, 9), (32, 7), (6, 27), (19, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618240", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 5), (30, 17), (6, 9), (11, 9), (30, 22), (25, 25), (30, 11), (27, 29), (12, 23), (29, 30), (30, 21), (14, 23), (18, 27), (28, 25), (0, 31), (18, 7), (25, 16), (13, 7), (12, 8), (9, 27), (9, 17), (31, 7), (21, 7), (9, 20), (4, 18), (2, 13), (8, 26), (7, 30), (18, 24), (18, 0), (16, 9), (11, 0), (27, 1), (9, 16), (29, 10), (4, 29), (28, 4), (18, 12), (9, 23), (22, 0), (14, 13), (24, 18), (21, 6), (14, 19), (10, 23), (1, 15), (19, 18), (6, 11), (29, 2), (0, 17), (4, 23), (0, 16), (3, 8), (4, 14), (7, 18), (27, 19), (7, 10), (1, 17), (9, 13), (17, 13), (8, 17), (31, 26), (6, 6), (25, 1), (26, 5), (27, 21), (32, 23), (6, 18), (23, 13), (24, 19), (8, 5), (14, 22), (3, 20), (20, 25), (5, 23), (1, 16), (29, 9), (9, 3), (8, 12), (14, 10), (27, 17), (22, 24), (14, 6), (22, 7), (5, 11), (15, 19), (12, 0), (13, 27), (25, 6), (9, 30), (1, 29), (2, 10), (9, 7), (1, 31), (27, 8), (2, 17), (15, 28), (30, 23), (4, 24), (2, 16), (27, 0), (7, 9), (18, 3), (17, 18), (15, 8), (21, 19), (24, 23), (20, 24), (20, 3), (12, 17), (21, 10), (7, 19), (23, 11), (10, 18), (5, 24), (12, 25), (1, 6), (29, 3), (31, 20), (2, 26), (3, 13), (7, 13), (3, 10), (1, 12), (3, 31), (7, 20), (8, 20), (30, 12), (32, 18), (21, 15), (31, 31), (20, 6), (20, 26), (15, 24), (29, 21), (0, 28), (19, 28), (20, 14), (26, 16), (28, 5), (4, 30), (17, 1), (7, 14), (1, 4), (30, 19), (6, 23), (30, 1), (5, 15), (11, 1), (19, 14), (23, 24), (6, 13), (5, 14), (11, 23), (31, 19), (16, 3), (2, 7), (2, 28), (0, 12), (0, 1), (7, 25), (30, 8), (25, 30), (24, 29), (20, 2), (13, 2), (15, 10), (6, 19), (11, 13), (24, 1), (10, 2), (28, 13), (12, 10), (25, 13), (11, 31), (0, 22), (3, 25), (26, 14), (18, 20), (23, 1), (13, 26), (18, 16), (0, 3), (28, 24), (12, 16), (19, 10), (23, 28), (22, 4), (5, 19), (14, 7), (30, 5), (20, 16), (26, 0), (25, 18), (13, 17), (2, 19), (29, 22), (25, 8), (29, 14), (19, 30), (9, 11), (25, 12), (30, 29), (26, 22), (12, 21), (3, 22), (18, 10), (19, 31), (25, 31), (9, 0), (31, 16), (14, 8), (28, 23), (9, 21), (26, 27), (4, 21), (18, 22), (8, 16), (14, 21), (22, 27), (31, 6), (18, 30), (4, 12), (3, 18), (11, 16), (7, 22), (31, 3), (0, 2), (21, 30), (15, 5), (31, 18), (14, 28), (3, 4), (4, 1), (22, 1), (1, 11), (23, 20), (5, 28), (30, 4), (4, 8), (23, 7), (13, 20), (31, 25), (9, 10), (20, 17), (17, 29), (20, 13), (7, 28), (17, 4), (20, 19), (1, 10), (31, 9), (15, 7), (28, 6), (28, 19), (22, 3), (4, 7), (6, 1), (3, 17), (30, 0), (29, 1), (7, 0), (26, 4), (10, 22), (13, 19), (17, 9), (5, 6), (14, 9), (10, 17), (22, 12), (19, 8), (16, 27), (11, 2), (10, 19), (1, 1), (8, 8), (11, 11), (3, 1), (25, 17), (8, 30), (17, 17), (15, 0), (16, 1), (23, 14), (8, 7), (8, 23), (19, 27), (8, 9), (13, 8), (15, 2), (1, 22), (13, 6), (12, 30), (16, 29), (27, 23), (11, 20), (15, 13), (1, 26), (26, 18), (31, 1), (23, 29), (16, 28), (5, 31), (32, 17), (31, 28), (22, 14), (29, 27), (6, 21), (26, 15), (13, 28), (22, 2), (20, 4), (30, 15), (8, 13), (31, 23), (25, 9), (18, 11), (6, 17), (24, 30), (16, 24), (18, 19), (19, 12), (2, 4), (11, 17), (14, 16), (21, 22), (3, 14), (13, 12), (7, 1), (21, 9), (30, 2), (27, 20), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 36), (20, 8), (12, 8), (20, 38), (24, 29), (19, 2), (0, 26), (29, 4), (2, 11), (23, 26), (11, 2), (28, 36), (29, 18), (2, 9), (1, 15), (32, 19), (14, 12), (19, 20), (1, 26), (16, 17), (14, 37), (3, 20), (27, 10), (20, 19), (10, 32), (31, 18), (23, 8), (9, 3), (8, 22), (22, 13), (8, 4), (25, 23), (18, 17), (11, 29), (24, 26), (1, 5), (13, 20), (15, 37), (29, 21), (15, 24), (4, 34), (14, 34), (32, 13), (27, 9), (30, 3), (21, 6), (26, 5), (3, 32), (9, 13), (25, 17), (27, 25), (26, 36), (25, 19), (22, 3), (8, 19), (2, 35), (0, 20), (25, 5), (7, 18), (30, 2), (31, 9), (5, 29), (8, 31), (19, 25), (20, 26), (8, 33), (13, 31), (6, 30), (31, 10), (16, 33), (21, 20), (12, 36), (25, 13), (28, 32), (9, 22), (1, 12), (10, 23), (4, 5), (11, 35), (17, 31), (1, 32), (10, 34), (15, 34), (11, 7), (13, 12), (27, 26), (4, 17), (11, 8), (14, 18), (5, 22), (27, 33), (26, 6), (28, 4), (22, 30), (3, 30), (27, 1), (14, 35), (3, 5), (27, 11), (4, 12), (27, 35), (10, 37), (3, 25), (4, 29), (14, 36), (24, 25), (16, 35), (5, 10), (23, 37), (13, 0), (32, 17), (23, 9), (27, 0), (21, 13), (1, 1), (27, 19), (0, 5), (21, 26), (15, 2), (6, 15), (4, 10), (2, 13), (7, 5), (9, 12), (10, 1), (5, 20), (20, 3), (17, 36), (11, 28), (31, 2), (2, 2), (28, 18), (28, 25), (7, 9), (13, 29), (17, 9), (31, 23), (22, 17), (12, 15), (14, 20), (32, 36), (18, 15), (12, 6), (32, 10), (21, 25), (32, 26), (11, 5), (29, 23), (1, 35), (10, 31), (30, 17), (20, 32), (26, 23), (9, 10), (22, 19), (19, 19), (24, 11), (5, 3), (16, 32), (17, 14), (28, 30), (28, 12), (19, 35), (10, 6), (0, 12), (0, 19), (0, 33), (11, 11), (23, 30), (1, 21), (16, 18), (26, 32), (12, 18), (16, 10), (1, 23), (27, 36), (8, 14), (25, 29), (6, 2), (31, 6), (22, 22), (12, 5), (8, 38), (29, 6), (15, 33), (5, 25), (9, 1), (28, 3), (31, 37), (26, 7), (14, 7), (0, 23), (24, 32), (15, 4), (32, 0), (26, 13), (26, 25), (9, 23), (18, 34), (26, 15), (8, 27), (13, 4), (10, 16), (25, 31), (5, 4), (15, 3), (3, 15), (2, 33), (3, 18), (3, 36), (7, 29), (18, 37), (17, 20), (2, 10), (31, 20), (2, 34), (18, 12), (9, 29), (19, 28), (15, 38), (8, 5), (5, 27), (28, 1), (3, 7), (22, 11), (8, 28), (29, 9), (9, 19), (4, 37), (7, 8), (20, 12), (8, 26), (7, 28), (29, 22), (19, 21), (23, 6), (21, 5), (2, 28), (18, 24), (20, 14), (1, 25), (26, 10), (27, 32), (6, 14), (24, 0), (20, 21), (9, 16), (18, 4), (3, 38), (22, 24), (9, 7), (29, 11), (25, 16), (25, 7), (30, 35), (18, 13), (7, 15), (23, 5), (28, 26), (16, 28), (9, 25), (15, 32), (9, 17), (30, 8), (30, 12), (18, 14), (3, 12), (21, 22), (31, 5), (31, 13), (5, 2), (16, 38), (30, 36), (5, 18), (0, 3), (5, 8), (10, 21), (13, 2), (19, 34), (32, 31), (1, 6), (23, 24), (5, 26), (16, 5), (32, 18), (7, 37), (4, 8), (23, 33), (3, 29), (17, 12), (22, 25), (10, 33), (2, 30), (5, 36), (22, 38), (5, 24), (7, 34), (19, 6), (8, 29), (10, 11), (32, 7), (23, 17), (17, 0), (7, 35), (4, 14), (19, 5), (14, 2), (11, 14), (27, 16), (14, 22), (26, 31), (32, 21), (30, 16), (3, 23), (1, 11), (31, 31), (24, 4), (25, 18), (30, 1), (29, 29), (13, 17), (0, 4), (19, 30), (8, 20), (32, 1), (2, 23), (6, 9), (22, 37), (19, 14), (1, 36), (17, 38), (9, 31), (17, 35), (24, 7), (30, 0), (19, 8), (22, 10), (15, 0), (18, 28), (22, 23), (13, 27), (5, 31), (23, 21), (22, 20), (30, 22), (31, 22), (29, 7), (5, 5), (14, 28), (21, 35), (30, 20), (10, 30), (1, 24), (4, 24), (0, 32), (11, 30), (7, 14), (21, 11), (7, 13), (28, 15), (8, 7), (4, 11), (24, 15), (4, 2), (24, 10), (0, 11), (12, 37), (25, 38), (2, 24), (20, 18), (1, 33), (5, 11), (16, 31), (5, 6), (27, 13), (11, 37), (13, 23), (17, 11), (22, 7), (28, 33), (27, 27), (9, 21), (20, 6), (22, 2), (25, 9), (1, 10), (0, 16), (11, 1), (7, 11), (6, 0), (4, 22), (31, 32), (12, 20), (11, 10), (27, 34), (32, 23), (15, 5), (2, 31), (27, 8), (8, 35), (13, 37), (7, 7), (21, 34), (21, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), 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), (24, 21), (7, 11), (11, 32), (23, 0), (21, 6), (24, 9), (3, 28), (3, 32), (33, 18), (17, 33), (8, 20), (26, 32), (11, 33), (26, 5), (14, 1), (16, 20), (29, 20), (10, 1), (7, 24), (0, 15), (0, 1), (17, 16), (0, 31), (23, 8), (31, 11), (13, 12), (32, 31), (25, 7), (22, 23), (22, 2), (29, 7), (16, 22), (12, 27), (34, 20), (16, 30), (22, 30), (6, 2), (12, 15), (13, 4), (33, 32), (28, 9), (28, 21), (35, 31), (20, 15), (25, 0), (0, 24), (32, 9), (13, 25), (32, 23), (11, 27), (4, 13), (24, 24), (18, 24), (8, 16), (35, 24), (4, 18), (1, 27), (12, 13), (17, 9), (4, 7), (10, 2), (17, 0), (29, 27), (34, 6), (18, 11), (14, 29), (21, 22), (12, 14), (2, 8), (27, 33), (28, 16), (18, 2), (3, 4), (24, 17), (29, 31), (11, 10), (26, 6), (21, 5), (11, 5), (14, 7), (12, 5), (21, 16), (14, 18), (13, 13), (3, 21), (14, 30), (30, 2), (4, 26), (4, 2), (26, 27), (16, 4), (10, 15), (8, 32), (26, 20), (10, 13), (23, 5), (8, 14), (19, 19), (23, 3), (24, 22), (1, 33), (33, 28), (19, 5), (11, 1), (9, 18), (13, 8), (15, 17), (1, 14), (18, 28), (27, 4), (2, 22), (9, 9), (0, 29), (5, 28), (16, 8), (23, 27), (31, 9), (1, 4), (29, 28), (28, 7), (19, 2), (16, 21), (16, 1), (7, 5), (30, 20), (34, 30), (22, 26), (32, 22), (4, 19), (14, 27), (23, 32), (4, 10), (32, 15), (25, 13), (29, 32), (13, 9), (14, 32), (12, 4), (24, 28), (3, 19), (33, 5), (20, 30), (31, 29), (31, 26), (20, 24), (28, 0), (28, 13), (24, 6), (3, 18), (6, 29), (25, 30), (35, 3), (25, 17), (34, 11), (3, 16), (27, 11), (27, 13), (25, 21), (35, 0), (16, 18), (24, 16), (14, 13), (20, 17), (11, 17), (15, 3), (12, 12), (34, 9), (19, 1), (5, 13), (1, 30), (31, 19), (2, 20), (20, 7), (1, 22), (18, 16), (6, 18), (22, 28), (13, 15), (29, 13), (28, 14), (11, 4), (24, 25), (32, 5), (31, 20), (33, 14), (12, 21), (31, 13), (13, 28), (22, 21), (4, 6), (8, 5), (5, 22), (22, 3), (9, 32), (25, 24), (34, 7), (3, 7), (11, 14), (11, 3), (18, 23), (29, 17), (31, 0), (30, 24), (10, 16), (8, 9), (2, 30), (27, 24), (13, 3), (15, 2), (8, 11), (10, 25), (26, 2), (22, 0), (32, 21), (15, 24), (17, 30), (24, 32), (21, 3), (12, 19), (8, 6), (11, 25), (23, 1), (26, 15), (7, 9), (9, 20), (25, 32), (4, 9), (13, 24), (26, 8), (19, 16), (7, 30), (20, 13), (18, 5), (0, 22), (24, 7), (6, 8), (18, 3), (32, 0), (11, 13), (29, 5), (28, 12), (19, 23), (23, 22), (35, 30), (0, 32), (2, 27), (5, 2), (14, 12), (2, 3), (22, 15), (13, 21), (21, 11), (3, 5), (2, 24), (16, 16), (14, 24), (29, 23), (13, 30), (22, 22), (19, 13), (25, 4), (19, 11), (8, 26), (2, 21), (21, 25), (22, 20), (32, 26), (17, 31), (7, 15), (12, 6), (15, 11), (1, 2), (13, 10), (10, 5), (0, 17), (35, 2), (19, 12), (7, 3), (29, 30), (22, 5), (13, 23), (2, 19), (33, 31), (23, 29), (35, 4), (22, 17), (21, 23), (7, 16), (5, 4), (14, 21), (4, 22), (9, 17), (18, 32), (31, 18), (6, 28), (1, 12), (15, 28), (20, 14), (2, 14), (26, 14), (30, 29), (29, 0), (23, 9), (0, 21), (27, 27), (1, 29), (33, 27), (11, 6), (0, 3), (6, 24), (7, 23), (17, 27), (3, 24), (24, 3), (8, 10), (8, 21), (4, 24), (26, 11), (17, 32), (35, 20), (29, 29), (34, 10), (25, 31), (5, 8), (20, 31), (31, 3), (17, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320850", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), 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), (32, 10), (22, 4), (32, 32), (34, 5), (23, 4), (36, 7), (2, 30), (31, 19), (18, 25), (7, 25), (35, 4), (4, 17), (3, 7), (13, 16), (2, 16), (3, 11), (29, 18), (1, 27), (29, 5), (33, 16), (34, 21), (14, 15), (14, 33), (34, 18), (19, 8), (33, 30), (13, 20), (14, 19), (35, 27), (31, 2), (37, 7), (34, 9), (36, 9), (8, 23), (18, 6), (37, 27), (12, 7), (32, 6), (6, 6), (25, 0), (3, 34), (13, 10), (26, 11), (23, 0), (2, 18), (1, 34), (33, 28), (10, 25), (30, 24), (33, 15), (11, 8), (37, 19), (14, 5), (24, 31), (23, 29), (15, 14), (13, 7), (33, 3), (23, 28), (8, 21), (21, 26), (11, 5), (11, 20), (35, 15), (28, 3), (11, 24), (29, 8), (16, 0), (8, 24), (36, 4), (20, 19), (0, 16), (22, 1), (25, 32), (33, 10), (13, 18), (18, 17), (4, 19), (28, 14), (24, 16), (2, 25), (36, 29), (20, 17), (7, 21), (6, 7), (7, 6), (13, 15), (0, 20), (26, 24), (17, 22), (35, 12), (3, 18), (5, 22), (24, 1), (5, 28), (25, 27), (0, 27), (12, 0), (25, 24), (6, 28), (30, 9), (2, 29), (17, 12), (4, 9), (4, 30), (0, 12), (9, 11), (17, 19), (30, 8), (3, 27), (16, 21), (0, 21), (3, 28), (22, 34), (13, 26), (31, 9), (21, 9), (27, 4), (5, 19), (31, 17), (17, 6), (29, 2), (3, 30), (31, 10), (14, 13), (9, 4), (26, 9), (8, 13), (18, 3), (8, 0), (15, 20), (33, 24), (27, 3), (26, 20), (9, 21), (37, 20), (0, 9), (37, 11), (27, 22), (11, 33), (14, 7), (23, 31), (3, 9), (21, 17), (17, 26), (9, 34), (8, 26), (7, 2), (27, 23), (8, 4), (21, 21), (19, 33), (2, 20), (9, 8), (9, 12), (12, 10), (24, 3), (20, 13), (11, 18), (0, 22), (16, 22), (16, 26), (2, 21), (8, 5), (29, 19), (34, 7), (28, 1), (16, 25), (13, 23), (6, 29), (3, 10), (32, 2), (34, 0), (11, 23), (21, 2), (13, 13), (32, 29), (36, 20), (8, 17), (12, 26), (26, 21), (18, 34), (36, 31), (23, 13), (2, 32), (25, 14), (25, 10), (34, 2), (15, 4), (22, 14), (23, 6), (25, 4), (37, 21), (21, 30), (3, 17), (7, 4), (9, 5), (6, 1), (27, 26), (10, 18), (34, 27), (36, 15), (1, 16), (32, 27), (28, 2), (36, 32), (10, 24), (20, 14), (10, 31), (23, 18), (21, 7), (7, 19), (18, 19), (22, 5), (10, 26), (9, 32), (14, 17), (14, 6), (6, 22), (26, 32), (14, 27), (12, 12), (14, 34), (23, 24), (9, 17), (36, 23), (6, 12), (33, 22), (15, 33), (27, 18), (28, 15), (4, 8), (24, 11), (19, 14), (0, 4), (6, 33), (32, 31), (33, 8), (27, 16), (26, 22), (18, 0), (9, 18), (21, 6), (3, 2), (7, 17), (24, 30), (7, 10), (19, 7), (9, 29), (35, 23), (17, 13), (15, 25), (33, 11), (28, 34), (26, 17), (2, 6), (25, 16), (3, 19), (12, 30), (2, 7), (8, 20), (36, 10), (21, 13), (19, 16), (14, 23), (5, 27), (36, 34), (24, 17), (13, 6), (15, 21), (30, 3), (16, 9), (14, 26), (21, 1), (2, 19), (8, 15), (28, 6), (36, 27), (7, 33), (16, 17), (37, 24), (24, 7), (30, 15), (12, 33), (24, 15), (16, 23), (10, 29), (14, 14), (12, 2), (17, 4), (30, 29), (34, 15), (9, 25), (15, 13), (23, 27), (11, 6), (16, 27), (12, 13), (31, 28), (10, 0), (32, 21), (24, 22), (15, 34), (18, 21), (3, 15), (3, 20), (17, 24), (6, 20), (29, 12), (12, 31), (21, 24), (30, 13), (20, 23), (19, 1), (11, 3), (1, 31), (28, 16), (6, 30), (33, 9), (34, 10), (4, 4), (18, 16), (10, 32), (16, 31), (22, 8), (2, 2), (23, 2), (1, 15), (7, 26), (14, 9), (0, 23), (0, 2), (27, 10), (30, 16), (31, 24), (4, 20), (15, 0), (36, 26), (31, 14), (3, 1), (18, 27), (15, 8), (11, 30), (10, 3), (22, 28), (21, 0), (9, 15), (31, 7), (25, 25), (29, 24), (17, 8), (30, 22), (22, 18), (11, 27), (31, 0), (27, 14), (5, 21), (3, 5), (11, 13), (10, 13), (15, 31), (6, 32), (8, 31), (19, 25), (32, 24), (35, 32), (28, 29), (3, 24), (31, 34), (20, 9), (3, 26), (25, 1), (30, 30), (32, 34), (1, 17), (8, 25), (23, 23), (15, 5), (28, 7), (15, 28), (29, 17), (34, 23), (16, 19), (20, 15), (0, 33), (10, 9), (29, 16), (20, 27), (35, 30), (34, 31), (35, 24), (27, 21), (34, 16), (37, 6), (35, 18), (6, 18), (36, 13), (24, 33), (0, 11), (24, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27648", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 5), (11, 28), (9, 0), (0, 4), (13, 27), (19, 25), (3, 0), (10, 4), (26, 22), (16, 8), (8, 22), (20, 8), (18, 31), (14, 23), (28, 22), (8, 31), (2, 29), (9, 9), (18, 15), (20, 6), (31, 6), (26, 29), (19, 10), (21, 23), (21, 25), (6, 8), (3, 1), (8, 13), (0, 21), (11, 19), (3, 2), (7, 12), (28, 16), (9, 32), (20, 13), (25, 0), (18, 5), (23, 1), (26, 30), (23, 16), (15, 17), (17, 23), (30, 27), (9, 8), (22, 25), (19, 24), (24, 11), (14, 6), (15, 3), (16, 26), (3, 16), (10, 11), (2, 7), (4, 6), (32, 29), (25, 24), (32, 5), (16, 2), (16, 9), (15, 27), (29, 13), (11, 15), (6, 14), (3, 17), (7, 21), (24, 31), (32, 12), (8, 0), (20, 2), (7, 13), (28, 30), (12, 25), (32, 4), (6, 6), (15, 20), (8, 2), (25, 12), (2, 4), (18, 7), (0, 2), (24, 18), (17, 31), (14, 1), (9, 10), (13, 11), (28, 0), (27, 24), (21, 17), (13, 18), (24, 25), (5, 30), (4, 23), (1, 21), (23, 2), (0, 24), (10, 8), (7, 24), (26, 28), (10, 22), (23, 0), (15, 19), (29, 19), (21, 4), (12, 3), (27, 8), (17, 18), (15, 18), (32, 30), (13, 21), (11, 17), (26, 8), (21, 27), (24, 2), (14, 31), (30, 3), (27, 17), (27, 19), (20, 24), (8, 3), (1, 9), (5, 10), (17, 21), (10, 23), (5, 24), (0, 25), (22, 26), (27, 32), (20, 32), (17, 10), (8, 30), (28, 13), (8, 9), (17, 0), (5, 9), (19, 6), (18, 13), (11, 5), (1, 0), (6, 12), (26, 2), (18, 6), (1, 17), (2, 18), (21, 11), (7, 14), (28, 20), (10, 2), (5, 32), (18, 29), (5, 16), (16, 6), (6, 28), (32, 1), (21, 1), (24, 4), (1, 13), (17, 29), (10, 20), (21, 22), (16, 29), (14, 21), (26, 1), (1, 29), (26, 19), (11, 1), (8, 11), (26, 27), (16, 24), (3, 11), (31, 21), (20, 14), (14, 2), (0, 28), (8, 21), (7, 15), (23, 23), (28, 9), (10, 5), (27, 0), (8, 24), (20, 31), (15, 28), (13, 4), (21, 20), (10, 13), (31, 9), (12, 27), (6, 11), (19, 11), (22, 7), (1, 28), (2, 10), (18, 3), (2, 21), (19, 7), (31, 24), (29, 17), (5, 2), (12, 23), (28, 14), (6, 25), (8, 20), (29, 28), (11, 29), (32, 3), (25, 21), (4, 7), (6, 27), (18, 30), (25, 29), (22, 11), (14, 28), (8, 7), (29, 22), (4, 4), (18, 28), (5, 4), (3, 7), (24, 22), (19, 21), (10, 0), (12, 12), (12, 10), (12, 6), (27, 20), (19, 20), (13, 31), (14, 25), (16, 5), (27, 6), (15, 14), (15, 7), (30, 8), (31, 4), (14, 3), (23, 13), (15, 12), (32, 21), (20, 23), (6, 29), (7, 0), (4, 27), (1, 18), (30, 4), (8, 29), (4, 17), (17, 17), (28, 5), (3, 19), (27, 25), (28, 15), (23, 5), (30, 17), (28, 26), (32, 17), (26, 0), (30, 1), (12, 7), (5, 26), (29, 20), (1, 6), (24, 0), (25, 8), (0, 17), (14, 19), (11, 14), (13, 7), (18, 0), (17, 6), (30, 21), (24, 8), (12, 5), (2, 28), (9, 21), (19, 0), (15, 9), (5, 7), (13, 28), (14, 8), (11, 2), (31, 5), (16, 19), (9, 16), (26, 21), (30, 18), (13, 24), (8, 26), (27, 1), (4, 28), (2, 25), (29, 32), (6, 2), (30, 22), (11, 26), (0, 9), (21, 29), (4, 19), (10, 31), (8, 15), (26, 5), (8, 8), (9, 22), (28, 11), (2, 0), (10, 28), (17, 28), (17, 22), (0, 19), (30, 19), (12, 11), (11, 21), (18, 1), (3, 3), (20, 18), (6, 10), (3, 15), (24, 32), (28, 23), (17, 32), (28, 10), (7, 30), (20, 15), (23, 30), (20, 30), (27, 18), (19, 22), (5, 19), (28, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720252", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 34), (35, 13), (24, 35), (34, 10), (27, 9), (30, 9), (19, 8), (4, 23), (17, 34), (16, 25), (19, 21), (3, 33), (19, 16), (13, 16), (11, 23), (26, 20), (3, 10), (28, 9), (5, 15), (25, 26), (9, 20), (31, 27), (32, 19), (6, 10), (8, 20), (9, 15), (17, 5), (2, 21), (8, 25), (22, 22), (1, 34), (26, 6), (1, 14), (29, 17), (9, 19), (34, 23), (10, 26), (20, 10), (0, 15), (25, 30), (12, 1), (14, 27), (1, 31), (24, 9), (0, 3), (28, 30), (5, 34), (12, 18), (22, 10), (10, 2), (32, 13), (35, 12), (14, 9), (35, 7), (7, 9), (25, 0), (28, 1), (12, 28), (5, 14), (6, 12), (14, 20), (1, 20), (10, 14), (35, 19), (14, 1), (6, 16), (17, 17), (17, 29), (27, 15), (15, 11), (28, 31), (9, 21), (34, 17), (36, 26), (31, 13), (26, 31), (30, 20), (12, 5), (28, 3), (22, 8), (12, 2), (34, 26), (24, 20), (13, 18), (21, 1), (8, 0), (37, 3), (25, 2), (19, 22), (23, 19), (12, 25), (4, 9), (20, 29), (32, 28), (7, 20), (19, 4), (17, 28), (23, 20), (2, 1), (37, 19), (11, 5), (29, 34), (12, 20), (12, 13), (3, 25), (33, 1), (22, 0), (24, 7), (0, 33), (0, 5), (2, 31), (27, 25), (6, 35), (28, 20), (1, 8), (19, 11), (37, 16), (37, 10), (13, 11), (22, 13), (21, 33), (18, 24), (10, 21), (14, 17), (6, 9), (10, 7), (32, 11), (5, 24), (0, 6), (37, 2), (12, 8), (29, 1), (5, 32), (29, 22), (22, 31), (28, 4), (1, 2), (22, 9), (24, 34), (23, 12), (30, 32), (4, 28), (20, 35), (4, 14), (12, 10), (18, 22), (30, 18), (3, 18), (25, 34), (30, 5), (5, 16), (25, 23), (2, 29), (30, 15), (30, 4), (35, 34), (21, 15), (19, 9), (15, 27), (21, 28), (7, 11), (14, 22), (32, 15), (6, 18), (20, 25), (16, 12), (10, 17), (0, 4), (11, 10), (24, 22), (8, 23), (15, 25), (2, 15), (19, 3), (32, 31), (19, 17), (34, 24), (30, 1), (23, 13), (19, 30), (15, 29), (37, 6), (9, 18), (1, 4), (2, 33), (36, 10), (7, 35), (8, 33), (24, 33), (30, 21), (7, 7), (7, 22), (15, 3), (5, 23), (26, 9), (22, 30), (6, 0), (7, 26), (13, 22), (25, 29), (15, 16), (24, 12), (27, 10), (15, 2), (35, 30), (8, 17), (18, 13), (29, 14), (7, 29), (19, 2), (32, 18), (0, 22), (4, 17), (15, 30), (16, 3), (34, 4), (33, 21), (9, 10), (5, 12), (11, 31), (9, 27), (32, 7), (13, 1), (32, 29), (24, 4), (25, 10), (26, 5), (31, 21), (13, 13), (16, 18), (33, 23), (11, 12), (24, 6), (28, 25), (17, 35), (27, 14), (2, 10), (11, 7), (20, 6), (15, 15), (21, 17), (3, 20), (37, 11), (5, 28), (33, 27), (34, 1), (29, 12), (32, 2), (25, 32), (25, 6), (32, 22), (29, 8), (3, 35), (20, 13), (31, 6), (37, 20), (8, 24), (30, 35), (23, 24), (31, 31), (14, 21), (16, 2), (32, 5), (1, 18), (37, 21), (12, 0), (25, 11), (10, 34), (23, 7), (35, 11), (31, 25), (2, 5), (32, 26), (6, 4), (33, 3), (9, 3), (28, 19), (21, 10), (13, 5), (27, 11), (7, 0), (28, 32), (21, 25), (18, 3), (29, 7), (4, 19), (8, 32), (12, 26), (36, 12), (32, 33), (12, 4), (15, 24), (24, 13), (30, 29), (9, 0), (12, 12), (37, 7), (35, 25), (33, 20), (29, 29), (30, 27), (11, 20), (15, 17), (18, 2), (27, 20), (0, 34), (24, 18), (11, 1), (31, 2), (24, 15), (4, 25), (36, 7), (26, 17), (12, 22), (27, 2), (31, 5), (4, 35), (15, 23), (29, 11), (21, 11), (9, 17), (20, 22), (10, 33), (15, 9), (10, 32), (11, 13), (14, 10), (5, 33), (12, 17), (6, 33), (11, 29), (28, 16), (4, 24), (4, 22), (10, 20), (33, 16), (16, 8), (24, 28), (3, 27), (22, 5), (16, 11), (31, 11), (8, 9), (33, 34), (0, 30), (18, 35), (25, 5), (13, 27), (22, 2), (0, 14), (37, 27), (13, 20), (7, 17), (2, 22), (18, 5), (25, 9), (30, 28), (20, 9), (29, 13), (7, 4), (0, 8), (6, 8), (27, 26), (12, 34), (36, 3), (33, 5), (35, 23), (24, 19), (30, 24), (30, 0), (30, 6), (22, 25), (7, 33), (26, 24), (8, 28), (36, 22), (10, 18), (20, 32), (21, 24), (9, 7), (32, 24), (21, 35), (11, 35), (17, 19), (26, 29), (2, 23), (19, 19), (28, 7), (16, 17), (0, 13), (33, 30), (15, 20), (24, 0), (8, 6), (37, 9), (17, 11), (30, 19), (13, 23), (12, 21), (23, 32), (5, 35), (36, 14), (13, 12), (0, 19), (16, 32), (5, 1), (9, 12), (1, 26), (10, 1), (21, 32), (32, 1), (11, 17), (25, 27), (17, 14), (9, 13), (21, 14), (23, 33), (5, 7), (1, 21), (11, 26), (26, 21), (5, 0), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864000", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 23), (17, 27), (30, 33), (27, 14), (11, 26), (31, 30), (11, 34), (24, 12), (22, 36), (10, 22), (6, 23), (20, 28), (2, 9), (4, 16), (9, 11), (1, 9), (30, 11), (34, 23), (33, 1), (17, 32), (33, 32), (12, 24), (17, 25), (14, 9), (17, 13), (24, 19), (33, 16), (6, 4), (22, 11), (9, 0), (22, 32), (23, 10), (22, 0), (21, 8), (9, 9), (31, 15), (25, 17), (21, 20), (12, 33), (0, 14), (30, 23), (22, 30), (30, 36), (16, 15), (4, 28), (26, 6), (5, 18), (23, 26), (1, 3), (23, 13), (30, 6), (14, 16), (5, 24), (25, 35), (8, 8), (10, 31), (30, 12), (11, 3), (9, 6), (29, 5), (30, 32), (20, 11), (23, 1), (15, 0), (19, 16), (26, 14), (5, 33), (21, 26), (12, 36), (27, 29), (19, 12), (25, 22), (4, 20), (10, 17), (12, 30), (0, 19), (29, 1), (22, 7), (32, 33), (17, 10), (2, 5), (23, 5), (20, 17), (10, 15), (28, 10), (18, 7), (9, 13), (31, 26), (13, 36), (14, 19), (20, 31), (15, 24), (14, 8), (14, 18), (16, 18), (31, 7), (6, 19), (25, 0), (18, 3), (10, 7), (34, 12), (35, 31), (1, 1), (5, 28), (34, 34), (35, 16), (11, 6), (35, 7), (29, 17), (20, 20), (8, 31), (10, 12), (29, 21), (6, 31), (27, 34), (28, 29), (0, 36), (21, 30), (4, 24), (6, 33), (16, 2), (34, 17), (7, 15), (4, 13), (20, 5), (27, 16), (31, 23), (32, 11), (5, 26), (7, 24), (25, 13), (8, 12), (18, 2), (17, 0), (35, 27), (18, 22), (32, 23), (6, 26), (14, 15), (24, 4), (12, 11), (22, 5), (27, 33), (1, 13), (18, 17), (11, 18), (2, 34), (28, 0), (31, 19), (26, 15), (1, 26), (19, 17), (6, 10), (25, 2), (24, 3), (7, 36), (3, 26), (29, 29), (8, 21), (34, 0), (10, 16), (19, 29), (13, 8), (2, 21), (25, 11), (0, 22), (28, 35), (30, 17), (21, 27), (13, 13), (10, 24), (34, 22), (7, 3), (7, 5), (33, 25), (13, 14), (24, 17), (5, 30), (22, 27), (26, 9), (1, 11), (13, 4), (15, 6), (0, 23), (1, 10), (32, 25), (0, 13), (18, 28), (1, 16), (21, 34), (27, 10), (22, 24), (9, 14), (26, 26), (1, 31), (21, 25), (10, 32), (21, 7), (15, 17), (33, 36), (4, 3), (26, 8), (24, 6), (10, 5), (35, 11), (13, 35), (2, 15), (32, 31), (26, 4), (8, 7), (19, 10), (26, 33), (28, 26), (2, 14), (34, 9), (3, 2), (21, 4), (4, 7), (35, 1), (18, 9), (32, 15), (8, 26), (29, 16), (29, 36), (17, 23), (16, 25), (24, 1), (29, 25), (33, 8), (32, 20), (27, 30), (24, 11), (25, 16), (19, 24), (3, 18), (35, 13), (29, 30), (18, 12), (29, 11), (18, 1), (30, 27), (7, 7), (14, 4), (22, 16), (11, 5), (4, 30), (28, 12), (11, 2), (13, 16), (27, 31), (13, 19), (32, 6), (22, 35), (2, 26), (16, 33), (20, 14), (22, 4), (5, 10), (26, 10), (35, 22), (6, 30), (28, 36), (23, 9), (28, 21), (8, 20), (8, 33), (3, 10), (32, 19), (26, 19), (17, 7), (13, 10), (0, 17), (32, 36), (13, 22), (1, 29), (2, 7), (8, 19), (25, 24), (0, 27), (34, 35), (7, 4), (10, 1), (17, 30), (19, 19), (11, 36), (1, 0), (3, 13), (12, 0), (1, 7), (17, 9), (15, 21), (24, 26), (32, 32), (20, 26), (14, 36), (0, 12), (26, 21), (34, 6), (28, 7), (29, 34), (21, 28), (30, 22), (17, 28), (24, 15), (2, 4), (16, 26), (33, 12), (25, 15), (12, 26), (5, 14), (18, 21), (11, 19), (0, 30), (12, 17), (7, 18), (16, 16), (6, 24), (31, 10), (22, 1), (31, 31), (9, 31), (14, 24), (7, 2), (17, 15), (3, 12), (22, 29), (15, 25), (16, 21), (24, 9), (35, 15), (12, 31), (24, 10), (1, 22), (3, 20), (34, 26), (9, 33), (30, 0), (3, 15), (25, 1), (4, 12), (9, 19), (26, 22), (34, 30), (17, 1), (10, 27), (8, 4), (19, 33), (2, 6), (29, 13), (35, 26), (13, 23), (27, 9), (6, 36), (0, 10), (12, 5), (17, 3), (29, 27), (25, 19), (1, 27), (25, 10), (15, 2), (6, 6), (34, 7), (13, 1), (16, 31), (15, 31), (10, 26), (4, 8), (10, 25), (31, 9), (12, 27), (28, 11), (14, 31), (14, 26), (12, 14), (25, 28), (30, 1), (23, 24), (0, 11), (22, 19), (14, 30), (22, 34), (14, 5), (25, 32), (5, 32), (3, 5), (9, 26), (8, 14), (1, 28), (12, 10), (18, 30), (15, 3), (34, 3), (17, 22), (3, 22), (17, 26), (10, 33), (30, 10), (35, 29), (28, 6), (1, 30), (24, 14), (23, 34), (2, 32), (8, 32), (26, 31), (15, 36), (32, 5), (14, 25), (34, 19), (9, 32), (5, 19), (12, 23), (23, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "218442", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 13), (34, 4), (9, 5), (8, 6), (17, 32), (8, 2), (15, 17), (26, 7), (33, 35), (6, 5), (21, 34), (15, 15), (5, 16), (7, 24), (23, 12), (33, 15), (32, 8), (7, 30), (1, 2), (24, 36), (9, 17), (7, 14), (15, 1), (22, 24), (6, 26), (11, 20), (3, 28), (11, 27), (24, 11), (31, 18), (2, 34), (14, 37), (30, 3), (14, 22), (36, 11), (5, 30), (18, 30), (1, 21), (31, 16), (14, 21), (5, 15), (21, 22), (23, 26), (0, 15), (23, 37), (19, 10), (18, 37), (14, 29), (5, 37), (3, 31), (23, 9), (13, 26), (20, 22), (11, 3), (3, 6), (32, 23), (7, 28), (7, 17), (2, 27), (25, 11), (36, 9), (6, 31), (25, 32), (20, 25), (32, 31), (31, 5), (20, 30), (31, 35), (8, 3), (1, 36), (36, 4), (6, 33), (1, 9), (26, 8), (17, 34), (22, 32), (33, 26), (7, 8), (1, 32), 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(29, 12), (10, 2), (24, 20), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333040", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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), (15, 22), (18, 4), (23, 16), (24, 33), (1, 9), (20, 0), (10, 10), (8, 3), (27, 35), (1, 17), (3, 15), (22, 30), (1, 19), (1, 16), (20, 16), (21, 12), (14, 14), (21, 22), (6, 25), (25, 6), (18, 27), (2, 2), (1, 28), (10, 27), (4, 18), (14, 6), (3, 4), (7, 33), (7, 3), (5, 21), (0, 29), (11, 6), (14, 0), (10, 14), (26, 17), (22, 16), (5, 3), (25, 1), (8, 35), (22, 12), (29, 36), (28, 27), (24, 24), (4, 11), (6, 5), (7, 1), (25, 20), (12, 24), (27, 28), (10, 3), (29, 22), (13, 2), (27, 1), (12, 35), (19, 20), (18, 17), (5, 35), (0, 36), (9, 6), (9, 34), (2, 4), (1, 6), (11, 34), (22, 19), (3, 16), (16, 34), (16, 11), (8, 13), (29, 2), (5, 30), (24, 36), (12, 21), (19, 13), (18, 29), (15, 2), (4, 26), (27, 9), (22, 10), (17, 16), (20, 8), (17, 30), (9, 26), (12, 2), (22, 27), (6, 29), (27, 31), (9, 24), (17, 21), (16, 36), (25, 22), (19, 30), (16, 22), (12, 30), (1, 24), (11, 26), (21, 0), (29, 25), (4, 21), (8, 21), (20, 24), (20, 34), (3, 21), (13, 19), (14, 35), (6, 30), (29, 16), (12, 26), (11, 8), (7, 8), (12, 13), (0, 22), (11, 21), (11, 17), (30, 24), (4, 16), (2, 34), (6, 3), (30, 9), (5, 5), (15, 28), (30, 20), (20, 17), (8, 4), (22, 8), (18, 11), (22, 31), (2, 11), (30, 28), (12, 7), (14, 34), (17, 19), (15, 33), (23, 23), (26, 19), (9, 0), (15, 35), (27, 36), (26, 0), (9, 8), (27, 11), (18, 26), (26, 10), (19, 31), (5, 10), (23, 24), (23, 28), (7, 18), (2, 20), (30, 34), (25, 29), (28, 35), (27, 6), (25, 18), (9, 27), (9, 10), (18, 32), (24, 5), (15, 29), (0, 31), (19, 7), (12, 1), (1, 5), (2, 8), (19, 23), (28, 9), (20, 27), (19, 4), (19, 29), (18, 8), (14, 26), (2, 0), (10, 35), (12, 6), (5, 18), (20, 19), (13, 33), (18, 0), (6, 7), (16, 4), (29, 27), (7, 36), (13, 34), (15, 8), (15, 0), (7, 25), (25, 34), (4, 6), (6, 1), (8, 20), (21, 26), (1, 1), (24, 19), (2, 3), (4, 1), (3, 34), (22, 15), (9, 5), (18, 3), (17, 29), (23, 31), (19, 0), (19, 17), (27, 34), (26, 13), (21, 5), (0, 30), (24, 1), (15, 10), (30, 3), (0, 10), (16, 30), (7, 31), (17, 15), (14, 36), (28, 19), (2, 24), (23, 36), (23, 27), (15, 26), (7, 29), (17, 3), (22, 0), (8, 5), (5, 28), (20, 3), (3, 35), (3, 10), (17, 9), (11, 35), (12, 15), (6, 12), (7, 32), (13, 21), (18, 21), (7, 13), (21, 18), (13, 27), (25, 28), (19, 9), (15, 5), (22, 32), (20, 11), (26, 6), (24, 35), (24, 13), (22, 21), (2, 18), (17, 12), (29, 30), (14, 11), (5, 13), (2, 31), (22, 25), (13, 31), (21, 14), (4, 15), (5, 2), (20, 10), (10, 25), (28, 29), (14, 21), (26, 11), (26, 7), (20, 35), (26, 18), (8, 14), (16, 25), (16, 0), (17, 18), (1, 10), (17, 5), (0, 13), (4, 29), (7, 14), (13, 18), (9, 1), (27, 24), (0, 32), (21, 27), (13, 24), (17, 28), (13, 28), (24, 8), (14, 16), (25, 24), (5, 4), (28, 2), (22, 5), (21, 21), (11, 15), (20, 14), (23, 32), (20, 36), (7, 10), (1, 21), (3, 12), (27, 0), (25, 14), (12, 29), (19, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931500", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 2), (0, 16), (5, 12), (0, 12), (26, 22), (3, 29), (15, 30), (21, 23), (5, 9), (12, 19), (19, 3), (8, 21), (13, 9), (28, 28), (1, 13), (24, 6), (16, 27), (4, 12), (29, 28), (28, 9), (20, 6), (18, 6), (12, 3), (27, 27), (0, 9), (14, 2), (4, 4), (0, 5), (25, 0), (28, 27), (4, 5), (13, 15), (29, 22), (22, 2), (4, 14), (28, 13), (7, 26), (5, 15), (4, 18), (22, 23), (1, 14), (23, 11), (12, 13), (9, 5), (10, 28), (14, 26), (8, 10), (9, 25), (15, 14), (21, 18), (28, 20), (22, 29), (7, 29), (21, 10), (12, 2), (9, 4), (3, 9), (11, 27), (19, 17), (27, 5), (2, 12), (27, 7), (24, 8), (25, 17), (8, 20), (5, 3), (1, 10), (0, 14), (4, 22), (16, 22), (2, 26), (15, 2), (12, 28), (21, 31), (23, 24), (16, 26), (15, 18), (13, 8), (19, 8), (2, 1), (15, 0), (3, 15), (29, 1), (17, 18), (10, 17), (6, 2), (7, 18), (12, 0), (1, 31), (20, 31), (28, 4), (18, 2), (27, 0), (8, 13), (27, 1), (26, 18), (25, 19), (29, 3), (19, 27), (26, 21), (12, 21), (24, 14), (4, 2), (15, 12), (22, 19), (24, 19), (24, 16), (23, 14), (15, 19), (5, 0), (7, 2), (12, 24), (26, 27), (27, 6), (0, 23), (24, 18), (20, 9), (19, 12), (6, 7), (4, 19), (23, 26), (12, 4), (28, 30), (29, 9), (12, 16), (16, 7), (26, 9), (27, 14), (6, 15), (4, 11), (1, 23), (21, 16), (5, 18), (23, 13), (5, 25), (19, 15), (29, 17), (6, 5), (17, 6), (5, 24), (17, 17), (25, 23), (17, 15), (14, 13), (1, 29), (14, 30), (6, 6), (6, 3), (11, 1), (6, 27), (7, 8), (10, 26), (5, 16), (12, 9), (4, 8), (23, 23), (20, 13), (21, 1), (3, 28), (2, 0), (4, 15), (11, 20), (1, 1), (15, 27), (22, 17), (4, 24), (1, 0), (3, 22), (23, 1), (29, 13), (10, 8), (22, 6), (18, 4), (21, 20), (14, 29), (27, 3), (6, 22), (28, 1), (27, 23), (5, 21), (7, 9), (23, 18), (7, 10), (24, 5), (15, 31), (8, 17), (29, 23), (23, 29), (19, 19), (17, 10), (19, 10), (18, 3), (14, 27), (15, 11), (17, 2), (28, 24), (1, 17), (16, 21), (20, 2), (15, 16), (25, 7), (18, 26), (15, 28), (11, 21), (24, 31), (20, 4), (25, 12), (0, 18), (11, 11), (27, 22), (5, 17), (29, 12), (15, 22), (24, 2), (8, 31), (25, 30), (22, 4), (12, 11), (17, 0), (1, 3), (17, 20), (18, 13), (21, 11), (9, 30), (12, 27), (24, 29), (0, 3), (9, 1), (20, 18), (6, 29), (7, 7), (14, 4), (20, 23), (13, 18), (28, 12), (26, 31), (23, 16), (12, 23), (12, 5), (3, 4), (11, 7), (4, 31), (25, 5), (15, 4), (19, 26), (17, 13), (25, 2), (2, 6), (27, 16), (16, 19), (23, 9), (5, 6), (14, 19), (9, 27), (19, 11), (20, 26), (9, 22), (27, 20), (27, 4), (26, 17), (6, 24), (23, 19), (18, 27), (4, 13), (18, 16), (23, 7), (15, 24), (6, 26), (13, 31), (23, 31), (16, 13), (14, 15), (16, 30), (24, 23), (10, 16), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "634368", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), 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), (21, 28), (30, 24), (3, 30), (16, 2), (5, 17), (5, 11), (27, 11), (0, 18), (24, 32), (37, 4), (28, 28), (30, 2), (32, 21), (1, 10), (23, 1), (13, 4), (27, 27), (11, 11), (33, 23), (17, 16), (30, 27), (5, 15), (20, 11), (0, 11), (23, 2), (6, 5), (1, 6), (30, 9), (38, 5), (3, 6), (7, 1), (35, 6), (1, 5), (17, 11), (24, 0), (6, 27), (16, 6), (3, 29), (14, 4), (11, 9), (23, 8), (11, 4), (14, 6), (6, 18), (19, 4), (17, 3), (23, 13), (19, 31), (16, 33), (2, 25), (1, 25), (7, 7), (25, 21), (30, 23), (34, 12), (32, 17), (36, 19), (1, 4), (7, 25), (5, 4), (2, 1), (23, 22), (0, 8), (15, 6), (17, 7), (18, 15), (17, 9), (6, 19), (38, 22), (27, 23), (20, 2), (14, 13), (34, 1), (13, 18), (23, 29), (26, 31), (12, 23), (25, 12), (4, 30), (24, 12), (34, 23), (37, 5), (5, 26), (27, 16), (30, 30), (9, 3), (35, 18), (25, 25), (5, 18), (29, 5), (31, 25), (29, 26), (5, 27), (1, 1), (31, 8), (16, 15), (31, 17), (0, 6), (34, 8), (29, 20), (26, 1), (15, 15), (27, 12), (28, 33), (23, 27), (36, 23), (15, 9), (25, 14), (11, 22), (36, 33), (9, 16), (13, 10), (16, 24), (31, 18), (35, 11), (25, 32), (2, 21), (19, 17), (13, 33), (0, 33), (33, 11), (25, 24), (36, 6), (10, 19), (9, 24), (30, 10), (27, 5), (25, 0), (8, 20), (13, 22), (31, 32), (22, 18), (9, 27), (14, 12), (5, 28), (19, 9), (15, 10), (24, 10), (19, 22), (12, 3), (18, 25), (37, 22), (17, 31), (24, 8), (19, 26), (31, 19), (15, 31), (1, 14), (29, 14), (36, 22), (22, 29), (28, 15), (32, 10), (38, 17), (21, 27), (27, 19), (1, 21), (1, 24), (2, 18), (11, 16), (38, 28), (31, 15), (34, 18), (22, 26), (30, 4), (16, 32), (0, 7), (8, 19), (33, 33), (25, 16), (8, 15), (31, 9), (7, 2), (9, 23), (38, 19), (16, 10), (35, 20), (30, 22), (30, 20), (33, 30), (6, 22), (30, 13), (20, 28), (7, 8), (10, 11), (27, 10), (35, 19), (13, 17), (35, 17), (17, 24), (34, 17), (9, 7), (2, 7), (37, 32), (7, 13), (14, 2), (26, 30), (38, 12), (26, 32), (31, 31), (33, 18), (19, 11), (30, 1), (2, 4), (11, 13), (24, 3), (28, 27), (4, 20), (10, 7), (32, 31), (16, 19), (37, 31), (15, 17), (5, 13), (9, 12), (21, 19), (22, 21), (26, 6), (22, 4), (20, 3), (32, 8), (15, 1), (18, 2), (26, 17), (20, 7), (20, 27), (18, 22), (36, 4), (7, 23), (34, 16), (26, 23), (29, 2), (28, 3), (10, 13), (21, 9), (0, 29), (28, 9), (15, 24), (21, 17), (32, 12), (2, 28), (21, 13), (24, 21), (8, 32), (2, 3), (5, 5), (33, 20), (12, 26), (1, 23), (21, 7), (14, 11), (27, 33), (27, 14), (32, 13), (24, 7), (20, 15), (12, 29), (18, 1), (25, 3), (6, 17), (29, 9), (38, 3), (9, 21), (8, 13), (10, 16), (17, 13), (16, 22), (38, 20), (0, 1), (29, 8), (0, 25), (32, 1), (0, 17), (12, 11), (2, 2), (31, 14), (18, 32), (2, 14), (3, 10), (18, 3), (34, 21), (27, 2), (25, 29), (17, 1), (12, 1), (14, 21), (0, 22), (16, 0), (22, 23), (25, 27), (38, 18), (12, 15), (35, 26), (6, 6), (6, 33), (33, 29), (3, 33), (7, 12), (27, 1), (7, 5), (21, 25), (15, 13), (2, 11), (6, 25), (36, 30), (38, 21), (36, 20), (23, 21), (35, 14), (24, 23), (26, 24), (23, 24), (7, 30), (1, 28), (0, 24), (33, 14), (22, 30), (12, 5), (29, 11), (32, 6), (37, 28), (23, 17), (0, 26), (3, 3), (3, 18), (21, 22), (1, 31), (6, 26), (28, 12), (19, 5), (5, 9), (12, 28), (28, 2), (35, 7), (23, 28), (27, 31), (32, 32), (9, 26), (34, 29), (37, 7), (11, 21), (19, 13), (20, 9), (5, 6), (8, 2), (24, 14), (36, 11), (31, 33), (29, 0), (13, 16), (12, 31), (28, 25), (23, 32), (23, 16), (21, 5), (13, 13), (4, 17), (27, 0), (8, 31), (21, 32), (17, 33), (2, 17), (12, 32), (14, 24), (31, 11), (23, 25), (35, 8), (1, 12), (9, 29), (23, 15), (27, 25), (35, 3), (17, 8), (7, 26), (5, 29), (38, 4), (14, 8), (2, 9), (3, 19), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303120", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (10, 11), (3, 9), (0, 21), (9, 23), (7, 27), (6, 29), (29, 0), (21, 15), (0, 3), (31, 27), (14, 27), (8, 3), (34, 2), (17, 8), (13, 7), (16, 22), (4, 24), (13, 24), (24, 28), (12, 9), (34, 6), (8, 28), (18, 24), (33, 17), (26, 19), (19, 30), (25, 28), (36, 22), (14, 28), (21, 9), (23, 28), (14, 13), (22, 18), (30, 27), (26, 7), (28, 0), (30, 29), (14, 4), (14, 26), (9, 11), (4, 26), (27, 1), (17, 19), (34, 21), (32, 1), (18, 28), (27, 23), (3, 8), (9, 7), (31, 20), (23, 14), (16, 20), (4, 7), (10, 2), (8, 9), (2, 13), (35, 10), (20, 4), (20, 5), (36, 5), (23, 6), (23, 26), (19, 6), (36, 2), (29, 31), (33, 21), (33, 30), (31, 6), (36, 8), (22, 11), (34, 13), (32, 12), (10, 29), (36, 20), (14, 15), (19, 29), (18, 26), (26, 31), (20, 17), (2, 6), (30, 16), (11, 29), (2, 27), (34, 20), (8, 0), (14, 17), (3, 2), (31, 15), (21, 31), (33, 1), (35, 15), (13, 6), (8, 10), (2, 3), (17, 17), (18, 8), (9, 24), (16, 11), (10, 19), (16, 4), (19, 15), (20, 13), (35, 2), (1, 20), (22, 20), (0, 13), (20, 31), (21, 29), (16, 14), (5, 30), (11, 2), (3, 20), (19, 3), (26, 4), (25, 30), (0, 8), (6, 25), (0, 27), (35, 9), (30, 30), (8, 4), (24, 14), (33, 26), (25, 1), (24, 29), (9, 26), (29, 25), (4, 29), (26, 13), (20, 29), (35, 25), (22, 12), (1, 1), (35, 21), (3, 27), (21, 20), (4, 1), (23, 27), (12, 4), (13, 21), (15, 10), (2, 23), (18, 4), (10, 17), (20, 22), (31, 28), (21, 30), (23, 25), (8, 8), (17, 11), (11, 11), (16, 18), (10, 27), (14, 19), (22, 9), (9, 25), (32, 15), (34, 30), (1, 7), (18, 31), (2, 25), (29, 20), (5, 25), (25, 16), (32, 7), (23, 31), (27, 26), (11, 19), (25, 11), (4, 2), (26, 29), (27, 8), (17, 14), (25, 7), (26, 16), (30, 8), (14, 29), (15, 3), (36, 25), (7, 8), (27, 16), (14, 8), (15, 30), (4, 4), (26, 10), (0, 9), (29, 17), (12, 27), (34, 18), (9, 17), (21, 14), (4, 18), (21, 21), (16, 5), (21, 1), (27, 11), (15, 22), (2, 28), (1, 24), (35, 22), (32, 18), (9, 31), (19, 11), (5, 1), (25, 4), (27, 5), (0, 1), (32, 8), (36, 28), (10, 21), (25, 9), (5, 13), (12, 23), (19, 22), (6, 2), (20, 27), (18, 22), (18, 17), (13, 31), (13, 16), (30, 9), (27, 20), (22, 22), (29, 18), (21, 5), (22, 23), (32, 14), (0, 7), (4, 23), (31, 3), (3, 5), (34, 9), (0, 14), (4, 20), (31, 7), (11, 0), (13, 17), (11, 4), (0, 18), (11, 9), (25, 31), (30, 19), (21, 8), (14, 2), (30, 24), (5, 3), (18, 15), (36, 30), (34, 14), (28, 26), (10, 15), (33, 12), (4, 15), (11, 5), (22, 5), (25, 3), (32, 21), (2, 22), (23, 1), (33, 15), (12, 6), (20, 15), (14, 16), (6, 11), (18, 23), (13, 4), (27, 14), (12, 19), (23, 21), (6, 15), (15, 26), (34, 1), (10, 3), (19, 18), (6, 23), (8, 25), (23, 29), (16, 15), (28, 4), (0, 10), (22, 25), (6, 3), (35, 1), (11, 15), (19, 20), (9, 16), (17, 12), (33, 13), (19, 25), (12, 2), (19, 0), (30, 15), (4, 19), (28, 6), (33, 3), (28, 31), (28, 3), (17, 0), (0, 30), (22, 1), (34, 22), (7, 28), (36, 27), (0, 16), (5, 9), (26, 0), (7, 7), (4, 21), (11, 22), (36, 4), (3, 30), (7, 21), (2, 17), (27, 31), (2, 24), (14, 25), (24, 23), (23, 17), (36, 23), (26, 22), (15, 11), (32, 26), (3, 12), (33, 18), (36, 7), (34, 0), (2, 1), (31, 2), (30, 12), (23, 4), (1, 25), (5, 26), (9, 10), (23, 24), (6, 31), (23, 8), (19, 23), (2, 7), (8, 5), (12, 13), (32, 4), (16, 23), (9, 27), (29, 13), (3, 29), (18, 5), (6, 1), (5, 2), (21, 0), (5, 22), (7, 5), (21, 10), (14, 14), (32, 30), (31, 26), (8, 26), (5, 17), (27, 6), (19, 19), (11, 17), (29, 3), (14, 20), (8, 1), (31, 25), (29, 24), (1, 6), (15, 21), (8, 31), (18, 25), (11, 27), (19, 10), (5, 28), (30, 23), (35, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514134", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (27, 27), (7, 18), (33, 1), (24, 17), (15, 25), (17, 29), (2, 32), (11, 34), (7, 5), (26, 28), (1, 3), (27, 6), (25, 16), (25, 15), (8, 21), (4, 2), (1, 7), (11, 31), (5, 8), (17, 3), (12, 26), (27, 5), (11, 33), (10, 12), (25, 10), (24, 33), (7, 12), (15, 32), (12, 24), (23, 4), (18, 12), (0, 24), (33, 16), (0, 21), (0, 13), (8, 20), (19, 30), (16, 14), (19, 25), (14, 11), (15, 3), (1, 18), (32, 33), (25, 14), (21, 20), (4, 29), (3, 0), (13, 18), (7, 15), (27, 16), (8, 18), (16, 13), (20, 14), (2, 26), (18, 31), (30, 0), (22, 4), (25, 33), (20, 22), (0, 1), (30, 30), (32, 8), (10, 24), (24, 4), (28, 13), (9, 25), (2, 27), (30, 17), (11, 13), (25, 12), (22, 7), (17, 11), (31, 8), (21, 22), (11, 8), (19, 32), (17, 7), (16, 0), (20, 19), (33, 23), (23, 2), (30, 8), (7, 31), (4, 18), (4, 31), (16, 31), (11, 0), (9, 29), (17, 14), (18, 23), (18, 18), (30, 27), (22, 16), (26, 29), (9, 28), (27, 20), (23, 25), (27, 32), (33, 14), (26, 19), (7, 22), (8, 0), (21, 10), (29, 25), (15, 33), (3, 34), (23, 10), (24, 25), (7, 17), (25, 13), (32, 7), (18, 13), (3, 24), (19, 12), (21, 29), (33, 10), (24, 32), (24, 3), (23, 19), (19, 0), (14, 34), (9, 0), (27, 30), (17, 22), (29, 12), (14, 22), (4, 12), (15, 23), (7, 9), (30, 11), (7, 6), (32, 24), (25, 17), (17, 30), (5, 11), (12, 2), (32, 4), (27, 2), (24, 28), (31, 18), (25, 18), (4, 16), (13, 15), (24, 12), (10, 16), (32, 21), (30, 26), (16, 20), (0, 31), (30, 28), (6, 17), (0, 18), (3, 10), (28, 34), (22, 34), (3, 5), (10, 17), (0, 14), (28, 31), (9, 34), (10, 21), (22, 20), (33, 11), (3, 12), (14, 30), (23, 30), (16, 9), (19, 31), (33, 18), (25, 32), (3, 9), (33, 12), (31, 17), (17, 13), (1, 16), (23, 31), (6, 13), (15, 15), (1, 15), (5, 1), (1, 31), (22, 21), (21, 8), (16, 34), (14, 26), (13, 29), (28, 20), (2, 14), (31, 6), (13, 22), (0, 32), (16, 1), (9, 4), (17, 15), (5, 9), (32, 29), (7, 28), (31, 13), (5, 19), (26, 20), (22, 12), (5, 18), (29, 20), (8, 2), (27, 9), (2, 10), (7, 21), (8, 32), (12, 9), (27, 34), (12, 27), (15, 9), (15, 34), (11, 20), (1, 23), (25, 4), (2, 12), (8, 27), (17, 8), (20, 5), (6, 20), (15, 5), (15, 31), (32, 30), (2, 21), (33, 22), (24, 1), (32, 0), (21, 28), (0, 9), (11, 1), (10, 33), (26, 30), (17, 33), (2, 19), (15, 2), (10, 6), (11, 28), (16, 15), (18, 34), (33, 27), (9, 33), (5, 17), (22, 13), (21, 25), (33, 25), (10, 23), (13, 5), (16, 18), (0, 25), (3, 23), (15, 22), (33, 28), (5, 20), (22, 25), (27, 29), (25, 7), (7, 4), (5, 34), (15, 24), (12, 18), (5, 0), (26, 21), (13, 2), (25, 28), (1, 29), (28, 23), (4, 19), (14, 9), (33, 24), (31, 20), (4, 0), (23, 13), (13, 26), (14, 5), (25, 0), (33, 4), (21, 17), (13, 8), (15, 6), (8, 17), (32, 10), (3, 7), (30, 2), (2, 1), (24, 31), (32, 2), (20, 21), (30, 16), (14, 23), (15, 27), (28, 1), (1, 6), (16, 5), (12, 16), (31, 7), (15, 7), (2, 18), (1, 13), (13, 28), (20, 0), (14, 3), (22, 9), (30, 10), (19, 7), (26, 27), (27, 28), (2, 7), (18, 8), (10, 5), (16, 26), (15, 29), (23, 7), (23, 8), (1, 8), (10, 19), (15, 26), (24, 10), (31, 22), (10, 8), (24, 0), (23, 21), (30, 5), (19, 14), (32, 5), (21, 13), (26, 26), (9, 17), (5, 10), (5, 30), (18, 2), (29, 9), (3, 32), (28, 15), (28, 32), (10, 32), (0, 2), (24, 6), (10, 15), (0, 12), (2, 31), (33, 6), (8, 8), (6, 14), (6, 8), (21, 6), (21, 4), (8, 29), (31, 31), (29, 16), (24, 26), (18, 24), (3, 15), (11, 14), (17, 34), (23, 3), (27, 21), (5, 16), (9, 6), (23, 18), (17, 2), (26, 16), (29, 3), (9, 15), (26, 13), (13, 3), (12, 30), (11, 32), (4, 7), (26, 23), (19, 29), (0, 30), (11, 15), (32, 16), (19, 1), (15, 0), (6, 34), (0, 10), (27, 23), (8, 31), (21, 21), (18, 9), (6, 31), (23, 12), (8, 19), (19, 17), (14, 28), (11, 27), (29, 27), (14, 29), (26, 6), (7, 23), (32, 6), (26, 11), (4, 6), (7, 32), (33, 5), (30, 33), (12, 8), (16, 29), (0, 7), (7, 19), (12, 23), (13, 1), (1, 19), (1, 5), (27, 12), (5, 23), (5, 7), (7, 25), (29, 0), (27, 3), (19, 26), (9, 13), (26, 31), (14, 10), (1, 25), (11, 26), (3, 4), (9, 14), (33, 2), (9, 16), (28, 29), (6, 15), (24, 21), (31, 15), (32, 17), (2, 30), (19, 16), (21, 2), (18, 32), (8, 28), (2, 6), (16, 8), (22, 30), (31, 1), (13, 13), (22, 6), (24, 18), (22, 32), (17, 26), (0, 27), (7, 14), (4, 13), (4, 4), (14, 24), (15, 17), (23, 26), (33, 33), (7, 11), (9, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980490", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (30, 10), (13, 2), (25, 22), (21, 17), (0, 17), (13, 13), (28, 14), (10, 28), (16, 21), (26, 27), (5, 7), (18, 29), (23, 16), (21, 25), (19, 11), (23, 21), (11, 29), (13, 23), (23, 20), (5, 1), (25, 25), (9, 25), (20, 14), (12, 28), (7, 16), (19, 3), (27, 30), (3, 14), (14, 30), (30, 29), (1, 27), (2, 28), (0, 9), (24, 12), (30, 20), (26, 21), (28, 4), (21, 15), (16, 13), (16, 7), (19, 5), (13, 5), (30, 4), (16, 30), (6, 5), (16, 14), (29, 16), (11, 9), (14, 16), (21, 0), (27, 22), (11, 0), (24, 0), (16, 25), (0, 12), (22, 26), (5, 29), (7, 27), (23, 1), (7, 9), (6, 13), (17, 8), (8, 27), (24, 28), (14, 22), (15, 25), (26, 28), (20, 23), (11, 28), (4, 28), (21, 22), (29, 11), (23, 29), (29, 5), (24, 7), (17, 25), (14, 4), (23, 30), (28, 8), (29, 12), (6, 29), (28, 17), (19, 30), (18, 19), (16, 8), (14, 10), (5, 14), (29, 8), (28, 6), (25, 10), (3, 13), (11, 30), (13, 11), (1, 21), (12, 21), (14, 25), (1, 22), (14, 24), (0, 7), (11, 3), (14, 12), (11, 5), (24, 21), (5, 12), (17, 9), (18, 13), (15, 13), (5, 11), (23, 8), (23, 12), (18, 22), (15, 8), (4, 18), (12, 29), (26, 29), (9, 26), (14, 26), (12, 27), (11, 17), (1, 8), (2, 12), (1, 28), (18, 3), (29, 19), (4, 23), (1, 2), (21, 18), (29, 15), (17, 4), (17, 15), (3, 19), (17, 27), (17, 12), (13, 19), (26, 26), (9, 1), (0, 27), (3, 16), (24, 3), (1, 0), (21, 20), (29, 22), (30, 6), (13, 12), (14, 11), (30, 3), (14, 0), (19, 15), (11, 6), (2, 30), (2, 11), (29, 6), (7, 10), (5, 5), (26, 3), (11, 2), (8, 9), (5, 4), (4, 15), (27, 12), (19, 20), (10, 8), (10, 20), (0, 10), (8, 1), (20, 8), (4, 13), (21, 10), (9, 7), (25, 6), (8, 6), (7, 22), (16, 26), (17, 28), (10, 21), (24, 20), (1, 26), (4, 5), (26, 12), (24, 26), (13, 10), (1, 18), (13, 7), (5, 6), (8, 17), (15, 2), (4, 8), (6, 22), (8, 5), (29, 2), (9, 14), (27, 15), (17, 5), (1, 4), (26, 1), (14, 7), (29, 0), (16, 17), (9, 16), (25, 29), (20, 22), (26, 11), (11, 1), (20, 1), (14, 18), (10, 24), (14, 5), (13, 24), (6, 6), (27, 18), (17, 24), (4, 21), (28, 20), (19, 0), (1, 19), (15, 17), (30, 18), (25, 30), (18, 6), (30, 19), (2, 5), (8, 30), (2, 9), (13, 16), (13, 6), (23, 13), (4, 1), (13, 3), (7, 28), (25, 15), (21, 19), (27, 7), (18, 10), (0, 16), (7, 6), (8, 4), (28, 16), (28, 12), (18, 9), (22, 14), (4, 26), (3, 22), (10, 5), (22, 12), (2, 15), (19, 25), (12, 23), (22, 24), (29, 7), (28, 27), (26, 15), (12, 24), (25, 21), (23, 11), (30, 25), (30, 7), (2, 24), (17, 30), (15, 19), (4, 16), (12, 2), (7, 12), (7, 8), (20, 9), (17, 20), (7, 17), (13, 27), (22, 5), (12, 12), (10, 25), (30, 2), (0, 5), (16, 5), (18, 14), (26, 22), (2, 7), (18, 21), (7, 14), (6, 14), (29, 27), (7, 18), (0, 25), (19, 18), (27, 24), (3, 12), (15, 27), (15, 30), (26, 9), (23, 14), (15, 24), (20, 10), (30, 27), (10, 26), (11, 4), (8, 18), (17, 21), (12, 26), (15, 9), (13, 0), (25, 19), (8, 23), (25, 9), (26, 8), (24, 19), (21, 7), (1, 24), (3, 15), (15, 0), (2, 14), (24, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "203200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 1), (0, 22), (1, 13), (25, 15), (27, 35), (32, 11), (27, 4), (0, 30), (4, 26), (29, 10), (32, 3), (24, 36), (30, 22), (27, 19), (11, 0), (16, 36), (8, 25), (17, 24), (2, 23), (29, 1), (23, 3), (8, 6), (16, 30), (17, 4), (4, 19), (17, 7), (28, 22), (32, 2), (16, 27), (1, 6), (20, 16), (11, 1), (20, 30), (27, 6), (17, 6), (24, 3), (22, 18), (22, 5), (12, 24), (10, 33), (2, 34), (22, 31), (5, 10), (12, 29), (31, 7), (12, 30), (5, 12), (1, 9), (9, 22), (0, 31), (4, 24), (26, 7), (6, 24), (22, 19), (26, 17), (18, 3), (32, 15), (0, 14), (29, 4), (8, 16), (24, 20), (2, 20), (26, 8), (26, 36), (6, 5), (7, 25), (24, 29), (17, 17), (12, 10), (31, 12), (32, 23), (26, 10), (13, 16), (16, 31), (9, 16), (28, 31), (28, 32), (27, 32), (9, 26), (18, 14), (24, 32), (24, 10), (25, 37), (12, 32), (11, 22), (5, 4), (21, 17), (3, 29), (22, 8), (15, 19), (15, 30), (21, 18), (19, 19), (4, 16), (8, 21), (31, 26), (27, 9), (17, 13), (29, 35), (17, 33), (27, 22), (5, 36), (16, 18), (29, 14), (16, 23), (30, 2), (24, 25), (21, 33), (26, 16), (27, 3), (7, 14), (25, 28), (19, 9), (0, 8), (14, 12), (21, 30), (27, 15), (6, 20), (14, 36), (5, 37), (10, 29), (13, 13), (25, 10), (9, 34), (2, 18), (22, 30), (26, 9), (30, 34), (16, 13), (2, 30), (22, 24), (30, 12), (11, 3), (1, 25), (29, 17), (24, 23), (27, 23), (11, 16), (17, 25), (16, 17), (19, 3), (19, 20), (20, 32), (14, 4), (0, 33), (28, 2), (3, 25), (11, 12), (3, 26), (18, 35), (11, 18), (23, 15), (11, 34), (2, 25), (22, 22), (13, 9), (21, 3), (29, 23), (7, 23), (7, 7), (6, 21), (26, 35), (22, 34), (15, 24), (13, 23), (12, 13), (28, 26), (12, 26), (16, 34), (29, 3), (14, 17), (28, 25), (32, 4), (15, 32), (9, 0), (12, 21), (29, 5), (27, 33), (6, 23), (5, 25), (31, 6), (9, 17), (29, 34), (24, 27), (25, 1), (5, 34), (0, 29), (0, 16), (32, 19), (5, 24), (23, 21), (3, 5), (4, 15), (26, 29), (16, 19), (15, 5), (26, 32), (7, 3), (1, 20), (6, 34), (21, 5), (22, 37), (14, 8), (12, 11), (22, 29), (11, 5), (28, 14), (27, 30), (7, 27), (21, 9), (30, 6), (5, 22), (30, 28), (8, 20), (19, 23), (16, 6), (30, 9), (19, 6), (18, 32), (16, 25), (1, 3), (1, 31), (18, 21), (4, 27), (4, 32), (4, 22), (28, 28), (16, 15), (5, 33), (9, 18), (8, 27), (25, 33), (7, 26), (8, 31), (10, 15), (4, 25), (16, 10), (10, 37), (20, 1), (20, 19), (26, 12), (6, 26), (29, 29), (11, 24), (24, 22), (13, 12), (28, 13), (25, 27), (7, 18), (22, 11), (13, 28), (26, 15), (17, 35), (31, 8), (31, 13), (13, 4), (9, 1), (25, 29), (29, 36), (27, 13), (18, 5), (15, 22), (0, 18), (17, 27), (5, 18), (30, 25), (26, 21), (8, 19), (18, 20), (15, 8), (11, 30), (6, 1), (23, 19), (32, 14), (30, 19), (8, 0), (21, 37), (3, 19), (2, 13), (23, 0), (5, 35), (25, 16), (23, 22), (0, 24), (7, 36), (21, 14), (1, 10), (27, 1), (14, 5), (18, 25), (23, 32), (7, 20), (22, 0), (11, 2), (6, 29), (8, 23), (4, 2), (12, 9), (31, 20), (13, 15), (32, 35), (29, 13), (31, 28), (19, 21), (16, 1), (15, 11), (23, 23), (20, 7), (29, 21), (19, 10), (12, 6), (2, 4), (9, 25), (9, 35), (1, 36), (3, 2), (31, 25), (13, 22), (11, 29), (14, 20), (11, 35), (28, 10), (21, 24), (3, 16), (22, 16), (30, 30), (3, 21), (27, 11), (13, 33), (2, 36), (32, 26), (30, 4), (20, 0), (29, 9), (5, 1), (8, 28), (32, 9), (9, 6), (5, 16), (6, 10), (1, 34), (14, 16), (24, 33), (14, 26), (21, 0), (20, 24), (30, 14), (26, 18), (6, 2), (31, 11), (1, 19), (14, 29), (12, 1), (16, 37), (8, 2), (12, 8), (7, 32), (7, 17), (32, 13), (4, 8), (11, 15), (25, 30), (12, 37), (30, 16), (2, 6), (3, 13), (5, 26), (19, 25), (0, 25), (28, 5), (18, 18), (29, 37), (31, 32), (14, 32), (17, 2), (5, 21), (30, 27), (4, 33), (6, 7), (20, 6), (24, 21), (3, 34), (7, 1), (20, 8), (0, 10), (13, 1), (29, 26), (1, 33), (18, 29), (20, 10), (31, 2), (9, 9), (20, 36), (24, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "813960", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (15, 22), (13, 9), (18, 17), (2, 31), (26, 18), (2, 12), (18, 34), (22, 21), (26, 8), (24, 1), (33, 1), (26, 28), (13, 29), (26, 20), (15, 28), (10, 10), (34, 16), (30, 19), (28, 27), (20, 7), (23, 28), (18, 12), (7, 29), (32, 20), (10, 16), (14, 5), (8, 19), (16, 33), (34, 25), (4, 29), (4, 5), (22, 0), (1, 21), (34, 31), (3, 6), (32, 18), (21, 0), (33, 25), (8, 25), (30, 14), (6, 25), (17, 17), (22, 33), (7, 14), (6, 27), (33, 24), (24, 0), (20, 15), (29, 6), (24, 27), (13, 0), (17, 28), (26, 12), (27, 7), (6, 32), (13, 20), (21, 29), (11, 14), (21, 8), (12, 24), (27, 10), (1, 1), (12, 2), (18, 21), (14, 7), (23, 30), (13, 4), (25, 0), (24, 15), (28, 13), (25, 1), (4, 22), (17, 21), (31, 9), (3, 24), (21, 32), (3, 12), (15, 32), (27, 33), (4, 6), (33, 3), (21, 13), (11, 11), (15, 33), (35, 24), (35, 33), (2, 21), (19, 20), (12, 13), (22, 31), (34, 26), (9, 34), (12, 27), (20, 19), (35, 6), (32, 16), (7, 23), (21, 1), (29, 34), (5, 23), (14, 3), (15, 9), (1, 17), (15, 24), (15, 4), (11, 15), (10, 15), (13, 30), (4, 28), (24, 11), (21, 25), (6, 0), (25, 3), (23, 25), (18, 31), (5, 29), (14, 30), (12, 34), (14, 9), (28, 28), (0, 17), (16, 17), (31, 11), (1, 10), (13, 27), (22, 5), (25, 10), (21, 28), (13, 21), (29, 12), (7, 19), (29, 3), (5, 0), (34, 23), (26, 19), (34, 5), (3, 33), (26, 5), (18, 33), (27, 15), (31, 3), (1, 34), (11, 22), (6, 3), (30, 28), (10, 7), (6, 15), (15, 6), (25, 20), (12, 26), (21, 4), (33, 10), (13, 24), (0, 5), (22, 16), (30, 10), (28, 12), (12, 18), (20, 10), (24, 31), (0, 13), (32, 7), (0, 26), (30, 11), (13, 8), (30, 17), (33, 23), (20, 11), (28, 22), (32, 26), (35, 27), (8, 10), (1, 30), (15, 17), (35, 5), (17, 15), (8, 20), (9, 32), (31, 32), (15, 13), (31, 25), (4, 30), (19, 24), (28, 1), (13, 32), (22, 18), (24, 14), (29, 30), (27, 17), (33, 11), (28, 30), (8, 2), (31, 26), (10, 12), (15, 18), (6, 1), (1, 15), (11, 8), (0, 29), (25, 2), (10, 3), (13, 5), (30, 30), (20, 28), (18, 14), (18, 2), (7, 32), (34, 19), (30, 0), (5, 24), (6, 22), (28, 24), (31, 22), (23, 4), (7, 10), (32, 17), (8, 0), (32, 31), (21, 14), (14, 19), (5, 2), (15, 15), (25, 14), (21, 18), (19, 34), (27, 23), (31, 12), (17, 19), (34, 0), (9, 20), (17, 26), (26, 25), (27, 4), (19, 2), (34, 28), (18, 22), (34, 9), (25, 34), (33, 30), (4, 15), (9, 28), (26, 4), (20, 29), (6, 30), (19, 33), (2, 0), (30, 31), (23, 19), (23, 24), (0, 24), (17, 16), (31, 6), (8, 23), (35, 1), (12, 1), (30, 7), (3, 0), (14, 8), (5, 18), (13, 18), (10, 11), (29, 23), (32, 5), (18, 29), (27, 5), (25, 30), (20, 16), (32, 3), (4, 7), (25, 6), (2, 18), (3, 3), (0, 30), (27, 3), (4, 34), (22, 32), (19, 7), (30, 18), (17, 3), (21, 6), (19, 22), (31, 15), (8, 4), (0, 22), (20, 31), (31, 10), (10, 22), (8, 14), (18, 7), (14, 29), (19, 28), (12, 32), (12, 20), (15, 30), (9, 9), (2, 7), (1, 31), (8, 28), (0, 4), (7, 28), (7, 16), (10, 20), (31, 1), (26, 16), (7, 11), (1, 5), (6, 19), (0, 12), (32, 24), (17, 34), (20, 0), (6, 4), (4, 25), (11, 10), (16, 22), (9, 14), (32, 22), (14, 21), (31, 30), (28, 10), (13, 19), (3, 29), (33, 0), (27, 13), (35, 4), (29, 0), (28, 16), (18, 26), (25, 12), (3, 30), (31, 19), (16, 12), (19, 3), (13, 15), (22, 13), (20, 27), (16, 25), (0, 7), (23, 5), (25, 9), (24, 32), (4, 11), (2, 34), (26, 31), (5, 7), (11, 34), (33, 34), (2, 3), (1, 11), (21, 21), (18, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979200", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 7), (28, 25), (6, 8), (3, 26), (10, 29), (14, 14), (33, 0), (25, 1), (9, 2), (1, 10), (25, 19), (32, 8), (23, 18), (22, 1), (30, 18), (2, 25), (19, 20), (19, 16), (19, 25), (17, 28), (21, 11), (27, 27), (2, 9), (28, 4), (33, 3), (12, 4), (24, 10), (15, 24), (1, 24), (7, 9), (7, 28), (0, 12), (29, 14), (8, 16), (17, 7), (18, 22), (19, 9), (14, 6), (9, 30), (11, 21), (14, 7), (31, 29), (16, 24), (9, 16), (18, 29), (23, 12), (4, 8), (16, 1), (18, 20), (7, 25), (27, 14), (19, 26), (8, 10), (0, 7), (3, 19), (15, 11), (5, 8), (0, 20), (31, 30), (20, 8), (29, 25), (7, 7), (0, 23), (8, 22), (26, 21), (26, 7), (28, 20), (19, 22), (0, 21), (16, 22), (10, 14), (1, 27), (19, 6), (1, 9), (11, 20), (0, 13), (12, 28), (17, 24), (22, 6), (33, 4), (17, 6), (5, 27), (27, 30), (22, 17), (3, 8), (32, 25), (1, 20), (27, 4), (3, 18), (12, 26), (11, 12), (20, 4), (31, 9), (12, 30), (3, 29), (28, 26), (32, 18), (28, 19), (8, 19), (14, 27), (30, 11), (27, 25), (14, 3), (5, 21), (29, 9), (21, 0), (22, 5), (28, 29), (3, 21), (12, 8), (6, 9), (29, 13), (20, 14), (22, 26), (4, 22), (8, 1), (16, 8), (26, 24), (8, 18), (30, 14), (17, 3), (27, 0), (32, 9), (33, 19), (1, 18), (20, 11), (7, 30), (6, 20), (7, 24), (26, 29), (0, 3), (9, 3), (1, 25), (4, 1), (2, 17), (11, 14), (9, 23), (10, 11), (30, 19), (2, 8), (10, 30), (22, 2), (15, 7), (15, 18), (11, 2), (11, 25), (15, 27), (2, 5), (14, 29), (10, 3), (28, 15), (0, 14), (23, 22), (22, 24), (24, 23), (10, 9), (29, 4), (14, 17), (19, 8), (9, 25), (6, 16), (7, 29), (27, 21), (8, 14), (27, 1), (16, 18), (17, 9), (11, 17), (20, 16), (4, 14), (15, 26), (8, 28), (13, 6), (13, 12), (0, 26), (28, 8), (33, 28), (18, 3), (6, 0), (2, 18), (21, 12), (12, 3), (3, 9), (0, 2), (18, 8), (23, 2), (17, 30), (14, 2), (33, 24), (30, 21), (28, 22), (32, 27), (11, 9), (27, 16), (0, 17), (22, 4), (5, 25), (2, 2), (33, 25), (31, 23), (29, 3), (24, 5), (8, 20), (21, 25), (2, 1), (12, 7), (20, 9), (4, 5), (8, 7), (22, 21), (21, 23), (1, 23), (5, 22), (23, 20), (21, 17), (9, 28), (20, 5), (28, 9), (10, 20), (25, 30), (17, 17), (16, 6), (24, 26), (20, 17), (13, 15), (16, 12), (14, 28), (9, 0), (22, 10), (27, 26), (15, 28), (16, 9), (30, 16), (11, 26), (13, 10), (26, 1), (11, 7), (2, 19), (6, 23), (15, 15), (16, 30), (6, 26), (24, 24), (1, 29), (14, 8), (9, 26), (25, 29), (24, 29), (22, 18), (27, 24), (24, 3), (20, 28), (6, 15), (20, 15), (8, 15), (18, 24), (18, 15), (1, 15), (2, 20), (33, 9), (25, 24), (17, 18), (17, 22), (26, 18), (29, 0), (20, 10), (1, 4), (10, 24), (29, 23), (19, 18), (20, 27), (20, 19), (32, 19), (27, 22), (5, 28), (15, 19), (20, 0), (28, 5), (13, 0), (9, 11), (25, 17), (4, 4), (8, 24), (30, 25), (18, 6), (0, 19), (27, 29), (12, 2), (14, 13), (15, 14), (1, 22), (26, 15), (22, 13), (21, 24), (23, 7), (1, 2), (25, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777304", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), 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), (24, 13), (35, 19), (30, 17), (11, 15), (9, 11), (38, 30), (21, 21), (33, 14), (38, 10), (11, 22), (13, 8), (1, 31), (26, 20), (22, 30), (33, 5), (13, 14), (35, 25), (26, 4), (36, 14), (0, 19), (17, 12), (31, 15), (3, 18), (3, 32), (27, 4), (28, 22), (33, 11), (21, 29), (7, 23), (7, 31), (0, 12), (8, 23), (37, 31), (7, 29), (6, 5), (23, 16), (29, 24), (24, 3), (22, 8), (13, 6), (0, 9), (18, 6), (23, 5), (27, 16), (2, 8), (11, 16), (5, 26), (30, 20), (0, 14), (17, 3), (33, 22), (1, 6), (0, 29), (14, 30), (12, 9), (32, 22), (15, 16), (19, 14), (17, 14), (2, 5), (4, 2), (32, 28), (24, 25), (14, 5), (26, 29), (11, 28), (25, 17), (31, 26), (2, 16), (15, 24), (33, 1), (14, 17), (15, 15), (2, 32), (17, 9), (36, 15), (26, 28), (25, 8), (0, 32), (28, 12), (8, 5), (16, 10), (6, 7), (22, 29), (3, 26), (24, 16), (10, 14), (26, 2), (5, 16), (38, 32), (2, 21), (25, 24), (9, 17), (34, 18), (25, 30), (29, 0), (26, 33), (13, 23), (25, 15), (26, 16), (21, 13), (7, 33), (18, 29), (3, 21), (36, 10), (15, 32), (3, 24), (0, 30), (21, 7), (15, 26), (14, 2), (2, 23), (20, 13), (8, 11), (11, 27), (16, 14), (19, 16), (1, 22), (33, 23), (0, 27), (16, 13), (21, 33), (3, 14), (31, 19), (10, 11), (25, 27), (29, 9), (16, 29), (36, 2), (5, 1), (11, 0), (29, 27), (20, 8), (38, 15), (17, 28), (7, 18), (16, 28), (2, 1), (0, 11), (26, 23), (9, 14), (30, 0), (10, 21), (18, 11), (0, 10), (6, 25), (23, 20), (9, 15), (33, 29), (17, 15), (35, 3), (33, 33), (19, 13), (31, 21), (24, 12), (31, 24), (21, 28), (3, 10), (4, 11), (20, 10), (19, 19), (24, 11), (35, 29), (28, 14), (7, 32), (1, 14), (21, 32), (12, 13), (18, 4), (21, 20), (24, 21), (5, 29), (16, 5), (32, 20), (14, 28), (29, 33), (36, 12), (16, 15), (11, 18), (20, 30), (1, 23), (10, 9), (3, 28), (7, 1), (9, 27), (17, 0), (23, 6), (11, 7), (38, 1), (19, 11), (27, 2), (0, 22), (25, 1), (18, 30), (37, 2), (6, 16), (13, 10), (28, 9), (1, 26), (30, 13), (1, 8), (9, 13), (8, 29), (30, 23), (21, 18), (29, 31), (32, 4), (30, 10), (4, 21), (19, 9), (24, 18), (11, 13), (20, 6), (4, 22), (29, 3), (5, 4), (24, 32), (24, 5), (8, 30), (11, 1), (31, 33), (28, 6), (17, 19), (19, 7), (22, 6), (21, 19), (6, 32), (34, 6), (4, 12), (34, 4), (7, 2), (37, 9), (7, 5), (8, 33), (18, 1), (1, 5), (2, 17), (13, 11), (33, 12), (4, 9), (32, 29), (32, 5), (36, 13), (2, 12), (27, 26), (18, 15), (10, 1), (3, 3), (36, 30), (0, 20), (34, 24), (33, 10), (20, 16), (29, 4), (12, 15), (37, 14), (28, 28), (36, 18), (29, 25), (2, 25), (21, 3), (18, 31), (34, 28), (35, 26), (9, 18), (19, 1), (30, 21), (10, 15), (1, 32), (14, 31), (2, 26), (24, 24), (34, 14), (19, 22), (26, 13), (15, 4), (11, 6), (22, 17), (36, 3), (32, 33), (17, 2), (30, 24), (37, 23), (5, 30), (23, 15), (23, 33), (34, 20), (22, 11), (27, 24), (9, 1), (16, 2), (12, 3), (35, 5), (26, 12), (23, 29), (29, 20), (15, 33), (20, 5), (26, 31), (11, 29), (18, 9), (28, 30), (10, 17), (27, 6), (26, 3), (35, 32), (8, 21), (38, 28), (2, 14), (1, 10), (31, 4), (28, 4), (25, 4), (23, 7), (30, 31), (37, 32), (27, 12), (12, 2), (38, 24), (38, 6), (17, 27), (19, 32), (17, 18), (0, 6), (4, 4), (9, 5), (33, 17), (35, 27), (27, 3), (3, 0), (32, 23), (37, 12), (18, 28), (22, 16), (38, 31), (22, 23), (21, 31), (37, 25), (34, 29), (26, 32), (6, 22), (1, 0), (26, 27), (5, 24), (34, 19), (11, 5), (6, 12), (27, 1), (15, 23), (7, 30), (14, 15), (20, 25), (33, 9), (0, 23), (36, 22), (18, 12), (17, 8), (30, 18), (36, 26), (7, 9), (23, 24), (6, 2), (12, 32), (13, 4), (4, 7), (17, 20), (15, 0), (0, 3), (10, 32), (15, 3), (13, 3), (35, 20), (9, 23), (5, 20), (13, 22), (28, 15), (37, 13), (28, 33), (37, 8), (3, 8), (9, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "699840", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 6), (27, 32), (20, 27), (0, 4), (5, 36), (16, 25), (19, 1), (1, 5), (22, 35), (29, 9), (13, 3), (15, 21), (29, 4), (2, 13), (17, 12), (27, 6), (22, 10), (18, 2), (28, 11), (30, 17), (26, 31), (16, 34), (9, 21), (12, 18), (3, 14), (29, 25), (12, 34), (11, 1), (25, 21), (20, 30), (7, 7), (18, 0), (31, 33), (24, 34), (13, 5), (26, 12), (18, 36), (7, 0), (27, 3), (18, 37), (1, 1), (17, 4), (8, 3), (22, 12), (30, 28), (27, 21), (8, 8), (14, 33), (1, 29), (23, 10), (22, 36), (8, 21), (7, 25), (30, 9), (14, 6), (27, 0), (5, 33), (15, 30), (16, 27), (20, 1), (18, 23), (19, 21), (27, 26), (25, 33), (19, 32), (21, 22), (16, 15), (27, 14), (20, 6), (4, 14), (28, 29), (30, 23), (19, 36), (18, 14), (8, 10), (9, 17), (26, 16), (28, 22), (28, 37), (4, 13), (3, 3), (31, 11), (8, 14), (28, 16), (3, 27), (24, 23), (9, 27), (17, 29), (9, 10), (3, 17), (0, 22), (30, 1), (20, 37), (12, 31), (20, 29), (10, 27), (29, 1), (31, 31), (4, 10), (20, 21), (15, 12), (23, 2), (19, 28), (17, 17), (21, 26), (20, 2), (29, 7), (3, 5), (12, 20), (11, 12), (21, 2), (29, 16), (15, 18), (24, 3), (9, 34), (25, 34), (23, 6), (21, 23), (12, 27), (26, 2), (26, 29), (0, 8), (16, 16), (4, 32), (15, 34), (19, 19), (0, 15), (23, 7), (11, 27), (27, 17), (29, 28), (9, 3), (15, 7), (3, 30), (15, 8), (20, 33), (26, 15), (11, 14), (30, 36), (14, 36), (16, 32), (25, 1), (3, 0), (20, 4), (25, 17), (5, 22), (4, 33), (26, 19), (19, 18), (0, 35), (22, 22), (23, 25), (25, 31), (20, 5), (23, 28), (15, 22), (25, 14), (6, 9), (6, 35), (28, 7), (29, 12), (28, 0), (15, 13), (20, 18), (3, 36), (3, 31), (23, 27), (1, 13), (29, 3), (1, 11), (1, 9), (14, 13), (6, 36), (22, 15), (11, 23), (0, 36), (29, 22), (14, 34), (19, 22), (0, 16), (24, 8), (29, 5), (29, 33), (29, 31), (27, 20), (19, 30), (11, 21), (8, 5), (2, 25), (7, 24), (14, 16), (0, 37), (26, 1), (29, 0), (18, 21), (7, 19), (27, 25), (24, 10), (13, 16), (19, 9), (25, 9), (21, 37), (19, 4), (14, 5), (15, 25), (23, 20), (24, 19), (10, 25), (12, 1), (30, 19), (27, 36), (9, 36), (7, 33), (6, 29), (30, 31), (25, 13), (20, 19), (5, 21), (26, 0), (18, 13), (6, 27), (5, 20), (13, 34), (16, 2), (24, 36), (2, 2), (24, 24), (28, 18), (12, 12), (27, 35), (25, 2), (9, 1), (17, 14), (10, 6), (7, 30), (13, 29), (30, 27), (2, 0), (30, 16), (27, 22), (27, 9), (9, 18), (31, 22), (3, 8), (15, 17), (18, 16), (29, 18), (21, 5), (26, 25), (31, 34), (13, 18), (2, 33), (10, 18), (9, 5), (0, 26), (3, 4), (14, 35), (23, 11), (8, 1), (0, 10), (13, 19), (20, 17), (14, 28), (19, 12), (4, 15), (2, 26), (20, 9), (3, 16), (3, 6), (30, 18), (22, 13), (10, 26), (7, 12), (11, 35), (3, 9), (15, 4), (28, 27), (2, 14), (12, 30), (28, 15), (30, 14), (21, 32), (19, 13), (22, 18), (8, 36), (9, 24), (3, 26), (7, 28), (4, 11), (1, 14), (18, 17), (20, 8), (7, 17), (11, 15), (8, 20), (28, 33), (20, 16), (13, 28), (5, 9), (27, 13), (16, 29), (23, 33), (5, 7), (6, 34), (30, 25), (20, 3), (6, 14), (9, 4), (12, 3), (21, 1), (26, 13), (14, 11), (2, 9), (13, 2), (11, 16), (17, 13), (21, 9), (22, 34), (7, 32), (14, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71712", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 4), (30, 23), (2, 5), (8, 26), (15, 0), (14, 27), (5, 30), (33, 36), (32, 1), (13, 15), (22, 18), (31, 15), (9, 30), (24, 28), (6, 1), (35, 30), (32, 7), (28, 6), (5, 3), (22, 19), (3, 20), (35, 16), (15, 36), (11, 24), (25, 28), (28, 28), (15, 30), (2, 36), (33, 31), (7, 10), (24, 27), (36, 17), (1, 23), (21, 0), (6, 32), (10, 17), (14, 31), (19, 34), (0, 8), (29, 31), (7, 1), (18, 22), (29, 14), (9, 26), (34, 16), (25, 30), (27, 20), (2, 4), (20, 8), (23, 15), (27, 8), (16, 33), (15, 21), (37, 32), (4, 32), (7, 11), (14, 36), (30, 26), (9, 27), (22, 26), (15, 4), (11, 18), (16, 25), (35, 31), (5, 5), (17, 2), (34, 13), (24, 33), (37, 0), (36, 36), (11, 22), (23, 9), (23, 24), (3, 9), (21, 31), (25, 24), (6, 21), (1, 18), (9, 25), (1, 32), (8, 13), (5, 34), (29, 36), (25, 32), (19, 14), (1, 31), (22, 24), (18, 21), (37, 28), (25, 22), (4, 4), (24, 22), (7, 14), (23, 25), (17, 29), (21, 33), (3, 17), (2, 10), (7, 21), (3, 4), (13, 9), (10, 26), (30, 3), (10, 35), (25, 3), (15, 3), (7, 32), (21, 10), (17, 0), (35, 36), (35, 33), (0, 7), (18, 27), (0, 2), (14, 29), (22, 27), (9, 32), (15, 11), (30, 10), (7, 23), (29, 9), (9, 22), (2, 31), (5, 1), (34, 9), (34, 14), (27, 33), (21, 5), (8, 20), (14, 30), (16, 13), (17, 32), (13, 5), (5, 23), (17, 9), (6, 7), (19, 32), (33, 24), (18, 7), (3, 12), (16, 36), (13, 35), (5, 12), (10, 5), (35, 18), (18, 25), (1, 36), (18, 5), (0, 5), (15, 18), (33, 22), (15, 28), (16, 4), (27, 24), (11, 23), (37, 3), (11, 29), (23, 27), (26, 2), (28, 3), (33, 23), (5, 35), (37, 18), (34, 27), (15, 27), (28, 1), (5, 18), (35, 20), (16, 0), (37, 10), (24, 7), (34, 18), (2, 19), (32, 22), (29, 26), (8, 3), (21, 23), (4, 14), (33, 28), (7, 31), (30, 13), (26, 34), (33, 15), (25, 17), (25, 27), (19, 30), (23, 8), (37, 30), (17, 8), (7, 18), (17, 14), (13, 7), (9, 9), (3, 33), (11, 33), (20, 9), (14, 34), (28, 15), (33, 13), (28, 29), (29, 22), (10, 33), (3, 25), (15, 6), (6, 4), (29, 3), (21, 3), (17, 36), (12, 20), (4, 2), (34, 24), (31, 36), (32, 15), (37, 1), (11, 34), (3, 21), (5, 11), (0, 21), (6, 31), (14, 23), (23, 34), (20, 3), (28, 16), (22, 6), (33, 32), (0, 31), (29, 15), (20, 5), (5, 22), (19, 2), (32, 24), (2, 34), (29, 28), (22, 17), (4, 9), (37, 15), (20, 27), (20, 13), (12, 28), (26, 5), (32, 32), (35, 12), (5, 2), (27, 28), (36, 32), (16, 22), (28, 26), (3, 23), (28, 23), (35, 27), (31, 33), (3, 7), (0, 29), (19, 0), (31, 29), (18, 17), (29, 7), (28, 9), (21, 22), (16, 10), (21, 4), (9, 28), (20, 16), (32, 36), (26, 17), (0, 14), (10, 6), (17, 7), (31, 5), (35, 34), (34, 23), (3, 19), (0, 30), (19, 36), (7, 2), (9, 1), (9, 24), (28, 27), (8, 18), (9, 10), (1, 16), (2, 6), (27, 14), (4, 22), (12, 36), (18, 30), (5, 21), (4, 19), (4, 1), (32, 23), (14, 20), (26, 6), (28, 12), (17, 18), (19, 16), (8, 29), (24, 5), (19, 12), (29, 2), (1, 35), (14, 7), (27, 22), (0, 33), (20, 23), (10, 18), (30, 2), (24, 0), (19, 19), (15, 29), (20, 12), (18, 34), (22, 25), (30, 22), (9, 23), (17, 31), (4, 6), (35, 10), (24, 6), (32, 9), (6, 16), (19, 8), (4, 10), (12, 9), (12, 19), (34, 6), (29, 25), (30, 33), (32, 13), (25, 15), (8, 27), (11, 0), (10, 32), (17, 22), (13, 30), (32, 8), (6, 9), (25, 16), (4, 0), (27, 30), (14, 9), (16, 8), (21, 1), (23, 4), (26, 10), (34, 36), (19, 35), (5, 19), (23, 26), (29, 5), (27, 34), (12, 35), (22, 8), (0, 15), (9, 21), (2, 0), (1, 22), (36, 3), (16, 32), (25, 29), (35, 2), (34, 0), (30, 8), (26, 11), (6, 11), (2, 13), (25, 13), (28, 2), (21, 15), (29, 8), (10, 28), (12, 5), (3, 16), (5, 24), (23, 18), (32, 25), (33, 25), (1, 30), (17, 34), (31, 27), (13, 26), (7, 36), (6, 35), (32, 12), (37, 2), (15, 2), (2, 14), (37, 29), (18, 23), (12, 0), (12, 11), (19, 26), (12, 3), (7, 25), (0, 22), (1, 21), (13, 24), (11, 25), (25, 23), (4, 8), (6, 12), (23, 3), (0, 19), (21, 2), (27, 32), (2, 8), (25, 31), (11, 4), (0, 18), (14, 1), (19, 18), (32, 19), (3, 6), (8, 23), (23, 5), (27, 5), (36, 14), (2, 30), (32, 35), (16, 28), (24, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "939672", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 5), (3, 19), (9, 29), (1, 9), (8, 20), (23, 17), (19, 24), (27, 30), (23, 4), (15, 28), (27, 23), (21, 9), (8, 15), (8, 5), (4, 5), (18, 23), (34, 1), (4, 3), (31, 6), (26, 24), (1, 14), (17, 28), (33, 16), (0, 27), (26, 28), (30, 15), (5, 14), (11, 18), (33, 18), (8, 21), (18, 31), (5, 1), (6, 26), (25, 19), (29, 23), (16, 14), (8, 10), (17, 2), (27, 5), (28, 19), (13, 21), (3, 20), (33, 19), (23, 1), (24, 15), (15, 27), (2, 13), (7, 1), (16, 11), (28, 11), (7, 16), (14, 21), (13, 28), (27, 15), (14, 15), (2, 16), (6, 22), (19, 16), (28, 28), (12, 8), (3, 16), (9, 25), (11, 19), (24, 9), (18, 21), (5, 20), (27, 18), (32, 23), (1, 4), (22, 30), (29, 30), (7, 12), (25, 11), (25, 1), (15, 26), (13, 8), (17, 27), (9, 20), (33, 31), (30, 17), (19, 0), (4, 20), (23, 25), (24, 21), (27, 1), (25, 12), (20, 16), (17, 14), (0, 4), (4, 27), (8, 1), (20, 18), (26, 18), (9, 9), (20, 9), (30, 12), (22, 6), (34, 3), (2, 19), (28, 0), (18, 6), (30, 1), (9, 2), (7, 14), (26, 8), (17, 22), (25, 20), (26, 16), (33, 24), (18, 13), (8, 19), (14, 26), (27, 9), (17, 1), (17, 25), (20, 28), (16, 24), (20, 8), (28, 4), (13, 29), (32, 18), (28, 26), (28, 16), (5, 23), (1, 5), (0, 24), (11, 10), (18, 2), (13, 23), (31, 7), (12, 19), (20, 5), (13, 15), (7, 26), (17, 9), (23, 2), (5, 29), (27, 4), (18, 29), (27, 25), (6, 5), (13, 20), (24, 16), (10, 19), (4, 16), (7, 17), (16, 18), (6, 12), (30, 21), (14, 14), (18, 10), (3, 12), (12, 6), (5, 8), (3, 10), (25, 6), (14, 13), (25, 22), (6, 21), (32, 20), (22, 11), (3, 13), (3, 3), (10, 10), (11, 0), (22, 12), (3, 8), (32, 30), (9, 19), (17, 16), (3, 22), (12, 3), (22, 1), (4, 9), (27, 31), (24, 30), (26, 21), (17, 19), (15, 7), (3, 11), (22, 16), (9, 14), (9, 15), (25, 30), (15, 29), (29, 8), (30, 20), (14, 17), (30, 8), (13, 19), (7, 2), (29, 27), (11, 13), (27, 2), (31, 26), (0, 13), (31, 13), (0, 25), (5, 18), (7, 24), (26, 20), (28, 15), (21, 3), (10, 25), (25, 31), (26, 22), (20, 6), (9, 31), (29, 22), (17, 15), (19, 14), (10, 24), (2, 4), (2, 23), (22, 14), (13, 12), (31, 22), (6, 8), (18, 9), (23, 9), (26, 5), (19, 21), (25, 4), (28, 18), (28, 6), (26, 2), (24, 17), (18, 18), (13, 26), (31, 23), (29, 17), (14, 10), (14, 6), (6, 28), (4, 26), (34, 10), (21, 23), (8, 6), (7, 6), (16, 4), (21, 4), (31, 25), (30, 25), (9, 6), (9, 13), (25, 10), (32, 9), (25, 9), (0, 5), (24, 0), (19, 12), (12, 17), (15, 20), (2, 21), (20, 4), (0, 10), (4, 17), (21, 18), (19, 10), (16, 25), (2, 7), (12, 29), (15, 2), (6, 4), (20, 11), (23, 10), (6, 17), (2, 31), (3, 1), (17, 7), (4, 7), (31, 9), (25, 13), (0, 21), (23, 23), (1, 15), (19, 18), (10, 6), (10, 22), (27, 13), (21, 6), (31, 21), (34, 7), (10, 13), (4, 24), (24, 2), (27, 21), (6, 16), (34, 26), (8, 11), (31, 19), (22, 20), (34, 23), (11, 22), (14, 7), (25, 8), (4, 4), (4, 18), (32, 16), (12, 27), (10, 26), (18, 25), (28, 7), (15, 23), (6, 27), (5, 6), (0, 29), (9, 12), (3, 27), (19, 29), (31, 4), (24, 18), (31, 24), (19, 2), (21, 30), (25, 3), (19, 25), (29, 0), (12, 7), (16, 26), (14, 18), (8, 25), (4, 1), (25, 23), (13, 6), (27, 26), (30, 7), (4, 19), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149400", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 37), (9, 14), (32, 4), (36, 14), (16, 28), (9, 2), (34, 2), (2, 2), (14, 25), (16, 9), (16, 4), (1, 25), (36, 16), (36, 22), (27, 36), (18, 27), (10, 23), (35, 19), (17, 25), (18, 8), (6, 8), (33, 36), (10, 20), (3, 1), (10, 24), (14, 0), (9, 11), (22, 16), (25, 30), (12, 32), (12, 28), (0, 8), (31, 30), (29, 20), (13, 11), (14, 2), (28, 11), (30, 15), (26, 3), (19, 11), (8, 35), (21, 0), (10, 21), (36, 18), (26, 15), (17, 13), (19, 15), (28, 26), (10, 15), (1, 20), (29, 10), (24, 0), (14, 3), (0, 9), (9, 26), (13, 23), (1, 14), (9, 10), (9, 9), (6, 33), (3, 20), (21, 28), (25, 4), (2, 34), (26, 28), (4, 31), (1, 22), (25, 36), (21, 37), (25, 3), (25, 15), (0, 20), (13, 36), (36, 15), (33, 4), (2, 8), (34, 11), (24, 4), (24, 20), (23, 30), (33, 28), (16, 20), (26, 6), (19, 30), (8, 17), (2, 23), (4, 32), (18, 31), (30, 30), (0, 12), (33, 20), (9, 32), (16, 10), (34, 9), (9, 22), (0, 23), (30, 19), (15, 33), (4, 29), (18, 15), (13, 16), (35, 20), (8, 20), (23, 18), (22, 5), (30, 4), (15, 3), (23, 24), (19, 26), (22, 36), (17, 18), (4, 15), (5, 30), (2, 27), (36, 17), (17, 10), (24, 12), (28, 19), (8, 28), (35, 26), (17, 35), (29, 6), (33, 23), (7, 17), (24, 17), (24, 3), (13, 22), (2, 33), (15, 22), (22, 10), (4, 30), (23, 27), (4, 8), (22, 14), (33, 30), (32, 15), (24, 26), (9, 34), (14, 14), (23, 17), (14, 18), (30, 5), (34, 13), (24, 21), (23, 31), (11, 26), (19, 18), (33, 17), (17, 7), (26, 22), (18, 2), (11, 25), (20, 35), (9, 6), (21, 31), (22, 34), (0, 32), (16, 11), (21, 4), (26, 1), (11, 24), (19, 33), (30, 27), (19, 23), (10, 4), (30, 3), (10, 36), (36, 33), (18, 20), (21, 19), (9, 16), (14, 17), (30, 16), (10, 32), (25, 5), (1, 4), (9, 17), (22, 37), (11, 31), (12, 13), (19, 20), (30, 36), (35, 21), (5, 26), (15, 19), (8, 1), (25, 16), (36, 5), (10, 12), (13, 25), (10, 19), (13, 19), (13, 24), (3, 29), (25, 1), (3, 30), (1, 21), (32, 36), (10, 16), (7, 9), (15, 0), (7, 34), (24, 10), (2, 22), (22, 1), (12, 9), (20, 31), (22, 4), (5, 35), (21, 24), (5, 32), (35, 16), (10, 14), (32, 2), (28, 21), (16, 6), (6, 11), (20, 0), (21, 10), (0, 21), (7, 26), (21, 34), (24, 27), (13, 35), (2, 4), (8, 21), (16, 14), (20, 23), (25, 12), (35, 14), (10, 2), (17, 30), (13, 5), (7, 32), (7, 29), (17, 24), (17, 15), (26, 33), (2, 35), (31, 12), (28, 22), (7, 7), (2, 14), (15, 1), (33, 35), (36, 3), (10, 6), (0, 27), (13, 30), (3, 25), (15, 8), (7, 2), (19, 9), (23, 11), (3, 26), (8, 23), (27, 13), (8, 24), (35, 2), (20, 27), (17, 29), (20, 37), (34, 24), (0, 26), (14, 22), (19, 19), (2, 13), (15, 16), (17, 9), (23, 33), (33, 8), (25, 24), (28, 15), (18, 28), (11, 29), (10, 10), (26, 5), (8, 15), (1, 0), (8, 16), (27, 7), (9, 15), (21, 14), (16, 15), (35, 18), (32, 10), (7, 37), (20, 26), (28, 1), (20, 7), (16, 13), (4, 26), (0, 16), (36, 11), (7, 14), (7, 4), (11, 36), (30, 8), (32, 27), (18, 17), (10, 26), (28, 13), (18, 9), (8, 26), (5, 17), (30, 35), (0, 31), (18, 23), (21, 17), (14, 33), (31, 17), (33, 14), (34, 36), (29, 21), (0, 24), (25, 2), (21, 23), (26, 8), (15, 21), (27, 17), (4, 21), (36, 7), (19, 4), (36, 35), (20, 36), (31, 14), (25, 25), (32, 16), (36, 26), (34, 16), (29, 36), (36, 25), (11, 5), (31, 22), (23, 35), (13, 28), (8, 37), (21, 5), (26, 18), (34, 26), (27, 33), (7, 10), (23, 9), (17, 8), (9, 28), (20, 1), (20, 14), (19, 27), (23, 10), (34, 22), (0, 25), (5, 1), (3, 31), (19, 3), (33, 0), (35, 3), (25, 17), (21, 6), (14, 35), (31, 34), (10, 17), (26, 19), (8, 8), (27, 22), (1, 33), (15, 36), (12, 34), (5, 29), (26, 30), (27, 35), (4, 35), (35, 30), (15, 17), (35, 28), (25, 7), (31, 33), (13, 8), (4, 18), (35, 12), (20, 3), (16, 37), (0, 17), (15, 32), (20, 19), (7, 12), (6, 2), (20, 29), (12, 19), (4, 20), (8, 22), (22, 28), (29, 35), (6, 18), (33, 7), (29, 2), (16, 17), (32, 1), (6, 22), (2, 16), (27, 14), (22, 35), (20, 24), (2, 10), (27, 0), (21, 7), (11, 4), (12, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "351600", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 8), (6, 19), (16, 5), (30, 29), (17, 26), (17, 15), (2, 2), (28, 17), (21, 4), (28, 21), (6, 16), (14, 4), (12, 19), (27, 19), (17, 21), (21, 11), (19, 18), (22, 4), (17, 0), (3, 4), (29, 29), (15, 29), (22, 29), (14, 25), (19, 6), (5, 1), (33, 21), (20, 3), (23, 14), (16, 0), (33, 27), (12, 13), (8, 28), (24, 8), (14, 23), (29, 17), (32, 24), (29, 11), (21, 2), (3, 8), (16, 1), (8, 22), (8, 14), (14, 2), (14, 16), (24, 23), (5, 13), (10, 18), (30, 9), (2, 22), (21, 28), (32, 29), (29, 3), (19, 25), (29, 6), (7, 20), (14, 22), (3, 20), (2, 5), (12, 2), (20, 0), (16, 7), (23, 23), (21, 9), (4, 1), (3, 12), (28, 6), (14, 11), (22, 14), (14, 17), (31, 23), (26, 26), (5, 4), (29, 5), (33, 16), (4, 14), (27, 11), (23, 19), (33, 6), (16, 14), (31, 13), (19, 17), (17, 2), (28, 0), (2, 23), (1, 0), (25, 15), (26, 18), (32, 23), (22, 19), (10, 26), (31, 21), (7, 8), (11, 3), (23, 2), (22, 12), (12, 18), (17, 9), (18, 3), (33, 0), (17, 25), (26, 17), (28, 26), (10, 14), (10, 12), (9, 14), (29, 19), (18, 20), (10, 8), (5, 5), (13, 13), (11, 8), (2, 9), (25, 25), (7, 1), (29, 15), (31, 11), (24, 2), (28, 22), (10, 9), (25, 16), (0, 10), (2, 21), (26, 5), (15, 3), (29, 7), (24, 9), (20, 4), (2, 10), (11, 24), (20, 10), (0, 2), (21, 26), (29, 13), (2, 25), (22, 24), (30, 14), (21, 1), (1, 6), (24, 21), (27, 16), (5, 21), (9, 27), (2, 14), (18, 26), (6, 0), (26, 3), (3, 28), (21, 16), (19, 21), (17, 27), (16, 25), (18, 14), (24, 24), (13, 8), (2, 12), (33, 9), (26, 16), (18, 7), (12, 24), (21, 25), (22, 1), (21, 8), (1, 17), (11, 18), (10, 15), (9, 13), (27, 23), (4, 27), (0, 5), (27, 9), (5, 2), (25, 3), (26, 8), (17, 20), (31, 2), (3, 29), (12, 7), (29, 26), (22, 5), (14, 3), (30, 13), (25, 8), (15, 2), (20, 25), (5, 26), (30, 18), (33, 5), (32, 9), (6, 13), (3, 13), (9, 9), (3, 26), (4, 12), (16, 29), (19, 26), (14, 14), (14, 19), (19, 23), (28, 23), (8, 27), (5, 19), (3, 24), (9, 26), (7, 18), (29, 2), (29, 21), (22, 10), (33, 13), (19, 10), (22, 26), (18, 6), (14, 27), (4, 25), (2, 11), (20, 26), (17, 19), (7, 24), (1, 20), (24, 3), (25, 29), (8, 3), (2, 15), (4, 7), (27, 26), (29, 1), (22, 21), (26, 9), (23, 4), (7, 14), (13, 2), (2, 17), (31, 27), (19, 22), (13, 5), (32, 14), (21, 6), (25, 1), (12, 4), (19, 19), (19, 16), (2, 7), (1, 9), (4, 0), (13, 12), (10, 29), (24, 5), (1, 23), (20, 1), (12, 16), (1, 29), (16, 26), (28, 20), (11, 7), (23, 16), (15, 18), (33, 12), (6, 1), (27, 28), (14, 10), (14, 0), (22, 27), (6, 17), (8, 24), (32, 13), (0, 26), (10, 17), (18, 12), (16, 28), (0, 20), (33, 15), (13, 21), (21, 13), (3, 15), (32, 10), (25, 21), (10, 19), (23, 3), (22, 20), (7, 2), (9, 2), (26, 27), (13, 16), (11, 9), (16, 8), (25, 6), (23, 27), (15, 20), (30, 0), (18, 2), (11, 11), (23, 5), (30, 22), (2, 27), (33, 11), (16, 18), (26, 0), (6, 12), (15, 5), (20, 9), (0, 16), (13, 22), (11, 14), (31, 8), (18, 21), (32, 5), (24, 0), (29, 14), (15, 6), (10, 20), (9, 10), (8, 0), (11, 13), (28, 28), (23, 24), (23, 1), (19, 20), (30, 27), (29, 28), (23, 0), (31, 0), (19, 8), (25, 24), (29, 9), (28, 3), (27, 22), (31, 10), (9, 1), (14, 29), (20, 14), (26, 22), (21, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "925344", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 2), (12, 32), (22, 12), (18, 33), (12, 5), (31, 29), (26, 18), (29, 15), (10, 3), (9, 2), (26, 23), (2, 7), (32, 9), (19, 28), (11, 27), (34, 9), (2, 21), (36, 12), (26, 13), (12, 18), (2, 5), (14, 1), (6, 7), (19, 9), (21, 33), (35, 26), (5, 6), (12, 26), (12, 3), (17, 25), (23, 3), (23, 8), (18, 21), (34, 3), (17, 23), (36, 33), (12, 29), (23, 0), (35, 31), (0, 6), (4, 2), (25, 1), (6, 24), (26, 16), (8, 3), (15, 23), (23, 17), (31, 5), (21, 8), (35, 9), (11, 4), (33, 12), (6, 35), (24, 26), (18, 22), (7, 10), (23, 21), (4, 18), (0, 7), (31, 20), (6, 20), (28, 24), (34, 0), (16, 25), (29, 0), (3, 7), (14, 25), (28, 27), (1, 20), (17, 27), (5, 3), (34, 35), (12, 6), (4, 12), (5, 21), (31, 27), (31, 1), (34, 12), (13, 34), (3, 18), (33, 27), (21, 16), (11, 10), (4, 19), (15, 6), (21, 19), (31, 22), (17, 19), (31, 15), (19, 23), (16, 17), (22, 35), (14, 19), (17, 2), (34, 8), (1, 7), (29, 27), (15, 31), (30, 32), (33, 8), (10, 14), (29, 20), (32, 8), (0, 31), (13, 33), (6, 21), (9, 35), (8, 15), (4, 25), (2, 15), (14, 20), (23, 7), (11, 21), (21, 10), (26, 29), (6, 22), (3, 12), (9, 10), (15, 4), (10, 24), (30, 12), (33, 34), (21, 30), (26, 33), (26, 6), (33, 15), (13, 13), (35, 11), (7, 25), (2, 1), (12, 31), (1, 35), (30, 7), (10, 12), (9, 18), (13, 1), (30, 21), (13, 15), (24, 19), (30, 4), (6, 3), (13, 18), (20, 0), (0, 14), (31, 24), (23, 34), (11, 16), (24, 8), (29, 9), (18, 27), (17, 0), (10, 1), (14, 2), (11, 34), (21, 25), (35, 17), (4, 33), (1, 15), (11, 13), (24, 5), (14, 32), (31, 3), (34, 19), (4, 24), (24, 6), (17, 12), (34, 7), (8, 16), (11, 12), (34, 31), (31, 33), (13, 27), (36, 30), (34, 10), (8, 34), (32, 12), (30, 20), (33, 31), (34, 30), (34, 2), (11, 6), (7, 8), (26, 17), (27, 19), (21, 35), (35, 15), (12, 20), (16, 4), (32, 7), (10, 27), (28, 15), (24, 3), (13, 35), (23, 19), (35, 0), (4, 9), (25, 33), (1, 5), (16, 34), (22, 3), (15, 21), (5, 18), (24, 30), (20, 18), (26, 27), (12, 2), (13, 11), (7, 28), (6, 18), (35, 30), (31, 34), (28, 33), (30, 5), (11, 2), (32, 16), (6, 15), (3, 22), (22, 31), (25, 35), (3, 32), (26, 1), (27, 28), (11, 18), (14, 9), (35, 29), (13, 8), (12, 25), (8, 4), (7, 3), (25, 26), (3, 15), (1, 32), (11, 24), (31, 7), (17, 15), (19, 6), (31, 13), (10, 0), (35, 7), (13, 28), (19, 5), (4, 3), (8, 28), (22, 29), (15, 17), (0, 16), (8, 1), (22, 4), (12, 34), (31, 14), (12, 22), (31, 12), (32, 30), (10, 10), (29, 2), (10, 21), (12, 10), (27, 8), (8, 32), (19, 29), (0, 3), (28, 9), (5, 26), (4, 7), (21, 27), (9, 21), (31, 17), (2, 28), (17, 28), (34, 16), (31, 21), (28, 19), (29, 21), (30, 22), (25, 31), (33, 26), (6, 34), (29, 16), (12, 35), (3, 33), (25, 28), (32, 15), (24, 11), (31, 28), (8, 20), (25, 24), (29, 7), (22, 22), (17, 13), (16, 31), (5, 15), (7, 4), (6, 28), (35, 14), (33, 29), (12, 33), (26, 34), (34, 28), (20, 16), (0, 5), (25, 34), (32, 14), (5, 27), (13, 4), (0, 30), (25, 4), (33, 22), (21, 29), (14, 14), (10, 6), (35, 25), (12, 0), (7, 27), (34, 1), (15, 7), (25, 19), (31, 6), (11, 8), (9, 20), (18, 9), (5, 22), (23, 35), (27, 10), (4, 21), (8, 23), (1, 9), (31, 9), (1, 21), (33, 0), (36, 3), (3, 20), (24, 1), (1, 22), (30, 10), (16, 16), (2, 35), (30, 34), (30, 24), (10, 8), (22, 8), (4, 6), (33, 1), (36, 1), (1, 2), (22, 5), (6, 14), (18, 1), (29, 19), (16, 7), (13, 2), (30, 33), (23, 16), (12, 4), (31, 4), (22, 7), (18, 35), (6, 25), (21, 1), (22, 27), (28, 30), (9, 30), (7, 21), (22, 18), (8, 18), (6, 30), (0, 11), (18, 4), (12, 11), (1, 13), (14, 6), (12, 24), (32, 24), (0, 28), (28, 0), (17, 18), (26, 21), (24, 10), (20, 13), (1, 33), (17, 5), (12, 16), (28, 1), (15, 10), (10, 31), (24, 24), (10, 20), (8, 12), (14, 7), (10, 9), (25, 13), (3, 16), (10, 16), (33, 16), (18, 19), (16, 35), (14, 12), (13, 24), (16, 30), (33, 2), (3, 21), (26, 7), (29, 1), (30, 25), (0, 19), (7, 19), (18, 32), (30, 30), (27, 24), (20, 7), (13, 7), (28, 7), (35, 5), (20, 1), (4, 17), (2, 22), (9, 6), (26, 26), (24, 4), (19, 18), (9, 28), (14, 10), (28, 28), (19, 15), (5, 23), (20, 15), (15, 33), (21, 15), (17, 3), (35, 23), (4, 1), (32, 5), (32, 13), (14, 23), (24, 2), (11, 3), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816480", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 9), (11, 19), (5, 17), (3, 10), (1, 17), (27, 22), (34, 23), (6, 28), (33, 15), (7, 26), (17, 9), (16, 20), (25, 2), (22, 26), (33, 17), (10, 4), (14, 5), (22, 24), (3, 24), (13, 15), (26, 18), (26, 20), (32, 2), (7, 1), (31, 5), (1, 26), (4, 0), (14, 17), (15, 18), (18, 3), (23, 28), (22, 19), (17, 29), (24, 18), (6, 16), (29, 25), (20, 28), (12, 19), (22, 16), (18, 9), (33, 10), (7, 7), (10, 0), (6, 26), (13, 29), (12, 5), (26, 27), (14, 4), (29, 18), (13, 7), (2, 19), (6, 31), (2, 31), (10, 29), (12, 26), (31, 9), (11, 28), (18, 14), (19, 22), (21, 9), (22, 11), (30, 18), (11, 4), (12, 7), (33, 20), (28, 25), (8, 5), (9, 28), (14, 23), (20, 30), (35, 4), (3, 23), (35, 14), (34, 8), (20, 1), (19, 14), (26, 22), (4, 3), (4, 14), (30, 27), (14, 22), (22, 23), (33, 18), (7, 24), (28, 2), (16, 12), (28, 4), (2, 24), (30, 2), (22, 3), (27, 21), (9, 6), (0, 11), (25, 6), (34, 15), (6, 23), (16, 26), (13, 10), (34, 5), (21, 8), (32, 11), (28, 28), (15, 29), (11, 25), (31, 4), (6, 22), (28, 21), (14, 13), (26, 28), (28, 3), (34, 6), (32, 13), (27, 3), (17, 12), (35, 16), (13, 20), (28, 11), (8, 1), (22, 2), (9, 3), (24, 8), (4, 20), (32, 27), (19, 12), (9, 8), (34, 3), (23, 20), (21, 17), (3, 18), (8, 24), (24, 30), (19, 31), (0, 6), (17, 20), (34, 12), (7, 19), (13, 8), (35, 24), (18, 1), (30, 14), (32, 19), (1, 4), (19, 21), (31, 23), (16, 7), (29, 2), (7, 16), (5, 0), (33, 16), (2, 13), (24, 26), (33, 22), (14, 28), (22, 21), (14, 25), (31, 27), (16, 25), (32, 4), (27, 26), (20, 23), (8, 29), (25, 16), (19, 17), (14, 20), (28, 18), (3, 26), (11, 29), (8, 20), (17, 27), (28, 20), (3, 0), (8, 9), (21, 16), (33, 26), (29, 30), (0, 15), (33, 12), (12, 16), (25, 22), (27, 13), (11, 12), (27, 7), (23, 19), (16, 14), (19, 26), (34, 25), (14, 19), (7, 10), (24, 11), (2, 12), (1, 28), (23, 0), (11, 5), (3, 5), (4, 17), (30, 19), (19, 6), (5, 30), (2, 27), (23, 13), (1, 16), (26, 8), (2, 30), (27, 14), (33, 23), (19, 10), (25, 5), (8, 16), (1, 6), (11, 26), (10, 12), (30, 0), (14, 27), (23, 7), (1, 8), (0, 9), (15, 13), (11, 14), (20, 11), (10, 31), (22, 8), (28, 27), (16, 3), (25, 18), (7, 25), (17, 22), (13, 4), (3, 29), (17, 13), (34, 11), (14, 16), (10, 5), (32, 18), (32, 30), (25, 25), (23, 8), (28, 13), (21, 14), (24, 31), (15, 9), (12, 27), (25, 28), (15, 25), (28, 6), (9, 10), (18, 11), (7, 0), (3, 30), (18, 4), (28, 5), (0, 31), (1, 14), (12, 23), (18, 5), (31, 20), (3, 2), (35, 10), (29, 6), (24, 1), (31, 1), (20, 15), (19, 5), (32, 28), (5, 15), (13, 23), (21, 20), (4, 4), (31, 2), (5, 25), (15, 15), (15, 6), (5, 29), (33, 28), (30, 24), (15, 17), (13, 24), (1, 30), (24, 3), (5, 2), (33, 9), (17, 11), (1, 29), (4, 16), (21, 19), (34, 4), (6, 12), (10, 17), (15, 16), (1, 11), (15, 10), (7, 17), (23, 31), (19, 28), (11, 9), (30, 7), (7, 12), (7, 28), (34, 17), (7, 8), (12, 31), (7, 23), (14, 30), (27, 8), (32, 22), (34, 0), (1, 22), (25, 7), (16, 22), (19, 3), (10, 25), (28, 7), (19, 2), (16, 13), (22, 27), (26, 3), (4, 13), (26, 17), (4, 15), (22, 17), (21, 5), (30, 25), (3, 19), (27, 15), (11, 17), (21, 0), (23, 5), (13, 22), (24, 22), (16, 30), (21, 27), (11, 24), (34, 20), (4, 2), (8, 22), (32, 6), (33, 4), (9, 19), (2, 21), (31, 16), (1, 10), (24, 4), (17, 28), (9, 9), (16, 31), (8, 19), (18, 26), (26, 12), (5, 24), (27, 9), (32, 15), (0, 5), (10, 24), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24795", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 31), (4, 11), (35, 16), (1, 7), (26, 29), (29, 19), (16, 13), (16, 25), (17, 11), (26, 8), (8, 30), (7, 5), (1, 3), (26, 24), (6, 27), (1, 21), (16, 20), (29, 0), (9, 9), (4, 22), (32, 0), (35, 18), (0, 23), (29, 16), (28, 0), (6, 9), (25, 5), (24, 1), (32, 12), (20, 12), (19, 28), (24, 0), (2, 23), (13, 11), (35, 27), (15, 20), (2, 13), (14, 16), (35, 22), (10, 14), (14, 21), (23, 13), (18, 29), (6, 23), (20, 5), (20, 18), (31, 6), (15, 8), (12, 28), (15, 29), (2, 19), (30, 13), (20, 9), (23, 9), (5, 6), (12, 15), (21, 3), (10, 19), (19, 29), (20, 4), (0, 32), (32, 28), (0, 22), (8, 1), (31, 8), (22, 27), (24, 19), (26, 3), (28, 30), (10, 17), (7, 1), (0, 19), (35, 17), (15, 9), (31, 10), (23, 31), (25, 22), (32, 2), (4, 3), (7, 0), (15, 11), (2, 30), (32, 29), (23, 29), (13, 1), (11, 8), (5, 26), (18, 12), (5, 18), (1, 5), (9, 23), (25, 18), (7, 23), (2, 21), (23, 6), (19, 20), (34, 32), (1, 25), (20, 25), (8, 7), (19, 25), (6, 3), (8, 20), (10, 26), (27, 17), (4, 9), (24, 7), (26, 9), (30, 3), (17, 32), (24, 27), (34, 16), (29, 22), (16, 5), (4, 18), (20, 14), (12, 30), (29, 21), (20, 28), (32, 23), (26, 12), (9, 0), (26, 30), (19, 4), (8, 25), (21, 26), (19, 9), (13, 8), (9, 11), (35, 28), (12, 23), (10, 15), (15, 16), (4, 6), (34, 6), (3, 9), (26, 27), (16, 18), (2, 2), (9, 10), (10, 12), (34, 5), (1, 27), (31, 25), (21, 12), (16, 29), (35, 26), (18, 26), (25, 16), (9, 4), (22, 11), (15, 13), (33, 19), (18, 7), (34, 25), (22, 8), (13, 10), (5, 1), (34, 27), (2, 3), (6, 6), (26, 4), (19, 18), (34, 24), (32, 15), (19, 22), (30, 29), (10, 4), (10, 23), (18, 18), (7, 16), (10, 10), (24, 16), (31, 18), (33, 29), (33, 4), (10, 3), (10, 31), (14, 5), (24, 30), (30, 24), (24, 8), (1, 32), (27, 2), (18, 20), (12, 3), (28, 15), (21, 6), (21, 9), (9, 15), (17, 21), (25, 1), (31, 9), (4, 14), (31, 11), (28, 25), (26, 31), (22, 16), (35, 19), (17, 29), (6, 22), (33, 24), (29, 24), (12, 14), (8, 26), (24, 22), (35, 8), (22, 1), (12, 32), (20, 16), (21, 22), (35, 6), (6, 24), (33, 23), (8, 0), (3, 11), (34, 30), (17, 2), (15, 32), (2, 10), (27, 3), (31, 3), (34, 28), (8, 15), (25, 24), (0, 29), (23, 28), (9, 20), (23, 4), (22, 25), (21, 2), (33, 16), (14, 27), (26, 0), (8, 19), (3, 4), (20, 0), (1, 11), (21, 8), (28, 4), (0, 30), (16, 24), (12, 20), (5, 7), (8, 16), (26, 26), (35, 11), (5, 29), (28, 26), (4, 23), (21, 32), (26, 19), (21, 7), (8, 22), (18, 16), (18, 9), (14, 17), (5, 24), (22, 28), (18, 23), (3, 22), (14, 4), (14, 26), (19, 7), (2, 17), (16, 32), (14, 6), (27, 8), (23, 27), (19, 15), (21, 20), (24, 28), (12, 10), (19, 5), (3, 19), (3, 10), (29, 27), (30, 18), (16, 15), (11, 15), (3, 27), (31, 1), (29, 25), (27, 13), (29, 30), (13, 30), (35, 29), (30, 17), (17, 20), (10, 13), (22, 3), (3, 26), (10, 25), (29, 11), (19, 13), (12, 27), (2, 0), (31, 19), (7, 22), (23, 14), (3, 31), (20, 29), (13, 24), (12, 13), (2, 20), (20, 23), (31, 14), (7, 6), (7, 13), (0, 1), (9, 26), (17, 7), (0, 8), (27, 14), (33, 13), (19, 8), (21, 11), (35, 20), (28, 22), (12, 16), (1, 24), (5, 30), (2, 29), (19, 16), (18, 27), (19, 21), (5, 11), (2, 12), (15, 21), (31, 7), (23, 18), (23, 12), (31, 24), (32, 31), (17, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "790248", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), 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), (8, 15), (31, 19), (29, 3), (5, 30), (9, 20), (26, 6), (4, 27), (32, 19), (18, 19), (4, 5), (25, 24), (5, 20), (6, 5), (16, 8), (26, 21), (30, 30), (16, 2), (22, 27), (27, 6), (29, 14), (8, 19), (23, 5), (18, 6), (26, 1), (22, 24), (27, 31), (0, 5), (0, 3), (20, 13), (17, 26), (12, 26), (23, 31), (19, 3), (9, 0), (3, 3), (33, 13), (11, 25), (19, 25), (22, 7), (1, 25), (22, 14), (4, 10), (18, 27), (10, 11), (29, 19), (17, 16), (31, 29), (8, 31), (26, 13), (14, 26), (32, 12), (22, 17), (5, 1), (4, 11), (27, 29), (3, 24), (7, 8), (23, 10), (0, 11), (3, 12), (10, 21), (26, 9), (27, 0), (7, 23), (0, 12), (30, 11), (21, 4), (21, 25), (29, 21), (22, 28), (7, 10), (9, 13), (30, 31), (18, 18), (26, 20), (25, 9), (9, 8), (33, 2), (30, 21), (30, 14), (21, 15), (8, 12), (33, 0), (20, 31), (27, 2), (28, 24), (21, 18), (8, 22), (11, 13), (20, 3), (13, 2), (5, 22), (24, 25), (9, 10), (24, 0), (0, 21), (26, 15), (19, 15), (33, 22), (30, 7), (31, 2), (10, 25), (28, 1), (30, 6), (23, 21), (9, 19), (16, 16), (14, 23), (9, 1), (4, 24), (30, 12), (33, 28), (21, 0), (19, 23), (12, 20), (20, 12), (21, 20), (22, 13), (21, 9), (18, 26), (20, 4), (4, 13), (7, 5), (19, 6), (26, 16), (1, 30), (6, 16), (23, 25), (3, 31), (9, 25), (8, 5), (24, 26), (27, 8), (6, 10), (10, 19), (10, 8), (7, 2), (20, 11), (11, 24), (13, 24), (25, 31), (4, 3), (1, 10), (15, 21), (4, 23), (16, 0), (4, 22), (24, 21), (3, 0), (15, 4), (28, 15), (5, 12), (9, 26), (26, 0), (26, 18), (33, 23), (6, 30), (6, 27), (12, 8), (13, 15), (31, 21), (6, 6), (17, 9), (2, 25), (3, 10), (28, 22), (20, 23), (1, 5), (9, 15), (28, 5), (19, 17), (15, 5), (0, 29), (11, 9), (8, 8), (4, 6), (19, 4), (21, 29), (31, 20), (14, 21), (9, 18), (22, 5), (33, 20), (25, 26), (32, 7), (22, 26), (27, 5), (23, 30), (23, 27), (7, 6), (8, 17), (28, 9), (1, 8), (10, 12), (12, 2), (22, 0), (15, 30), (28, 17), (30, 24), (29, 2), (15, 27), (8, 18), (31, 0), (26, 28), (10, 22), (13, 1), (25, 29), (17, 23), (24, 12), (21, 23), (24, 27), (14, 16), (12, 29), (0, 13), (21, 16), (13, 0), (27, 26), (14, 30), (8, 30), (6, 9), (27, 27), (3, 22), (33, 10), (22, 3), (23, 20), (2, 9), (28, 2), (20, 29), (14, 31), (20, 27), (10, 4), (33, 27), (6, 25), (15, 8), (22, 31), (25, 19), (13, 29), (21, 8), (31, 11), (3, 2), (21, 7), (15, 22), (18, 16), (4, 12), (9, 22), (4, 19), (19, 11), (15, 11), (27, 28), (28, 31), (11, 6), (19, 7), (6, 8), (21, 12), (7, 1), (10, 7), (2, 1), (0, 27), (28, 21), (13, 20), (8, 23), (3, 27), (6, 28), (12, 11), (8, 11), (17, 25), (20, 6), (7, 25), (16, 25), (3, 18), (6, 3), (1, 15), (31, 25), (29, 22), (0, 25), (11, 11), (4, 0), (30, 8), (18, 4), (18, 12), (3, 28), (28, 16), (9, 27), (14, 27), (31, 24), (1, 22), (31, 18), (15, 10), (23, 4), (5, 31), (29, 29), (6, 24), (16, 9), (13, 5), (29, 26), (15, 17), (12, 25), (17, 20), (32, 14), (5, 6), (33, 1), (13, 30), (31, 5), (30, 10), (16, 1), (13, 10), (0, 8), (11, 20), (33, 14), (1, 11), (17, 15), (28, 3), (10, 0), (28, 7), (20, 9), (19, 21), (29, 24), (12, 31), (12, 14), (1, 23), (33, 25), (31, 7), (11, 28), (16, 11), (15, 28), (23, 13), (5, 2), (26, 19), (24, 20), (8, 13), (30, 0), (2, 3), (5, 26), (28, 19), (18, 0), (5, 28), (11, 3), (4, 15), (26, 4), (12, 13), (2, 8), (8, 7), (23, 7), (0, 16), (10, 16), (9, 11), (14, 17), (17, 22), (29, 20), (32, 17), (10, 1), (30, 20), (3, 5), (25, 16), (7, 27), (19, 29), (3, 11), (22, 19), (1, 1), (20, 8), (31, 3), (26, 26), (16, 14), (2, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10368", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 7), (6, 29), (13, 17), (2, 6), (5, 5), (29, 14), (19, 12), (14, 2), (10, 11), (9, 8), (21, 3), (12, 31), (6, 32), (32, 3), (5, 17), (28, 31), (11, 12), (9, 13), (29, 7), (21, 2), (29, 16), (27, 27), (29, 13), (6, 22), (28, 6), (3, 16), (3, 23), (9, 10), (22, 10), (7, 25), (25, 7), (19, 30), (24, 14), (18, 6), (9, 14), (14, 17), (12, 8), (26, 30), (21, 16), (16, 1), (10, 29), (15, 18), (27, 26), (25, 10), (11, 30), (23, 16), (4, 1), (18, 1), (13, 7), (21, 17), (0, 14), (13, 27), (0, 20), (20, 2), (6, 30), (11, 23), (16, 21), (26, 5), (1, 6), (1, 23), (9, 19), (19, 14), (8, 12), (23, 7), (28, 2), (26, 29), (28, 4), (9, 12), (28, 11), (8, 15), (9, 27), (25, 27), (31, 19), (17, 17), (17, 25), (14, 9), (6, 23), (4, 23), (0, 27), (13, 1), (2, 17), (12, 16), (28, 12), (13, 3), (28, 25), (3, 27), (8, 16), (7, 2), (27, 18), (1, 15), (26, 21), (29, 20), (9, 6), (19, 18), (9, 3), (6, 17), (31, 11), (23, 26), (23, 20), (31, 17), (10, 21), (18, 24), (29, 32), (6, 9), (0, 17), (13, 23), (21, 30), (24, 13), (27, 25), (17, 21), (31, 31), (7, 19), (3, 4), (18, 21), (29, 3), (28, 24), (16, 29), (22, 20), (30, 24), (31, 24), (28, 10), (29, 29), (6, 15), (2, 20), (4, 17), (16, 5), (1, 31), (8, 25), (19, 19), (29, 23), (21, 14), (14, 12), (11, 29), (13, 28), (3, 20), (23, 21), (23, 24), (29, 31), (21, 31), (6, 1), (10, 0), (22, 23), (0, 8), (7, 3), (1, 29), (8, 8), (3, 28), (10, 19), (4, 2), (1, 0), (16, 14), (18, 19), (15, 17), (5, 23), (17, 18), (24, 12), (30, 0), (12, 32), (0, 5), (12, 5), (14, 21), (6, 24), (28, 20), (7, 14), (9, 26), (29, 11), (18, 2), (12, 25), (22, 27), (13, 29), (28, 27), (30, 7), (11, 21), (10, 23), (16, 19), (32, 19), (18, 15), (21, 24), (1, 32), (12, 18), (7, 6), (16, 4), (6, 4), (21, 18), (23, 31), (1, 9), (2, 32), (17, 1), (20, 27), (22, 0), (9, 16), (4, 21), (3, 24), (5, 13), (10, 16), (14, 4), (17, 13), (8, 26), (15, 6), (32, 23), (15, 31), (27, 21), (29, 2), (26, 27), (12, 14), (29, 10), (32, 30), (13, 15), (19, 10), (5, 21), (30, 8), (16, 22), (25, 9), (32, 14), (18, 9), (27, 22), (3, 22), (14, 16), (16, 28), (22, 22), (1, 4), (0, 2), (4, 7), (5, 22), (26, 18), (4, 29), (18, 22), (20, 5), (2, 28), (31, 27), (2, 27), (30, 18), (21, 12), (5, 15), (28, 0), (31, 26), (9, 1), (28, 16), (23, 25), (19, 32), (18, 7), (8, 4), (24, 17), (7, 15), (5, 7), (9, 9), (16, 20), (19, 9), (20, 30), (32, 29), (27, 31), (17, 23), (25, 1), (28, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887712", "dataset": "MATH"}
{"messages": [{"content": "In a 32x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 37), 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), (1, 27), (16, 2), (23, 25), (9, 9), (2, 32), (30, 7), (7, 6), (11, 31), (6, 37), (26, 18), (21, 24), (11, 19), (24, 15), (22, 22), (29, 22), (2, 24), (25, 2), (9, 21), (9, 25), (13, 29), (10, 11), (13, 16), (1, 9), (1, 36), (6, 31), (23, 7), (9, 3), (23, 28), (7, 33), (26, 0), (12, 29), (30, 29), (1, 26), (21, 2), (20, 16), (20, 34), (19, 1), (2, 25), (25, 28), (3, 36), (29, 15), (14, 23), (21, 5), (16, 29), (9, 13), (24, 25), (27, 12), (15, 24), (0, 31), (7, 9), (7, 34), (28, 2), (26, 34), (10, 9), (18, 2), (2, 26), (5, 35), (1, 18), (15, 5), (22, 14), (30, 4), (14, 6), (16, 22), (26, 31), (9, 26), (9, 7), (8, 22), (19, 0), (2, 8), (17, 17), (24, 4), (15, 31), (7, 15), (7, 4), (3, 8), (15, 8), (24, 31), (3, 11), (2, 6), (22, 34), (0, 14), (13, 27), (15, 19), (17, 28), (3, 17), (15, 25), (0, 32), (4, 18), (29, 19), (0, 10), (29, 32), (4, 0), (4, 10), (20, 22), (30, 27), (27, 3), (21, 19), (21, 14), (27, 8), (13, 26), (16, 17), (11, 12), (31, 12), (4, 36), (18, 32), (20, 15), (11, 15), (22, 21), (31, 19), (1, 21), (24, 29), (14, 13), (24, 26), (28, 27), (20, 26), (13, 3), (26, 13), (11, 24), (23, 5), (25, 8), (1, 14), (20, 20), (31, 1), (29, 25), (9, 30), (24, 3), (6, 25), (6, 16), (14, 1), (7, 30), (14, 0), (23, 2), (24, 27), (4, 13), (17, 3), (23, 33), (19, 5), (30, 21), (19, 23), (27, 2), (28, 6), (19, 35), (26, 14), (5, 31), (14, 37), (21, 18), (4, 35), (3, 1), (23, 26), (20, 21), (17, 23), (0, 28), (2, 22), (18, 24), (4, 22), (24, 24), (3, 34), (27, 15), (13, 1), (6, 15), (25, 25), (25, 29), (7, 22), (19, 7), (22, 37), (14, 20), (21, 26), (19, 28), (20, 1), (2, 18), (16, 27), (17, 11), (19, 15), (18, 27), (26, 33), (6, 26), (7, 26), (2, 16), (5, 6), (0, 33), (2, 2), (3, 29), (23, 29), (30, 19), (28, 26), (9, 31), (8, 32), (26, 23), (11, 10), (12, 2), (5, 15), (31, 8), (29, 12), (26, 1), (8, 20), (13, 28), (15, 20), (4, 34), (8, 34), (13, 35), (5, 33), (25, 1), (8, 30), (14, 17), (14, 18), (30, 16), (10, 30), (4, 27), (0, 21), (10, 17), (28, 21), (9, 24), (24, 11), (8, 14), (31, 5), (27, 13), (10, 33), (6, 23), (16, 1), (4, 15), (22, 26), (31, 14), (3, 0), (10, 19), (8, 21), (13, 33), (7, 2), (4, 25), (24, 12), (20, 33), (9, 1), (17, 6), (14, 22), (9, 14), (3, 18), (7, 10), (15, 30), (11, 20), (3, 3), (30, 23), (12, 8), (18, 35), (0, 4), (10, 12), (25, 4), (26, 35), (28, 15), (29, 31), (4, 14), (25, 12), (17, 7), (18, 37), (8, 4), (4, 24), (13, 12), (3, 35), (24, 37), (13, 4), (6, 4), (17, 18), (21, 36), (15, 16), (29, 0), (8, 13), (19, 10), (23, 1), (10, 1), (4, 19), (29, 26), (27, 37), (11, 14), (18, 18), (2, 12), (18, 16), (2, 30), (19, 13), (22, 35), (20, 35), (5, 14), (21, 12), (25, 36), (24, 35), (9, 28), (5, 7), (20, 13), (5, 34), (25, 32), (1, 22), (29, 14), (11, 27), (22, 6), (19, 26), (12, 22), (26, 16), (7, 12), (5, 1), (15, 23), (25, 7), (21, 23), (9, 33), (6, 27), (13, 30), (25, 34), (22, 15), (31, 26), (7, 14), (16, 37), (30, 30), (4, 2), (23, 31), (14, 7), (13, 10), (9, 23), (5, 2), (19, 8), (5, 32), (6, 9), (24, 6), (24, 32), (28, 25), (2, 23), (23, 34), (27, 0), (27, 4), (15, 21), (9, 6), (1, 37), (6, 36), (28, 0), (26, 22), (18, 19), (10, 6), (10, 26), (5, 25), (0, 26), (19, 31), (28, 37), (11, 4), (8, 26), (18, 28), (26, 12), (12, 30), (11, 11), (16, 14), (18, 1), (28, 19), (18, 23), (16, 13), (28, 23), (16, 21), (15, 13), (12, 3), (2, 29), (11, 0), (22, 33), (15, 9), (27, 22), (6, 35), (6, 14), (18, 22), (28, 24), (18, 20), (9, 11), (3, 15), (6, 8), (13, 5), (28, 33), (8, 25), (3, 26), (1, 29), (27, 20), (11, 6), (0, 8), (4, 17), (22, 19), (19, 21), (18, 17), (13, 0), (28, 31), (15, 37), (6, 20), (18, 13), (10, 16), (21, 32), (8, 5), (20, 36), (16, 33), (22, 17), (27, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522288", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (23, 14), (13, 16), (23, 22), (11, 22), (4, 0), (13, 25), (8, 29), (28, 14), (18, 13), (1, 28), (31, 28), (6, 21), (2, 20), (8, 26), (13, 10), (19, 8), (25, 17), (22, 11), (18, 16), (4, 15), (4, 9), (28, 22), (27, 21), (11, 23), (28, 7), (23, 20), (23, 5), (18, 4), (4, 29), (23, 15), (22, 2), (27, 28), (0, 25), (10, 14), (19, 26), (30, 23), (22, 4), (6, 2), (26, 18), (13, 24), (8, 21), (11, 28), (14, 24), (3, 19), (20, 17), (31, 11), (17, 2), (6, 11), (31, 5), (17, 20), (30, 18), (5, 13), (15, 16), (31, 4), (15, 18), (28, 23), (17, 21), (30, 15), (28, 27), (26, 16), (3, 10), (15, 7), (16, 26), (31, 3), (20, 15), (15, 20), (4, 5), (4, 8), (31, 27), (31, 19), (13, 18), (11, 26), (25, 18), (25, 1), (7, 14), (18, 25), (9, 9), (2, 24), (30, 26), (27, 19), (5, 6), (6, 18), (25, 15), (17, 4), (22, 24), (24, 19), (12, 8), (14, 12), (7, 7), (12, 4), (30, 21), (26, 13), (29, 8), (6, 10), (14, 22), (14, 2), (16, 15), (31, 9), (31, 20), (20, 16), (12, 10), (20, 6), (29, 3), (24, 12), (21, 19), (29, 1), (5, 26), (20, 26), (24, 23), (27, 5), (31, 0), (18, 17), (18, 6), (16, 10), (29, 10), (8, 13), (8, 23), (12, 11), (15, 25), (26, 2), (18, 27), (24, 9), (14, 6), (26, 20), (2, 12), (8, 27), (2, 18), (9, 19), (0, 10), (18, 7), (22, 7), (31, 24), (28, 17), (8, 5), (4, 19), (3, 9), (11, 7), (14, 28), (5, 3), (24, 20), (13, 29), (20, 27), (30, 4), (17, 6), (27, 14), (2, 2), (9, 20), (22, 6), (23, 11), (22, 12), (1, 3), (16, 13), (1, 0), (26, 23), (16, 6), (27, 29), (21, 6), (12, 15), (19, 6), (9, 1), (21, 28), (14, 23), (17, 1), (5, 27), (4, 14), (7, 4), (1, 17), (9, 21), (5, 1), (31, 15), (7, 27), (8, 15), (20, 22), (10, 15), (16, 4), (1, 13), (25, 5), (7, 13), (0, 6), (25, 12), (25, 21), (28, 10), (13, 17), (6, 20), (17, 9), (27, 23), (6, 28), (19, 17), (24, 11), (21, 20), (3, 25), (29, 19), (8, 0), (10, 23), (15, 12), (2, 15), (20, 29), (26, 6), (19, 7), (28, 1), (23, 12), (5, 25), (3, 5), (29, 24), (16, 7), (5, 12), (26, 12), (7, 22), (13, 3), (11, 14), (7, 12), (15, 1), (7, 0), (17, 22), (7, 19), (4, 10), (25, 7), (4, 25), (16, 18), (6, 3), (0, 22), (14, 13), (6, 29), (29, 11), (16, 25), (26, 29), (9, 29), (15, 19), (1, 20), (26, 3), (10, 0), (22, 16), (29, 15), (10, 22), (12, 25), (2, 26), (29, 20), (19, 23), (27, 27), (10, 7), (25, 23), (22, 3), (12, 22), (19, 11), (22, 0), (21, 7), (26, 28), (20, 5), (30, 14), (22, 10), (21, 8), (24, 8), (9, 8), (0, 24), (27, 22), (3, 1), (15, 27), (14, 27), (0, 14), (4, 11), (19, 1), (1, 6), (28, 13), (19, 19), (4, 16), (18, 22), (12, 9), (1, 15), (20, 18), (11, 19), (23, 29), (29, 28), (15, 28), (0, 15), (23, 7), (31, 14), (27, 13), (26, 19), (27, 20), (21, 16), (1, 25), (3, 8), (0, 19), (9, 15), (26, 17), (28, 26), (26, 27), (8, 8), (31, 6), (25, 29), (23, 10), (18, 11), (18, 21), (4, 28), (20, 2), (21, 9), (31, 26), (25, 20), (27, 7), (30, 8), (12, 18), (7, 29), (9, 25), (30, 3), (8, 1), (17, 27), (13, 8), (23, 3), (9, 4), (17, 24), (8, 17), (24, 1), (11, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559483", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 23), (12, 1), (30, 4), (3, 8), (32, 29), (15, 2), (4, 9), (32, 18), (24, 14), (13, 5), (9, 30), (29, 18), (5, 21), (31, 27), (13, 30), (11, 26), (23, 6), (25, 25), (25, 19), (30, 26), (29, 14), (19, 17), (25, 21), (15, 29), (33, 6), (8, 24), (9, 24), (27, 20), (5, 26), (14, 10), (5, 9), (30, 14), (25, 1), (16, 16), (3, 29), (7, 7), (26, 20), (19, 5), (22, 31), (13, 7), (5, 4), (30, 0), (3, 10), (0, 18), (19, 30), (25, 28), (32, 20), (18, 21), (30, 2), (8, 26), (25, 2), (26, 21), (3, 13), (12, 20), (7, 3), (20, 15), (22, 6), (6, 25), (33, 26), (8, 20), (13, 14), (24, 20), (30, 23), (29, 7), (2, 21), (33, 20), (25, 6), (2, 25), (10, 6), (24, 8), (29, 22), (23, 5), (13, 27), (20, 6), (1, 14), (33, 15), (30, 22), (17, 28), (31, 15), (23, 11), (15, 7), (9, 18), (7, 5), (30, 1), (28, 22), (5, 3), (4, 11), (16, 28), (0, 20), (33, 3), (27, 2), (6, 16), (24, 11), (27, 25), (20, 8), (3, 28), (6, 31), (21, 12), (5, 13), (23, 9), (20, 20), (3, 5), (22, 4), (22, 0), (0, 14), (29, 11), (30, 11), (13, 0), (9, 28), (32, 16), (30, 27), (0, 17), (18, 1), (8, 17), (11, 16), (32, 17), (26, 11), (6, 8), (24, 9), (7, 0), (24, 10), (18, 5), (10, 17), (19, 24), (27, 26), (30, 3), (20, 22), (0, 3), (32, 31), (6, 7), (12, 10), (0, 29), (7, 21), (11, 1), (15, 16), (8, 27), (29, 16), (22, 12), (10, 4), (17, 4), (5, 16), (22, 21), (11, 6), (21, 2), (33, 0), (0, 11), (11, 7), (17, 23), (14, 12), (6, 19), (26, 12), (12, 8), (20, 17), (11, 11), (31, 29), (25, 12), (0, 28), (4, 0), (2, 26), (27, 16), (1, 10), (21, 23), (13, 13), (8, 1), (28, 27), (32, 30), (10, 30), (14, 8), (26, 5), (27, 21), (9, 8), (15, 9), (28, 16), (22, 7), (31, 3), (5, 8), (8, 3), (5, 23), (23, 19), (26, 19), (28, 23), (21, 26), (20, 14), (2, 0), (5, 6), (11, 28), (21, 18), (33, 12), (6, 26), (17, 21), (28, 21), (27, 10), (33, 8), (5, 10), (10, 2), (28, 13), (11, 24), (3, 18), (31, 14), (20, 30), (3, 14), (33, 17), (29, 27), (29, 31), (18, 24), (8, 19), (23, 21), (12, 15), (0, 24), (16, 29), (23, 14), (10, 15), (14, 1), (3, 16), (26, 8), (17, 25), (21, 29), (27, 4), (30, 31), (22, 18), (10, 0), (11, 31), (9, 9), (22, 11), (18, 26), (7, 1), (14, 28), (6, 29), (3, 11), (33, 22), (5, 19), (20, 12), (16, 14), (23, 2), (20, 23), (16, 31), (24, 24), (24, 0), (6, 28), (23, 3), (6, 4), (2, 4), (24, 17), (19, 4), (8, 6), (31, 16), (21, 28), (25, 4), (0, 15), (13, 18), (31, 13), (30, 16), (20, 5), (31, 7), (26, 25), (2, 24), (32, 6), (27, 23), (26, 4), (18, 13), (17, 11), (2, 1), (6, 5), (1, 28), (25, 26), (16, 21), (12, 29), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451620", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 6), (6, 35), (14, 17), (19, 13), (5, 20), (11, 15), (14, 13), (18, 28), (29, 10), (4, 30), (1, 10), (11, 16), (25, 33), (14, 12), (17, 33), (26, 17), (26, 26), (24, 22), (5, 23), (29, 29), (7, 22), (12, 16), (2, 27), (21, 6), (8, 27), (20, 23), (3, 35), (1, 18), (18, 17), (2, 9), (5, 9), (6, 6), (16, 22), (23, 20), (3, 2), (19, 27), (0, 30), (11, 13), (16, 14), (3, 20), (20, 27), (17, 11), (0, 16), (13, 26), (4, 14), (6, 7), (23, 5), (17, 25), (25, 24), (23, 24), (4, 35), (15, 8), (20, 13), (25, 26), (28, 32), (11, 33), (17, 31), (22, 35), (18, 14), (16, 1), (16, 25), (22, 10), (14, 29), (20, 3), (12, 24), (0, 15), (15, 20), (11, 28), (8, 4), (29, 28), (5, 1), (1, 32), (7, 33), (21, 35), (4, 23), (1, 24), (18, 35), (20, 21), (19, 24), (11, 14), (8, 22), (19, 16), (22, 4), (0, 34), (0, 7), (9, 2), (0, 6), (8, 18), (11, 2), (10, 14), (17, 1), (21, 28), (29, 24), (4, 25), (17, 14), (19, 31), (3, 0), (22, 28), (10, 15), (18, 5), (17, 24), (16, 6), (17, 8), (24, 13), (26, 31), (5, 22), (24, 19), (1, 23), (13, 23), (27, 6), (5, 12), (24, 11), (27, 33), (1, 2), (28, 19), (10, 25), (28, 22), (10, 5), (28, 12), (2, 16), (4, 27), (25, 25), (16, 15), (25, 18), (1, 29), (15, 30), (23, 15), (27, 16), (20, 32), (25, 10), (0, 14), (28, 4), (1, 22), (9, 19), (24, 10), (13, 17), (14, 16), (22, 6), (23, 11), (16, 18), (28, 0), (8, 12), (17, 15), (2, 24), (16, 16), (13, 1), (12, 20), (0, 26), (0, 31), (26, 16), (3, 9), (20, 14), (4, 16), (7, 24), (18, 7), (28, 15), (9, 9), (12, 12), (10, 16), (1, 31), (5, 19), (8, 35), (25, 23), (1, 19), (15, 27), (6, 5), (24, 35), (0, 18), (18, 25), (27, 11), (27, 30), (13, 30), (20, 26), (26, 5), (17, 10), (28, 25), (5, 28), (17, 32), (10, 31), (7, 34), (3, 13), (26, 20), (7, 8), (27, 26), (27, 35), (27, 31), (18, 27), (28, 31), (5, 0), (11, 34), (14, 30), (17, 6), (20, 1), (28, 30), (14, 24), (12, 25), (12, 15), (5, 13), (6, 21), (15, 34), (29, 7), (27, 23), (18, 2), (16, 10), (9, 23), (0, 35), (8, 34), (10, 26), (7, 29), (7, 23), (23, 22), (28, 26), (14, 11), (15, 0), (3, 7), (28, 17), (15, 31), (17, 13), (13, 35), (3, 17), (3, 15), (18, 9), (6, 13), (11, 26), (4, 28), (17, 29), (13, 31), (25, 20), (1, 20), (28, 18), (29, 5), (6, 0), (14, 18), (16, 19), (3, 32), (18, 0), (18, 4), (22, 24), (12, 11), (20, 22), (21, 1), (4, 10), (22, 8), (1, 25), (7, 25), (3, 12), (13, 13), (23, 2), (19, 26), (13, 10), (29, 3), (10, 23), (17, 21), (6, 10), (13, 15), (16, 31), (0, 25), (4, 20), (28, 5), (27, 4), (20, 29), (6, 23), (2, 22), (26, 18), (19, 8), (18, 12), (16, 34), (23, 16), (16, 27), (25, 13), (8, 15), (2, 3), (20, 30), (12, 27), (22, 27), (13, 34), (15, 1), (10, 9), (28, 27), (26, 13), (29, 26), (13, 0), (8, 30), (24, 33), (4, 24), (22, 21), (13, 21), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73440", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (2, 0), (36, 13), (18, 10), (24, 23), (12, 14), (29, 3), (33, 32), (37, 14), (8, 11), (34, 6), (11, 24), (29, 6), (2, 12), (17, 17), (36, 16), (8, 17), (6, 10), (16, 23), (15, 4), (4, 23), (25, 10), (32, 21), (30, 24), (10, 26), (18, 0), (10, 0), (16, 24), (16, 3), (6, 12), (11, 8), (5, 19), (4, 26), (10, 9), (9, 32), (19, 2), (34, 23), (16, 11), (23, 3), (15, 16), (23, 26), (33, 11), (37, 15), (35, 30), (8, 13), (34, 32), (21, 19), (31, 0), (6, 18), (3, 10), (20, 1), (20, 20), (33, 14), (5, 33), (30, 10), (31, 30), (1, 24), (35, 8), (9, 20), (19, 25), (0, 3), (6, 29), (32, 12), (3, 2), (10, 16), (32, 4), (19, 29), (34, 1), (19, 7), (22, 22), (20, 17), (1, 0), (11, 27), (28, 23), (21, 16), (11, 19), (19, 8), (12, 15), (23, 13), (26, 7), (6, 20), (8, 7), (3, 27), (36, 8), (0, 32), (27, 6), (27, 33), (34, 26), (23, 15), (20, 8), (37, 28), (4, 25), (4, 22), (35, 25), (31, 20), (23, 19), (0, 13), (36, 24), (7, 20), (10, 21), (20, 33), (23, 0), (17, 14), (11, 18), (37, 6), (31, 6), (8, 31), (4, 27), (21, 9), (13, 22), (17, 26), (28, 18), (29, 23), (10, 29), (29, 0), (22, 11), (29, 2), (28, 4), (15, 3), (3, 22), (20, 26), (22, 31), (17, 4), (13, 0), (25, 17), (7, 0), (34, 17), (17, 11), (4, 13), (28, 6), (21, 21), (16, 30), (33, 10), (33, 33), (19, 6), (12, 8), (13, 18), (21, 12), (10, 18), (0, 6), (14, 9), (4, 28), (6, 13), (21, 7), (31, 8), (24, 6), (0, 23), (27, 8), (14, 2), (12, 17), (20, 5), (18, 17), (11, 33), (17, 18), (34, 2), (33, 27), (22, 33), (24, 14), (4, 21), (19, 12), (8, 22), (5, 24), (28, 8), (30, 13), (21, 4), (6, 22), (34, 7), (35, 1), (20, 32), (3, 23), (16, 12), (28, 26), (33, 8), (5, 20), (19, 26), (23, 14), (5, 7), (1, 17), (29, 15), (24, 4), (34, 3), (18, 33), (17, 7), (28, 33), (28, 2), (16, 2), (30, 16), (30, 6), (23, 8), (4, 24), (19, 30), (35, 10), (35, 21), (13, 20), (21, 30), (29, 33), (6, 7), (22, 16), (1, 31), (33, 18), (23, 33), (16, 28), (19, 5), (13, 6), (23, 31), (18, 13), (0, 29), (14, 10), (10, 19), (35, 29), (2, 22), (36, 4), (14, 28), (9, 21), (8, 9), (15, 2), (11, 25), (1, 32), (30, 11), (22, 14), (13, 1), (23, 25), (1, 6), (30, 3), (14, 5), (31, 7), (0, 18), (2, 27), (22, 15), (22, 28), (2, 20), (5, 11), (27, 15), (28, 30), (3, 3), (25, 2), (17, 29), (3, 26), (2, 28), (20, 25), (15, 12), (36, 12), (6, 16), (23, 20), (19, 31), (8, 18), (28, 11), (35, 7), (23, 4), (25, 1), (24, 15), (37, 1), (28, 12), (27, 10), (23, 1), (6, 32), (7, 5), (1, 25), (34, 29), (11, 13), (24, 21), (27, 0), (23, 23), (31, 24), (23, 18), (9, 14), (21, 15), (3, 31), (2, 4), (5, 32), (11, 0), (36, 29), (14, 16), (15, 20), (7, 14), (28, 14), (35, 18), (28, 22), (7, 28), (20, 6), (16, 6), (23, 5), (32, 17), (28, 31), (13, 5), (5, 9), (4, 32), (9, 26), (10, 15), (18, 19), (13, 23), (16, 25), (25, 13), (33, 6), (8, 8), (15, 8), (36, 23), (37, 20), (12, 30), (3, 28), (18, 23), (2, 30), (14, 14), (35, 14), (21, 6), (3, 19), (27, 1), (9, 5), (3, 32), (34, 22), (0, 21), (12, 7), (22, 8), (25, 22), (6, 3), (21, 22), (6, 27), (15, 18), (20, 19), (0, 33), (20, 22), (26, 11), (36, 17), (16, 14), (3, 0), (36, 31), (28, 16), (10, 32), (12, 23), (34, 13), (5, 26), (16, 15), (19, 24), (18, 4), (3, 15), (0, 26), (4, 29), (20, 31), (17, 28), (16, 21), (24, 8), (13, 8), (13, 14), (19, 19), (18, 6), (12, 19), (16, 0), (4, 14), (17, 30), (12, 6), (23, 2), (10, 4), (26, 21), (30, 26), (20, 13), (1, 3), (1, 5), (22, 6), (26, 4), (11, 31), (9, 29), (32, 3), (15, 5), (29, 14), (37, 22), (22, 10), (0, 22), (15, 29), (32, 2), (31, 17), (32, 18), (24, 19), (19, 21), (15, 33), (22, 20), (14, 26), (10, 24), (11, 23), (11, 29), (33, 30), (21, 26), (30, 17), (31, 2), (20, 14), (34, 18), (12, 0), (2, 5), (9, 33), (26, 15), (23, 24), (9, 10), (13, 19), (9, 25), (11, 30), (33, 24), (23, 9), (33, 7), (10, 7), (21, 18), (29, 20), (14, 21), (29, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842520", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (38, 4), (32, 26), (28, 19), (19, 3), (25, 23), (18, 1), (16, 15), (17, 24), (5, 7), (27, 17), (10, 20), (14, 24), (5, 9), (29, 22), (21, 11), (18, 16), (35, 10), (35, 5), (21, 6), (14, 3), (22, 1), (29, 6), (29, 11), (34, 13), (22, 17), (16, 12), (6, 4), (10, 24), (7, 23), (23, 24), (38, 24), (18, 30), (27, 28), (22, 3), (9, 4), (26, 12), (20, 24), (17, 2), (0, 15), (29, 9), (10, 7), (8, 29), (15, 1), (28, 14), (23, 0), (18, 11), (27, 25), (15, 7), (13, 16), (33, 6), (6, 9), (14, 16), (33, 21), (6, 7), (23, 22), (22, 6), (30, 32), (27, 3), (31, 1), (6, 21), (12, 3), (38, 31), (29, 28), (20, 16), (2, 4), (25, 16), (32, 14), (28, 28), (37, 32), (8, 23), (38, 0), (23, 11), (18, 20), (31, 23), (18, 26), (24, 25), (30, 26), (3, 12), (31, 22), (0, 34), (2, 5), (9, 1), (9, 24), (27, 21), (35, 18), (27, 31), (14, 25), (1, 22), (32, 9), (22, 8), (4, 1), (22, 23), (18, 2), (14, 29), (4, 5), (28, 23), (14, 27), (10, 21), (21, 4), (17, 8), (26, 26), (18, 9), (7, 19), (23, 13), (29, 34), (28, 24), (13, 17), (18, 34), (33, 4), (5, 28), (26, 32), (15, 23), (17, 10), (15, 18), (13, 26), (9, 28), (19, 16), (12, 12), (27, 4), (22, 31), (22, 25), (10, 3), (16, 18), (31, 3), (0, 7), (9, 18), (33, 12), (32, 24), (16, 10), (20, 22), (21, 15), (5, 0), (31, 14), (37, 6), (36, 31), (26, 20), (24, 11), (13, 34), (33, 11), (36, 21), (33, 3), (28, 21), (31, 29), (16, 3), (23, 29), (30, 23), (7, 5), (38, 1), (19, 7), (14, 8), (13, 8), (35, 32), (7, 25), (19, 25), (20, 25), (0, 13), (28, 27), (4, 27), (13, 10), (14, 32), (0, 10), (32, 2), (35, 31), (31, 7), (16, 1), (2, 8), (4, 9), (7, 6), (22, 28), (4, 13), (12, 24), (25, 34), (37, 20), (38, 22), (23, 12), (30, 18), (6, 31), (1, 13), (11, 21), (0, 29), (13, 29), (26, 23), (24, 13), (12, 10), (29, 1), (35, 30), (35, 8), (8, 9), (28, 32), (0, 9), (28, 22), (26, 14), (7, 13), (23, 7), (28, 33), (10, 17), (11, 1), (17, 20), (37, 21), (3, 30), (19, 18), (14, 30), (24, 7), (13, 25), (38, 19), (38, 13), (5, 8), (29, 20), (33, 30), (11, 10), (8, 7), (24, 33), (0, 30), (13, 4), (12, 8), (36, 8), (24, 5), (19, 24), (35, 26), (22, 27), (29, 3), (31, 28), (7, 11), (10, 29), (38, 7), (8, 17), (32, 32), (25, 14), (3, 21), (27, 27), (34, 1), (27, 29), (8, 24), (1, 15), (19, 15), (31, 18), (29, 25), (38, 5), (28, 20), (33, 18), (12, 34), (31, 9), (37, 24), (31, 11), (23, 26), (28, 6), (13, 27), (20, 12), (26, 27), (26, 4), (1, 20), (26, 0), (11, 23), (6, 10), (19, 33), (12, 0), (13, 7), (36, 12), (6, 27), (21, 31), (35, 7), (5, 6), (3, 22), (19, 31), (30, 14), (2, 7), (1, 24), (21, 20), (26, 24), (15, 15), (35, 29), (9, 29), (6, 16), (11, 11), (2, 9), (27, 18), (37, 2), (1, 11), (18, 28), (33, 31), (11, 17), (36, 27), (24, 6), (16, 30), (26, 11), (27, 7), (21, 21), (26, 33), (8, 12), (19, 30), (22, 19), (17, 21), (19, 10), (4, 3), (18, 27), (13, 12), (27, 2), (35, 15), (36, 18), (19, 27), (21, 18), (12, 33), (11, 3), (4, 30), (19, 1), (31, 24), (18, 18), (7, 28), (16, 9), (0, 17), (19, 29), (6, 5), (27, 19), (5, 3), (31, 17), (28, 17), (21, 29), (6, 14), (20, 33), (13, 24), (35, 20), (16, 6), (18, 17), (9, 0), (32, 29), (24, 31), (23, 23), (10, 22), (34, 23), (12, 2), (5, 5), (12, 4), (19, 28), (15, 16), (20, 20), (12, 18), (1, 19), (16, 5), (21, 32), (20, 2), (15, 21), (6, 15), (36, 5), (28, 5), (14, 5), (25, 9), (35, 4), (15, 34), (12, 28), (6, 30), (8, 14), (27, 0), (22, 20), (25, 0), (23, 10), (1, 4), (11, 6), (14, 1), (11, 25), (36, 28), (5, 18), (34, 0), (9, 17), (10, 15), (24, 22), (34, 6), (4, 24), (26, 9), (17, 27), (36, 32), (11, 29), (7, 9), (33, 19), (16, 32), (17, 31), (2, 10), (37, 5), (35, 19), (14, 10), (26, 2), (6, 18), (15, 14), (1, 9), (12, 21), (28, 1), (28, 10), (9, 13), (36, 14), (3, 26), (1, 31), (24, 8), (29, 21), (5, 12), (1, 32), (35, 23), (28, 12), (23, 21), (3, 32), (30, 0), (25, 28), (15, 24), (27, 6), (37, 1), (34, 3), (6, 6), (26, 30), (20, 28), (32, 13), (11, 7), (17, 13), (20, 21), (34, 12), (21, 10), (9, 21), (22, 33), (13, 23), (13, 14), (26, 16), (11, 28), (20, 18), (31, 30), (36, 9), (1, 5), (8, 6), (34, 5), (8, 32), (37, 22), (33, 25), (19, 12), (29, 12), (12, 27), (22, 10), (1, 16), (9, 19), (34, 16), (17, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540000", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 37), (30, 30), (26, 31), (11, 32), (26, 4), (10, 0), (20, 5), (25, 27), (20, 10), (16, 9), (7, 29), (32, 31), (27, 7), (29, 14), (17, 35), (26, 37), (24, 9), (22, 9), (31, 14), (14, 27), (9, 4), (18, 11), (5, 31), (3, 35), (4, 28), (33, 14), (12, 18), (7, 31), (32, 18), (16, 0), (13, 21), (15, 23), (26, 0), (7, 30), (19, 19), (0, 10), (19, 23), (14, 15), (23, 34), (12, 16), (13, 36), (6, 37), (25, 10), (11, 30), (15, 10), (36, 13), (33, 30), (0, 32), (35, 5), (32, 28), (8, 22), (24, 20), (12, 29), (15, 11), (34, 2), (35, 18), (20, 31), (1, 25), (5, 27), (22, 21), (36, 22), (24, 23), (33, 1), (4, 2), (15, 26), (13, 7), (2, 16), (17, 31), (26, 36), (8, 9), (29, 26), (4, 25), (29, 22), (28, 21), (8, 14), (23, 2), (11, 10), (0, 18), (32, 11), (5, 7), (8, 24), (3, 29), (23, 4), (34, 12), (34, 22), (1, 17), (4, 36), (16, 17), (5, 5), (13, 27), (14, 37), (3, 10), (6, 9), (20, 11), (23, 22), (21, 9), (24, 28), (6, 16), (8, 8), (34, 9), (23, 7), (25, 28), (12, 0), (2, 19), (20, 7), (11, 22), (14, 32), (15, 34), (2, 36), (4, 0), (13, 19), (8, 1), (17, 30), (13, 12), (11, 31), (34, 30), (21, 3), (4, 14), (24, 11), (21, 29), (18, 22), (17, 5), (31, 5), (31, 4), (11, 13), (27, 30), (1, 26), (32, 23), (9, 13), (34, 20), (26, 33), (27, 22), (14, 7), (7, 28), (33, 6), (15, 29), (23, 27), (5, 19), (0, 13), (30, 8), (36, 11), (3, 20), (19, 22), (24, 7), (1, 13), (24, 3), (11, 14), (7, 13), (4, 5), (28, 29), (35, 6), (25, 19), (32, 29), (0, 30), (11, 17), (23, 0), (12, 10), (1, 20), (34, 28), (3, 19), (13, 8), (35, 9), (8, 17), (31, 30), (18, 0), (19, 18), (18, 27), (2, 2), (26, 19), (19, 11), (22, 5), (20, 24), (22, 33), (33, 10), (0, 31), (17, 29), (34, 29), (26, 15), (17, 33), (1, 19), (24, 15), (32, 8), (8, 0), (7, 8), (13, 6), (25, 15), (4, 10), (20, 34), (5, 4), (10, 12), (20, 2), (13, 23), (0, 21), (30, 4), (19, 33), (9, 26), (14, 17), (35, 19), (19, 29), (7, 10), (20, 25), (10, 30), (30, 33), (16, 23), (13, 30), (27, 9), (14, 23), (18, 19), (35, 14), (24, 16), (18, 23), (6, 19), (6, 7), (28, 15), (27, 24), (25, 0), (27, 13), (2, 32), (9, 21), (29, 34), (24, 35), (17, 6), (24, 22), (11, 7), (5, 11), (31, 16), (2, 37), (0, 22), (3, 27), (17, 17), (30, 9), (21, 37), (28, 12), (6, 1), (31, 11), (26, 6), (32, 4), (33, 18), (28, 33), (11, 36), (6, 13), (8, 16), (12, 26), (0, 36), (33, 35), (36, 9), (5, 9), (21, 36), (29, 29), (31, 34), (18, 14), (23, 5), (29, 19), (2, 28), (10, 8), (1, 27), (1, 29), (6, 28), (15, 18), (22, 4), (26, 24), (21, 14), (10, 17), (1, 37), (2, 21), (3, 34), (0, 1), (33, 23), (13, 35), (30, 16), (11, 4), (23, 31), (10, 26), (11, 34), (11, 26), (34, 26), (30, 23), (20, 22), (13, 20), (32, 16), (13, 11), (14, 16), (8, 7), (13, 0), (24, 1), (36, 8), (28, 20), (8, 4), (36, 35), (23, 26), (17, 3), (17, 10), (13, 33), (21, 8), (25, 30), (20, 18), (25, 6), (2, 9), (22, 1), (3, 32), (18, 20), (7, 34), (30, 11), (22, 10), (26, 35), (33, 3), (5, 33), (18, 37), (29, 15), (23, 21), (31, 7), (32, 21), (8, 25), (12, 21), (20, 36), (32, 33), (12, 6), (17, 25), (3, 24), (31, 33), (32, 9), (15, 37), (36, 23), (10, 15), (2, 14), (12, 20), (3, 31), (3, 3), (29, 5), (34, 24), (1, 18), (15, 7), (28, 9), (28, 5), (9, 28), (26, 13), (7, 33), (21, 27), (22, 35), (16, 16), (7, 3), (22, 34), (25, 16), (11, 3), (10, 7), (5, 14), (35, 12), (21, 17), (18, 35), (22, 28), (21, 25), (21, 20), (1, 21), (13, 26), (14, 29), (15, 36), (30, 17), (18, 31), (25, 2), (7, 15), (33, 20), (35, 11), (9, 11), (27, 35), (8, 34), (12, 2), (14, 3), (0, 33), (3, 28), (13, 15), (14, 14), (10, 16), (12, 36), (21, 4), (15, 17), (9, 36), (13, 17), (14, 25), (9, 12), (33, 19), (29, 7), (13, 4), (28, 2), (30, 3), (21, 32), (4, 1), (28, 0), (8, 33), (4, 19), (7, 0), (8, 21), (28, 13), (23, 37), (30, 10), (12, 1), (8, 6), (19, 16), (16, 18), (19, 28), (21, 15), (16, 5), (12, 27), (6, 5), (6, 36), (11, 11), (12, 8), (25, 26), (30, 27), (0, 37), (20, 0), (21, 0), (34, 10), (35, 16), (30, 13), (6, 30), (32, 27), (36, 15), (24, 0), (7, 26), (22, 36), (31, 26), (10, 23), (1, 12), (15, 1), (20, 6), (3, 23), (36, 18), (24, 24), (30, 18), (25, 22), (34, 16), (34, 32), (26, 7), (23, 13), (15, 30), (32, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401280", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 16), (0, 4), (15, 35), (14, 2), (18, 7), (16, 17), (15, 16), (19, 6), (28, 20), (12, 19), (5, 4), (27, 17), (2, 0), (19, 28), (9, 22), (3, 34), (16, 23), (20, 19), (1, 5), (20, 32), (25, 28), (1, 18), (24, 29), (29, 24), (4, 35), (8, 23), (7, 5), (8, 25), (14, 3), (20, 29), (25, 6), (17, 8), (21, 10), (21, 2), (8, 30), (16, 19), (29, 31), (23, 36), (20, 6), (17, 2), (10, 18), (4, 15), (20, 24), (25, 3), (17, 16), (18, 31), (15, 17), (5, 13), (8, 3), (5, 29), (16, 3), (21, 12), (0, 20), (14, 10), (3, 36), (11, 13), (19, 5), (23, 5), (26, 3), (29, 18), (28, 36), (17, 34), (12, 10), (8, 17), (19, 18), (9, 24), (19, 17), (0, 36), (8, 31), (18, 33), (27, 0), (14, 17), (9, 11), (15, 32), (2, 26), (17, 22), (28, 14), (13, 10), (7, 21), (9, 21), (22, 23), (25, 35), (21, 30), (8, 19), (12, 32), (26, 34), (5, 32), (0, 25), (28, 30), (2, 5), (10, 4), (28, 15), (19, 22), (17, 11), (29, 28), (8, 15), (19, 25), (8, 22), (13, 35), (24, 5), (5, 30), (3, 14), (8, 18), (1, 11), (23, 35), (13, 32), (19, 29), (5, 2), (26, 29), (28, 0), (3, 33), (22, 5), (4, 17), (2, 15), (14, 16), (21, 11), (11, 19), (20, 2), (26, 4), (17, 23), (25, 20), (26, 1), (8, 32), (15, 11), (13, 7), (19, 10), (2, 32), (13, 1), (6, 33), (9, 1), (9, 3), (29, 22), (14, 28), (1, 31), (6, 32), (18, 25), (10, 1), (27, 20), (10, 6), (20, 17), (29, 29), (29, 19), (1, 15), (4, 16), (3, 35), (0, 26), (23, 19), (13, 12), (23, 16), (10, 11), (26, 25), (24, 17), (0, 6), (22, 36), (20, 9), (27, 10), (2, 17), (7, 18), (25, 12), (3, 5), (15, 23), (1, 33), (17, 13), (25, 7), (25, 16), (13, 27), (20, 16), (9, 25), (2, 19), (13, 14), (4, 25), (11, 28), (17, 3), (18, 5), (3, 18), (2, 16), (10, 33), (14, 27), (14, 25), (2, 11), (2, 12), (15, 25), (7, 7), (22, 14), (3, 8), (9, 13), (13, 18), (16, 5), (0, 30), (2, 8), (19, 33), (22, 10), (6, 34), (10, 3), (14, 32), (17, 25), (2, 14), (10, 36), (18, 34), (28, 22), (5, 21), (13, 13), (19, 24), (0, 8), (22, 8), (29, 33), (13, 17), (12, 17), (16, 15), (1, 25), (11, 30), (23, 4), (27, 25), (26, 16), (29, 27), (17, 10), (3, 29), (21, 21), (10, 5), (22, 11), (8, 28), (21, 36), (4, 27), (29, 21), (7, 2), (6, 15), (17, 12), (6, 3), (22, 33), (20, 35), (23, 30), (1, 13), (14, 4), (12, 25), (13, 20), (10, 10), (6, 8), (23, 1), (15, 12), (16, 9), (15, 7), (19, 7), (26, 24), (14, 22), (9, 10), (5, 7), (10, 15), (8, 8), (28, 7), (29, 20), (22, 32), (3, 28), (7, 6), (20, 15), (18, 26), (5, 22), (3, 0), (17, 6), (24, 35), (19, 2), (12, 14), (14, 8), (18, 27), (7, 19), (26, 8), (7, 9), (4, 9), (12, 12), (19, 14), (22, 12), (13, 16), (29, 12), (10, 12), (9, 16), (10, 8), (21, 27), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712152", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 31), (26, 25), (3, 16), (9, 35), (6, 19), (6, 36), (23, 31), (5, 15), (0, 9), (22, 15), (4, 1), (3, 36), (2, 12), (12, 35), (10, 20), (16, 15), (13, 25), (3, 18), (31, 20), (2, 21), (6, 22), (7, 14), (26, 26), (18, 31), (17, 14), (20, 34), (0, 14), (5, 7), (20, 29), (13, 23), (21, 0), (21, 3), (11, 5), (2, 19), (0, 17), (21, 12), (7, 24), (30, 33), (10, 5), (13, 26), (29, 16), (2, 14), (3, 30), (11, 22), (32, 5), (28, 10), (25, 20), (30, 23), (22, 20), (12, 5), (5, 33), (20, 26), (4, 10), (1, 13), (32, 28), (19, 21), (32, 35), (12, 33), (12, 28), (22, 23), (21, 6), (5, 12), (3, 19), (11, 10), (31, 7), (4, 9), (23, 2), (25, 7), (19, 11), (19, 20), (9, 7), (29, 12), (3, 35), (23, 9), (7, 36), (25, 19), (22, 6), (22, 18), (2, 2), (11, 4), (15, 6), (5, 3), (5, 29), (0, 31), (15, 29), (8, 12), (24, 29), (22, 0), (18, 18), (12, 26), (28, 23), (11, 24), (29, 17), (22, 29), (13, 21), (17, 25), (15, 16), (12, 14), (10, 29), (24, 28), (22, 30), (6, 27), (18, 17), (0, 23), (31, 31), (4, 34), (10, 27), (20, 4), (16, 16), (14, 32), (23, 36), (27, 3), (16, 2), (15, 3), (9, 28), (28, 33), (30, 17), (8, 13), (14, 20), (11, 23), (29, 35), (22, 25), (4, 36), (16, 11), (24, 35), (15, 14), (25, 17), (9, 16), (20, 22), (17, 0), (21, 5), (7, 11), (21, 33), (20, 1), (14, 33), (18, 20), (5, 34), (14, 31), (17, 24), (14, 6), (17, 15), (32, 25), (13, 12), (8, 23), (10, 19), (10, 7), (1, 20), (26, 20), (24, 27), (16, 34), (14, 5), (14, 4), (1, 28), (19, 15), (15, 34), (8, 19), (17, 23), (29, 13), (20, 0), (24, 24), (3, 1), (3, 14), (1, 8), (4, 8), (7, 8), (29, 31), (0, 7), (1, 4), (3, 9), (27, 23), (10, 11), (30, 21), (7, 5), (23, 13), (21, 32), (29, 5), (29, 22), (23, 15), (16, 26), (28, 5), (17, 5), (31, 10), (24, 23), (19, 4), (9, 33), (25, 22), (13, 6), (20, 10), (25, 33), (1, 35), (17, 32), (10, 12), (5, 19), (28, 11), (7, 34), (18, 12), (30, 18), (15, 0), (32, 12), (1, 31), (29, 8), (4, 29), (7, 32), (14, 8), (15, 4), (22, 5), (31, 25), (13, 0), (7, 20), (24, 19), (11, 31), (4, 21), (9, 1), (30, 5), (31, 29), (18, 16), (26, 36), (5, 26), (32, 33), (15, 13), (15, 9), (26, 21), (23, 1), (5, 22), (3, 13), (5, 30), (3, 12), (5, 4), (10, 35), (26, 17), (30, 36), (13, 34), (29, 24), (13, 16), (19, 36), (6, 9), (5, 35), (8, 2), (32, 16), (30, 35), (18, 3), (18, 5), (13, 10), (16, 32), (10, 25), (11, 11), (30, 19), (16, 35), (25, 29), (28, 26), (23, 16), (7, 21), (1, 7), (7, 15), (16, 24), (30, 31), (6, 2), (27, 19), (16, 27), (13, 1), (15, 28), (10, 22), (27, 15), (11, 6), (10, 10), (6, 20), (2, 35), (18, 4), (0, 32), (12, 3), (23, 7), (11, 21), (31, 8), (15, 32), (26, 18), (31, 1), (19, 27), (20, 21), (28, 32), (5, 20), (28, 36), (16, 10), (9, 2), (12, 17), (30, 13), (23, 33), (5, 32), (2, 32), (11, 28), (5, 6), (23, 11), (5, 16), (9, 36), (0, 30), (25, 35), (4, 6), (22, 36), (32, 8), (0, 8), (29, 23), (23, 21), (19, 19), (10, 28), (15, 12), (6, 14), (5, 13), (27, 24), (13, 14), (28, 21), (14, 1), (3, 4), (31, 30), (1, 23), (0, 16), (6, 5), (14, 26), (24, 0), (10, 8), (5, 11), (8, 15), (22, 35), (27, 31), (3, 8), (31, 4), (7, 23), (29, 2), (6, 13), (7, 17), (21, 25), (30, 9), (14, 9), (14, 10), (7, 31), (31, 17), (17, 35), (28, 30), (19, 8), (31, 6), (27, 28), (2, 29), (29, 7), (12, 36), (18, 0), (19, 35), (9, 22), (20, 25), (20, 14), (23, 23), (29, 26), (23, 29), (30, 4), (32, 31), (21, 22), (30, 11), (20, 32), (10, 2), (32, 10), (11, 26), (11, 30), (0, 12), (21, 13), (32, 21), (6, 0), (18, 7), (25, 1), (25, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991600", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), 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), (18, 2), (25, 26), (16, 9), (19, 12), (29, 28), (21, 17), (32, 22), (20, 19), (16, 4), (33, 12), (1, 17), (29, 6), (14, 20), (25, 17), (16, 15), (6, 24), (34, 11), (14, 15), (23, 27), (10, 14), (12, 23), (0, 5), (5, 23), (6, 8), (33, 2), (6, 9), (22, 6), (19, 15), (17, 7), (15, 9), (22, 20), (11, 23), (6, 14), (22, 22), (21, 10), (26, 14), (25, 8), (3, 27), (29, 22), (0, 11), (33, 7), (4, 15), (26, 5), (23, 0), (4, 25), (14, 4), (7, 12), (23, 9), (4, 14), (8, 9), (27, 17), (17, 5), (15, 6), (6, 26), (21, 30), (17, 20), (6, 23), (26, 21), (16, 27), (29, 5), (1, 21), (2, 20), (31, 10), (17, 22), (32, 24), (19, 26), (26, 28), (29, 14), (27, 11), (28, 11), (26, 20), (3, 26), (31, 3), (9, 27), (0, 24), (1, 29), (4, 21), (30, 9), (9, 2), (20, 11), (13, 2), (25, 10), (20, 23), (15, 10), (21, 13), (2, 8), (16, 0), (31, 23), (12, 4), (20, 3), (2, 0), (28, 20), (15, 14), (8, 29), (13, 28), (0, 10), (15, 8), (17, 12), (11, 17), (28, 0), (26, 25), (31, 26), (32, 14), (18, 11), (29, 29), (0, 19), (17, 9), (16, 23), (15, 7), (30, 4), (3, 30), (15, 26), (28, 2), (16, 16), (32, 5), (28, 24), (6, 27), (18, 8), (22, 9), (8, 27), (26, 24), (0, 26), (25, 7), (6, 18), (29, 25), (29, 4), (10, 6), (3, 29), (2, 18), (0, 30), (5, 17), (21, 6), (0, 28), (5, 2), (17, 18), (2, 23), (19, 18), (24, 9), (5, 7), (12, 18), (12, 20), (35, 25), (18, 14), (26, 19), (3, 1), (32, 12), (12, 12), (22, 11), (11, 8), (14, 21), (7, 10), (28, 17), (34, 25), (30, 10), (3, 0), (5, 26), (10, 16), (33, 29), (7, 5), (17, 0), (4, 24), (12, 0), (30, 28), (7, 28), (25, 6), (9, 14), (34, 18), (12, 26), (27, 1), (18, 17), (10, 23), (6, 3), (33, 13), (17, 2), (8, 10), (32, 23), (30, 22), (14, 2), (13, 20), (33, 14), (30, 20), (19, 29), (31, 22), (2, 28), (16, 10), (23, 14), (5, 24), (6, 28), (21, 24), (16, 25), (13, 10), (35, 12), (23, 1), (27, 2), (26, 13), (1, 27), (3, 10), (15, 2), (6, 13), (16, 17), (8, 25), (15, 27), (2, 30), (12, 9), (19, 27), (7, 4), (34, 29), (9, 21), (24, 11), (14, 7), (23, 18), (15, 1), (18, 15), (33, 4), (5, 6), (29, 12), (33, 11), (35, 10), (35, 9), (35, 18), (29, 26), (24, 5), (34, 0), (27, 29), (29, 20), (25, 4), (13, 5), (21, 14), (1, 0), (9, 24), (9, 25), (7, 8), (8, 8), (27, 7), (9, 12), (30, 27), (25, 5), (7, 6), (14, 8), (21, 16), (24, 26), (2, 3), (27, 0), (15, 28), (4, 17), (17, 6), (17, 1), (30, 16), (12, 11), (32, 4), (0, 23), (28, 6), (23, 30), (9, 3), (3, 13), (20, 8), (25, 16), (8, 23), (4, 28), (14, 6), (33, 22), (21, 9), (21, 25), (3, 21), (33, 9), (18, 22), (18, 24), (19, 2), (18, 0), (16, 14), (23, 23), (16, 5), (20, 20), (6, 11), (15, 23), (11, 6), (31, 25), (4, 8), (30, 6), (6, 22), (9, 0), (22, 4), (8, 18), (6, 17), (11, 13), (2, 13), (3, 25), (34, 5), (11, 28), (32, 10), (24, 13), (9, 17), (32, 17), (13, 1), (22, 2), (30, 8), (25, 30), (21, 21), (10, 27), (21, 28), (12, 15), (35, 1), (22, 17), (31, 16), (34, 1), (23, 3), (10, 1), (33, 15), (10, 3), (22, 12), (24, 15), (29, 10), (27, 3), (14, 19), (27, 26), (19, 11), (26, 4), (27, 4), (5, 10), (9, 8), (19, 25), (13, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841230", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 9), (0, 12), (10, 26), (29, 19), (26, 5), (20, 18), (21, 26), (33, 15), (2, 2), (22, 25), (20, 7), (6, 15), (20, 22), (7, 4), (15, 21), (14, 2), (24, 13), (28, 16), (23, 20), (16, 26), (28, 22), (17, 15), (12, 6), (3, 8), (23, 16), (0, 5), (16, 27), (21, 22), (18, 11), (30, 18), (0, 22), (5, 7), (17, 12), (9, 14), (10, 12), (22, 22), (27, 25), (27, 9), (13, 18), (12, 18), (13, 17), (24, 25), (10, 1), (20, 14), (0, 15), (6, 28), (26, 4), (4, 6), (19, 12), (3, 3), (31, 28), (28, 24), (32, 6), (11, 17), (33, 24), (23, 1), (13, 8), (9, 2), (15, 24), (24, 9), (27, 26), (1, 3), (31, 12), (24, 6), (26, 6), (1, 14), (4, 16), (31, 9), (32, 26), (20, 16), (6, 14), (22, 8), (27, 20), (33, 6), (6, 7), (32, 14), (29, 2), (19, 24), (14, 1), (20, 17), (4, 29), (0, 11), (0, 23), (10, 13), (29, 22), (7, 24), (11, 16), (15, 8), (25, 21), (24, 11), (12, 8), (30, 14), (5, 3), (16, 13), (14, 8), (15, 28), (22, 2), (17, 21), (8, 28), (4, 20), (17, 1), (3, 14), (30, 10), (8, 7), (28, 20), (14, 16), (17, 11), (4, 19), (29, 16), (27, 18), (33, 2), (19, 8), (10, 18), (31, 7), (14, 25), (30, 26), (10, 0), (14, 21), (31, 25), (7, 19), (21, 16), (4, 7), (14, 7), (6, 27), (31, 1), (7, 26), (7, 13), (13, 13), (33, 28), (12, 12), (31, 26), (0, 13), (14, 5), (16, 17), (21, 3), (29, 17), (8, 22), (27, 10), (31, 24), (22, 18), (9, 19), (16, 24), (15, 0), (14, 9), (9, 9), (4, 17), (23, 2), (2, 9), (7, 9), (4, 12), (24, 10), (5, 19), (14, 20), (25, 9), (27, 27), (32, 24), (27, 6), (30, 21), (27, 5), (27, 23), (14, 14), (8, 17), (33, 5), (20, 27), (28, 23), (33, 16), (27, 4), (25, 2), (5, 22), (17, 0), (19, 0), (0, 19), (12, 25), (28, 29), (5, 0), (2, 23), (32, 3), (6, 6), (7, 15), (21, 15), (19, 27), (26, 7), (25, 11), (14, 4), (4, 27), (18, 23), (26, 18), (21, 18), (9, 29), (9, 18), (21, 17), (5, 26), (0, 3), (5, 10), (18, 26), (20, 21), (15, 5), (3, 12), (8, 14), (12, 5), (10, 21), (11, 21), (28, 1), (15, 13), (7, 29), (0, 17), (7, 27), (19, 2), (30, 16), (30, 28), (22, 21), (28, 12), (19, 14), (20, 0), (33, 26), (11, 3), (3, 24), (26, 17), (28, 2), (21, 0), (10, 28), (10, 24), (26, 22), (17, 3), (19, 17), (5, 14), (10, 19), (4, 11), (22, 12), (3, 2), (8, 15), (19, 22), (3, 13), (19, 4), (30, 9), (25, 4), (16, 28), (30, 13), (14, 18), (12, 2), (10, 15), (10, 3), (9, 21), (30, 19), (12, 9), (4, 2), (33, 9), (23, 14), (26, 15), (7, 7), (3, 25), (10, 8), (21, 10), (21, 25), (21, 11), (27, 16), (10, 22), (15, 11), (3, 9), (30, 5), (19, 11), (29, 4), (31, 27), (33, 25), (18, 28), (18, 29), (14, 11), (0, 14), (22, 7), (25, 25), (9, 25), (14, 28), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "702525", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), 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), (19, 14), (7, 9), (20, 12), (30, 25), (32, 1), (21, 3), (21, 6), (21, 29), (36, 24), (6, 29), (7, 22), (14, 7), (17, 26), (35, 9), (37, 34), (18, 22), (19, 2), (16, 27), (27, 35), (38, 2), (12, 29), (0, 17), (34, 31), (18, 24), (2, 34), (17, 7), (0, 33), (31, 12), (6, 3), (33, 12), (35, 32), (34, 6), (8, 10), (29, 18), (16, 15), (21, 25), (32, 29), (0, 26), (31, 26), (6, 18), (23, 0), (21, 26), (23, 8), (26, 24), (31, 21), (8, 30), (33, 35), (8, 9), (5, 16), (28, 6), (28, 25), (12, 8), (27, 0), (36, 14), (12, 7), (23, 16), (12, 16), (34, 14), (22, 23), (2, 24), (11, 4), (38, 9), (37, 14), (14, 14), (34, 18), (18, 3), (7, 28), (3, 26), (6, 9), (15, 11), (13, 20), (32, 17), (34, 27), (6, 25), (7, 19), (2, 18), (27, 1), (10, 22), (17, 33), (14, 18), (14, 29), (14, 19), (27, 32), (1, 0), (28, 10), (17, 29), (29, 28), (31, 5), (3, 28), (22, 2), (20, 14), (10, 4), (10, 24), (0, 28), (14, 28), (3, 9), (6, 35), (24, 21), (22, 4), (5, 19), (29, 12), (16, 21), (36, 27), (35, 33), (33, 8), (23, 7), (0, 14), (30, 1), (24, 35), (14, 1), (18, 11), (22, 30), (34, 33), (30, 35), (34, 12), (14, 31), (37, 21), (12, 32), (14, 35), (32, 12), (4, 3), (5, 20), (11, 8), (33, 28), (14, 12), (11, 34), (15, 32), (16, 16), (29, 33), (31, 32), (30, 32), (10, 30), (29, 23), (25, 32), (6, 22), (32, 11), (1, 14), (38, 18), (0, 5), (34, 4), (14, 25), (20, 23), (7, 11), (8, 23), (20, 16), (17, 27), (12, 20), (32, 35), (26, 21), (25, 9), (12, 11), (18, 14), (26, 28), (19, 28), (29, 30), (38, 29), (30, 8), (21, 16), (29, 27), (36, 4), (31, 33), (20, 35), (28, 13), (3, 29), (15, 13), (23, 30), (35, 18), (15, 3), (1, 19), (38, 19), (24, 28), (29, 25), (15, 30), (37, 0), (27, 11), (22, 34), (27, 34), (24, 4), (11, 25), (37, 17), (0, 21), (15, 28), (28, 26), (28, 15), (16, 32), (11, 11), (28, 30), (1, 13), (3, 17), (33, 24), (32, 14), (14, 0), (13, 33), (23, 35), (28, 16), (1, 17), (24, 6), (2, 11), (25, 7), (7, 35), (18, 32), (20, 13), (34, 26), (10, 35), (11, 24), (36, 31), (32, 34), (17, 12), (21, 0), (21, 24), (0, 7), (26, 4), (2, 26), (2, 8), (36, 32), (25, 33), (31, 18), (4, 6), (12, 34), (10, 27), (10, 31), (35, 24), (1, 33), (5, 10), (25, 22), (18, 35), (27, 6), (32, 16), (21, 2), (10, 21), (2, 6), (35, 2), (15, 29), (25, 3), (9, 24), (6, 34), (9, 34), (26, 17), (12, 9), (15, 12), (3, 0), (23, 33), (7, 30), (2, 20), (21, 14), (38, 20), (3, 33), (19, 7), (5, 11), (24, 20), (13, 12), (24, 15), (25, 13), (18, 16), (27, 28), (1, 23), (34, 24), (10, 20), (9, 18), (26, 0), (16, 0), (25, 27), (30, 13), (15, 2), (30, 15), (18, 4), (27, 29), (30, 23), (24, 12), (1, 29), (24, 29), (5, 15), (13, 14), (13, 31), (24, 23), (15, 19), (26, 11), (24, 3), (25, 26), (1, 9), (31, 28), (8, 14), (1, 1), (11, 30), (24, 27), (3, 21), (4, 1), (19, 29), (21, 20), (13, 10), (27, 14), (8, 19), (11, 3), (13, 9), (37, 18), (32, 2), (26, 3), (36, 0), (35, 0), (35, 14), (13, 25), (35, 23), (14, 11), (19, 10), (31, 17), (36, 33), (8, 0), (0, 27), (2, 33), (7, 12), (22, 24), (24, 2), (1, 32), (16, 3), (15, 22), (8, 6), (5, 26), (16, 5), (29, 15), (9, 5), (34, 0), (33, 19), (31, 29), (18, 29), (36, 3), (28, 23), (17, 8), (35, 28), (4, 23), (34, 20), (33, 5), (5, 3), (1, 22), (38, 24), (38, 22), (17, 22), (27, 17), (23, 12), (16, 20), (33, 21), (27, 26), (5, 24), (33, 25), (34, 23), (24, 19), (38, 5), (5, 7), (5, 18), (9, 14), (33, 18), (26, 26), (36, 12), (33, 13), (29, 21), (3, 15), (21, 33), (17, 21), (26, 18), (4, 34), (32, 15), (28, 19), (38, 16), (8, 26), (14, 15), (17, 14), (16, 8), (20, 18), (18, 13), (17, 35), (37, 8), (26, 1), (20, 20), (1, 11), (22, 32), (7, 1), (14, 3), (15, 16), (20, 34), (22, 14), (27, 27), (13, 4), (11, 35), (31, 1), (25, 4), (32, 4), (19, 12), (33, 16), (22, 22), (11, 21), (16, 35), (34, 15), (24, 11), (23, 22), (14, 8), (30, 34), (25, 0), (22, 18), (11, 0), (37, 7), (24, 9), (23, 23), (11, 9), (34, 17), (20, 11), (24, 5), (13, 6), (21, 15), (2, 13), (38, 28), (6, 13), (38, 1), (25, 10), (33, 6), (0, 24), (36, 1), (37, 6), (4, 13), (3, 16), (2, 3), (7, 21), (23, 20), (20, 3), (26, 7), (15, 20), (18, 1), (6, 14), (21, 23), (19, 4), (20, 28), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30720", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), 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), (26, 5), (23, 9), (15, 4), (8, 18), (19, 2), (10, 2), (29, 17), (12, 10), (27, 25), (27, 20), (28, 12), (4, 1), (13, 15), (2, 30), (12, 23), (10, 11), (1, 8), (4, 16), (18, 24), (19, 18), (10, 7), (13, 17), (19, 24), (14, 25), (5, 2), (7, 21), (4, 21), (16, 27), (13, 6), (3, 13), (17, 12), (29, 21), (10, 15), (5, 30), (8, 28), (22, 1), (10, 4), (9, 22), (10, 24), (12, 6), (2, 24), (22, 10), (2, 12), (27, 19), (3, 23), (21, 20), (1, 4), (26, 21), (8, 22), (17, 17), (28, 14), (19, 1), (14, 26), (25, 22), (21, 0), (29, 2), (10, 18), (19, 21), (16, 6), (26, 27), (8, 6), (22, 30), (8, 24), (1, 2), (12, 30), (19, 6), (12, 2), (16, 13), (9, 17), (12, 16), (18, 23), (3, 8), (25, 28), (7, 15), (7, 8), (13, 27), (23, 17), (14, 0), (10, 17), (21, 29), (0, 28), (25, 18), (14, 3), (2, 28), (24, 2), (3, 10), (11, 1), (18, 14), (29, 16), (0, 22), (18, 30), (28, 1), (14, 6), (24, 16), (4, 11), (27, 29), (12, 11), (28, 0), (4, 6), (27, 26), (9, 1), (29, 27), (2, 10), (4, 5), (21, 18), (17, 0), (26, 23), (5, 29), (10, 8), (20, 20), (10, 13), (1, 29), (25, 25), (16, 9), (13, 22), (15, 3), (10, 28), (4, 18), (19, 15), (21, 27), (26, 28), (6, 19), (8, 12), (22, 26), (6, 24), (16, 12), (20, 8), (12, 19), (7, 16), (17, 10), (18, 6), (2, 18), (25, 23), (17, 7), (18, 28), (9, 8), (5, 24), (19, 10), (28, 24), (4, 7), (0, 15), (12, 25), (27, 0), (12, 18), (28, 21), (6, 14), (6, 1), (10, 0), (20, 3), (22, 11), (28, 10), (15, 26), (1, 13), (6, 20), (13, 29), (17, 21), (21, 12), (26, 14), (15, 12), (24, 19), (26, 0), (14, 2), (29, 7), (26, 12), (18, 17), (10, 19), (6, 23), (15, 14), (8, 0), (2, 8), (19, 3), (25, 1), (13, 5), (24, 20), (7, 10), (23, 20), (18, 26), (27, 23), (12, 0), (28, 26), (15, 28), (15, 18), (9, 12), (23, 12), (7, 6), (16, 10), (0, 16), (15, 23), (12, 24), (22, 20), (17, 1), (1, 6), (28, 20), (24, 17), (26, 4), (17, 13), (15, 1), (7, 5), (2, 7), (22, 23), (2, 22), (15, 10), (26, 26), (14, 17), (0, 12), (23, 29), (26, 8), (16, 24), (22, 0), (20, 14), (4, 24), (24, 30), (23, 22), (3, 16), (10, 12), (5, 6), (24, 14), (11, 24), (18, 11), (28, 18), (20, 21), (8, 3), (17, 3), (18, 16), (29, 25), (1, 9), (5, 3), (7, 3), (21, 4), (3, 12), (10, 9), (13, 7), (3, 9), (11, 11), (5, 4), (6, 25), (29, 29), (28, 13), (20, 19), (29, 3), (21, 10), (2, 13), (4, 4), (26, 19), (0, 30), (5, 17), (7, 12), (25, 13), (26, 16), (29, 13), (26, 18), (4, 20), (24, 0), (25, 2), (1, 19), (20, 11), (19, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 28), (22, 17), (19, 15), (1, 25), (19, 20), (20, 4), (18, 29), (16, 5), (26, 29), (6, 3), (10, 2), (30, 11), (7, 9), (5, 3), (12, 27), (27, 22), (24, 26), (15, 21), (27, 13), (11, 14), (26, 7), (12, 24), (15, 18), (8, 14), (4, 2), (20, 0), (7, 7), (3, 23), (20, 6), (26, 24), (15, 20), (4, 15), (11, 13), (13, 4), (20, 27), (30, 25), (10, 19), (15, 28), (18, 28), (22, 18), (17, 29), (8, 22), (0, 1), (0, 26), (21, 26), (19, 6), (4, 30), (28, 23), (0, 17), (7, 18), (11, 20), (28, 22), (5, 4), (9, 21), (14, 14), (16, 19), (20, 21), (20, 26), (19, 3), (15, 27), (19, 12), (8, 11), (4, 20), (18, 10), (7, 11), (23, 12), (15, 2), (13, 21), (9, 2), (19, 19), (16, 14), (11, 26), (10, 1), (6, 22), (5, 8), (7, 29), (25, 5), (18, 16), (7, 14), (28, 1), (0, 19), (13, 3), (24, 7), (26, 15), (17, 13), (27, 8), (13, 29), (25, 19), (0, 27), (6, 12), (8, 26), (8, 6), (8, 28), (1, 4), (6, 1), (9, 7), (22, 29), (23, 6), (20, 28), (24, 15), (20, 20), (3, 21), (23, 2), (0, 30), (18, 9), (21, 18), (29, 18), (10, 9), (27, 24), (16, 21), (28, 8), (16, 29), (11, 21), (3, 25), (17, 4), (21, 9), (22, 1), (30, 17), (24, 9), (14, 23), (6, 6), (30, 1), (2, 10), (22, 27), (20, 3), (9, 19), (18, 25), (5, 10), (28, 13), (8, 0), (8, 4), (17, 11), (17, 18), (28, 25), (5, 30), (12, 22), (11, 29), (22, 6), (5, 2), (5, 24), (27, 25), (22, 19), (19, 24), (4, 11), (2, 22), (9, 25), (21, 25), (13, 28), (17, 6), (23, 30), (1, 19), (1, 9), (24, 22), (30, 14), (2, 17), (9, 1), (2, 29), (8, 19), (10, 25), (24, 19), (24, 13), (26, 10), (14, 8), (30, 27), (0, 20), (6, 11), (6, 25), (22, 23), (9, 14), (15, 30), (0, 12), (7, 4), (28, 10), (20, 13), (17, 16), (30, 3), (24, 0), (26, 0), (0, 8), (7, 30), (2, 15), (24, 28), (30, 6), (15, 29), (28, 14), (19, 25), (19, 13), (11, 6), (6, 14), (15, 13), (25, 29), (8, 10), (6, 4), (5, 22), (14, 15), (25, 12), (4, 16), (1, 8), (19, 28), (10, 26), (21, 24), (11, 15), (19, 10), (22, 0), (28, 3), (22, 16), (28, 19), (6, 23), (4, 13), (23, 20), (4, 4), (14, 20), (3, 4), (27, 20), (14, 11), (18, 8), (8, 15), (18, 12), (11, 3), (23, 17), (23, 18), (23, 23), (26, 2), (12, 25), (18, 21), (28, 18), (11, 0), (4, 7), (14, 30), (20, 9), (13, 12), (24, 23), (8, 17), (23, 4), (0, 3), (9, 22), (19, 18), (0, 16), (7, 19), (8, 9), (29, 3), (5, 0), (3, 19), (14, 28), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "854112", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 33), (32, 29), (33, 22), (12, 10), (10, 22), (26, 19), (13, 5), (14, 20), (28, 18), (4, 4), (21, 6), (5, 29), (3, 34), (15, 0), (2, 0), (32, 34), (7, 33), (3, 7), (18, 7), (6, 12), (20, 12), (19, 28), (11, 20), (15, 10), (15, 4), (8, 27), (0, 19), (5, 11), (3, 26), (29, 6), (5, 22), (31, 6), (6, 31), (16, 10), (9, 19), (14, 34), (15, 34), (30, 28), (17, 3), (11, 23), (35, 8), (23, 2), (26, 33), (34, 33), (30, 6), (14, 8), (31, 24), (26, 21), (13, 1), (17, 17), (24, 16), (9, 3), (22, 17), (26, 16), (14, 7), (30, 34), (19, 11), (28, 35), (23, 12), (20, 0), (11, 34), (12, 8), (12, 4), (24, 1), (33, 5), (15, 16), (27, 16), (12, 14), (17, 19), (24, 22), (10, 30), (21, 25), (5, 8), (18, 17), (29, 33), (16, 29), (21, 28), (1, 21), (17, 30), (32, 8), (21, 27), (8, 11), (9, 29), (32, 25), (22, 12), (2, 14), (17, 16), (15, 27), (34, 3), (16, 30), (31, 12), (3, 14), (26, 14), (26, 18), (23, 0), (14, 0), (27, 10), (1, 22), (14, 4), (18, 14), (18, 2), (5, 0), (6, 27), (7, 24), (29, 10), (19, 18), (16, 24), (23, 20), (18, 30), (10, 10), (28, 1), (25, 5), (19, 16), (32, 3), (17, 2), (5, 21), (24, 21), (28, 11), (14, 5), (34, 26), (0, 30), (7, 7), (7, 5), (4, 1), (28, 19), (3, 19), (4, 32), (16, 6), (2, 16), (24, 30), (20, 13), (14, 24), (32, 33), (12, 15), (22, 7), (14, 19), (27, 18), (23, 16), (11, 22), (9, 22), (22, 25), (7, 9), (32, 24), (0, 12), (3, 0), (16, 17), (10, 35), (20, 27), (2, 17), (21, 16), (22, 32), (25, 2), (20, 7), (35, 28), (15, 18), (7, 17), (31, 16), (13, 2), (22, 6), (6, 11), (33, 11), (4, 25), (18, 5), (16, 7), (10, 13), (26, 0), (29, 30), (27, 22), (9, 6), (33, 25), (25, 29), (15, 21), (2, 28), (30, 35), (4, 11), (5, 4), (22, 35), (34, 34), (22, 34), (8, 18), (17, 27), (17, 25), (0, 17), (32, 22), (26, 20), (1, 3), (1, 5), (15, 8), (0, 2), (31, 32), (21, 33), (16, 19), (18, 13), (13, 19), (30, 17), (16, 8), (22, 29), (27, 26), (21, 8), (24, 18), (28, 14), (25, 8), (20, 3), (29, 0), (23, 21), (26, 23), (28, 5), (7, 4), (28, 0), (27, 35), (5, 10), (26, 5), (13, 6), (4, 12), (35, 9), (34, 6), (8, 20), (5, 2), (18, 12), (9, 0), (35, 33), (6, 7), (30, 14), (35, 18), (11, 21), (34, 32), (9, 11), (14, 16), (24, 11), (24, 24), (19, 8), (13, 27), (17, 1), (11, 35), (8, 30), (23, 5), (34, 23), (4, 31), (12, 11), (18, 22), (1, 32), (24, 0), (28, 29), (21, 26), (4, 26), (15, 30), (16, 35), (27, 11), (33, 29), (20, 5), (13, 11), (33, 14), (28, 28), (3, 35), (33, 9), (27, 27), (4, 15), (29, 19), (34, 24), (2, 20), (19, 22), (25, 21), (5, 1), (25, 25), (24, 9), (21, 3), (7, 20), (31, 10), (6, 1), (2, 22), (35, 31), (5, 31), (23, 23), (31, 18), (0, 3), (12, 30), (25, 33), (16, 3), (15, 12), (4, 8), (10, 0), (15, 29), (1, 7), (33, 3), (2, 27), (22, 3), (2, 7), (1, 11), (30, 1), (14, 29), (12, 19), (27, 0), (16, 32), (13, 3), (5, 24), (0, 11), (33, 8), (6, 15), (25, 12), (13, 15), (2, 26), (30, 33), (4, 13), (9, 23), (1, 16), (34, 21), (9, 5), (16, 9), (12, 33), (16, 5), (32, 23), (8, 31), (11, 1), (31, 19), (12, 0), (15, 23), (4, 0), (26, 22), (8, 8), (10, 18), (22, 22), (19, 33), (26, 34), (8, 21), (27, 5), (3, 30), (33, 24), (21, 5), (4, 30), (24, 31), (14, 11), (28, 30), (27, 33), (21, 10), (2, 25), (25, 30), (33, 21), (4, 16), (35, 14), (1, 4), (23, 25), (5, 32), (11, 26), (17, 22), (6, 22), (23, 9), (35, 19), (31, 4), (2, 34), (6, 5), (8, 16), (28, 23), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "842400", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), 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), (30, 29), (30, 4), (18, 20), (8, 15), (24, 7), (25, 0), (4, 24), (24, 1), (23, 18), (10, 4), (12, 13), (32, 12), (33, 6), (19, 27), (32, 14), (23, 5), (32, 5), (7, 26), (19, 1), (33, 24), (22, 15), (31, 6), (33, 27), (28, 6), (10, 0), (8, 25), (25, 20), (29, 19), (4, 28), (29, 14), (15, 24), (4, 9), (18, 1), (33, 16), (31, 18), (31, 29), (9, 25), (20, 17), (0, 2), (19, 15), (19, 23), (20, 3), (2, 22), (1, 28), (20, 1), (15, 8), (1, 18), (8, 22), (28, 0), (18, 14), (32, 20), (27, 22), (22, 2), (2, 12), (23, 27), (27, 21), (7, 9), (33, 9), (28, 21), (5, 13), (24, 21), (31, 0), (5, 17), (9, 6), (1, 14), (13, 5), (25, 1), (27, 23), (3, 9), (12, 12), (14, 9), (13, 26), (22, 29), (0, 6), (16, 23), (27, 14), (23, 16), (29, 23), (12, 20), (6, 4), (32, 19), (24, 24), (1, 26), (7, 10), (25, 23), (15, 1), (24, 27), (31, 12), (20, 23), (7, 5), (32, 4), (13, 17), (8, 6), (0, 9), (29, 25), (4, 16), (20, 22), (2, 8), (1, 12), (0, 5), (3, 0), (12, 0), (16, 25), (32, 23), (13, 2), (21, 12), (20, 16), (19, 19), (14, 12), (19, 5), (17, 3), (11, 6), (2, 17), (16, 27), (14, 4), (30, 16), (29, 3), (9, 7), (25, 18), (30, 3), (14, 29), (6, 8), (12, 4), (11, 20), (26, 2), (23, 6), (17, 10), (26, 27), (17, 0), (33, 13), (23, 7), (9, 1), (19, 11), (30, 26), (9, 18), (1, 8), (17, 4), (14, 18), (27, 26), (22, 25), (13, 23), (25, 15), (9, 15), (17, 8), (23, 13), (14, 6), (5, 0), (2, 1), (32, 8), (15, 12), (7, 24), (23, 3), (22, 9), (29, 0), (2, 19), (24, 5), (27, 27), (21, 26), (33, 26), (26, 1), (24, 14), (17, 7), (15, 22), (3, 7), (25, 28), (0, 11), (0, 20), (13, 20), (19, 4), (25, 19), (8, 11), (22, 0), (13, 28), (20, 25), (7, 17), (10, 20), (28, 25), (8, 7), (0, 16), (17, 18), (2, 29), (7, 27), (19, 9), (29, 24), (23, 17), (13, 6), (28, 13), (33, 11), (25, 8), (11, 25), (4, 7), (22, 19), (9, 21), (7, 3), (25, 3), (10, 15), (19, 18), (24, 3), (12, 1), (11, 27), (1, 9), (10, 2), (5, 24), (20, 13), (12, 23), (2, 11), (17, 12), (30, 22), (30, 17), (24, 4), (24, 17), (15, 0), (28, 8), (12, 18), (30, 28), (21, 10), (29, 15), (8, 23), (11, 16), (5, 16), (24, 12), (15, 25), (8, 20), (16, 19), (23, 23), (33, 5), (13, 24), (22, 5), (7, 6), (25, 6), (15, 29), (32, 15), (22, 18), (31, 9), (19, 14), (12, 21), (18, 27), (31, 13), (10, 17), (15, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 18), (32, 29), (22, 28), (31, 24), (8, 13), (31, 27), (20, 18), (35, 24), (17, 8), (14, 8), (8, 25), (15, 20), (25, 25), (20, 29), (12, 17), (29, 30), (34, 17), (21, 22), (2, 22), (15, 9), (25, 12), (22, 27), (34, 26), (6, 10), (19, 23), (34, 2), (35, 26), (27, 19), (11, 13), (18, 27), (12, 25), (25, 18), (14, 0), (31, 29), (5, 8), (13, 6), (33, 20), (18, 21), (22, 24), (8, 15), (7, 19), (28, 2), (23, 20), (5, 24), (18, 15), (14, 9), (34, 7), (21, 23), (7, 0), (8, 14), (32, 15), (2, 23), (31, 15), (35, 16), (0, 2), (10, 17), (2, 4), (1, 10), (33, 12), (19, 5), (24, 23), (13, 26), (32, 26), (21, 15), (10, 8), (0, 21), (17, 12), (17, 18), (17, 17), (7, 17), (22, 2), (5, 16), (23, 14), (13, 25), (23, 13), (9, 5), (29, 25), (35, 9), (14, 21), (13, 10), (2, 19), (23, 27), (2, 9), (27, 11), (25, 8), (17, 0), (8, 12), (29, 26), (31, 22), (0, 5), (18, 3), (29, 13), (32, 21), (15, 8), (22, 6), (26, 9), (3, 14), (2, 18), (8, 7), (20, 21), (23, 5), (18, 23), (5, 7), (35, 7), (22, 8), (25, 15), (25, 21), (16, 6), (2, 10), (33, 7), (25, 29), (9, 10), (12, 5), (16, 13), (34, 4), (28, 5), (31, 16), (15, 22), (28, 25), (23, 28), (1, 29), (29, 24), (15, 11), (3, 19), (6, 29), (12, 28), (3, 18), (8, 30), (11, 18), (25, 27), (6, 2), (27, 10), (7, 21), (7, 27), (14, 22), (23, 4), (28, 26), (5, 11), (15, 4), (34, 1), (14, 13), (23, 26), (0, 13), (10, 14), (1, 30), (24, 22), (22, 26), (1, 28), (10, 18), (29, 9), (22, 4), (18, 5), (2, 0), (3, 16), (17, 13), (26, 3), (5, 5), (14, 7), (2, 6), (7, 5), (13, 3), (17, 7), (4, 12), (4, 0), (20, 9), (2, 28), (5, 19), (5, 13), (18, 22), (29, 11), (29, 12), (11, 14), (31, 23), (15, 27), (1, 8), (21, 21), (25, 23), (2, 14), (3, 25), (21, 25), (12, 3), (33, 13), (34, 28), (17, 15), (33, 19), (33, 15), (33, 8), (2, 24), (33, 16), (9, 13), (21, 11), (33, 3), (34, 23), (20, 10), (11, 1), (10, 0), (14, 15), (4, 3), (22, 7), (27, 15), (26, 12), (12, 6), (34, 5), (0, 25), (1, 6), (35, 20), (12, 20), (20, 15), (1, 9), (31, 4), (1, 17), (26, 26), (5, 14), (8, 19), (14, 12), (29, 23), (24, 28), (5, 18), (26, 1), (28, 3), (9, 29), (22, 15), (19, 3), (24, 3), (5, 28), (11, 27), (10, 15), (34, 10), (31, 14), (8, 6), (21, 19), (7, 26), (35, 14), (27, 22), (17, 16), (28, 24), (4, 9), (9, 3), (7, 1), (26, 15), (0, 16), (22, 16), (25, 17), (33, 18), (18, 17), (3, 10), (21, 0), (30, 12), (23, 19), (12, 4), (16, 3), (9, 23), (9, 9), (1, 27), (9, 18), (7, 10), (35, 3), (1, 24), (35, 27), (7, 13), (28, 27), (35, 8), (34, 16), (18, 0), (18, 28), (30, 28), (16, 1), (31, 11), (3, 8), (31, 8), (4, 16), (9, 20), (16, 27), (0, 4), (6, 28), (21, 4), (16, 5), (9, 22), (32, 16), (13, 17), (2, 13), (35, 1), (7, 30), (5, 12), (17, 25), (3, 15), (18, 12), (4, 26), (15, 28), (22, 12), (20, 16), (14, 17), (28, 23), (10, 16), (18, 18), (20, 4), (4, 7), (30, 20), (29, 28), (31, 9), (31, 18), (33, 25), (11, 30), (28, 28), (27, 0), (12, 11), (4, 19), (6, 9), (15, 15), (24, 6), (11, 2), (12, 29), (29, 15), (34, 0), (4, 8), (6, 30), (1, 18), (34, 24), (34, 19), (7, 20), (9, 2), (4, 10), (10, 3), (16, 12), (0, 20), (8, 24), (0, 18), (33, 9), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180960", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (35, 2), (27, 16), (35, 3), (10, 27), (33, 19), (4, 12), (18, 3), (23, 26), (4, 25), (34, 0), (4, 22), (3, 11), (33, 25), (13, 18), (25, 24), (1, 29), (35, 29), (17, 26), (34, 33), (30, 16), (27, 19), (29, 6), (14, 8), (34, 5), (14, 17), (2, 6), (15, 15), (31, 2), (33, 10), (20, 31), (8, 9), (11, 17), (25, 20), (10, 21), (34, 8), (18, 27), (18, 24), (33, 7), (20, 4), (33, 24), (6, 7), (21, 6), (15, 27), (28, 17), (20, 25), (31, 1), (0, 24), (10, 19), (28, 32), (19, 32), (25, 6), (27, 1), (2, 15), (22, 20), (32, 26), (2, 22), (20, 27), (17, 4), (3, 3), (24, 34), (9, 4), (24, 23), (9, 20), (9, 24), (11, 7), (27, 33), (0, 25), (17, 15), (10, 14), (8, 13), (24, 4), (24, 30), (7, 25), (29, 7), (2, 16), (11, 5), (4, 23), (16, 23), (6, 23), (13, 4), (8, 30), (3, 17), (6, 13), (12, 6), (34, 9), (31, 31), (35, 11), (13, 17), (16, 25), (6, 34), (34, 7), (31, 6), (10, 10), (27, 22), (14, 4), (17, 33), (11, 23), (25, 8), (25, 0), (15, 2), (11, 8), (13, 14), (32, 25), (28, 34), (7, 1), (16, 20), (24, 3), (17, 18), (21, 33), (25, 19), (10, 34), (18, 31), (24, 20), (32, 34), (2, 27), (17, 34), (1, 11), (15, 1), (30, 0), (0, 20), (22, 11), (22, 24), (7, 34), (6, 5), (34, 34), (3, 23), (16, 18), (32, 16), (20, 5), (31, 4), (17, 10), (4, 8), (2, 14), (22, 13), (13, 11), (30, 30), (23, 18), (0, 33), (17, 3), (33, 20), (18, 19), (33, 8), (22, 7), (13, 12), (15, 34), (20, 20), (5, 13), (9, 19), (23, 17), (9, 2), (26, 12), (23, 4), (21, 26), (2, 23), (8, 23), (14, 14), (22, 6), (33, 33), (33, 29), (13, 22), (7, 8), (7, 4), (6, 31), (25, 11), (7, 5), (23, 15), (6, 1), (28, 21), (25, 21), (21, 32), (33, 12), (26, 5), (14, 24), (28, 19), (33, 30), (6, 28), (11, 6), (16, 33), (33, 6), (20, 18), (21, 4), (32, 24), (5, 20), (11, 2), (26, 25), (23, 33), (9, 1), (22, 4), (34, 26), (24, 15), (5, 8), (20, 3), (17, 24), (8, 16), (5, 5), (34, 3), (27, 3), (19, 31), (8, 33), (9, 7), (12, 18), (1, 24), (35, 5), (7, 11), (31, 16), (35, 0), (1, 2), (34, 19), (35, 21), (31, 21), (3, 2), (23, 24), (8, 8), (34, 25), (2, 17), (17, 9), (27, 29), (32, 4), (10, 2), (3, 28), (1, 20), (16, 26), (28, 9), (22, 12), (25, 28), (0, 31), (17, 25), (10, 24), (31, 22), (34, 20), (22, 23), (32, 21), (23, 11), (16, 16), (1, 19), (17, 17), (5, 23), (6, 17), (33, 17), (1, 26), (8, 19), (22, 34), (34, 22), (12, 4), (3, 12), (22, 27), (17, 23), (27, 12), (12, 16), (8, 27), (22, 9), (1, 22), (11, 4), (4, 27), (8, 10), (22, 32), (15, 28), (34, 27), (13, 21), (2, 11), (23, 25), (7, 31), (15, 25), (27, 34), (12, 1), (12, 21), (18, 12), (24, 6), (4, 5), (22, 25), (19, 30), (2, 33), (8, 5), (9, 14), (7, 0), (30, 24), (23, 23), (8, 6), (30, 26), (5, 9), (17, 13), (29, 30), (21, 12), (9, 8), (17, 7), (3, 24), (12, 10), (15, 20), (32, 30), (35, 10), (26, 34), (2, 0), (16, 15), (3, 13), (7, 12), (20, 23), (26, 33), (17, 19), (26, 15), (35, 14), (0, 26), (14, 1), (1, 14), (32, 1), (34, 31), (19, 6), (5, 2), (14, 20), (0, 11), (35, 4), (3, 7), (0, 29), (28, 28), (15, 5), (15, 18), (3, 29), (32, 29), (35, 17), (6, 15), (7, 15), (13, 28), (15, 13), (0, 13), (14, 29), (10, 23), (12, 26), (3, 30), (27, 9), (6, 21), (16, 30), (22, 21), (26, 1), (35, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38920", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), 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), (25, 2), (16, 24), (1, 6), (11, 12), (26, 12), (25, 12), (2, 8), (13, 33), (36, 0), (29, 5), (1, 13), (15, 17), (0, 6), (5, 15), (11, 7), (2, 25), (5, 31), (13, 34), (16, 34), (17, 5), (1, 17), (23, 29), (28, 23), (23, 16), (25, 3), (31, 19), (32, 3), (17, 35), (2, 2), (2, 1), (33, 31), (21, 15), (30, 4), (8, 4), (20, 31), (21, 4), (7, 35), (19, 15), (20, 4), (8, 15), (15, 3), (24, 19), (20, 22), (8, 27), (31, 10), (27, 5), (35, 33), (30, 31), (27, 32), (24, 31), (2, 9), (13, 35), (16, 6), (22, 7), (7, 5), (27, 18), (14, 30), (6, 33), (15, 11), (36, 29), (27, 2), (4, 1), (33, 5), (30, 5), (1, 19), (26, 25), (26, 20), (24, 23), (7, 29), (29, 18), (31, 23), (31, 8), (6, 2), (31, 4), (16, 35), (10, 4), (4, 2), (5, 24), (12, 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format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538704", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), 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), (27, 20), (14, 29), (1, 2), (28, 28), (8, 16), (16, 22), (17, 9), (14, 16), (8, 5), (2, 14), (18, 11), (16, 35), (20, 30), (9, 19), (29, 18), (21, 1), (14, 0), (12, 28), (6, 36), (2, 25), (23, 1), (9, 34), (27, 23), (31, 35), (15, 16), (29, 12), (27, 5), (27, 17), (13, 33), (3, 9), (6, 31), (11, 7), (0, 26), (25, 11), (21, 27), (16, 6), (22, 32), (2, 1), (9, 28), (28, 0), (11, 22), (28, 35), (2, 11), (14, 9), (27, 25), (32, 22), (19, 27), (11, 3), (18, 34), (7, 15), (10, 16), (26, 12), (30, 17), (4, 8), (10, 22), (25, 12), (1, 19), (21, 2), (30, 21), (5, 20), (24, 23), (31, 8), (4, 12), (7, 36), (4, 2), (31, 34), (11, 25), (31, 3), (6, 2), (30, 1), (6, 27), (31, 27), (19, 31), (13, 23), (27, 22), (15, 3), (16, 37), (9, 14), (5, 30), (4, 13), (15, 11), (13, 26), (16, 20), (30, 35), (15, 25), (30, 8), (30, 14), (23, 20), (17, 13), (0, 30), (5, 29), (3, 22), (4, 25), (27, 14), (28, 32), (25, 29), (2, 16), (30, 33), (17, 29), (25, 23), (21, 30), (2, 20), (20, 37), (15, 20), (13, 15), (28, 20), (14, 6), (4, 26), (6, 4), (17, 10), (22, 8), (22, 16), (20, 35), (32, 23), (19, 21), (7, 30), (10, 23), (23, 26), (9, 9), (0, 24), (32, 5), (27, 35), (29, 6), (0, 23), (2, 33), (13, 9), (26, 24), (32, 12), (16, 10), (26, 25), (29, 16), (9, 21), (13, 31), (20, 0), (4, 14), (31, 20), (9, 13), (12, 17), (18, 24), (22, 17), (28, 17), (2, 21), (7, 7), (22, 10), (19, 0), (18, 29), (22, 15), (14, 12), (22, 12), (26, 15), (18, 27), (3, 34), (1, 27), (12, 26), (10, 0), (11, 1), (31, 32), (30, 12), (21, 4), (4, 28), (20, 15), (17, 5), (15, 12), (19, 6), (20, 25), (32, 11), (16, 0), (20, 3), (9, 6), (27, 0), (1, 20), (4, 21), (18, 12), (28, 7), (24, 36), (15, 28), (31, 17), (24, 20), (17, 22), (19, 4), (11, 18), (30, 32), (3, 17), (29, 20), (0, 28), (4, 18), (11, 10), (22, 31), (12, 14), (20, 32), (3, 10), (23, 37), (7, 12), (30, 19), (23, 18), (5, 17), (22, 0), (26, 17), (30, 31), (16, 24), (2, 23), (5, 12), (16, 33), (2, 9), (24, 3), (19, 17), (25, 13), (4, 35), (29, 5), (32, 31), (31, 7), (29, 11), (5, 2), (15, 19), (8, 33), (7, 9), (16, 7), (8, 2), (22, 23), (9, 17), (32, 0), (29, 4), (27, 3), (4, 31), (24, 30), (0, 29), (12, 25), (16, 19), (14, 19), (19, 10), (9, 25), (15, 2), (1, 31), (21, 15), (12, 6), (22, 1), (15, 27), (7, 37), (16, 27), (6, 8), (16, 9), (21, 5), (3, 12), (7, 27), (26, 26), (30, 4), (8, 24), (29, 15), (31, 2), (1, 4), (28, 24), (10, 29), (25, 25), (0, 16), (0, 12), (25, 2), (18, 15), (5, 9), (8, 4), (24, 2), (21, 20), (8, 17), (18, 23), (21, 26), (14, 23), (22, 36), (11, 6), (12, 30), (10, 11), (20, 36), (14, 14), (6, 10), (24, 27), (20, 23), (13, 25), (24, 8), (9, 18), (32, 28), (30, 23), (0, 36), (19, 7), (0, 19), (20, 6), (30, 2), (17, 16), (31, 31), (25, 26), (25, 3), (27, 27), (7, 8), (20, 18), (22, 37), (0, 8), (20, 22), (6, 32), (24, 26), (5, 28), (20, 1), (20, 24), (7, 19), (21, 8), (19, 23), (23, 35), (26, 20), (4, 15), (15, 13), (15, 0), (22, 20), (27, 32), (25, 14), (30, 20), (18, 10), (29, 2), (30, 10), (18, 20), (21, 24), (5, 19), (25, 31), (0, 11), (31, 25), (17, 28), (18, 9), (25, 21), (14, 24), (29, 36), (23, 3), (32, 9), (18, 31), (17, 27), (1, 0), (32, 21), (4, 29), (23, 2), (15, 34), (29, 35), (5, 18), (24, 11), (13, 5), (8, 32), (31, 5), (10, 14), (13, 28), (25, 1), (18, 36), (27, 4), (24, 12), (14, 7), (10, 34), (4, 19), (13, 4), (23, 11), (23, 36), (16, 3), (15, 7), (5, 24), (1, 32), (9, 4), (10, 18), (3, 30), (15, 33), (23, 8), (13, 29), (31, 30), (22, 6), (7, 23), (30, 9), (27, 15), (1, 35), (31, 0), (10, 35), (18, 6), (17, 0), (14, 30), (0, 14), (14, 31), (13, 37), (24, 13), (1, 13), (8, 36), (6, 11), (17, 37), (28, 36), (32, 35), (17, 36), (25, 36), (29, 14), (0, 35), (20, 12), (27, 24), (22, 33), (25, 19), (10, 32), (14, 13), (8, 30), (13, 8), (9, 32), (30, 16), (12, 5), (19, 25), (18, 37), (30, 28), (22, 35), (29, 32), (22, 5), (11, 31), (2, 6), (21, 32), (28, 18), (8, 19), (2, 18), (23, 27), (2, 4), (30, 13), (0, 21), (9, 26), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "898416", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 32), (30, 31), (33, 25), (17, 21), (0, 11), (16, 21), (0, 29), (3, 17), (12, 14), (21, 30), (34, 7), (19, 23), (16, 17), (11, 9), (30, 22), (18, 18), (29, 9), (16, 29), (11, 31), (18, 10), (0, 8), (30, 27), (9, 14), (12, 0), (4, 14), (19, 33), (3, 35), (25, 26), (18, 33), (35, 25), (4, 13), (24, 16), (11, 33), (13, 6), (18, 20), (10, 24), (5, 30), (15, 28), (12, 34), (24, 35), (11, 17), (11, 32), (16, 19), (29, 6), (33, 12), (20, 6), (19, 17), (27, 30), (2, 12), (17, 23), (18, 1), (30, 3), (12, 37), (31, 16), (17, 2), (3, 37), (14, 29), (10, 32), (11, 28), (4, 36), (7, 25), (14, 37), (32, 18), (20, 28), (17, 9), (20, 15), (9, 9), (32, 15), (18, 37), (34, 26), (20, 20), (5, 32), (12, 20), (23, 24), (13, 27), (2, 11), (0, 1), (12, 24), (29, 26), (35, 8), (9, 23), (20, 29), (4, 32), (32, 12), (23, 34), (28, 19), (30, 12), (5, 3), (8, 36), (26, 2), (19, 34), (2, 14), (24, 18), (23, 3), (14, 21), (25, 20), (21, 0), (34, 33), (21, 24), (15, 5), (8, 18), (29, 29), (5, 24), (0, 34), (29, 2), (26, 31), (27, 31), (30, 16), (11, 22), (29, 14), (26, 16), (27, 5), (12, 13), (31, 0), (7, 13), (21, 17), (31, 34), (2, 15), (28, 4), (1, 28), (33, 2), (2, 32), (22, 10), (9, 35), (14, 8), (34, 4), (28, 33), (23, 1), (24, 28), (29, 20), (31, 6), (19, 27), (8, 33), (13, 29), (23, 31), (22, 30), (20, 1), (11, 35), (13, 34), (3, 33), (16, 14), (18, 13), (9, 2), (25, 28), (5, 22), (26, 28), (12, 32), (16, 23), (25, 33), (11, 6), (30, 10), (24, 29), (20, 16), (29, 37), (11, 23), (29, 8), (30, 36), (23, 26), (31, 27), (15, 9), (2, 9), (35, 4), (11, 5), (32, 22), (14, 11), (6, 12), (2, 35), (8, 3), (27, 0), (12, 35), (9, 27), (13, 22), (4, 30), (13, 0), (14, 5), (20, 27), (34, 23), (24, 23), (4, 35), (6, 8), (19, 1), (4, 18), (32, 0), (21, 12), (25, 22), (29, 25), (30, 21), (7, 5), (26, 23), (2, 7), (33, 20), (1, 19), (15, 34), (33, 26), (18, 14), (35, 16), (27, 24), (2, 16), (27, 29), (7, 3), (33, 16), (27, 11), (17, 16), (11, 24), (8, 5), (0, 24), (18, 11), (26, 30), (11, 3), (32, 28), (30, 5), (35, 11), (15, 15), (31, 13), (27, 19), (19, 5), (1, 26), (22, 20), (19, 37), (22, 3), (21, 16), (13, 12), (23, 11), (10, 19), (0, 10), (21, 25), (4, 3), (19, 7), (30, 0), (34, 17), (7, 33), (6, 37), (0, 5), (12, 7), (9, 21), (33, 21), (26, 1), (15, 21), (24, 13), (31, 11), (27, 28), (5, 12), (9, 25), (29, 32), (16, 12), (9, 34), (31, 3), (27, 32), (35, 27), (7, 8), (3, 26), (13, 5), (5, 35), (13, 2), (27, 3), (16, 27), (25, 25), (12, 1), (0, 19), (23, 30), (19, 22), (13, 23), (7, 37), (20, 10), (1, 35), (24, 1), (5, 11), (2, 26), (26, 8), (32, 24), (18, 19), (13, 18), (24, 3), (4, 16), (1, 12), (21, 11), (13, 13), (24, 26), (14, 25), (8, 7), (14, 31), (24, 12), (4, 11), (23, 4), (20, 19), (19, 4), (13, 28), (9, 3), (35, 31), (3, 24), (4, 26), (35, 7), (11, 2), (12, 10), (12, 2), (23, 17), (15, 7), (11, 37), (6, 27), (1, 21), (9, 10), (6, 10), (8, 29), (18, 17), (7, 26), (15, 20), (2, 3), (32, 25), (24, 31), (19, 0), (8, 17), (35, 35), (17, 26), (25, 6), (13, 21), (34, 8), (1, 34), (17, 0), (34, 1), (12, 36), (13, 4), (25, 37), (21, 14), (21, 23), (9, 22), (9, 26), (19, 26), (20, 13), (19, 21), (17, 36), (14, 36), (4, 33), (32, 9), (15, 17), (10, 33), (26, 32), (5, 0), (35, 1), (1, 10), (12, 4), (9, 29), (34, 32), (1, 17), (6, 13), (28, 25), (20, 32), (22, 32), (0, 2), (27, 26), (14, 3), (34, 9), (2, 23), (11, 19), (5, 36), (18, 8), (5, 25), (15, 32), (28, 5), (1, 9), (21, 2), (14, 33), (26, 33), (12, 31), (17, 8), (8, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "963144", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (6, 3), (2, 8), (30, 12), (15, 28), (5, 15), (29, 22), (0, 1), (16, 10), (9, 20), (12, 14), (12, 22), (6, 4), (12, 31), (26, 25), (27, 12), (0, 26), (14, 17), (27, 10), (21, 2), (25, 1), (24, 12), (27, 25), (14, 19), (26, 19), (10, 5), (4, 29), (20, 20), (25, 17), (4, 15), (11, 28), (8, 15), (5, 20), (8, 7), (21, 15), (13, 9), (20, 23), (18, 23), (1, 22), (0, 8), (29, 16), (17, 22), (5, 17), (16, 2), (30, 14), (9, 30), (23, 29), (12, 7), (5, 26), (22, 25), (20, 21), (5, 11), (20, 22), (6, 29), (25, 6), (17, 31), (9, 26), (2, 21), (1, 23), (11, 31), (4, 1), (4, 17), (18, 18), (29, 6), (11, 0), (12, 29), (7, 25), (3, 16), (29, 27), (17, 13), (14, 10), (1, 17), (25, 15), (7, 27), (27, 6), (3, 0), (1, 6), (4, 7), (16, 13), (1, 5), (20, 0), (2, 23), (16, 5), (24, 29), (21, 25), (24, 8), (13, 2), (1, 12), (4, 21), (7, 19), (18, 16), (16, 8), (22, 12), (17, 5), (25, 18), (11, 1), (13, 19), (2, 20), (12, 28), (15, 25), (18, 22), (15, 30), (28, 10), (9, 21), (20, 10), (2, 16), (28, 17), (22, 30), (13, 8), (29, 20), (28, 5), (10, 4), (21, 21), (0, 18), (4, 26), (21, 6), (10, 18), (22, 24), (30, 15), (18, 3), (13, 12), (7, 9), (16, 21), (0, 21), (11, 19), (12, 3), (28, 18), (1, 24), (3, 15), (3, 11), (21, 1), (30, 11), (4, 25), (2, 19), (6, 24), (19, 15), (22, 2), (18, 5), (11, 4), (3, 12), (5, 13), (8, 30), (18, 24), (27, 31), (25, 20), (27, 17), (7, 11), (29, 14), (21, 16), (1, 28), (9, 3), (21, 9), (30, 8), (17, 1), (14, 11), (23, 31), (18, 17), (10, 6), (7, 21), (22, 0), (26, 16), (3, 4), (2, 10), (2, 30), (24, 15), (23, 11), (13, 5), (28, 22), (18, 21), (19, 29), (14, 18), (24, 28), (9, 5), (21, 5), (17, 0), (13, 23), (30, 28), (23, 12), (26, 26), (5, 7), (19, 8), (25, 16), (17, 2), (22, 1), (10, 9), (24, 19), (30, 25), (0, 29), (28, 4), (0, 31), (26, 28), (28, 0), (7, 2), (4, 16), (22, 3), (4, 27), (5, 4), (8, 1), (11, 14), (2, 0), (8, 16), (19, 19), (2, 2), (2, 17), (22, 20), (4, 28), (13, 11), (8, 4), (27, 2), (17, 17), (6, 9), (15, 6), (22, 29), (24, 31), (29, 4), (17, 12), (15, 29), (19, 12), (14, 0), (1, 21), (22, 16), (28, 28), (25, 28), (13, 29), (25, 2), (21, 19), (8, 12), (3, 30), (13, 15), (2, 12), (24, 9), (8, 26), (14, 15), (26, 13), (15, 8), (27, 14), (29, 11), (29, 12), (29, 31), (16, 16), (30, 22), (11, 18), (4, 9), (15, 21), (3, 19), (22, 10), (5, 0), (12, 27), (27, 13), (22, 6), (13, 1), (14, 14), (26, 0), (5, 12), (6, 20), (26, 21), (19, 23), (0, 14), (21, 8), (17, 3), (3, 6), (4, 18), (6, 28), (18, 30), (12, 6), (25, 10), (18, 19), (14, 6), (3, 24), (21, 31), (23, 19), (20, 1), (5, 25), (10, 7), (12, 13), (4, 20), (6, 30), (6, 8), (14, 27), (10, 31), (25, 13), (21, 29), (9, 15), (14, 8), (0, 11), (26, 24), (27, 26), (30, 2), (13, 7), (5, 1), (10, 1), (30, 6), (2, 31), (19, 18), (18, 29), (3, 1), (30, 19), (14, 24), (10, 3), (0, 9), (22, 18), (12, 23), (19, 30), (28, 24), (27, 18), (4, 4), (19, 11), (9, 23), (22, 22), (15, 12), (16, 24), (23, 30), (24, 22), (26, 23), (23, 25), (1, 18), (0, 25), (28, 3), (4, 11), (6, 25), (22, 21), (28, 2), (16, 25), (23, 8), (6, 1), (26, 5), (15, 24), (2, 14), (19, 24), (3, 20), (20, 14), (17, 27), (11, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743808", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 34), (22, 3), (13, 29), (14, 14), (4, 11), (33, 12), (18, 33), (27, 35), (9, 31), (30, 17), (1, 23), (7, 19), (6, 24), (28, 29), (23, 17), (8, 27), (18, 27), (1, 29), (22, 15), (35, 13), (0, 4), (5, 23), (9, 15), (22, 7), (12, 2), (37, 19), (20, 36), (9, 3), (20, 20), (31, 18), (15, 18), (11, 4), (37, 28), (29, 13), (33, 4), (37, 32), (2, 17), (26, 24), (5, 1), (3, 35), (21, 32), (21, 7), (28, 1), (2, 13), (21, 36), (16, 28), (37, 4), (25, 10), (5, 14), (12, 30), (29, 4), (30, 20), (12, 4), (22, 4), (27, 12), (17, 13), (13, 5), (34, 12), (6, 5), (19, 22), (12, 20), (25, 22), (14, 35), (9, 20), (29, 20), (21, 31), (32, 17), (2, 6), (27, 1), (14, 26), (5, 16), (15, 19), (17, 3), (4, 4), (21, 8), (0, 23), (29, 16), (30, 34), (19, 28), (27, 33), (21, 29), (29, 25), (25, 36), (3, 3), (17, 35), (36, 36), (35, 35), (36, 32), (19, 35), (14, 18), (31, 30), (33, 28), (34, 11), (34, 26), (24, 7), (31, 19), (3, 14), (29, 9), (16, 33), (23, 26), (33, 31), (20, 22), (23, 19), (36, 0), (17, 25), (28, 8), (10, 10), (9, 2), (7, 4), (24, 33), (17, 23), (35, 2), (1, 18), (2, 24), (32, 6), (6, 16), (10, 27), (32, 19), (35, 36), (2, 20), (28, 24), (24, 5), (2, 4), (3, 17), (3, 2), (8, 8), (33, 10), (36, 12), (18, 24), (37, 26), (11, 12), (12, 10), (35, 7), (26, 0), (26, 17), (20, 17), (21, 1), (20, 24), (12, 34), (15, 7), (30, 10), (37, 33), (22, 33), (4, 33), (15, 25), (17, 36), (21, 25), (4, 35), (29, 18), (11, 15), (25, 7), (22, 2), (28, 11), (15, 2), (33, 23), (19, 5), (11, 13), (13, 10), (1, 33), (20, 11), (8, 21), (22, 22), (0, 14), (30, 19), (37, 6), (16, 20), (13, 13), (30, 9), (23, 16), (3, 1), (22, 31), (10, 9), (32, 25), (29, 33), (13, 17), (29, 23), (2, 31), (31, 1), (7, 7), (30, 33), (32, 35), (31, 17), (27, 25), (0, 10), (30, 12), (2, 3), (6, 7), (27, 32), (27, 5), (36, 4), (3, 12), (19, 10), (19, 19), (27, 21), (36, 10), (20, 29), (0, 24), (8, 32), (7, 18), (4, 7), (26, 28), (4, 29), (25, 8), (32, 13), (20, 32), (14, 16), (6, 0), (15, 11), (15, 4), (28, 35), (25, 2), (10, 8), (5, 24), (34, 8), (28, 19), (6, 23), (6, 33), (35, 6), (10, 0), (30, 3), (7, 35), (9, 36), (30, 15), (16, 35), (16, 31), (12, 7), (10, 18), (14, 4), (33, 29), (18, 31), (15, 8), (0, 3), (24, 21), (1, 27), (34, 32), (20, 2), (33, 25), (30, 13), (18, 25), (24, 34), (0, 17), (16, 32), (32, 20), (13, 1), (25, 34), (26, 23), (11, 23), (8, 3), (7, 9), (29, 8), (8, 29), (3, 18), (4, 8), (23, 33), (18, 34), (9, 17), (1, 11), (27, 18), (21, 33), (26, 21), (37, 1), (34, 31), (5, 10), (26, 1), (25, 29), (1, 22), (13, 12), (17, 16), (24, 31), (8, 14), (28, 14), (30, 11), (24, 6), (16, 6), (9, 27), (7, 25), (32, 29), (27, 34), (34, 35), (0, 35), (27, 28), (9, 13), (15, 20), (32, 4), (12, 14), (11, 32), (2, 32), (35, 24), (24, 24), (33, 16), (30, 23), (6, 11), (2, 10), (7, 28), (32, 18), (5, 28), (30, 30), (28, 20), (1, 34), (4, 26), (0, 13), (15, 22), (24, 18), (32, 26), (37, 14), (14, 19), (35, 28), (19, 30), (3, 0), (9, 10), (29, 36), (33, 24), (28, 27), (32, 32), (13, 11), (29, 3), (22, 34), (33, 2), (15, 23), (7, 20), (27, 0), (19, 13), (0, 16), (4, 30), (15, 9), (30, 16), (10, 6), (25, 9), (17, 7), (16, 22), (7, 1), (6, 9), (2, 26), (35, 29), (0, 6), (28, 10), (31, 36), (8, 23), (1, 19), (35, 23), (20, 6), (23, 18), (14, 6), (21, 22), (1, 30), (7, 15), (6, 30), (35, 20), (9, 14), (0, 19), (3, 20), (24, 4), (0, 8), (25, 17), (33, 34), (6, 10), (9, 29), (34, 14), (18, 36), (12, 22), (34, 28), (19, 33), (9, 0), (3, 4), (21, 13), (22, 12), (15, 21), (32, 27), (26, 30), (15, 32), (17, 10), (13, 0), (2, 7), (3, 28), (21, 28), (9, 25), (3, 19), (17, 18), (34, 6), (7, 11), (7, 0), (14, 17), (21, 16), (33, 7), (5, 4), (31, 10), (32, 24), (8, 2), (32, 10), (28, 4), (27, 31), (30, 32), (31, 27), (11, 3), (28, 28), (25, 6), (21, 35), (5, 33), (0, 5), (36, 35), (24, 20), (23, 31), (5, 30), (5, 7), (7, 10), (32, 2), (30, 27), (20, 7), (15, 15), (14, 29), (16, 3), (0, 15), (1, 16), (14, 28), (10, 25), (16, 9), (13, 3), (16, 29), (37, 23), (17, 0), (9, 12), (12, 16), (16, 13), (19, 34), (25, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475632", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 12), (3, 34), (7, 36), (1, 3), (3, 27), (32, 1), (14, 14), (36, 7), (4, 37), (33, 12), (36, 35), (23, 13), (35, 0), (32, 21), (30, 31), (3, 31), (35, 26), (12, 23), (18, 2), (11, 1), (17, 17), (9, 13), (33, 8), (11, 9), (29, 35), (4, 23), (9, 28), (32, 26), (15, 30), (30, 19), (16, 24), (21, 20), (17, 12), (31, 34), (3, 21), (31, 21), (14, 30), (31, 24), (0, 4), (35, 22), (34, 35), (14, 2), (26, 8), (35, 1), (8, 30), (33, 36), (4, 9), (37, 6), (31, 9), (30, 29), (33, 9), (6, 9), (18, 6), (27, 9), (31, 2), (14, 32), (9, 32), (32, 20), (5, 37), (14, 23), (8, 0), (6, 27), (25, 20), (13, 10), (0, 3), (8, 22), (14, 34), (33, 0), (13, 34), (34, 19), (36, 32), (28, 26), (19, 1), (4, 16), (29, 7), (12, 26), (25, 2), (1, 26), (21, 5), 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18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "184680", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 15), (0, 11), (28, 0), (24, 30), (37, 7), (13, 6), (0, 8), (29, 24), (31, 23), (7, 30), (6, 31), (17, 30), (16, 9), (17, 33), (31, 27), (9, 20), (28, 11), (14, 8), (21, 25), (15, 2), (6, 5), (26, 32), (1, 29), (14, 31), (22, 25), (29, 15), (7, 1), (21, 12), (22, 10), (30, 33), (19, 24), (1, 25), (36, 8), (22, 16), (2, 22), (32, 1), (20, 33), (7, 11), (21, 17), (20, 28), (24, 16), (2, 14), (12, 32), (24, 24), (27, 32), (15, 0), (33, 23), (17, 20), (27, 13), (29, 18), (38, 12), (8, 30), (27, 30), (34, 32), (4, 27), (33, 33), (10, 16), (26, 3), (22, 32), (36, 15), (7, 24), (19, 8), (5, 32), (20, 26), (7, 26), (4, 5), (36, 27), (35, 10), (7, 23), (18, 27), (31, 22), (30, 7), (35, 2), (17, 9), (36, 32), (13, 19), (7, 4), (28, 24), (33, 22), (12, 2), (26, 33), (35, 31), (13, 12), (0, 1), (11, 12), (2, 16), (26, 28), (34, 0), (19, 10), (15, 33), (23, 17), (8, 16), (6, 0), (17, 24), (30, 21), (1, 2), (23, 9), (20, 8), (21, 2), (27, 8), (21, 0), (12, 26), (31, 20), (6, 24), (38, 23), (10, 0), (29, 29), (1, 31), (25, 26), (16, 28), (21, 7), (1, 32), (25, 15), (25, 10), (33, 25), (7, 8), (3, 17), (20, 11), (35, 20), (4, 25), (26, 17), (31, 19), (37, 14), (8, 5), (19, 20), (29, 30), (37, 10), (16, 2), (26, 27), (7, 21), (4, 10), (14, 27), (24, 5), (3, 22), (23, 18), (37, 24), (9, 4), (26, 30), (27, 10), (22, 1), (32, 21), (15, 8), (37, 22), (21, 19), (38, 15), (13, 18), (8, 22), (17, 1), (34, 18), (15, 11), (35, 14), (34, 31), (33, 26), (9, 12), (19, 26), (16, 1), (22, 9), (13, 21), (16, 27), (36, 12), (0, 19), (12, 33), (21, 13), (29, 25), (12, 11), (3, 16), (37, 5), (3, 33), (14, 10), (20, 21), (30, 9), (38, 25), (25, 29), (27, 21), (21, 1), (21, 5), (37, 12), (19, 9), (6, 11), (2, 23), (34, 28), (2, 1), (36, 16), (23, 28), (9, 5), (27, 29), (33, 8), (16, 6), (31, 3), (10, 27), (37, 18), (3, 18), (23, 30), (29, 14), (6, 12), (3, 26), (13, 0), (22, 20), (33, 20), (4, 28), (25, 23), (28, 32), (18, 26), (11, 25), (9, 25), (38, 4), (26, 21), (15, 31), (10, 33), (38, 5), (36, 7), (23, 1), (13, 15), (6, 13), (36, 19), (20, 10), (24, 7), (2, 19), (22, 21), (24, 20), (4, 26), (31, 1), (9, 10), (16, 25), (29, 4), (18, 28), (24, 31), (6, 4), (31, 12), (2, 30), (4, 13), (19, 16), (29, 28), (9, 17), (31, 21), (25, 16), (37, 6), (7, 2), (22, 29), (16, 23), (29, 8), (31, 31), (19, 23), (38, 21), (37, 25), (34, 1), (23, 19), (5, 0), (14, 23), (25, 22), (18, 10), (24, 3), (35, 1), (14, 3), (5, 16), (3, 20), (36, 28), (29, 2), (13, 17), (3, 5), (35, 29), (37, 13), (19, 29), (12, 15), (11, 8), (30, 25), (9, 15), (29, 11), (24, 15), (19, 17), (28, 26), (13, 28), (36, 24), (18, 18), (15, 30), (36, 6), (28, 4), (25, 13), (6, 7), (14, 13), (24, 25), (15, 28), (16, 8), (5, 18), (16, 22), (8, 11), (13, 32), (19, 12), (17, 12), (6, 29), (1, 21), (34, 15), (13, 33), (25, 0), (22, 31), (12, 18), (30, 3), (0, 20), (14, 12), (35, 28), (32, 10), (14, 2), (20, 23), (3, 28), (29, 27), (24, 21), (9, 1), (3, 4), (13, 27), (6, 16), (38, 26), (32, 22), (9, 9), (4, 7), (21, 6), (28, 22), (24, 4), (22, 6), (6, 10), (24, 28), (24, 14), (16, 15), (25, 30), (37, 11), (27, 9), (15, 5), (6, 21), (15, 22), (5, 24), (10, 25), (36, 4), (35, 15), (33, 5), (4, 21), (25, 24), (35, 17), (32, 17), (8, 1), (23, 15), (11, 16), (0, 15), (26, 20), (2, 5), (28, 8), (10, 10), (32, 0), (37, 30), (31, 10), (5, 30), (21, 20), (34, 2), (1, 7), (30, 10), (35, 5), (25, 6), (19, 19), (9, 21), (3, 11), (34, 22), (14, 22), (36, 21), (35, 0), (34, 33), (34, 7), (30, 26), (29, 32), (33, 19), (28, 16), (10, 26), (36, 18), (17, 13), (2, 21), (21, 9), (10, 5), (23, 21), (32, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "760320", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (17, 19), (0, 23), (12, 13), (11, 2), (5, 27), (14, 6), (28, 24), (24, 3), (13, 21), (27, 0), (24, 16), (2, 17), (4, 14), (18, 24), (11, 18), (28, 36), (4, 15), (22, 36), (28, 34), (24, 21), (27, 30), (19, 4), (2, 9), (7, 21), (0, 29), (15, 36), (21, 18), (13, 28), (27, 33), (22, 23), (19, 35), (13, 11), (3, 18), (22, 9), (4, 18), (13, 2), (10, 22), (28, 10), (23, 28), (17, 21), (10, 8), (22, 27), (4, 4), (8, 10), (4, 33), (29, 20), (2, 2), (9, 1), (6, 34), (8, 21), (7, 25), (0, 34), (19, 29), (21, 11), (28, 0), (17, 35), (23, 29), (29, 5), (12, 1), (24, 27), (15, 4), (20, 10), (1, 20), (13, 24), (16, 10), (0, 4), (6, 3), (4, 7), (3, 20), (12, 25), (25, 29), (22, 30), (24, 22), (22, 15), (10, 1), (11, 9), (10, 35), (8, 36), (11, 21), (26, 11), (18, 7), (14, 25), (21, 15), (14, 23), (5, 9), (26, 36), (8, 11), (29, 27), (7, 32), (2, 11), (29, 8), (1, 35), (3, 11), (3, 2), (9, 15), (1, 33), (27, 21), (23, 2), (1, 19), (20, 12), (24, 20), (18, 16), (19, 12), (26, 13), (22, 13), (24, 18), (19, 9), (23, 23), (12, 34), (20, 15), (3, 26), (0, 35), (12, 26), (8, 2), (22, 18), (7, 16), (19, 28), (20, 1), (11, 32), (7, 8), (1, 27), (6, 12), (26, 24), (28, 18), (12, 31), (1, 26), (1, 1), (16, 9), (21, 25), (19, 20), (18, 15), (13, 20), (19, 7), (9, 19), (26, 0), (29, 7), (29, 24), (14, 15), (22, 4), (21, 33), (12, 15), (13, 31), (10, 10), (1, 6), (21, 5), (22, 25), (10, 14), (20, 11), (28, 14), (29, 3), (23, 26), (25, 5), (23, 15), (29, 1), (3, 8), (9, 16), (19, 23), (9, 31), (17, 3), (26, 8), (5, 14), (26, 25), (27, 22), (4, 1), (16, 4), (13, 3), (0, 26), (14, 31), (16, 2), (7, 3), (16, 23), (23, 17), (16, 20), (17, 23), (27, 34), (2, 7), (2, 21), (7, 0), (25, 28), (6, 17), (17, 9), (3, 4), (19, 26), (2, 3), (22, 24), (13, 7), (9, 11), (19, 0), (7, 11), (10, 34), (3, 21), (12, 24), (9, 0), (13, 19), (11, 23), (6, 26), (6, 4), (28, 32), (11, 25), (0, 15), (16, 34), (9, 28), (27, 20), (9, 24), (14, 27), (0, 7), (10, 11), (14, 32), (26, 29), (20, 9), (8, 14), (26, 35), (23, 12), (4, 29), (1, 31), (24, 28), (14, 29), (17, 24), (6, 0), (5, 31), (25, 33), (16, 33), (27, 3), (27, 28), (6, 9), (6, 23), (26, 22), (15, 29), (8, 17), (25, 30), (14, 5), (7, 20), (0, 33), (21, 3), (25, 32), (8, 34), (21, 0), (25, 6), (25, 34), (20, 24), (6, 14), (6, 27), (5, 28), (22, 31), (7, 15), (8, 13), (6, 16), (24, 0), (8, 0), (11, 33), (5, 19), (21, 32), (23, 32), (18, 9), (16, 3), (2, 19), (28, 13), (3, 33), (27, 27), (27, 16), (17, 0), (20, 23), (4, 26), (28, 15), (8, 24), (14, 11), (28, 25), (7, 28), (26, 15), (4, 24), (8, 4), (3, 22), (22, 3), (25, 3), (24, 7), (4, 22), (13, 22), (11, 3), (25, 13), (27, 18), (25, 9), (5, 0), (26, 30), (24, 1), (2, 20), (5, 34), (7, 29), (9, 9), (8, 27), (1, 17), (25, 36), (26, 27), (17, 11), (3, 29), (5, 30), (16, 24), (16, 13), (27, 35), (24, 24), (0, 36), (5, 35), (20, 31), (4, 28), (2, 31), (21, 36), (23, 31), (25, 26), (19, 25), (15, 34), (11, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501952", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 37), (15, 28), (23, 3), (22, 25), (13, 37), (21, 31), (7, 9), (0, 33), (14, 36), (1, 10), (4, 15), (29, 19), (2, 9), (3, 32), (26, 17), (3, 14), (8, 25), (7, 3), (24, 31), (23, 18), (11, 2), (0, 17), (27, 18), (9, 16), (14, 35), (16, 35), (6, 25), (22, 19), (30, 23), (27, 5), (25, 3), (22, 34), (1, 25), (4, 34), (21, 5), (1, 29), (4, 25), (19, 32), (14, 20), (5, 19), (7, 29), (12, 25), (3, 8), (3, 1), (2, 33), (3, 35), (21, 14), (3, 22), (15, 18), (23, 20), (21, 1), (15, 15), (17, 34), (15, 0), (22, 32), (24, 7), (6, 36), (19, 17), (25, 14), (0, 11), (19, 37), (9, 22), (28, 0), (13, 15), (0, 35), (17, 16), (18, 7), (14, 33), (19, 35), (5, 27), (21, 24), (29, 9), (29, 37), (17, 3), (12, 10), (8, 11), (26, 34), (12, 35), (18, 31), (10, 20), (9, 37), (20, 5), (20, 10), (10, 14), (10, 19), (8, 36), (27, 31), (24, 9), (13, 34), (22, 16), (28, 7), (0, 6), (2, 14), (19, 6), (29, 33), (21, 35), (14, 34), (7, 27), (23, 19), (27, 10), (4, 14), (3, 9), (25, 34), (3, 6), (25, 33), (17, 14), (2, 6), (23, 28), (15, 21), (4, 28), (13, 21), (27, 33), (7, 2), (18, 27), (15, 19), (24, 28), (4, 9), (0, 15), (19, 30), (20, 15), (14, 32), (9, 15), (20, 16), (10, 31), (1, 15), (18, 0), (15, 14), (26, 29), (3, 29), (20, 29), (12, 24), (27, 17), (14, 27), (23, 6), (9, 29), (22, 14), (9, 0), (4, 6), (4, 18), (7, 31), (17, 18), (29, 3), (21, 9), (1, 21), (29, 25), (14, 21), (14, 4), (14, 37), (25, 1), (19, 29), (14, 23), (7, 5), (23, 16), (15, 30), (8, 7), (5, 24), (24, 24), (12, 31), (16, 31), (14, 2), (20, 4), (16, 25), (16, 10), (20, 13), (29, 26), (23, 26), (15, 29), (30, 17), (8, 27), (20, 36), (26, 24), (26, 1), (28, 26), (3, 10), (23, 13), (20, 35), (17, 10), (14, 13), (1, 2), (7, 30), (29, 23), (22, 27), (15, 16), (26, 16), (10, 6), (17, 29), (1, 36), (21, 33), (0, 2), (28, 14), (11, 31), (25, 5), (19, 34), (27, 28), (24, 34), (0, 8), (1, 8), (7, 19), (8, 23), (21, 19), (2, 17), (16, 22), (18, 32), (10, 5), (16, 28), (23, 33), (0, 30), (10, 26), (18, 6), (6, 35), (19, 8), (4, 4), (29, 35), (27, 4), (26, 18), (26, 36), (0, 31), (23, 23), (5, 15), (11, 19), (28, 8), (12, 9), (1, 4), (12, 8), (21, 28), (3, 31), (4, 1), (3, 25), (18, 10), (23, 37), (2, 21), (22, 4), (16, 1), (23, 8), (2, 23), (18, 24), (18, 35), (17, 22), (12, 11), (24, 16), (19, 14), (10, 23), (5, 2), (20, 25), (30, 13), (25, 8), (1, 28), (27, 27), (7, 33), (8, 19), (0, 23), (11, 37), (26, 27), (10, 29), (2, 35), (1, 32), (19, 19), (0, 21), (9, 1), (13, 19), (25, 10), (26, 28), (28, 24), (24, 23), (2, 5), (12, 7), (6, 8), (9, 8), (30, 24), (26, 20), (20, 30), (12, 0), (3, 16), (28, 5), (13, 13), (14, 16), (28, 32), (26, 22), (27, 22), (1, 30), (28, 15), (11, 5), (30, 11), (4, 26), (0, 26), (2, 25), (12, 29), (14, 31), (8, 26), (2, 18), (14, 12), (13, 23), (15, 9), (5, 28), (11, 12), (30, 21), (17, 25), (15, 1), (16, 29), (22, 24), (30, 5), (29, 36), (17, 11), (20, 31), (11, 20), (8, 16), (5, 26), (7, 11), (10, 32), (29, 28), (22, 15), (28, 37), (2, 8), (29, 24), (12, 16), (24, 1), (9, 23), (23, 5), (25, 4), (24, 12), (18, 33), (23, 9), (28, 28), (13, 17), (14, 28), (6, 5), (27, 7), (23, 14), (5, 35), (29, 32), (21, 27), (8, 28), (9, 14), (20, 12), (11, 9), (30, 27), (22, 29), (2, 20), (10, 25), (22, 3), (7, 16), (28, 31), (30, 10), (13, 36), (29, 15), (18, 18), (28, 36), (2, 27), (2, 24), (22, 26), (28, 27), (30, 8), (23, 11), (30, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913824", "dataset": "MATH"}
{"messages": [{"content": "In a 39x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 30), (28, 11), (38, 14), (3, 11), (28, 25), (12, 10), (38, 2), (6, 2), (18, 4), (23, 15), (19, 25), (14, 28), (26, 16), (17, 7), (33, 13), (29, 15), (16, 29), (14, 8), (16, 17), (8, 11), (33, 1), (13, 30), (9, 4), (36, 3), (37, 18), (21, 10), (33, 22), (20, 20), (25, 11), (20, 18), (35, 21), (9, 22), (18, 16), (16, 20), (29, 18), (28, 21), (12, 7), (26, 10), (30, 11), (2, 25), (3, 17), (26, 13), (26, 17), (33, 30), (25, 19), (18, 9), (18, 13), (0, 30), (17, 21), (0, 25), (18, 29), (37, 7), (13, 16), (8, 26), (27, 12), (26, 4), (30, 1), (19, 22), (23, 0), (10, 0), (20, 16), (37, 21), (12, 9), (35, 19), (1, 16), (4, 20), (29, 19), (1, 25), (35, 20), (15, 11), (29, 0), (1, 17), (23, 27), (16, 6), (10, 21), (11, 21), (25, 5), (6, 22), (18, 11), (23, 5), (35, 0), (18, 3), (16, 25), (1, 27), (13, 11), (17, 12), (30, 0), (24, 30), (13, 22), (19, 8), (3, 4), (18, 12), (36, 20), (20, 24), (25, 25), (24, 2), (20, 3), (25, 15), (14, 23), (23, 17), (19, 18), (20, 7), (11, 28), (20, 19), (2, 2), (25, 8), (33, 5), (2, 26), (36, 28), (18, 27), (32, 11), (36, 7), (24, 21), (29, 9), (18, 21), (1, 24), (34, 30), (29, 5), (24, 8), (5, 12), (8, 20), (31, 18), (32, 28), (32, 9), (12, 11), (1, 10), (21, 21), (1, 21), (33, 23), (28, 22), (26, 2), (5, 6), (2, 21), (33, 11), (23, 23), (30, 6), (10, 20), (6, 30), (11, 13), (0, 5), (30, 23), (21, 30), (15, 24), (32, 2), (2, 24), (38, 18), (0, 24), (15, 20), (24, 11), (13, 1), (29, 21), (24, 12), (34, 8), (15, 18), (13, 3), (5, 1), (0, 21), (3, 29), (14, 30), (24, 29), (12, 24), (31, 2), (28, 12), (14, 20), (5, 23), (36, 16), (32, 12), (30, 12), (31, 19), (12, 27), (18, 25), (5, 17), (23, 20), (14, 26), (35, 25), (34, 28), (6, 13), (25, 4), (28, 8), (6, 6), (10, 24), (31, 29), (37, 25), (12, 13), (30, 14), (7, 0), (5, 8), (20, 23), (31, 27), (5, 3), (31, 21), (13, 15), (38, 10), (17, 3), (38, 15), (6, 14), (37, 29), (22, 28), (36, 24), (23, 6), (18, 14), (11, 1), (23, 10), (8, 12), (21, 6), (1, 8), (9, 5), (9, 13), (30, 16), (1, 5), (32, 0), (34, 11), (9, 7), (4, 30), (19, 14), (4, 26), (1, 6), (4, 21), (29, 25), (36, 26), (20, 12), (6, 28), (26, 22), (32, 15), (24, 4), (9, 14), (7, 29), (3, 9), (37, 11), (8, 7), (27, 23), (16, 1), (11, 25), (33, 12), (12, 25), (30, 25), (14, 18), (10, 3), (16, 3), (4, 28), (24, 7), (30, 18), (24, 24), (26, 18), (20, 9), (34, 26), (13, 7), (0, 27), (15, 22), (19, 5), (19, 2), (38, 12), (21, 7), (14, 25), (32, 10), (31, 7), (10, 27), (29, 14), (35, 22), (29, 8), (21, 11), (35, 4), (27, 24), (4, 17), (23, 30), (8, 22), (9, 24), (12, 12), (6, 20), (3, 8), (26, 8), (24, 18), (21, 13), (34, 16), (15, 9), (1, 13), (36, 4), (33, 21), (7, 8), (32, 23), (20, 17), (2, 4), (26, 3), (26, 28), (21, 2), (35, 27), (12, 22), (28, 19), (9, 10), (6, 7), (3, 28), (35, 9), (7, 28), (10, 8), (8, 19), (1, 29), (12, 5), (9, 29), (11, 20), (9, 27), (34, 10), (1, 4), (17, 15), (3, 21), (30, 30), (6, 3), (2, 9), (7, 11), (0, 15), (1, 3), (23, 24), (14, 24), (8, 2), (31, 23), (36, 15), (13, 29), (34, 0), (13, 18), (19, 3), (26, 30), (4, 13), (24, 25), (25, 29), (18, 8), (0, 14), (28, 15), (19, 7), (21, 3), (12, 18), (17, 29), (28, 28), (4, 7), (25, 26), (32, 13), (9, 20), (33, 10), (28, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528640", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (1, 9), (19, 8), (5, 1), (21, 32), (29, 1), (1, 18), (21, 10), (19, 26), (26, 4), (19, 28), (31, 32), (17, 23), (28, 0), (6, 15), (32, 27), (5, 27), (28, 16), (23, 23), (15, 17), (19, 22), (19, 16), (25, 0), (20, 26), (28, 15), (30, 23), (15, 2), (24, 17), (29, 27), (10, 19), (32, 0), (15, 18), (22, 17), (20, 4), (9, 5), (33, 21), (5, 21), (6, 29), (33, 2), (17, 10), (21, 15), (33, 27), (26, 22), (6, 4), (27, 28), (13, 11), (16, 29), (14, 9), (3, 26), (25, 19), (11, 21), (17, 33), (9, 7), (30, 33), (30, 24), (10, 11), (8, 30), (3, 22), (15, 4), (21, 14), (0, 13), (30, 14), (7, 5), (27, 17), (0, 6), (7, 33), (22, 28), (25, 32), (19, 4), (5, 33), (16, 25), (13, 12), (9, 14), (19, 1), (23, 26), (29, 6), (10, 7), (15, 7), (1, 17), (7, 10), (4, 20), (23, 19), (16, 13), (10, 10), (21, 6), (18, 2), (4, 28), (25, 8), (20, 15), (22, 25), (10, 1), (0, 8), (11, 19), (21, 19), (7, 28), (3, 21), (15, 25), (14, 29), (14, 1), (6, 17), (30, 30), (31, 23), (28, 6), (4, 8), (26, 30), (24, 10), (4, 7), (33, 0), (6, 27), (29, 3), (11, 16), (13, 21), (32, 5), (32, 11), (1, 12), (20, 14), (16, 5), (19, 0), (4, 5), (26, 13), (5, 10), (19, 11), (7, 1), (0, 3), (1, 19), (2, 13), (4, 15), (12, 32), (32, 24), (32, 21), (23, 15), (13, 0), (22, 18), (21, 4), (10, 20), (9, 4), (8, 16), (13, 19), (28, 1), (4, 17), (6, 1), (13, 20), (3, 0), (23, 28), (12, 30), (24, 28), (13, 22), (0, 28), (24, 25), (7, 30), (0, 27), (15, 21), (31, 12), (18, 14), (11, 18), (33, 9), (9, 2), (19, 24), (32, 22), (14, 5), (25, 18), (9, 19), (17, 25), (18, 13), (17, 3), (19, 27), (31, 19), (12, 31), (26, 25), (18, 20), (0, 19), (3, 15), (20, 18), (17, 29), (25, 23), (33, 30), (1, 14), (12, 18), (32, 13), (29, 17), (5, 5), (18, 29), (25, 10), (1, 24), (8, 5), (13, 17), (3, 32), (0, 4), (10, 12), (6, 20), (27, 14), (26, 31), (33, 1), (8, 2), (1, 8), (22, 19), (28, 31), (17, 20), (23, 11), (6, 28), (27, 22), (5, 30), (4, 0), (4, 19), (18, 11), (12, 21), (24, 3), (4, 6), (14, 3), (21, 20), (9, 21), (12, 25), (10, 25), (10, 4), (10, 5), (10, 15), (31, 10), (31, 0), (7, 0), (29, 5), (31, 25), (33, 15), (30, 27), (7, 2), (1, 2), (8, 12), (28, 7), (5, 0), (7, 12), (6, 9), (31, 31), (3, 33), (17, 6), (20, 5), (19, 21), (29, 13), (28, 4), (27, 2), (7, 19), (3, 9), (2, 12), (30, 25), (4, 25), (25, 24), (21, 24), (27, 32), (30, 5), (1, 3), (10, 30), (2, 11), (33, 29), (21, 9), (8, 21), (17, 5), (2, 6), (25, 6), (29, 22), (11, 15), (21, 29), (18, 10), (23, 1), (0, 12), (32, 6), (13, 14), (30, 15), (18, 30), (2, 20), (24, 14), (9, 10), (3, 2), (4, 22), (20, 0), (11, 2), (2, 31), (26, 26), (7, 21), (21, 13), (7, 20), (30, 9), (29, 15), (2, 17), (32, 4), (15, 14), (25, 25), (26, 0), (19, 33), (0, 31), (29, 20), (27, 19), (9, 31), (0, 20), (0, 10), (28, 20), (26, 17), (29, 19), (18, 5), (32, 18), (30, 7), (14, 20), (27, 21), (10, 0), (5, 4), (25, 7), (15, 11), (22, 31), (18, 27), (23, 4), (5, 25), (30, 13), (20, 32), (32, 32), (3, 24), (21, 3), (31, 3), (31, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "303672", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), 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), (31, 29), (5, 35), (25, 27), (14, 11), (17, 9), (5, 25), (25, 5), (27, 18), (6, 1), (1, 21), (30, 18), (2, 23), (6, 31), (10, 6), (17, 33), (3, 35), (21, 18), (27, 35), (27, 13), (4, 31), (6, 16), (15, 30), (30, 17), (24, 19), (20, 8), (4, 5), (19, 26), (16, 7), (2, 18), (6, 14), (7, 10), (13, 23), (29, 19), (22, 7), (3, 0), (27, 3), (18, 16), (26, 28), (8, 10), (23, 32), (4, 4), (7, 27), (20, 1), (25, 21), (30, 15), (8, 25), (7, 16), (29, 27), (11, 24), (22, 19), (9, 34), (13, 34), (12, 3), (12, 17), (21, 24), (6, 9), (7, 14), (27, 33), (24, 30), (23, 14), (14, 8), (27, 20), (17, 14), (4, 3), (23, 33), (24, 33), (2, 1), (3, 4), (30, 26), (18, 22), (22, 4), (1, 17), (10, 19), (5, 4), (20, 22), (14, 7), (22, 11), (31, 12), (10, 25), (7, 11), (25, 30), (4, 19), (21, 25), (31, 19), (31, 4), (19, 7), (1, 12), (11, 0), (5, 31), (14, 17), (9, 1), (10, 13), (7, 33), (11, 18), (29, 1), (3, 23), (26, 12), (12, 33), (30, 12), (8, 23), (20, 19), (2, 32), (11, 6), (29, 5), (29, 22), (19, 0), (21, 21), (29, 6), (21, 27), (17, 12), (16, 13), (7, 30), (3, 32), (30, 1), (7, 2), (7, 8), (4, 17), (28, 2), (19, 19), (24, 29), (31, 1), (26, 6), (31, 34), (8, 12), (3, 20), (20, 14), (4, 21), (18, 18), (4, 15), (8, 5), (1, 13), (8, 26), (1, 30), (31, 16), (15, 18), (5, 15), (28, 30), (13, 8), (15, 16), (9, 33), (6, 17), (18, 32), (10, 0), (9, 25), (7, 19), (15, 29), (30, 21), (25, 15), (8, 34), (29, 15), (3, 7), (22, 35), (1, 7), (25, 18), (31, 8), (23, 2), (22, 34), (20, 31), (11, 10), (30, 23), (6, 32), (5, 22), (20, 24), (4, 33), (17, 29), (5, 28), (10, 10), (27, 16), (22, 29), (7, 0), (4, 30), (21, 16), (22, 1), (9, 21), (26, 31), (1, 16), (0, 8), (6, 6), (10, 29), (0, 14), (9, 26), (10, 27), (26, 4), (12, 34), (22, 27), (27, 15), (20, 25), (21, 26), (0, 34), (17, 22), (22, 17), (3, 18), (20, 4), (10, 21), (15, 28), (10, 5), (30, 9), (6, 26), (9, 27), (3, 27), (28, 4), (19, 24), (24, 20), (16, 4), (16, 26), (19, 31), (28, 5), (20, 5), (16, 8), (24, 13), (22, 15), (25, 29), (10, 14), (15, 25), (14, 1), (2, 14), (23, 24), (3, 17), (15, 9), (29, 29), (29, 18), (12, 8), (9, 13), (18, 33), (16, 28), (22, 10), (23, 8), (16, 15), (2, 34), (2, 6), (26, 0), (31, 9), (8, 22), (22, 20), (10, 28), (18, 26), (22, 6), (21, 29), (23, 7), (23, 25), (8, 2), (28, 19), (4, 34), (9, 9), (18, 1), (4, 13), (3, 2), (2, 12), (23, 27), (7, 29), (25, 31), (16, 6), (30, 27), (27, 2), (13, 33), (18, 13), (22, 25), (14, 26), (12, 22), (13, 18), (29, 35), (14, 20), (12, 29), (0, 9), (24, 6), (4, 12), (26, 20), (2, 29), (17, 28), (29, 34), (13, 22), (14, 35), (5, 29), (14, 31), (19, 16), (4, 9), (1, 23), (22, 22), (27, 14), (4, 0), (15, 34), (8, 35), (9, 5), (16, 32), (4, 20), (27, 17), (26, 7), (17, 35), (2, 15), (27, 25), (28, 22), (18, 30), (22, 32), (25, 14), (28, 1), (29, 31), (15, 4), (22, 26), (17, 5), (24, 9), (28, 18), (0, 5), (9, 22), (3, 22), (21, 20), (31, 18), (4, 18), (10, 9), (25, 20), (5, 6), (4, 32), (15, 20), (12, 25), (25, 33), (6, 20), (9, 35), (9, 8), (12, 18), (0, 20), (19, 35), (25, 3), (20, 29), (7, 32), (23, 4), (24, 17), (12, 26), (3, 8), (19, 22), (16, 23), (25, 9), (8, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "462672", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 3), (27, 17), (25, 21), (15, 8), (14, 33), (17, 7), (30, 20), (10, 7), (9, 19), (32, 22), (35, 31), (1, 33), (11, 33), (16, 25), (24, 8), (28, 24), (35, 29), (20, 15), (34, 30), (8, 28), (24, 20), (23, 5), (35, 17), (1, 20), (6, 13), (19, 29), (24, 24), (31, 18), (23, 33), (32, 11), (36, 2), (21, 19), (27, 18), (33, 0), (0, 9), (15, 19), (33, 30), (22, 24), (1, 17), (18, 3), (9, 7), (17, 11), (11, 25), (30, 7), (21, 17), (25, 20), (31, 20), (1, 14), (33, 12), (29, 33), (20, 24), (30, 11), (35, 12), (9, 29), (30, 3), (25, 3), (34, 5), (31, 6), (18, 15), (29, 22), (21, 3), (26, 26), (27, 13), (24, 7), (29, 21), (25, 13), (14, 16), (21, 1), (7, 30), (20, 23), (32, 3), (36, 32), (24, 26), (8, 12), (34, 24), (30, 29), (21, 9), (19, 23), (11, 31), (2, 2), (14, 27), (7, 22), (33, 21), (2, 15), (6, 7), (6, 31), (28, 0), (16, 18), (28, 12), (5, 30), (32, 10), (7, 26), (25, 18), (23, 6), (20, 8), (13, 30), (14, 25), (22, 13), (32, 9), (24, 18), (17, 6), (25, 26), (18, 11), (5, 2), (9, 27), (3, 16), (23, 19), (5, 12), (7, 18), (19, 0), (32, 24), (5, 18), (12, 13), (30, 22), (5, 11), (5, 17), (15, 14), (16, 26), (17, 12), (29, 0), (32, 15), (32, 19), (34, 19), (3, 4), (29, 8), (17, 4), (13, 14), (31, 13), (7, 11), (31, 28), (1, 21), (19, 4), (10, 10), (7, 2), (25, 17), (30, 21), (7, 29), (33, 18), (7, 33), (4, 20), (16, 14), (21, 29), (32, 33), (26, 31), (5, 28), (34, 33), (12, 16), (2, 19), (21, 28), (31, 12), (15, 6), (1, 15), (29, 11), (3, 20), (8, 19), (5, 4), (36, 11), (29, 10), (35, 26), (3, 8), (17, 24), (7, 28), (17, 3), (34, 21), (19, 31), (0, 7), (7, 1), (24, 30), (35, 21), (27, 24), (31, 2), (14, 30), (8, 13), (4, 27), (3, 25), (33, 24), (22, 31), (29, 14), (7, 9), (21, 26), (3, 31), (4, 6), (17, 21), (28, 1), (16, 17), (22, 15), (33, 15), (11, 0), (6, 9), (18, 7), (11, 9), (21, 20), (21, 25), (11, 10), (30, 33), (28, 9), (17, 9), (17, 28), (15, 26), (2, 10), (9, 17), (11, 14), (2, 20), (18, 16), (27, 5), (3, 9), (10, 30), (7, 17), (25, 15), (6, 4), (3, 28), (10, 14), (25, 23), (23, 14), (3, 10), (20, 12), (17, 16), (13, 21), (16, 24), (7, 7), (13, 23), (24, 0), (34, 13), (18, 1), (28, 5), (20, 29), (31, 3), (25, 7), (8, 29), (19, 18), (16, 33), (9, 4), (18, 5), (22, 5), (11, 27), (17, 31), (30, 10), (6, 23), (27, 29), (16, 8), (29, 13), (31, 22), (15, 33), (32, 21), (32, 4), (23, 31), (0, 23), (0, 10), (1, 18), (28, 7), (22, 26), (35, 22), (17, 10), (26, 12), (36, 16), (0, 32), (14, 31), (25, 4), (19, 24), (7, 27), (5, 23), (25, 29), (30, 17), (34, 26), (26, 25), (7, 0), (6, 14), (22, 16), (3, 14), (8, 21), (13, 5), (1, 11), (19, 16), (15, 25), (2, 22), (12, 1), (25, 24), (20, 7), (16, 5), (14, 20), (26, 0), (24, 33), (31, 19), (27, 3), (20, 28), (5, 31), (6, 20), (4, 0), (6, 15), (13, 25), (30, 4), (0, 28), (17, 8), (25, 32), (13, 28), (15, 9), (20, 6), (19, 28), (4, 22), (35, 28), (14, 15), (4, 5), (0, 14), (4, 1), (33, 11), (36, 1), (30, 32), (2, 30), (34, 3), (35, 27), (29, 9), (17, 0), (33, 31), (7, 5), (29, 20), (28, 4), (1, 3), (29, 5), (12, 23), (24, 31), (1, 5), (1, 29), (36, 26), (24, 13), (8, 31), (18, 23), (4, 25), (14, 17), (24, 19), (13, 26), (27, 8), (20, 1), (33, 20), (12, 26), (22, 23), (29, 19), (4, 7), (22, 8), (13, 9), (19, 9), (28, 16), (15, 11), (21, 32), (15, 1), (27, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998400", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), 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, 30), (16, 30), (15, 25), (17, 27), (12, 30), (24, 33), (11, 23), (7, 4), (34, 28), (15, 22), (32, 18), (35, 35), (11, 9), (0, 6), (9, 0), (20, 28), (1, 23), (34, 14), (32, 30), (10, 36), (1, 1), (31, 22), (26, 25), (8, 9), (24, 35), (30, 2), (20, 11), (14, 38), (21, 33), (1, 22), (27, 8), (7, 31), (28, 11), (30, 26), (3, 29), (24, 19), (3, 23), (27, 31), (24, 20), (15, 6), (6, 28), (13, 6), (2, 7), (15, 8), (12, 17), (13, 27), (11, 6), (6, 8), (13, 14), (12, 33), (14, 25), (4, 7), (25, 21), (16, 26), (31, 27), (28, 1), (1, 7), (0, 22), (3, 38), (21, 34), (19, 4), (21, 7), (7, 10), (16, 23), (4, 23), (28, 3), (32, 29), (4, 5), (21, 28), (27, 9), (15, 34), (28, 12), (19, 34), (4, 28), (2, 15), (14, 32), (25, 14), (0, 10), (32, 11), (34, 8), (24, 14), (17, 16), (13, 3), (24, 9), (13, 34), (23, 11), (17, 25), (27, 16), (12, 2), (16, 10), (4, 29), (4, 33), (20, 8), (6, 17), (10, 10), (6, 11), (28, 37), (30, 30), (8, 22), (17, 21), (9, 31), (35, 27), (12, 36), (19, 10), (11, 19), (19, 0), (13, 16), (21, 25), (5, 6), (17, 0), (23, 3), (8, 27), (23, 1), (10, 5), (12, 19), (16, 4), (7, 36), (12, 13), (8, 20), (26, 21), (32, 15), (27, 37), (30, 22), (31, 32), (5, 38), (3, 20), (33, 29), (14, 8), (10, 17), (26, 22), (8, 7), (5, 3), (13, 0), (32, 14), (23, 30), (24, 11), (20, 34), (21, 5), (12, 21), (29, 7), (35, 21), (24, 15), (23, 16), (7, 28), (8, 6), (26, 12), (22, 27), (35, 34), (17, 17), (27, 32), (20, 30), (32, 34), (6, 34), (27, 5), (13, 23), (18, 8), (28, 19), (11, 36), (34, 23), (22, 33), (20, 16), (30, 19), (29, 26), (31, 28), (11, 11), (9, 28), (25, 38), (12, 3), (6, 16), (0, 15), (28, 6), (4, 8), (29, 25), (22, 36), (29, 5), (7, 17), (16, 34), (5, 2), (34, 30), (1, 24), (30, 5), (22, 15), (27, 29), (0, 17), (10, 9), (15, 7), (19, 5), (3, 18), (21, 3), (15, 16), (2, 34), (10, 35), (26, 14), (21, 26), (5, 8), (23, 29), (14, 17), (15, 36), (23, 5), (11, 5), (17, 28), (4, 22), (8, 4), (20, 26), (32, 6), (30, 1), (0, 12), (26, 16), (22, 17), (3, 35), (5, 26), (23, 27), (35, 1), (8, 5), (9, 2), (6, 24), (32, 19), (34, 31), (33, 19), (20, 36), (33, 13), (12, 5), (5, 23), (20, 7), (33, 34), (21, 20), (18, 11), (5, 35), (16, 12), (25, 36), (29, 3), (2, 13), (10, 38), (27, 34), (9, 6), (28, 26), (7, 14), (10, 4), (12, 29), (4, 18), (35, 23), (13, 8), (10, 8), (28, 15), (23, 13), (17, 6), (1, 27), (29, 37), (15, 19), (6, 18), (18, 13), (19, 28), (4, 21), (28, 18), (26, 33), (2, 17), (33, 22), (34, 27), (4, 16), (10, 20), (33, 20), (8, 12), (2, 25), (25, 18), (32, 26), (26, 18), (10, 15), (5, 10), (33, 36), (29, 29), (30, 9), (21, 37), (7, 30), (12, 18), (0, 13), (26, 3), (30, 31), (10, 18), (25, 26), (23, 32), (34, 15), (14, 20), (6, 7), (17, 15), (30, 16), (16, 37), (13, 29), (15, 17), (18, 5), (33, 38), (1, 18), (16, 21), (14, 1), (2, 22), (33, 11), (1, 31), (21, 18), (29, 34), (25, 8), (12, 38), (25, 30), (12, 31), (3, 11), (5, 37), (31, 6), (26, 15), (18, 27), (32, 21), (17, 24), (30, 17), (12, 15), (10, 30), (24, 37), (11, 15), (8, 11), (17, 14), (5, 1), (22, 2), (25, 27), (24, 31), (34, 20), (4, 12), (14, 6), (0, 36), (30, 23), (23, 25), (31, 38), (25, 6), (28, 21), (24, 12), (32, 4), (12, 27), (33, 0), (27, 23), (18, 6), (17, 26), (16, 32), (32, 1), (13, 9), (20, 22), (31, 2), (20, 10), (18, 1), (2, 12), (14, 34), (27, 1), (8, 34), (7, 13), (3, 25), (1, 14), (33, 18), (23, 10), (32, 31), (16, 27), (24, 16), (3, 27), (17, 20), (20, 9), (23, 21), (19, 17), (18, 18), (26, 36), (30, 18), (22, 37), (15, 21), (16, 13), (23, 23), (16, 9), (17, 7), (20, 38), (34, 12), (34, 13), (32, 27), (4, 34), (28, 29), (19, 13), (28, 13), (23, 8), (22, 38), (18, 22), (29, 32), (15, 31), (24, 36), (4, 19), (20, 0), (0, 27), (8, 13), (6, 0), (11, 38), (7, 21), (3, 4), (16, 11), (22, 11), (14, 31), (10, 33), (11, 30), (1, 2), (5, 34), (21, 27), (31, 7), (3, 15), (29, 30), (3, 37), (26, 9), (34, 19), (14, 11), (17, 22), (0, 33), (18, 30), (6, 23), (8, 2), (28, 34), (23, 6), (26, 27), (14, 13), (25, 29), (13, 17), (34, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734976", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (11, 31), (20, 22), (13, 25), (29, 16), (28, 17), (27, 7), (18, 2), (15, 22), (23, 33), (11, 28), (13, 18), (27, 9), (25, 24), (20, 9), (29, 7), (14, 9), (3, 9), (30, 32), (7, 21), (27, 2), (12, 15), (1, 27), (23, 8), (4, 29), (19, 8), (28, 10), (11, 29), (28, 4), (26, 2), (25, 5), (19, 11), (13, 15), (4, 9), (27, 34), (4, 34), (29, 9), (21, 23), (8, 6), (24, 4), (11, 12), (10, 15), (12, 29), (26, 31), (19, 36), (7, 1), (6, 23), (10, 25), (17, 28), (23, 10), (7, 7), (4, 19), (12, 36), (0, 34), (24, 11), (7, 35), (28, 31), (21, 3), (25, 19), (31, 2), (12, 5), (9, 30), (27, 26), (19, 14), (19, 9), (15, 2), (29, 8), (25, 13), (27, 30), (31, 1), (26, 8), (7, 33), (13, 33), (1, 13), (16, 23), (23, 7), (5, 17), (1, 22), (23, 27), (19, 1), (9, 20), (4, 31), (5, 5), (27, 25), (7, 9), (20, 4), (7, 12), (21, 24), (5, 31), (20, 26), (30, 19), (14, 27), (13, 11), (25, 2), (26, 7), (31, 22), (31, 13), (30, 7), (5, 26), (0, 20), (15, 30), (18, 20), (17, 21), (16, 29), (1, 11), (17, 9), (1, 29), (1, 25), (15, 10), (2, 12), (22, 21), (7, 27), (21, 22), (15, 34), (25, 15), (13, 29), (14, 21), (4, 18), (10, 5), (31, 33), (26, 6), (8, 32), (28, 29), (14, 24), (23, 21), (7, 4), (19, 3), (9, 8), (28, 11), (31, 20), (23, 25), (2, 3), (6, 22), (17, 27), (8, 21), (26, 23), (11, 2), (7, 20), (3, 27), (16, 33), (20, 6), (29, 11), (18, 6), (17, 2), (16, 24), (7, 16), (9, 27), (26, 0), (18, 31), (22, 11), (29, 29), (3, 36), (1, 18), (1, 20), (0, 7), (29, 18), (18, 24), (29, 30), (28, 25), (5, 23), (29, 23), (26, 3), (19, 25), (24, 15), (0, 1), (29, 35), (0, 31), (17, 30), (17, 16), (2, 25), (13, 10), (19, 24), (0, 13), (16, 17), (18, 9), (23, 20), (19, 35), (14, 33), (2, 36), (24, 7), (4, 6), (1, 12), (12, 11), (4, 28), (7, 0), (11, 30), (3, 22), (6, 11), (2, 23), (15, 6), (10, 13), (3, 11), (7, 6), (19, 4), (31, 8), (9, 19), (27, 31), (20, 11), (16, 15), (25, 18), (2, 2), (12, 22), (14, 36), (13, 21), (17, 0), (16, 22), (6, 34), (8, 23), (21, 0), (11, 35), (6, 32), (19, 20), (11, 13), (5, 9), (0, 4), (6, 33), (2, 34), (3, 26), (15, 24), (1, 7), (6, 5), (9, 24), (22, 14), (5, 22), (0, 30), (25, 36), (24, 22), (15, 32), (13, 12), (14, 32), (1, 1), (23, 11), (21, 1), (29, 34), (21, 9), (11, 36), (30, 22), (8, 10), (22, 25), (6, 25), (15, 31), (20, 29), (30, 35), (8, 12), (16, 2), (13, 7), (17, 29), (8, 36), (23, 4), (12, 21), (10, 1), (24, 14), (16, 30), (19, 6), (10, 27), (27, 35), (1, 35), (5, 1), (10, 21), (13, 9), (30, 20), (24, 23), (13, 27), (22, 0), (16, 31), (28, 22), (18, 25), (18, 19), (14, 4), (27, 14), (22, 5), (14, 2), (9, 32), (31, 4), (15, 28), (8, 35), (25, 6), (23, 19), (21, 28), (9, 1), (12, 14), (1, 32), (20, 18), (31, 29), (17, 36), (15, 29), (2, 5), (3, 10), (7, 23), (3, 34), (7, 28), (30, 31), (7, 34), (2, 22), (12, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "997360", "dataset": "MATH"}
{"messages": [{"content": "In a 31x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 24), (27, 10), (6, 13), (21, 19), (3, 7), (18, 11), (27, 29), (24, 6), (5, 22), (10, 15), (27, 19), (1, 16), (28, 8), (18, 4), (9, 28), (4, 11), (23, 12), (25, 27), (14, 14), (17, 18), (14, 9), (3, 6), (9, 19), (4, 31), (8, 19), (26, 28), (8, 22), (8, 15), (0, 12), (10, 29), (29, 21), (30, 21), (11, 24), (0, 11), (9, 30), (20, 11), (24, 18), (7, 7), (30, 31), (25, 2), (12, 16), (23, 26), (10, 11), (14, 32), (12, 26), (12, 5), (25, 12), (9, 24), (16, 23), (6, 32), (5, 29), (12, 0), (4, 21), (12, 6), (17, 6), (11, 1), (28, 5), (19, 9), (16, 24), (22, 22), (5, 30), (2, 26), (3, 27), (26, 4), (17, 12), (20, 27), (6, 10), (13, 31), (23, 3), (11, 18), (19, 24), (17, 16), (15, 28), (15, 24), (26, 10), (13, 5), (23, 32), (18, 2), (20, 6), (17, 28), (13, 17), (28, 22), (19, 11), (18, 10), (2, 10), (18, 20), (12, 31), (25, 7), (20, 2), (8, 2), (11, 6), (28, 4), (16, 25), (29, 18), (29, 22), (3, 3), (30, 18), (11, 3), (0, 28), (9, 8), (28, 20), (11, 4), (2, 16), (12, 3), (13, 16), (1, 17), (30, 5), (15, 5), (19, 10), (22, 2), (2, 30), (25, 21), (1, 9), (1, 28), (21, 2), (8, 5), (16, 12), (25, 20), (0, 2), (16, 31), (10, 8), (26, 14), (21, 0), (30, 28), (15, 13), (22, 21), (1, 3), (11, 23), (8, 21), (27, 2), (15, 4), (30, 25), (20, 9), (5, 17), (30, 1), (25, 3), (15, 32), (11, 26), (30, 2), (9, 1), (12, 20), (25, 28), (12, 18), (15, 7), (8, 18), (21, 4), (6, 24), (29, 5), (25, 0), (3, 15), (16, 2), (1, 4), (14, 19), (30, 26), (14, 27), (21, 10), (30, 3), (17, 23), (23, 27), (17, 0), (2, 20), (27, 8), (25, 5), (11, 9), (24, 7), (12, 7), (19, 1), (25, 1), (23, 15), (28, 30), (20, 22), (30, 12), (2, 0), (24, 14), (10, 22), (2, 5), (2, 19), (27, 20), (19, 7), (7, 13), (3, 9), (19, 30), (29, 2), (8, 25), (11, 27), (10, 7), (16, 4), (1, 27), (24, 2), (1, 25), (14, 1), (3, 24), (21, 32), (24, 21), (27, 13), (30, 13), (14, 2), (16, 1), (4, 19), (11, 8), (14, 10), (27, 7), (27, 24), (10, 5), (17, 26), (3, 4), (8, 13), (7, 11), (4, 17), (11, 30), (26, 32), (20, 13), (6, 15), (15, 6), (13, 23), (9, 17), (5, 8), (7, 31), (26, 9), (12, 2), (13, 3), (29, 26), (29, 19), (9, 14), (19, 8), (23, 25), (1, 23), (0, 30), (8, 9), (29, 12), (23, 22), (5, 9), (22, 6), (14, 5), (11, 0), (28, 23), (15, 27), (10, 17), (1, 31), (3, 2), (26, 15), (29, 9), (26, 30), (19, 19), (20, 19), (27, 18), (10, 10), (28, 13), (13, 21), (11, 29), (11, 13), (14, 20), (20, 24), (24, 26), (13, 9), (22, 9), (4, 6), (3, 32), (26, 6), (13, 6), (29, 24), (6, 5), (29, 3), (24, 4), (26, 16), (24, 31), (11, 17), (29, 15), (3, 20), (4, 27), (23, 28), (3, 18), (17, 24), (11, 28), (12, 25), (25, 14), (8, 6), (15, 0), (6, 17), (13, 10), (18, 1), (7, 17), (9, 16), (25, 16), (9, 18), (27, 5), (30, 23), (1, 21), (28, 0), (17, 31), (23, 0), (18, 23), (4, 24), (25, 13), (16, 21), (14, 11), (1, 10), (2, 22), (13, 0), (19, 22), (15, 21), (15, 22), (8, 4), (20, 28), (30, 27), (24, 0), (22, 1), (12, 21), (25, 10), (9, 29), (26, 20), (17, 13), (25, 30), (17, 7), (0, 13), (0, 14), (27, 6), (19, 27), (26, 11), (7, 4), (17, 2), (5, 20), (30, 15), (0, 23), (6, 12), (7, 8), (29, 25), (25, 22), (15, 30), (11, 16), (0, 22), (21, 11), (21, 8), (29, 17), (10, 30), (12, 4), (17, 14), (20, 7), (5, 13), (2, 12), (2, 29), (7, 29), (5, 12), (5, 4), (4, 32), (23, 19), (9, 2), (5, 15), (24, 3), (7, 19), (2, 9), (0, 6), (2, 14), (19, 18), (8, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "610560", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 14), (33, 4), (21, 28), (13, 32), (34, 26), (14, 15), (25, 20), (32, 19), (8, 29), (7, 20), (7, 23), (7, 1), (7, 25), (22, 2), (6, 23), (29, 27), (36, 12), (28, 22), (14, 30), (13, 19), (10, 25), (17, 1), (8, 21), (28, 14), (20, 25), (8, 8), (29, 4), (35, 2), (34, 29), (23, 21), (20, 20), (9, 6), (2, 15), (29, 9), (15, 20), (19, 30), (8, 11), (21, 25), (10, 22), (1, 32), (16, 23), (10, 30), (18, 1), (8, 3), (35, 21), (17, 31), (36, 2), (10, 32), (24, 2), (7, 4), (1, 22), (8, 10), (28, 0), (2, 25), (32, 15), (14, 18), (2, 24), (8, 30), (10, 20), (36, 5), (33, 3), (28, 19), (8, 27), (24, 29), (5, 4), (6, 3), (24, 7), (13, 28), (36, 17), (30, 24), (21, 32), (1, 13), (30, 13), (4, 26), (32, 27), (31, 9), (16, 5), (0, 1), (9, 27), (24, 16), (24, 20), (13, 22), (3, 16), (2, 9), (24, 32), (5, 31), (25, 29), (30, 28), (15, 14), (9, 2), (14, 17), (16, 32), (33, 19), (20, 29), (33, 9), (2, 10), (15, 6), (12, 14), (25, 13), (12, 17), (24, 9), (3, 11), (10, 18), (3, 31), (4, 32), (29, 23), (23, 28), (33, 14), (5, 0), (24, 30), (36, 19), (14, 19), (16, 7), (11, 16), (25, 3), (10, 13), (33, 26), (15, 4), (19, 13), (31, 6), (35, 15), (25, 1), (3, 13), (18, 29), (28, 26), (19, 7), (28, 15), (26, 29), (4, 18), (9, 15), (9, 18), (34, 25), (5, 6), (14, 24), (36, 22), (31, 26), (12, 27), (31, 17), (31, 0), (14, 29), (4, 31), (21, 2), (26, 32), (11, 23), (15, 7), (22, 31), (16, 29), (35, 5), (7, 17), (10, 5), (21, 1), (9, 8), (27, 5), (34, 16), (6, 19), (16, 18), (36, 24), (23, 32), (18, 10), (4, 30), (23, 12), (2, 2), (12, 13), (34, 11), (20, 3), (13, 17), (6, 5), (21, 4), (35, 6), (32, 12), (27, 12), (8, 9), (36, 0), (22, 12), (11, 31), (0, 17), (21, 19), (11, 8), (14, 4), (22, 19), (12, 1), (8, 1), (15, 27), (6, 7), (36, 3), (21, 6), (17, 24), (25, 16), (5, 28), (16, 15), (20, 10), (21, 21), (4, 4), (18, 19), (32, 1), (20, 12), (15, 28), (3, 2), (35, 8), (34, 2), (27, 1), (20, 31), (2, 26), (10, 7), (34, 1), (26, 16), (15, 25), (16, 21), (4, 24), (25, 0), (33, 1), (3, 8), (6, 29), (6, 32), (29, 21), (32, 17), (13, 16), (31, 13), (32, 21), (7, 10), (11, 4), (25, 21), (0, 19), (11, 3), (5, 10), (32, 28), (22, 8), (18, 26), (14, 9), (5, 15), (35, 0), (34, 22), (35, 29), (27, 23), (4, 27), (6, 13), (31, 31), (18, 21), (35, 27), (21, 15), (28, 30), (18, 6), (15, 1), (19, 21), (29, 7), (25, 28), (19, 27), (31, 15), (2, 0), (7, 11), (10, 28), (6, 18), (1, 14), (18, 2), (0, 22), (26, 6), (32, 4), (8, 14), (4, 16), (20, 2), (22, 23), (26, 21), (28, 29), (1, 15), (25, 22), (27, 27), (14, 16), (27, 16), (28, 4), (8, 6), (0, 29), (16, 10), (26, 10), (6, 15), (7, 19), (17, 28), (31, 19), (35, 19), (27, 10), (2, 3), (4, 2), (20, 14), (0, 9), (10, 29), (32, 16), (30, 32), (7, 24), (18, 0), (31, 5), (28, 2), (17, 7), (25, 18), (33, 22), (30, 0), (21, 23), (8, 13), (20, 32), (16, 4), (13, 5), (1, 25), (12, 4), (17, 22), (25, 5), (11, 5), (9, 11), (14, 7), (35, 18), (20, 28), (29, 26), (9, 13), (1, 8), (13, 20), (34, 17), (26, 14), (12, 22), (34, 31), (9, 12), (9, 10), (13, 6), (22, 0), (14, 23), (17, 12), (5, 32), (10, 26), (36, 11), (30, 11), (9, 25), (35, 1), (13, 1), (19, 14), (9, 5), (34, 23), (27, 19), (6, 24), (31, 24), (23, 4), (23, 14), (30, 9), (13, 25), (26, 18), (27, 4), (21, 7), (6, 16), (25, 10), (10, 15), (33, 5), (22, 16), (33, 23), (22, 27), (17, 2), (3, 21), (36, 10), (35, 26), (23, 17), (19, 15), (15, 3), (28, 23), (0, 25), (24, 24), (27, 21), (3, 4), (19, 4), (21, 22), (12, 25), (7, 8), (14, 0), (18, 11), (11, 10), (24, 22), (22, 5), (35, 22), (35, 24), (7, 28), (2, 32), (15, 9), (12, 2), (12, 32), (32, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940032", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 29), (34, 7), (32, 17), (32, 0), (5, 17), (26, 23), (19, 37), (13, 35), (32, 30), (19, 16), (35, 17), (2, 20), (31, 25), (35, 28), (28, 32), (11, 12), (7, 10), (5, 19), (32, 2), (15, 19), (33, 20), (13, 28), (21, 21), (1, 21), (27, 37), (2, 4), (31, 5), (19, 10), (26, 20), (29, 28), (22, 1), (17, 19), (5, 30), (30, 37), (14, 20), (17, 4), (10, 28), (21, 29), (10, 30), (34, 3), (3, 14), (28, 24), (3, 4), (18, 36), (23, 22), (13, 15), (13, 10), (27, 1), (15, 16), (32, 22), (2, 23), (6, 33), (2, 28), (29, 14), (12, 22), (26, 16), (12, 10), (26, 34), (27, 21), (7, 4), (17, 8), (3, 35), (15, 11), (29, 17), (1, 30), (20, 37), (3, 17), (1, 31), (31, 34), (27, 29), (21, 24), (17, 7), (29, 33), (2, 26), (34, 24), (23, 33), (25, 21), (23, 24), (8, 23), (16, 34), (1, 29), (2, 18), (2, 17), (32, 4), (19, 7), (15, 31), (31, 0), (30, 15), (1, 23), (13, 31), (20, 4), (30, 23), (29, 35), (15, 5), (26, 19), (3, 3), (15, 17), (34, 30), (27, 25), (12, 24), (14, 4), (22, 26), (29, 37), (14, 37), (19, 25), (30, 19), (15, 9), (29, 7), (12, 30), (0, 4), (33, 3), (21, 9), (0, 18), (11, 18), (33, 26), (5, 23), (10, 25), (11, 14), (30, 26), (31, 28), (1, 17), (9, 15), (15, 27), (20, 30), (22, 0), (7, 29), (28, 34), (15, 22), (10, 15), (22, 7), (18, 29), (18, 34), (12, 11), (31, 22), (9, 37), (0, 29), (16, 7), (18, 13), (11, 26), (2, 29), (26, 24), (1, 19), (10, 37), (1, 8), (35, 3), (9, 23), (16, 2), (4, 37), (2, 27), (17, 34), (16, 26), (7, 18), (21, 18), (11, 0), (19, 2), (18, 25), (31, 1), (7, 31), (23, 12), (17, 25), (35, 12), (28, 36), (14, 1), (27, 11), (32, 15), (21, 13), (30, 22), (6, 37), (1, 12), (26, 29), (6, 29), (23, 2), (35, 6), (8, 8), (30, 25), (32, 27), (11, 17), (1, 34), (35, 30), (10, 26), (19, 28), (3, 22), (29, 2), (1, 28), (0, 26), (4, 17), (28, 21), (34, 27), (32, 11), (12, 26), (8, 37), (24, 13), (3, 32), (30, 31), (33, 37), (4, 31), (27, 32), (6, 2), (15, 14), (15, 32), (7, 13), (19, 13), (22, 22), (17, 9), (34, 10), (22, 17), (19, 27), (9, 1), (33, 17), (16, 12), (8, 7), (18, 28), (20, 8), (27, 31), (32, 7), (13, 18), (34, 26), (27, 19), (13, 3), (25, 11), (20, 3), (7, 12), (20, 5), (27, 36), (8, 33), (10, 27), (24, 12), (34, 1), (13, 37), (2, 11), (16, 21), (10, 16), (13, 27), (7, 17), (9, 34), (34, 0), (31, 35), (35, 4), (6, 32), (23, 9), (35, 20), (16, 29), (16, 28), (25, 6), (20, 1), (4, 12), (35, 2), (14, 15), (17, 6), (19, 15), (18, 3), (14, 31), (6, 9), (29, 31), (26, 14), (2, 7), (35, 24), (30, 21), (22, 19), (5, 10), (17, 28), (29, 5), (35, 7), (10, 21), (33, 14), (8, 3), (29, 12), (18, 11), (22, 5), (25, 33), (31, 20), (14, 18), (3, 37), (1, 2), (33, 36), (20, 11), (4, 22), (4, 25), (5, 0), (22, 3), (24, 27), (13, 11), (18, 14), (18, 18), (14, 26), (28, 27), (16, 24), (0, 22), (1, 5), (26, 0), (28, 12), (20, 27), (7, 5), (25, 36), (34, 13), (2, 33), (0, 31), (19, 8), (13, 23), (11, 7), (22, 33), (29, 25), (18, 6), (1, 33), (27, 23), (3, 6), (34, 32), (19, 18), (26, 33), (9, 0), (3, 12), (8, 32), (32, 10), (15, 8), (27, 12), (18, 32), (29, 21), (26, 9), (0, 10), (27, 5), (26, 22), (33, 8), (5, 7), (6, 5), (19, 29), (32, 33), (18, 10), (19, 14), (4, 35), (22, 20), (9, 12), (23, 21), (18, 5), (27, 0), (13, 13), (4, 21), (4, 2), (24, 22), (0, 30), (29, 18), (16, 6), (19, 34), (17, 20), (27, 24), (8, 30), (26, 10), (34, 18), (25, 0), (35, 25), (35, 29), (30, 24), (7, 16), (15, 13), (7, 11), (16, 15), (23, 32), (19, 20), (8, 35), (12, 15), (24, 16), (1, 32), (30, 4), (2, 21), (34, 31), (34, 33), (28, 16), (24, 35), (33, 2), (24, 15), (7, 0), (6, 31), (10, 19), (23, 28), (19, 3), (28, 4), (4, 6), (26, 21), (12, 2), (2, 13), (25, 29), (11, 4), (22, 23), (7, 19), (27, 17), (31, 8), (33, 13), (21, 15), (25, 34), (23, 17), (5, 18), (30, 6), (20, 16), (27, 13), (8, 6), (33, 23), (9, 32), (23, 10), (10, 1), (32, 19), (16, 3), (16, 18), (18, 24), (16, 16), (4, 4), (9, 35), (34, 9), (34, 11), (22, 9), (9, 16), (14, 12), (32, 24), (24, 8), (9, 5), (0, 32), (6, 11), (4, 34), (29, 9), (14, 9), (30, 7), (24, 2), (27, 9), (0, 8), (2, 22), (16, 8), (32, 13), (30, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 30), (9, 31), (27, 15), (14, 2), (25, 3), (15, 21), (7, 14), (5, 25), (11, 16), (15, 31), (4, 11), (8, 15), (2, 12), (0, 11), (2, 5), (10, 0), (32, 8), (21, 6), (23, 4), (24, 5), (15, 33), (14, 5), (29, 28), (29, 1), (7, 17), (10, 27), (26, 26), (26, 29), (16, 29), (9, 27), (20, 26), (12, 9), (16, 9), (28, 3), (12, 22), (15, 7), (10, 20), (27, 6), (14, 9), (8, 10), (12, 16), (31, 3), (30, 15), (2, 0), (17, 33), (19, 10), (16, 32), (27, 3), (1, 31), (25, 28), (5, 12), (26, 25), (13, 9), (21, 21), (11, 27), (17, 11), (4, 8), (15, 25), (6, 31), (20, 4), (0, 32), (32, 14), (13, 13), (28, 24), (9, 26), (16, 19), (20, 6), (14, 20), (23, 6), (32, 0), (12, 26), (20, 28), (27, 16), (22, 5), (10, 13), (21, 1), (8, 2), (31, 20), (30, 22), (12, 3), (17, 6), (3, 34), (13, 5), (2, 16), (26, 18), (6, 34), (14, 7), (3, 7), (18, 11), (6, 9), (33, 7), (1, 15), (0, 22), (6, 14), (0, 25), (27, 11), (13, 22), (0, 12), (13, 14), (14, 31), (24, 25), (0, 28), (2, 2), (6, 24), (6, 27), (29, 33), (8, 9), (8, 16), (11, 1), (21, 8), (19, 11), (17, 31), (2, 32), (1, 10), (6, 12), (22, 13), (9, 12), (23, 22), (17, 22), (26, 8), (8, 17), (12, 6), (29, 11), (22, 21), (16, 33), (33, 14), (2, 17), (16, 5), (12, 13), (28, 32), (5, 3), (24, 6), (2, 13), (16, 26), (2, 26), (12, 14), (31, 34), (25, 0), (5, 1), (18, 20), (12, 24), (23, 3), (33, 15), (13, 20), (28, 27), (3, 31), (13, 10), (7, 25), (19, 6), (25, 33), (10, 24), (19, 32), (1, 3), (31, 31), (3, 11), (26, 9), (20, 12), (11, 11), (10, 9), (1, 22), (14, 1), (4, 21), (14, 33), (33, 19), (3, 8), (21, 3), (23, 13), (9, 0), (21, 15), (21, 33), (33, 29), (17, 27), (17, 19), (18, 34), (18, 8), (8, 33), (28, 11), (19, 26), (16, 22), (6, 21), (17, 20), (9, 18), (13, 30), (9, 13), (7, 20), (22, 15), (26, 0), (2, 10), (24, 31), (28, 30), (4, 34), (30, 5), (3, 16), (9, 16), (26, 6), (13, 34), (0, 26), (0, 29), (24, 30), (16, 27), (16, 14), (10, 25), (24, 10), (23, 19), (11, 14), (7, 32), (19, 17), (28, 10), (12, 32), (15, 19), (21, 14), (7, 10), (17, 2), (30, 13), (9, 21), (5, 22), (7, 0), (32, 19), (17, 28), (4, 32), (27, 23), (14, 19), (18, 12), (31, 15), (0, 17), (17, 29), (14, 21), (22, 17), (20, 29), (9, 2), (28, 13), (18, 9), (6, 33), (17, 1), (11, 9), (4, 4), (3, 1), (1, 32), (32, 13), (1, 14), (10, 10), (6, 4), (20, 2), (13, 8), (15, 14), (14, 32), (3, 30), (25, 24), (28, 14), (15, 1), (13, 18), (4, 27), (12, 0), (20, 17), (15, 32), (10, 5), (4, 29), (20, 23), (21, 10), (32, 27), (33, 30), (11, 25), (20, 31), (18, 32), (28, 9), (31, 11), (28, 12), (9, 8), (16, 2), (1, 5), (12, 2), (30, 3), (14, 0), (20, 32), (16, 23), (11, 2), (4, 17), (20, 18), (24, 1), (33, 3), (26, 30), (27, 12), (7, 31), (14, 28), (33, 23), (20, 1), (25, 18), (6, 19), (32, 32), (24, 15), (13, 16), (7, 28), (0, 13), (33, 21), (7, 23), (17, 12), (6, 10), (1, 0), (13, 24), (32, 26), (2, 19), (1, 19), (13, 6), (15, 18), (32, 20), (10, 32), (33, 12), (10, 22), (21, 7), (23, 14), (3, 22), (24, 21), (28, 34), (3, 0), (8, 30), (31, 2), (12, 25), (28, 17), (25, 19), (19, 7), (32, 15), (1, 9), (3, 6), (4, 0), (24, 20), (31, 32), (9, 34), (16, 31), (5, 6), (1, 1), (30, 4), (27, 4), (31, 25), (14, 27), (18, 25), (21, 9), (33, 26), (19, 16), (4, 10), (29, 19), (21, 25), (17, 4), (21, 31), (12, 31), (4, 3), (25, 34), (28, 25), (9, 22), (27, 34), (4, 13), (29, 4), (0, 20), (1, 7), (24, 3), (8, 11), (12, 21), (25, 6), (27, 28), (6, 29), (32, 24), (28, 2), (27, 27), (31, 10), (4, 22), (1, 17), (22, 16), (23, 5), (2, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347456", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 29), (27, 14), (2, 24), (26, 8), (25, 0), (33, 19), (11, 18), (7, 27), (16, 5), (15, 12), (35, 25), (17, 23), (4, 3), (17, 12), (21, 26), (7, 6), (7, 22), (23, 23), (3, 12), (12, 4), (10, 2), (28, 3), (2, 21), (17, 7), (4, 21), (25, 6), (7, 16), (5, 21), (31, 14), (34, 3), (2, 22), (5, 1), (5, 31), (8, 27), (23, 17), (21, 13), (28, 20), (2, 16), (14, 29), (2, 15), (14, 11), (20, 15), (9, 5), (20, 0), (23, 12), (1, 13), (10, 18), (11, 0), (27, 8), (12, 23), (2, 7), (23, 13), (22, 28), (30, 23), (14, 9), (25, 24), (33, 25), (8, 2), (29, 14), (13, 17), (12, 7), (2, 27), (19, 30), (0, 28), (12, 15), (28, 18), (2, 25), (12, 22), (19, 18), (1, 22), (26, 18), (19, 31), (14, 24), (10, 17), (21, 21), (0, 25), (33, 31), (13, 31), (10, 7), (10, 19), (35, 8), (30, 19), (31, 16), (22, 16), (21, 7), (11, 26), (19, 1), (31, 21), (0, 9), (31, 5), (7, 9), (29, 17), (35, 13), (0, 23), (22, 3), (15, 21), (9, 30), (1, 12), (6, 12), (26, 27), (14, 8), (26, 25), (22, 21), (1, 26), (28, 2), (33, 7), (24, 12), (18, 5), (11, 2), (21, 29), (30, 10), (7, 11), (22, 2), (31, 19), (14, 4), (29, 9), (24, 15), (20, 5), (28, 17), (18, 16), (27, 22), (8, 9), (4, 22), (2, 12), (20, 8), (32, 14), (4, 31), (32, 3), (24, 21), (0, 6), (12, 9), (26, 3), (0, 31), (23, 3), (28, 21), (9, 25), (6, 21), (7, 8), (25, 28), (5, 26), (25, 31), (9, 28), (3, 24), (4, 1), (34, 31), (29, 22), (18, 3), (33, 9), (26, 0), (22, 27), (27, 31), (9, 1), (16, 19), (19, 19), (20, 16), (34, 4), (17, 27), (14, 31), (2, 5), (17, 5), (4, 16), (26, 12), (2, 13), (9, 29), (5, 8), (29, 10), (2, 29), (19, 0), (23, 15), (32, 17), (24, 1), (2, 2), (31, 31), (29, 24), (23, 26), (31, 0), (25, 11), (14, 21), (4, 27), (16, 18), (34, 27), (19, 7), (11, 5), (13, 13), (6, 8), (10, 14), (34, 10), (16, 25), (16, 20), (34, 15), (1, 9), (1, 18), (13, 3), (8, 25), (26, 26), (17, 16), (33, 17), (1, 0), (18, 8), (17, 19), (4, 19), (28, 12), (22, 20), (16, 22), (28, 8), (15, 4), (23, 10), (17, 21), (4, 11), (33, 8), (2, 9), (0, 7), (21, 6), (32, 28), (22, 19), (3, 26), (5, 24), (8, 6), (25, 16), (15, 0), (25, 18), (22, 11), (18, 23), (25, 27), (15, 31), (25, 10), (4, 5), (30, 29), (7, 13), (15, 18), (15, 26), (19, 22), (22, 15), (28, 7), (10, 27), (24, 11), (4, 26), (20, 18), (18, 20), (7, 31), (33, 12), (35, 9), (34, 29), (6, 6), (7, 3), (15, 15), (13, 6), (30, 28), (35, 0), (9, 31), (26, 7), (33, 5), (11, 4), (25, 17), (27, 13), (1, 19), (30, 15), (32, 9), (24, 10), (32, 0), (27, 2), (0, 14), (6, 15), (23, 30), (3, 29), (25, 3), (34, 30), (11, 19), (26, 24), (11, 21), (34, 6), (16, 4), (34, 11), (27, 28), (1, 1), (19, 26), (19, 6), (29, 11), (9, 20), (4, 17), (3, 5), (21, 11), (26, 23), (16, 12), (20, 6), (33, 28), (3, 16), (28, 14), (16, 17), (33, 30), (18, 27), (30, 25), (4, 4), (4, 6), (27, 7), (18, 28), (32, 13), (12, 28), (9, 19), (3, 13), (31, 6), (30, 8), (10, 21), (9, 22), (5, 29), (25, 15), (30, 27), (23, 8), (29, 18), (29, 16), (35, 11), (0, 26), (20, 4), (33, 20), (18, 22), (8, 14), (3, 6), (32, 21), (28, 1), (15, 11), (19, 12), (3, 23), (24, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556920", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 27), (12, 28), (8, 6), (14, 21), (11, 23), (2, 18), (8, 21), (2, 9), (11, 8), (1, 21), (4, 11), (7, 27), (12, 29), (15, 13), (5, 7), (24, 5), (15, 15), (12, 8), (25, 7), (21, 27), (14, 24), (9, 27), (6, 13), (33, 4), (20, 1), (14, 20), (1, 10), (6, 19), (30, 14), (12, 18), (17, 23), (12, 1), (4, 23), (17, 0), (3, 26), (34, 27), (6, 10), (25, 9), (5, 22), (26, 10), (13, 10), (23, 2), (31, 2), (10, 17), (4, 17), (33, 10), (9, 17), (4, 28), (22, 0), (16, 25), (0, 3), (3, 4), (24, 2), (13, 19), (21, 23), (23, 22), (28, 16), (11, 14), (21, 25), (24, 23), (30, 1), (15, 24), (3, 7), (33, 1), (22, 23), (23, 18), (34, 19), (30, 21), (21, 15), (35, 18), (20, 7), (0, 4), (35, 12), (28, 1), (1, 2), (21, 9), (27, 14), (17, 15), (12, 14), (4, 0), (19, 12), (33, 6), (34, 8), (29, 21), (32, 12), (24, 10), (15, 27), (31, 14), (31, 4), (21, 4), (28, 24), (20, 20), (20, 26), (29, 17), (6, 2), (14, 19), (4, 10), (3, 22), (3, 10), (29, 20), (0, 11), (34, 7), (0, 9), (33, 22), (21, 21), (2, 2), (33, 28), (33, 29), (22, 26), (11, 19), (22, 5), (29, 9), (12, 27), (16, 16), (23, 23), (25, 26), (28, 17), (6, 5), (7, 22), (7, 14), (9, 26), (6, 24), (16, 8), (7, 13), (12, 5), (11, 25), (21, 29), (25, 22), (27, 21), (17, 3), (31, 23), (5, 13), (26, 24), (11, 15), (1, 3), (3, 21), (27, 29), (34, 29), (30, 10), (33, 17), (2, 12), (26, 4), (13, 16), (31, 9), (8, 10), (20, 5), (33, 19), (25, 0), (18, 3), (22, 12), (32, 24), (11, 16), (26, 16), (22, 24), (29, 6), (22, 19), (34, 1), (12, 13), (32, 11), (31, 27), (13, 21), (2, 0), (9, 0), (32, 4), (23, 9), (30, 17), (17, 20), (1, 13), (6, 27), (25, 23), (28, 18), (22, 17), (5, 2), (24, 20), (24, 7), (16, 18), (33, 21), (10, 13), (6, 20), (25, 21), (1, 29), (27, 15), (35, 5), (12, 3), (28, 0), (8, 0), (5, 27), (9, 23), (7, 16), (34, 18), (35, 21), (31, 17), (35, 19), (30, 5), (13, 15), (31, 16), (5, 12), (17, 9), (10, 21), (16, 10), (2, 29), (33, 7), (23, 6), (4, 21), (11, 4), (26, 7), (33, 15), (0, 29), (27, 10), (3, 13), (14, 27), (31, 20), (25, 15), (14, 18), (5, 9), (9, 20), (26, 25), (34, 17), (34, 15), (23, 27), (23, 16), (34, 4), (28, 22), (23, 7), (24, 0), (17, 5), (35, 6), (12, 6), (23, 28), (35, 15), (28, 2), (17, 28), (4, 4), (12, 0), (28, 21), (30, 19), (29, 5), (23, 19), (9, 29), (35, 20), (27, 5), (16, 21), (18, 11), (20, 15), (22, 6), (8, 13), (15, 21), (32, 23), (19, 7), (26, 1), (26, 23), (34, 0), (33, 16), (30, 25), (0, 20), (30, 7), (18, 21), (29, 14), (5, 0), (32, 21), (19, 13), (0, 26), (2, 5), (9, 24), (1, 7), (16, 2), (8, 23), (30, 15), (33, 0), (2, 26), (13, 7), (32, 28), (2, 15), (10, 8), (32, 27), (15, 16), (27, 23), (32, 1), (29, 18), (20, 28), (35, 16), (5, 6), (29, 13), (6, 12), (22, 29), (2, 4), (32, 2), (7, 26), (14, 14), (15, 7), (30, 16), (19, 21), (26, 11), (9, 4), (1, 27), (24, 22), (19, 18), (31, 8), (8, 16), (30, 8), (26, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541800", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 29), (33, 26), (32, 37), (30, 10), (2, 23), (34, 14), (10, 37), (9, 23), (18, 20), (11, 24), (28, 36), (22, 10), (1, 33), (28, 13), (5, 15), (20, 32), (19, 7), (5, 37), (18, 6), (3, 4), (21, 13), (34, 17), (14, 35), (15, 20), (4, 7), (8, 0), (0, 6), (8, 17), (6, 6), (20, 20), (31, 27), (35, 30), (4, 22), (2, 22), (11, 33), (8, 24), (31, 21), (6, 20), (23, 11), (24, 20), (0, 34), (11, 11), (22, 0), (26, 4), (14, 36), (30, 35), (25, 34), (31, 17), (9, 30), (32, 38), (18, 34), (24, 15), (1, 34), (10, 31), (27, 7), (35, 7), (7, 1), (16, 34), (29, 31), (0, 38), (4, 16), (4, 19), (4, 27), (1, 30), (10, 19), (25, 8), (28, 28), (19, 31), (9, 35), (0, 18), (28, 18), (2, 36), (19, 20), (3, 27), (14, 7), (35, 23), (6, 3), (12, 3), (23, 33), (12, 26), (31, 35), (33, 32), (12, 20), (15, 30), (7, 16), (33, 34), (9, 4), (27, 23), (26, 32), (16, 32), (19, 33), (9, 10), (31, 38), (36, 18), (35, 19), (4, 31), (1, 12), (20, 35), (15, 14), (24, 6), (32, 36), (29, 13), (18, 17), (4, 23), (31, 18), (11, 2), (3, 33), (33, 23), (36, 32), (4, 24), (30, 3), (23, 37), (21, 30), (5, 28), (22, 3), (15, 9), (14, 32), (6, 35), (13, 29), (19, 25), (22, 27), (19, 9), (16, 36), (14, 11), (2, 30), (22, 6), (7, 26), (34, 29), (10, 6), (1, 11), (30, 18), (26, 31), (35, 17), (17, 33), (24, 28), (12, 10), (23, 18), (27, 2), (21, 37), (1, 4), (30, 29), (23, 9), (12, 36), (18, 23), (13, 24), (19, 32), (14, 19), (0, 30), (2, 27), (2, 9), (20, 11), (23, 29), (16, 12), (11, 12), (12, 15), (26, 17), (13, 15), (10, 18), (7, 12), (28, 15), (0, 12), (9, 20), (27, 17), (22, 13), (9, 12), (10, 27), (23, 38), (11, 14), (8, 28), (29, 1), (10, 20), (25, 13), (20, 10), (31, 33), (2, 13), (35, 0), (19, 11), (22, 30), (30, 23), (5, 3), (23, 13), (17, 8), (5, 26), (12, 6), (29, 21), (34, 24), (31, 31), (27, 13), (1, 5), (18, 32), (13, 3), (13, 18), (22, 29), (29, 2), (17, 37), (18, 31), (23, 27), (20, 34), (19, 23), (0, 21), (21, 28), (29, 24), (5, 22), (6, 5), (6, 14), (10, 30), (29, 36), (15, 7), (22, 14), (2, 20), (5, 1), (31, 2), (10, 12), (29, 18), (26, 26), (18, 24), (8, 1), (22, 16), (0, 7), (36, 37), (2, 11), (33, 35), (4, 1), (9, 33), (5, 19), (32, 4), (3, 9), (34, 1), (20, 25), (34, 27), (23, 5), (7, 21), (21, 19), (18, 2), (27, 30), (32, 13), (12, 12), (31, 12), (22, 21), (1, 25), (30, 1), (12, 31), (3, 12), (14, 34), (0, 27), (4, 30), (12, 29), (29, 7), (7, 0), (16, 38), (12, 18), (17, 15), (35, 6), (13, 1), (11, 29), (5, 16), (16, 19), (15, 6), (0, 23), (26, 30), (26, 10), (22, 28), (36, 4), (33, 25), (32, 16), (14, 25), (1, 0), (10, 29), (4, 6), (29, 22), (24, 4), (5, 14), (10, 5), (1, 38), (30, 36), (33, 19), (5, 27), (6, 24), (36, 20), (4, 18), (11, 21), (35, 9), (27, 10), (3, 0), (10, 33), (20, 23), (9, 36), (19, 34), (25, 17), (15, 15), (7, 8), (27, 19), (33, 27), (11, 22), (15, 28), (9, 7), (30, 15), (15, 21), (3, 22), (25, 3), (3, 23), (4, 32), (27, 26), (29, 28), (23, 10), (4, 14), (6, 22), (24, 12), (17, 10), (22, 35), (20, 12), (4, 8), (35, 34), (1, 32), (8, 30), (17, 30), (2, 26), (20, 33), (21, 27), (13, 23), (5, 20), (10, 21), (34, 9), (24, 5), (23, 3), (21, 18), (7, 24), (28, 12), (30, 21), (13, 25), (21, 12), (0, 14), (34, 11), (29, 35), (19, 2), (35, 13), (28, 32), (16, 20), (9, 18), (35, 3), (5, 23), (29, 38), (24, 29), (21, 2), (6, 8), (24, 14), (6, 29), (36, 9), (20, 6), (22, 20), (23, 4), (8, 6), (23, 7), (7, 25), (12, 19), (13, 35), (29, 9), (34, 8), (5, 12), (2, 33), (16, 28), (10, 22), (29, 29), (4, 33), (15, 1), (31, 24), (33, 6), (7, 38), (24, 22), (17, 25), (28, 3), (24, 31), (33, 16), (5, 25), (2, 2), (15, 11), (1, 16), (8, 32), (32, 22), (35, 10), (5, 2), (1, 7), (8, 2), (31, 26), (11, 10), (19, 30), (25, 21), (17, 32), (12, 30), (1, 13), (17, 36), (33, 10), (22, 23), (6, 7), (13, 34), (8, 37), (18, 35), (27, 27), (21, 25), (22, 24), (2, 18), (2, 0), (6, 0), (33, 0), (6, 32), (23, 24), (9, 9), (25, 29), (11, 18), (19, 12), (19, 0), (6, 38), (24, 13), (24, 19), (27, 31), (5, 13), (6, 12), (10, 2), (22, 31), (18, 11), (21, 34), (17, 20), (36, 19), (26, 9), (35, 37), (28, 21), (15, 2), (14, 29), (30, 33), (18, 30), (8, 38), (19, 27), (12, 34), (36, 15), (35, 4), (3, 37), (36, 33), (28, 23), (8, 3), (23, 19), (5, 24), (16, 35), (27, 38), (8, 36), (30, 6), (6, 10), (1, 19), (14, 4), (20, 8), (32, 32), (7, 14), (17, 28), (9, 28), (20, 14), (1, 26), (3, 13), (2, 14), (2, 29), (35, 27), (23, 2), (4, 4), (10, 32), (7, 34), (19, 18), (30, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "702000", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 1), (16, 13), (15, 26), (0, 17), (19, 32), (18, 5), (11, 9), (27, 12), (31, 11), (17, 30), (19, 29), (14, 3), (0, 18), (12, 31), (20, 12), (12, 17), (32, 10), (10, 11), (11, 6), (9, 22), (18, 13), (2, 7), (4, 8), (2, 20), (31, 14), (30, 28), (1, 13), (27, 11), (18, 31), (22, 14), (13, 29), (31, 1), (21, 21), (9, 4), (17, 8), (32, 22), (16, 1), (3, 22), (2, 23), (13, 8), (21, 16), (5, 11), (13, 4), (32, 14), (18, 6), (28, 8), (0, 26), (5, 22), (18, 1), (9, 10), (11, 28), (19, 9), (1, 19), (19, 2), (19, 22), (22, 9), (9, 32), (22, 26), (31, 13), (18, 29), (6, 29), (22, 32), (20, 16), (15, 11), (26, 10), (0, 5), (27, 22), (10, 3), (29, 13), (18, 18), (23, 31), (24, 21), (17, 11), (1, 30), (28, 5), (23, 1), (6, 3), (26, 6), (20, 21), (31, 17), (3, 31), (29, 8), (21, 3), (30, 3), (3, 5), (8, 1), (26, 1), (6, 31), (5, 15), (4, 20), (7, 6), (11, 19), (31, 20), (27, 14), (2, 8), (14, 11), (7, 20), (20, 17), (27, 31), (11, 32), (16, 32), (11, 13), (6, 20), (17, 27), (26, 7), (3, 30), (31, 19), (19, 17), (8, 30), (19, 5), (23, 20), (27, 5), (6, 1), (11, 30), (32, 5), (17, 24), (5, 18), (17, 31), (27, 20), (16, 31), (12, 12), (26, 3), (6, 32), (27, 4), (1, 9), (10, 23), (1, 32), (0, 16), (6, 17), (1, 17), (8, 2), (26, 24), (8, 4), (28, 27), (12, 29), (21, 23), (29, 22), (21, 17), (10, 10), (29, 2), (24, 19), (26, 23), (20, 31), (5, 29), (24, 17), (17, 4), (20, 22), (13, 30), (17, 10), (14, 28), (2, 2), (14, 16), (30, 7), (20, 4), (4, 28), (27, 13), (30, 22), (7, 12), (11, 17), (23, 2), (7, 18), (5, 1), (16, 23), (3, 14), (3, 20), (10, 25), (20, 13), (15, 24), (18, 20), (3, 26), (15, 21), (21, 9), (1, 2), (5, 16), (5, 32), (15, 10), (26, 18), (12, 0), (14, 27), (6, 7), (24, 10), (5, 31), (7, 25), (16, 9), (21, 18), (29, 21), (5, 27), (4, 1), (1, 6), (8, 23), (31, 31), (17, 6), (2, 15), (19, 10), (6, 25), (16, 27), (10, 2), (12, 14), (14, 0), (20, 3), (7, 21), (14, 9), (22, 8), (9, 23), (1, 8), (4, 22), (17, 18), (9, 24), (11, 15), (24, 0), (14, 22), (21, 27), (19, 13), (16, 14), (15, 14), (5, 2), (4, 24), (7, 9), (13, 0), (5, 20), (31, 32), (13, 7), (30, 12), (31, 22), (6, 15), (14, 21), (19, 20), (20, 28), (5, 19), (17, 5), (22, 10), (15, 12), (10, 6), (29, 23), (13, 17), (30, 20), (23, 12), (22, 23), (7, 30), (24, 15), (14, 26), (3, 2), (28, 21), (31, 21), (31, 10), (5, 5), (5, 21), (14, 12), (26, 25), (25, 17), (28, 29), (11, 27), (1, 28), (10, 9), (20, 8), (12, 1), (9, 17), (13, 5), (9, 28), (2, 30), (32, 17), (7, 2), (0, 9), (23, 5), (19, 14), (17, 19), (8, 7), (7, 4), (11, 8), (26, 0), (17, 21), (12, 10), (28, 18), (30, 8), (8, 17), (4, 10), (9, 16), (29, 15), (29, 11), (15, 18), (6, 26), (20, 30), (11, 4), (25, 6), (30, 29), (19, 7), (16, 19), (2, 17), (22, 28), (16, 10), (26, 19), (31, 24), (23, 4), (21, 25), (28, 26), (9, 26), (32, 28), (11, 23), (1, 18), (27, 18), (10, 29), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58104", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 23), (8, 26), (15, 17), (3, 23), (33, 18), (4, 7), (26, 0), (21, 24), (5, 5), (5, 33), (31, 11), (29, 23), (30, 3), (18, 34), (2, 11), (26, 15), (14, 2), (16, 5), (7, 22), (6, 6), (33, 17), (18, 22), (32, 7), (15, 16), (1, 25), (10, 32), (31, 4), (7, 10), (16, 11), (2, 16), (15, 24), (24, 29), (13, 15), (10, 27), (5, 29), (17, 21), (7, 23), (12, 8), (25, 10), (24, 7), (7, 20), (0, 26), (33, 3), (16, 32), (12, 5), (25, 8), (18, 28), (9, 13), (5, 20), (18, 2), (33, 22), (31, 5), (27, 16), (31, 6), (27, 7), (26, 7), (14, 34), (7, 16), (7, 4), (29, 24), (4, 2), (21, 26), (14, 11), (23, 27), (29, 9), (9, 20), (18, 10), (17, 15), (3, 18), (24, 27), (8, 20), (11, 13), (30, 21), (11, 6), (16, 14), (20, 1), (25, 17), (23, 10), (6, 30), (25, 13), (20, 30), (1, 1), (5, 23), (10, 11), (9, 32), (27, 14), (16, 8), (21, 14), (7, 11), (19, 30), (8, 25), (32, 23), (29, 0), (25, 11), (24, 22), (6, 15), (18, 23), (31, 8), (12, 12), (19, 7), (9, 7), (5, 16), (29, 13), (15, 26), (26, 5), (0, 6), (26, 3), (33, 14), (24, 23), (29, 18), (2, 27), (11, 4), (15, 33), (24, 2), (5, 25), (23, 34), (12, 15), (30, 25), (23, 18), (21, 22), (10, 19), (22, 17), (22, 31), (19, 24), (26, 17), (22, 7), (16, 29), (31, 28), (22, 3), (29, 11), (16, 19), (33, 25), (30, 5), (32, 18), (7, 27), (11, 1), (27, 21), (24, 20), (17, 28), (19, 17), (23, 29), (2, 33), (20, 21), (4, 14), (25, 3), (26, 12), (9, 27), (21, 6), (16, 15), (20, 18), (20, 22), (9, 28), (14, 26), (7, 34), (18, 29), (12, 16), (33, 21), (28, 34), (14, 24), (15, 0), (22, 33), (24, 24), (7, 7), (14, 13), (33, 16), (5, 34), (28, 15), (12, 32), (25, 28), (9, 22), (5, 14), (9, 18), (0, 8), (2, 25), (4, 3), (26, 9), (1, 24), (30, 28), (18, 4), (12, 21), (29, 21), (12, 3), (33, 6), (10, 23), (10, 8), (1, 4), (3, 31), (15, 2), (24, 1), (22, 32), (23, 9), (18, 21), (2, 10), (14, 19), (27, 6), (32, 4), (10, 5), (32, 33), (26, 21), (32, 6), (31, 0), (20, 15), (27, 30), (13, 32), (10, 26), (8, 11), (23, 1), (15, 21), (29, 3), (0, 25), (4, 12), (3, 13), (10, 29), (22, 10), (24, 26), (18, 20), (13, 14), (9, 15), (31, 3), (18, 33), (23, 14), (18, 1), (20, 25), (7, 0), (27, 25), (2, 2), (11, 16), (11, 3), (20, 12), (13, 1), (0, 9), (6, 14), (0, 29), (22, 30), (17, 8), (0, 34), (9, 17), (7, 28), (29, 25), (9, 21), (0, 7), (21, 3), (33, 13), (30, 18), (5, 6), (25, 16), (29, 16), (3, 6), (3, 26), (2, 6), (33, 12), (15, 14), (1, 12), (7, 18), (3, 22), (6, 0), (20, 2), (32, 12), (25, 29), (5, 4), (9, 1), (11, 26), (15, 28), (9, 34), (9, 9), (25, 25), (25, 4), (31, 26), (5, 11), (28, 14), (6, 5), (17, 18), (5, 30), (0, 1), (9, 24), (14, 10), (1, 14), (1, 34), (2, 30), (23, 6), (15, 7), (22, 16), (14, 28), (26, 24), (8, 24), (28, 30), (9, 3), (24, 30), (1, 17), (8, 14), (30, 12), (9, 10), (14, 9), (33, 11), (24, 19), (2, 15), (11, 24), (24, 31), (28, 8), (10, 30), (27, 26), (19, 19), (3, 24), (30, 16), (28, 26), (8, 27), (8, 2), (3, 19), (15, 15), (3, 3), (5, 32), (14, 27), (22, 12), (2, 26), (11, 5), (33, 0), (31, 7), (10, 0), (25, 9), (7, 31), (27, 20), (18, 3), (3, 30), (20, 7), (3, 7), (14, 32), (26, 1), (23, 3), (0, 10), (24, 13), (10, 18), (33, 30), (2, 8), (17, 11), (27, 28), (7, 12), (17, 3), (10, 24), (28, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "815616", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 5), (7, 3), (17, 31), (11, 20), (9, 30), (22, 16), (19, 9), (28, 25), (2, 31), (24, 18), (32, 7), (33, 10), (8, 9), (20, 17), (14, 20), (8, 12), (9, 8), (13, 26), (0, 6), (12, 20), (9, 14), (36, 22), (30, 24), (36, 21), (28, 11), (2, 30), (28, 1), (31, 26), (32, 13), (33, 2), (25, 20), (8, 8), (37, 28), (25, 18), (29, 24), (23, 26), (15, 25), (37, 26), (2, 22), (14, 26), (30, 30), (27, 15), (5, 31), (18, 31), (20, 25), (27, 24), (8, 15), (0, 13), (19, 17), (27, 26), (1, 29), (6, 5), (16, 16), (22, 1), (25, 10), (29, 31), (30, 28), (25, 5), (21, 17), (15, 7), (11, 15), (3, 5), (15, 3), (14, 14), (29, 6), (4, 22), (23, 6), (19, 6), (10, 16), (37, 27), (27, 2), (31, 11), (20, 19), (18, 24), (24, 19), (11, 17), (16, 28), (24, 9), (34, 13), (30, 25), (16, 2), (2, 9), (19, 25), (2, 15), (25, 21), (22, 25), (1, 8), (8, 11), (17, 26), (10, 4), (34, 14), (3, 23), (27, 22), (36, 23), (23, 15), (25, 12), (38, 14), (38, 6), (27, 30), (0, 23), (23, 14), (25, 1), (10, 23), (21, 23), (13, 1), (33, 19), (4, 10), (25, 28), (38, 28), (37, 4), (14, 21), (5, 2), (13, 12), (26, 30), (26, 25), (31, 24), (10, 15), (11, 4), (18, 19), (18, 6), (31, 3), (38, 18), (17, 25), (9, 18), (28, 15), (6, 17), (14, 0), (20, 6), (12, 24), (27, 12), (22, 23), (1, 7), (26, 12), (21, 0), (26, 9), (20, 13), (6, 21), (15, 15), (18, 0), (22, 7), (32, 1), (14, 25), (6, 13), (21, 16), (26, 10), (26, 8), (28, 19), (7, 10), (2, 3), (12, 28), (9, 23), (34, 5), (22, 22), (22, 18), (26, 20), (5, 19), (9, 2), (32, 31), (34, 2), (15, 29), (28, 2), (35, 1), (22, 30), (32, 21), (24, 3), (15, 21), (24, 25), (15, 27), (18, 1), (13, 7), (11, 7), (22, 8), (2, 27), (24, 6), (30, 4), (19, 16), (19, 10), (16, 6), (35, 13), (38, 16), (7, 19), (8, 25), (28, 26), (32, 5), (4, 19), (26, 1), (32, 3), (4, 12), (24, 14), (14, 4), (4, 2), (9, 29), (6, 9), (5, 17), (36, 4), (28, 0), (1, 21), (22, 4), (37, 25), (29, 10), (37, 0), (18, 16), (0, 16), (20, 31), (34, 28), (25, 6), (3, 19), (32, 20), (34, 31), (35, 16), (30, 5), (28, 21), (20, 2), (0, 21), (0, 12), (24, 7), (6, 6), (7, 2), (3, 6), (23, 3), (20, 27), (13, 22), (5, 30), (0, 5), (7, 1), (34, 8), (28, 16), (30, 15), (0, 7), (29, 1), (11, 24), (31, 6), (11, 22), (34, 1), (13, 9), (9, 26), (11, 31), (16, 21), (13, 17), (6, 28), (33, 24), (23, 5), (25, 27), (9, 19), (29, 7), (6, 24), (30, 6), (27, 21), (26, 22), (22, 13), (0, 4), (9, 6), (8, 13), (15, 12), (17, 8), (8, 14), (29, 26), (26, 18), (10, 14), (24, 23), (35, 8), (7, 5), (26, 4), (10, 6), (27, 31), (29, 5), (35, 3), (2, 7), (38, 30), (9, 24), (5, 1), (26, 11), (33, 21), (8, 17), (5, 21), (35, 19), (6, 31), (30, 29), (18, 17), (21, 12), (13, 8), (27, 23), (27, 3), (34, 19), (20, 12), (2, 21), (14, 5), (5, 16), (24, 0), (31, 28), (14, 9), (2, 20), (13, 23), (27, 17), (0, 15), (8, 10), (14, 11), (24, 10), (1, 0), (38, 25), (5, 3), (28, 18), (36, 26), (28, 20), (35, 23), (20, 9), (38, 19), (15, 2), (9, 16), (12, 7), (33, 7), (17, 3), (37, 9), (16, 8), (7, 21), (1, 9), (11, 12), (3, 28), (35, 31), (9, 22), (18, 26), (10, 30), (32, 17), (20, 24), (1, 31), (10, 5), (38, 11), (32, 14), (24, 8), (15, 24), (10, 12), (23, 1), (6, 15), (32, 27), (20, 1), (2, 28), (26, 16), (15, 20), (29, 16), (26, 31), (6, 22), (36, 24), (27, 10), (38, 13), (37, 23), (31, 1), (18, 5), (33, 11), (6, 30), (35, 17), (38, 8), (18, 20), (22, 12), (21, 25), (38, 15), (25, 0), (36, 8), (8, 24), (5, 4), (1, 26), (33, 16), (17, 16), (24, 28), (2, 16), (23, 20), (5, 14), (35, 14), (14, 2), (20, 30), (8, 5), (23, 4), (1, 23), (33, 17), (0, 31), (1, 2), (37, 15), (23, 23), (4, 14), (10, 27), (18, 25), (3, 17), (37, 24), (21, 27), (15, 13), (32, 8), (15, 9), (7, 11), (29, 15), (33, 25), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393120", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 33), (19, 14), (32, 24), (9, 5), (20, 19), (15, 34), (2, 9), (4, 35), (7, 33), (30, 32), (37, 24), (0, 15), (24, 25), (7, 18), (7, 5), (18, 31), (11, 24), (23, 27), (16, 16), (12, 16), (5, 29), (38, 9), (4, 2), (10, 13), (25, 27), (24, 2), (33, 6), (28, 32), (34, 1), (4, 32), (6, 20), (29, 1), (8, 32), (22, 29), (13, 22), (24, 9), (20, 30), (20, 31), (13, 31), (3, 4), (23, 12), (33, 26), (27, 9), (1, 26), (34, 27), (9, 4), (1, 10), (25, 12), (16, 23), (21, 9), (25, 22), (13, 35), (23, 24), (1, 23), (34, 26), (36, 21), (22, 13), (32, 9), (15, 29), (6, 3), (16, 17), (18, 20), (15, 24), (7, 35), (5, 27), (33, 10), (21, 1), (9, 25), (28, 29), (24, 35), (32, 2), (18, 29), (34, 9), (6, 18), (36, 3), (17, 16), (3, 35), (32, 18), (25, 1), (27, 19), (22, 24), (15, 25), (29, 9), (19, 22), (0, 8), (13, 20), (6, 27), (16, 3), (19, 23), (32, 26), (2, 16), (8, 34), (35, 2), (34, 22), (19, 13), (2, 1), (7, 0), (29, 25), (31, 24), (23, 0), (11, 26), (15, 21), (8, 6), (23, 8), (33, 21), (34, 3), (3, 1), (12, 6), (7, 11), (2, 5), (36, 26), (30, 26), (27, 22), (5, 20), (0, 23), (26, 7), (10, 4), (14, 20), (5, 35), (24, 20), (25, 26), (11, 27), (13, 10), (27, 24), (15, 20), (4, 9), (6, 11), (18, 7), (28, 30), (2, 21), (29, 6), (35, 35), (8, 15), (30, 18), (13, 12), (32, 33), (36, 22), (1, 11), (5, 11), (38, 31), (13, 8), (36, 29), (24, 15), (23, 1), (16, 11), (16, 19), (26, 14), (35, 9), (17, 31), (20, 28), (1, 18), (9, 20), (27, 30), (7, 1), (1, 22), (16, 26), (32, 7), (7, 16), (22, 23), (37, 22), (34, 5), (38, 11), (4, 25), (25, 7), (35, 25), (24, 6), (19, 9), (5, 17), (20, 32), (25, 25), (30, 5), (26, 25), (8, 25), (34, 15), (16, 34), (31, 10), (38, 25), (15, 11), (6, 28), (32, 11), (31, 17), (27, 0), (6, 25), (8, 7), (29, 28), (34, 19), (6, 31), (35, 3), (37, 6), (8, 33), (27, 20), (22, 19), (29, 13), (30, 29), (21, 8), (21, 12), (1, 9), (2, 6), (35, 31), (5, 1), (21, 14), (14, 34), (18, 1), (17, 30), (4, 10), (25, 0), (9, 31), (10, 19), (20, 3), (33, 27), (24, 18), (30, 11), (2, 24), (27, 28), (21, 3), (9, 28), (17, 10), (8, 5), (18, 5), (35, 28), (13, 3), (16, 18), (1, 20), (10, 27), (27, 3), (15, 12), (0, 26), (19, 11), (29, 0), (4, 1), (5, 8), (25, 4), (12, 21), (37, 28), (21, 31), (16, 2), (0, 20), (25, 14), (2, 4), (21, 33), (22, 0), (7, 20), (19, 0), (20, 0), (30, 20), (8, 10), (19, 33), (3, 22), (3, 32), (8, 23), (33, 32), (30, 12), (36, 1), (10, 21), (21, 17), (28, 22), (20, 18), (26, 27), (37, 11), (17, 15), (18, 17), (2, 22), (19, 2), (18, 14), (2, 33), (13, 32), (5, 5), (0, 9), (29, 11), (37, 13), (9, 26), (35, 20), (38, 3), (27, 11), (36, 18), (37, 7), (22, 30), (35, 7), (35, 27), (12, 8), (25, 31), (20, 10), (8, 2), (1, 32), (11, 8), (1, 21), (8, 11), (34, 16), (32, 29), (9, 16), (13, 9), (8, 27), (22, 21), (8, 8), (38, 33), (1, 0), (16, 0), (28, 16), (15, 3), (15, 5), (31, 27), (9, 24), (12, 19), (29, 15), (22, 2), (20, 9), (5, 6), (28, 25), (9, 14), (26, 15), (19, 26), (9, 8), (6, 9), (14, 24), (17, 4), (17, 18), (10, 17), (36, 11), (6, 17), (7, 27), (24, 30), (34, 18), (1, 13), (13, 0), (24, 29), (0, 24), (16, 30), (4, 31), (28, 2), (33, 22), (5, 28), (4, 28), (23, 28), (4, 3), (8, 18), (0, 12), (1, 8), (20, 25), (29, 26), (35, 14), (29, 33), (6, 8), (7, 21), (11, 10), (12, 24), (10, 7), (11, 23), (21, 26), (25, 16), (12, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602910", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (4, 16), (23, 23), (11, 22), (26, 30), (29, 13), (26, 24), (11, 3), (7, 23), (20, 8), (0, 17), (25, 12), (30, 14), (15, 8), (20, 3), (18, 5), (15, 10), (19, 12), (23, 22), (29, 24), (28, 6), (1, 12), (6, 0), (24, 0), (23, 1), (18, 18), (29, 19), (20, 22), (5, 28), (9, 28), (30, 23), (8, 5), (12, 23), (9, 5), (2, 5), (26, 23), (19, 28), (10, 2), (16, 0), (26, 21), (22, 6), (14, 13), (14, 18), (19, 17), (14, 21), (9, 24), (3, 13), (12, 28), (13, 18), (0, 14), (20, 21), (23, 29), (25, 3), (23, 21), (9, 31), (6, 9), (29, 14), (11, 11), (2, 17), (12, 6), (14, 4), (14, 20), (22, 17), (14, 19), (15, 30), (18, 14), (12, 5), (25, 26), (10, 19), (20, 5), (20, 12), (3, 15), (19, 30), (24, 16), (14, 11), (9, 30), (11, 14), (15, 25), (17, 8), (7, 31), (12, 24), (4, 31), (27, 18), (15, 6), (22, 25), (30, 17), (0, 15), (12, 11), (19, 21), (19, 0), (6, 1), (26, 13), (7, 12), (9, 6), (20, 30), (29, 15), (4, 30), (3, 6), (11, 25), (7, 22), (0, 8), (15, 14), (3, 25), (20, 16), (17, 31), (0, 28), (1, 13), (3, 2), (29, 8), (25, 18), (9, 23), (17, 18), (29, 22), (12, 9), (6, 11), (20, 25), (13, 30), (23, 3), (16, 10), (16, 15), (28, 27), (20, 29), (10, 6), (28, 5), (5, 19), (4, 13), (1, 28), (1, 0), (11, 7), (10, 26), (27, 14), (8, 21), (16, 29), (24, 5), (17, 19), (2, 11), (4, 11), (8, 28), (5, 25), (29, 2), (21, 13), (28, 16), (1, 23), (10, 27), (13, 16), (5, 13), (26, 5), (6, 12), (28, 9), (10, 1), (14, 10), (18, 29), (21, 27), (9, 1), (15, 23), (14, 16), (3, 5), (4, 27), (19, 23), (1, 8), (20, 2), (1, 14), (15, 21), (12, 10), (18, 15), (22, 2), (26, 7), (1, 21), (19, 6), (13, 4), (4, 17), (15, 27), (16, 13), (14, 9), (26, 14), (9, 16), (9, 17), (4, 10), (1, 17), (11, 9), (13, 17), (22, 29), (9, 14), (26, 20), (13, 23), (6, 8), (25, 21), (6, 20), (3, 31), (22, 18), (16, 6), (2, 4), (7, 29), (4, 15), (24, 29), (3, 27), (21, 12), (21, 10), (4, 26), (17, 21), (14, 31), (19, 20), (21, 28), (9, 15), (6, 18), (14, 6), (3, 14), (17, 30), (27, 27), (30, 2), (25, 17), (28, 2), (6, 24), (25, 24), (13, 5), (7, 19), (8, 4), (14, 23), (21, 18), (1, 25), (11, 10), (3, 16), (27, 11), (23, 17), (12, 30), (25, 27), (2, 31), (5, 5), (22, 26), (11, 16), (25, 10), (28, 18), (13, 19), (0, 16), (15, 9), (7, 11), (18, 0), (17, 12), (9, 26), (8, 3), (19, 8), (14, 17), (30, 6), (28, 26), (8, 9), (18, 21), (4, 21), (5, 30), (22, 27), (30, 5), (0, 23), (21, 6), (23, 10), (2, 28), (22, 5), (23, 20), (21, 7), (26, 1), (16, 4), (0, 30), (27, 22), (0, 22), (14, 26), (11, 18), (17, 26), (18, 31), (10, 17), (23, 6), (15, 12), (18, 30), (9, 21), (16, 31), (15, 16), (12, 2), (15, 15), (9, 4), (9, 18), (27, 5), (17, 0), (13, 25), (3, 8), (17, 6), (5, 8), (18, 13), (3, 23), (30, 21), (6, 10), (16, 19), (20, 26), (3, 11), (25, 28), (4, 12), (28, 10), (1, 30), (26, 27), (22, 16), (1, 15), (15, 20), (29, 31), (5, 11), (26, 6), (9, 27), (10, 28), (25, 29), (29, 6), (6, 16), (19, 19), (9, 9), (21, 0), (10, 4), (8, 12), (10, 8), (2, 9), (8, 20), (25, 9), (9, 29), (3, 28), (30, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "725760", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 6), (30, 13), (9, 33), (29, 23), (16, 35), (12, 26), (34, 13), (17, 23), (5, 38), (10, 34), (4, 18), (2, 38), (28, 23), (8, 20), (5, 33), (11, 14), (16, 1), (7, 24), (3, 24), (20, 5), (1, 2), (18, 8), (17, 22), (32, 34), (30, 32), (28, 12), (20, 9), (29, 36), (9, 3), (1, 14), (8, 21), (15, 3), (10, 18), (19, 15), (28, 38), (14, 6), (9, 36), (7, 18), (25, 30), (35, 26), (21, 8), (31, 12), (20, 22), (37, 1), (23, 17), (29, 22), (24, 24), (2, 7), (8, 14), (37, 2), (10, 1), (27, 8), (8, 12), (34, 27), (9, 9), (21, 27), (32, 4), (30, 38), (20, 17), (27, 0), (8, 32), (1, 16), (34, 26), (26, 31), (27, 9), (0, 26), (18, 23), (10, 7), (37, 12), (35, 27), (21, 11), (2, 14), (26, 35), (3, 16), (9, 5), (25, 8), (4, 21), (1, 9), (23, 36), (36, 23), (25, 25), (0, 22), (3, 37), (6, 11), (29, 31), (5, 31), (34, 31), (34, 21), (6, 30), (20, 36), (27, 13), (17, 31), (33, 3), (38, 12), (32, 36), (27, 6), (23, 35), (28, 28), (35, 0), (22, 0), (14, 28), (29, 7), (4, 36), (3, 31), (31, 9), (7, 32), (16, 21), (1, 1), (22, 18), (5, 34), (3, 5), (37, 28), (17, 5), (24, 2), (5, 10), (27, 29), (36, 28), (12, 25), (27, 15), (8, 9), (26, 18), (33, 2), (36, 7), (7, 2), (19, 11), (9, 15), (2, 20), (29, 14), (1, 33), (22, 7), (5, 36), (34, 30), (4, 26), (34, 23), (27, 20), (12, 17), (18, 14), (9, 16), (2, 31), (11, 7), (27, 18), (9, 2), (22, 20), (35, 23), (8, 1), (30, 0), (5, 37), (28, 7), (38, 34), (2, 33), (0, 20), (4, 29), (17, 9), (7, 27), (32, 22), (9, 10), (15, 19), (34, 6), (7, 10), (25, 13), (21, 9), (5, 14), (9, 31), (11, 10), (33, 8), (35, 13), (33, 29), (35, 14), (35, 34), (1, 20), (0, 13), (31, 21), (16, 12), (31, 16), (15, 1), (23, 27), (14, 21), (18, 33), (23, 13), (28, 0), (5, 6), (21, 2), (17, 6), (27, 7), (26, 6), (31, 38), (18, 29), (15, 9), (32, 33), (3, 2), (38, 7), (21, 37), (35, 12), (37, 19), (14, 9), (8, 27), (17, 38), (23, 33), (15, 27), (18, 2), (25, 27), (28, 33), (8, 7), (30, 5), (14, 30), (14, 4), (21, 26), (38, 23), (22, 9), (36, 15), (16, 20), (33, 38), (13, 20), (17, 35), (15, 30), (34, 1), (2, 18), (29, 0), (30, 36), (9, 17), (6, 26), (17, 14), (13, 28), (26, 2), (18, 19), (13, 32), (24, 1), (31, 4), (13, 33), (13, 14), (37, 9), (34, 35), (18, 0), (35, 17), (20, 4), (9, 14), (19, 14), (30, 8), (13, 26), (0, 5), (3, 10), (13, 1), (9, 32), (36, 29), (35, 33), (4, 35), (9, 27), (20, 18), (3, 12), (27, 22), (14, 13), (5, 19), (35, 9), (0, 10), (37, 26), (4, 9), (20, 26), (4, 17), (33, 11), (29, 13), (11, 4), (36, 10), (27, 21), (14, 8), (32, 2), (35, 21), (6, 6), (32, 19), (13, 5), (18, 7), (30, 31), (11, 27), (26, 1), (33, 36), (28, 19), (27, 10), (27, 31), (3, 7), (26, 10), (4, 6), (37, 18), (19, 28), (5, 27), (3, 8), (31, 27), (16, 30), (15, 31), (34, 11), (1, 12), (22, 21), (5, 26), (12, 5), (16, 24), (5, 29), (24, 27), (15, 37), (20, 6), (12, 1), (11, 22), (2, 0), (17, 0), (36, 22), (19, 1), (4, 12), (20, 30), (13, 18), (17, 13), (23, 11), (4, 24), (13, 16), (5, 30), (20, 20), (5, 3), (15, 26), (11, 31), (25, 0), (26, 20), (36, 36), (14, 14), (22, 36), (27, 2), (0, 24), (28, 34), (24, 23), (32, 9), (5, 0), (16, 7), (35, 31), (34, 7), (7, 25), (29, 5), (37, 27), (30, 12), (34, 34), (6, 12), (8, 28), (13, 4), (16, 15), (30, 17), (28, 24), (1, 11), (8, 10), (27, 17), (17, 21), (12, 38), (27, 23), (20, 16), (33, 4), (28, 26), (37, 15), (28, 15), (4, 22), (8, 4), (15, 16), (34, 36), (24, 19), (4, 14), (35, 18), (31, 13), (13, 3), (6, 34), (15, 10), (15, 25), (6, 13), (7, 26), (23, 23), (27, 16), (26, 22), (21, 19), (28, 5), (4, 34), (18, 20), (1, 17), (7, 0), (23, 20), (23, 25), (6, 37), (23, 14), (21, 32), (28, 30), (29, 2), (32, 32), (13, 29), (28, 27), (31, 32), (33, 19), (19, 2), (6, 14), (14, 7), (23, 6), (12, 23), (26, 3), (25, 7), (4, 25), (20, 31), (36, 0), (16, 34), (32, 29), (26, 17), (8, 22), (32, 17), (37, 10), (7, 31), (11, 29), (12, 14), (14, 1), (14, 23), (18, 34), (5, 21), (28, 35), (22, 3), (37, 29), (35, 35), (15, 5), (21, 21), (26, 36), (1, 29), (11, 36), (29, 3), (4, 32), (33, 35), (16, 5), (18, 37), (2, 21), (16, 3), (13, 12), (17, 11), (29, 10), (20, 0), (24, 33), (3, 28), (23, 3), (0, 38), (33, 21), (30, 15), (21, 23), (6, 32), (10, 26), (36, 17), (10, 21), (29, 6), (32, 7), (2, 19), (32, 1), (34, 17), (7, 13), (36, 16), (20, 32), (18, 6), (31, 6), (16, 36), (7, 33), (7, 36), (3, 29), (1, 15), (4, 1), (32, 3), (26, 33), (36, 2), (27, 26), (31, 33), (12, 31), (35, 38), (38, 21), (12, 30), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "959040", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 5), (11, 2), (24, 6), (0, 14), (21, 34), (31, 7), (0, 20), (21, 3), (32, 13), (25, 32), (10, 30), (29, 35), (12, 27), (15, 15), (8, 20), (18, 32), (27, 35), (29, 6), (10, 29), (34, 9), (18, 24), (10, 25), (15, 30), (31, 20), (30, 12), (9, 30), (12, 13), (23, 11), (12, 22), (11, 31), (32, 18), (0, 17), (30, 5), (28, 32), (33, 20), (1, 7), (2, 26), (18, 10), (4, 34), (31, 17), (29, 26), (18, 21), (17, 12), (16, 24), (22, 21), (10, 7), (10, 23), (6, 27), (19, 33), (29, 33), (23, 20), (1, 32), (5, 4), (8, 28), (10, 13), (23, 7), (31, 34), (31, 23), (10, 28), (25, 17), (28, 22), (2, 25), (28, 28), (27, 5), (0, 1), (34, 29), (21, 18), (33, 5), (27, 21), (8, 25), (26, 20), (32, 3), (11, 18), (20, 17), (5, 19), (18, 13), (27, 4), (32, 8), (26, 2), (22, 1), (6, 26), (0, 30), (30, 25), (25, 15), (5, 22), (32, 5), (28, 20), (25, 10), (34, 15), (25, 19), (15, 17), (2, 20), (5, 1), (26, 15), (4, 32), (13, 7), (24, 11), (27, 11), (28, 13), (1, 9), (33, 31), (22, 13), (6, 30), (24, 4), (12, 35), (11, 33), (9, 18), (13, 26), (2, 9), (18, 15), (14, 8), (4, 31), (25, 21), (26, 25), (0, 27), (13, 32), (1, 16), (22, 22), (23, 30), (4, 27), (28, 7), (9, 31), (8, 21), (9, 15), (14, 4), (17, 23), (23, 35), (11, 25), (31, 0), (0, 15), (34, 28), (29, 28), (20, 34), (27, 14), (32, 32), (17, 16), (23, 28), (18, 19), (29, 0), (8, 15), (26, 14), (15, 2), (20, 22), (20, 12), (32, 27), (8, 26), (28, 5), (25, 13), (25, 23), (21, 16), (18, 4), (19, 30), (23, 14), (23, 6), (15, 11), (16, 22), (6, 21), (6, 25), (5, 8), (17, 6), (0, 3), (16, 19), (26, 3), (3, 31), (30, 0), (19, 14), (29, 18), (32, 25), (17, 18), (27, 16), (19, 3), (8, 27), (4, 21), (13, 9), (2, 29), (34, 8), (29, 1), (21, 25), (24, 24), (19, 21), (32, 24), (29, 12), (8, 22), (3, 26), (20, 31), (11, 22), (31, 15), (11, 20), (4, 12), (2, 22), (3, 17), (17, 15), (24, 32), (33, 29), (33, 25), (22, 10), (12, 15), (20, 21), (7, 21), (12, 20), (33, 35), (12, 6), (12, 10), (34, 16), (21, 27), (7, 16), (20, 30), (29, 30), (12, 21), (20, 4), (3, 18), (11, 5), (19, 18), (26, 4), (33, 33), (2, 17), (21, 24), (19, 6), (25, 3), (29, 19), (34, 3), (19, 22), (21, 7), (31, 3), (21, 17), (7, 31), (12, 8), (12, 19), (17, 34), (12, 5), (22, 31), (27, 32), (24, 20), (29, 24), (22, 8), (25, 26), (34, 6), (19, 5), (31, 14), (15, 4), (0, 31), (16, 9), (4, 13), (31, 31), (34, 11), (11, 10), (20, 13), (5, 31), (6, 3), (26, 9), (2, 27), (18, 12), (11, 16), (12, 4), (3, 1), (15, 19), (14, 31), (25, 31), (9, 0), (29, 32), (8, 14), (7, 1), (10, 34), (33, 2), (30, 20), (32, 26), (20, 14), (25, 30), (8, 2), (10, 17), (1, 19), (17, 30), (27, 0), (19, 10), (9, 10), (22, 28), (22, 11), (27, 20), (5, 16), (5, 9), (30, 15), (33, 0), (32, 19), (28, 12), (5, 14), (24, 18), (17, 27), (10, 31), (10, 1), (3, 23), (24, 21), (7, 8), (26, 24), (14, 0), (7, 22), (27, 22), (9, 29), (3, 16), (33, 7), (5, 13), (16, 10), (12, 18), (0, 9), (30, 22), (4, 20), (1, 22), (18, 2), (23, 12), (27, 18), (11, 7), (30, 26), (8, 29), (24, 17), (12, 34), (25, 6), (20, 29), (11, 15), (26, 11), (7, 3), (17, 29), (24, 15), (14, 15), (15, 22), (20, 35), (24, 19), (26, 10), (15, 28), (16, 15), (21, 15), (9, 6), (10, 24), (12, 1), (24, 5), (24, 3), (7, 34), (18, 34), (18, 18), (18, 22), (23, 10), (13, 1), (21, 8), (8, 31), (3, 29), (17, 1), (2, 12), (28, 34), (3, 6), (19, 9), (20, 18), (0, 35), (11, 34), (33, 26), (15, 27), (34, 7), (14, 10), (6, 28), (22, 34), (10, 26), (1, 13), (29, 15), (10, 21), (16, 27), (26, 5), (3, 4), (7, 19), (5, 28), (10, 11), (15, 18), (19, 32), (30, 23), (19, 24), (2, 2), (27, 7), (23, 34), (1, 35), (0, 8), (1, 4), (33, 10), (1, 34), (16, 0), (30, 19), (0, 12), (18, 31), (25, 16), (6, 31), (18, 29), (17, 19), (6, 1), (5, 6), (18, 0), (21, 9), (17, 10), (31, 16), (4, 11), (20, 33), (27, 26), (11, 0), (21, 6), (1, 30), (2, 24), (22, 26), (32, 11), (28, 10), (6, 16), (25, 14), (13, 2), (16, 33), (31, 33), (29, 7), (5, 30), (22, 7), (4, 28), (22, 24), (20, 23), (9, 5), (27, 34), (31, 29), (28, 31), (13, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155445", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 17), (7, 31), (9, 28), (30, 28), (20, 24), (22, 16), (16, 8), (24, 4), (17, 0), (6, 7), (8, 17), (10, 31), (26, 18), (10, 20), (14, 18), (1, 10), (0, 29), (30, 14), (12, 28), (24, 0), (20, 11), (8, 27), (16, 22), (15, 4), (23, 18), (24, 17), (2, 24), (13, 9), (8, 25), (1, 12), (22, 0), (22, 21), (15, 1), (29, 22), (20, 25), (1, 22), (20, 6), (5, 11), (15, 20), (5, 27), (1, 23), (15, 14), (10, 21), (3, 29), (22, 27), (13, 17), (13, 1), (23, 6), (21, 23), (13, 30), (13, 19), (3, 14), (4, 24), (15, 27), (18, 4), (29, 15), (23, 31), (1, 15), (9, 23), (8, 30), (26, 17), (8, 20), (6, 14), (22, 30), (4, 4), (21, 31), (1, 29), (23, 3), (22, 7), (27, 2), (4, 7), (3, 20), (1, 25), (14, 17), (12, 1), (22, 19), (4, 9), (17, 18), (24, 31), (0, 10), (17, 28), (19, 2), (27, 28), (26, 11), (5, 3), (2, 25), (6, 12), (21, 15), (16, 27), (5, 18), (16, 3), (18, 28), (10, 12), (14, 3), (2, 7), (20, 20), (28, 7), (0, 24), (14, 15), (18, 9), (25, 29), (25, 12), (8, 21), (23, 19), (29, 18), (10, 1), (23, 7), (18, 15), (11, 11), (24, 19), (4, 2), (4, 0), (7, 16), (22, 5), (20, 22), (9, 19), (9, 18), (27, 12), (10, 2), (15, 30), (5, 15), (22, 17), (3, 8), (25, 4), (6, 28), (16, 0), (10, 18), (12, 14), (29, 12), (21, 20), (19, 22), (13, 11), (3, 0), (20, 31), (13, 21), (15, 17), (11, 23), (2, 18), (0, 21), (19, 20), (6, 29), (17, 12), (0, 30), (27, 15), (2, 17), (10, 4), (11, 25), (18, 8), (11, 30), (1, 7), (26, 25), (6, 11), (4, 14), (26, 20), (22, 25), (24, 27), (6, 4), (2, 4), (4, 28), (21, 26), (8, 28), (26, 16), (4, 16), (12, 6), (28, 31), (17, 31), (2, 1), (3, 5), (15, 25), (14, 16), (29, 19), (23, 10), (5, 24), (15, 5), (21, 13), (26, 22), (24, 28), (11, 5), (9, 24), (0, 27), (19, 25), (25, 8), (29, 7), (14, 0), (7, 20), (14, 12), (29, 21), (28, 6), (5, 25), (21, 11), (8, 31), (8, 8), (9, 21), (6, 13), (20, 0), (17, 25), (11, 24), (30, 8), (21, 24), (22, 8), (22, 26), (21, 2), (21, 5), (16, 21), (8, 23), (3, 27), (26, 21), (1, 31), (25, 21), (14, 13), (23, 30), (25, 28), (24, 26), (4, 20), (17, 11), (5, 4), (23, 24), (22, 9), (29, 0), (25, 11), (30, 0), (30, 9), (30, 25), (30, 10), (13, 24), (16, 24), (8, 7), (7, 13), (19, 9), (18, 11), (21, 8), (27, 22), (1, 20), (0, 25), (2, 5), (18, 17), (28, 17), (10, 7), (13, 31), (0, 20), (15, 6), (4, 25), (20, 7), (18, 25), (17, 13), (20, 21), (25, 24), (0, 5), (6, 20), (3, 28), (25, 14), (24, 16), (21, 14), (9, 0), (28, 12), (12, 22), (30, 29), (19, 28), (15, 31), (12, 25), (25, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "487200", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 24), (23, 34), (0, 5), (3, 34), (15, 0), (0, 23), (13, 25), (19, 35), (23, 27), (9, 13), (24, 13), (4, 31), (27, 12), (14, 28), (14, 4), (16, 6), (1, 10), (31, 14), (27, 21), (27, 0), (32, 19), (9, 15), (15, 26), (23, 11), (18, 25), (31, 20), (28, 1), (30, 2), (1, 0), (3, 3), (3, 14), (23, 29), (7, 0), (8, 21), (31, 2), (23, 4), (2, 5), (30, 13), (18, 27), (25, 22), (30, 4), (4, 30), (19, 1), (16, 27), (21, 32), (19, 34), (9, 33), (25, 18), (8, 0), (15, 19), (1, 21), (6, 8), (9, 25), (24, 31), (24, 25), (3, 7), (26, 10), (9, 12), (33, 33), (16, 29), (2, 23), (8, 20), (22, 35), (28, 17), (17, 11), (11, 35), (3, 20), (31, 35), (33, 31), (31, 9), (30, 20), (9, 14), (7, 6), (12, 4), (29, 8), (13, 7), (32, 4), (11, 29), (34, 12), (22, 9), (18, 24), (17, 12), (12, 11), (9, 21), (31, 4), (34, 0), (11, 27), (17, 35), (6, 1), (17, 34), (2, 2), (7, 11), (18, 34), (16, 18), (15, 9), (31, 33), (32, 22), (10, 20), (26, 27), (0, 29), (25, 21), (7, 18), (32, 5), (27, 27), (2, 32), (16, 0), (31, 32), (2, 17), (14, 24), (2, 27), (23, 9), (34, 17), (15, 21), (25, 8), (13, 18), (34, 10), (2, 15), (26, 5), (31, 19), (22, 6), (13, 34), (22, 32), (17, 31), (15, 8), (30, 22), (12, 32), (12, 3), (23, 35), (2, 29), (26, 31), (22, 8), (28, 13), (28, 3), (14, 25), (8, 14), (9, 7), (17, 25), (13, 0), (32, 1), (1, 35), (28, 22), (2, 18), (29, 34), (20, 9), (10, 27), (6, 32), (32, 17), (21, 24), (29, 1), (33, 24), (10, 32), (10, 18), (24, 27), (8, 32), (30, 12), (18, 11), (3, 24), (2, 33), (10, 8), (15, 13), (21, 6), (10, 12), (7, 25), (34, 21), (25, 13), (5, 19), (20, 32), (15, 11), (33, 3), (3, 18), (27, 20), (6, 12), (13, 29), (10, 16), (28, 29), (27, 7), (29, 25), (3, 27), (34, 15), (26, 9), (11, 21), (30, 18), (4, 25), (0, 20), (9, 8), (34, 23), (22, 15), (27, 1), (31, 24), (12, 5), (6, 20), (5, 22), (9, 24), (28, 30), (20, 19), (12, 31), (25, 17), (31, 0), (5, 0), (34, 7), (32, 21), (9, 28), (23, 20), (5, 13), (18, 26), (1, 17), (23, 13), (25, 6), (31, 16), (10, 1), (32, 14), (7, 32), (27, 35), (9, 2), (26, 2), (15, 27), (30, 11), (13, 4), (24, 9), (1, 20), (16, 16), (18, 35), (24, 3), (33, 26), (17, 0), (24, 6), (13, 30), (27, 30), (15, 5), (6, 17), (22, 1), (32, 32), (10, 35), (25, 1), (32, 26), (9, 16), (15, 33), (8, 16), (28, 9), (16, 31), (16, 17), (20, 33), (26, 30), (11, 16), (5, 9), (18, 23), (26, 4), (20, 21), (16, 32), (12, 20), (20, 28), (21, 17), (30, 26), (13, 17), (34, 27), (21, 1), (28, 2), (22, 16), (18, 30), (7, 13), (26, 0), (29, 13), (15, 20), (32, 20), (4, 27), (26, 15), (33, 28), (1, 30), (33, 20), (7, 8), (4, 6), (16, 3), (15, 7), (23, 0), (12, 28), (33, 5), (26, 35), (19, 3), (34, 9), (22, 33), (12, 0), (17, 23), (18, 20), (10, 5), (19, 5), (15, 18), (28, 6), (11, 25), (29, 0), (14, 26), (5, 21), (27, 32), (9, 20), (27, 15), (26, 32), (6, 11), (23, 7), (2, 24), (21, 31), (19, 18), (28, 15), (7, 23), (18, 6), (6, 16), (5, 24), (34, 5), (23, 5), (7, 9), (25, 34), (22, 7), (11, 12), (8, 6), (1, 13), (34, 2), (17, 13), (4, 20), (6, 14), (0, 30), (33, 4), (6, 29), (32, 9), (33, 14), (11, 10), (22, 22), (10, 3), (32, 12), (25, 33), (6, 28), (8, 1), (26, 11), (7, 3), (2, 9), (27, 4), (3, 25), (30, 30), (8, 17), (27, 11), (30, 19), (4, 2), (25, 9), (30, 16), (10, 19), (11, 9), (13, 31), (4, 18), (30, 3), (24, 12), (23, 24), (30, 35), (9, 35), (1, 25), (1, 5), (18, 22), (26, 1), (20, 11), (16, 1), (13, 11), (0, 15), (0, 12), (7, 17), (6, 27), (19, 25), (26, 21), (27, 17), (8, 15), (20, 17), (11, 7), (27, 8), (0, 10), (15, 22), (24, 20), (24, 19), (20, 34), (29, 24), (30, 15), (17, 29), (29, 7), (16, 23), (31, 3), (14, 35), (28, 19), (22, 30), (6, 7), (5, 18), (2, 13), (8, 19), (29, 10), (6, 9), (16, 7), (19, 12), (7, 2), (3, 11), (12, 21), (29, 15), (7, 10), (4, 11), (5, 34), (1, 9), (16, 10), (18, 9), (28, 8), (28, 20), (2, 11), (5, 31), (18, 32), (2, 22), (23, 32), (6, 5), (6, 3), (7, 29), (3, 32), (12, 17), (20, 18), (9, 0), (21, 19), (34, 1), (19, 2), (26, 22), (1, 33), (22, 28), (19, 20), (2, 21), (27, 26), (16, 13), (9, 4), (13, 20), (11, 33), (24, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206976", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 29), (25, 27), (28, 32), (20, 14), (7, 2), (3, 5), (29, 22), (4, 18), (24, 6), (11, 21), (13, 1), (31, 28), (30, 11), (7, 25), (32, 32), (30, 30), (2, 28), (24, 24), (13, 32), (4, 34), (30, 12), (14, 13), (16, 18), (8, 26), (7, 8), (0, 25), (6, 21), (8, 19), (24, 35), (24, 16), (24, 21), (12, 27), (30, 20), (17, 31), (21, 25), (11, 25), (22, 4), (25, 31), (22, 30), (14, 0), (3, 35), (8, 32), (18, 1), (24, 29), (3, 32), (7, 6), (32, 14), (24, 26), (24, 2), (2, 13), (1, 6), (4, 11), (28, 2), (27, 32), (11, 4), (20, 2), (18, 12), (5, 12), (29, 7), (11, 5), (18, 34), (2, 5), (28, 28), (17, 25), (21, 15), (25, 3), (16, 23), (11, 31), (17, 29), (26, 29), (11, 17), (30, 35), (13, 22), (16, 1), (19, 23), (10, 4), (14, 21), (28, 5), (22, 34), (15, 4), (28, 14), (22, 1), (14, 6), (7, 9), (23, 4), (5, 32), (23, 14), (20, 5), (19, 33), (28, 13), (10, 5), (11, 30), (32, 10), (26, 1), (11, 7), (27, 6), (30, 2), (8, 28), (4, 9), (27, 5), (13, 2), (6, 34), (23, 0), (15, 30), (2, 8), (24, 1), (19, 24), (15, 10), (32, 17), (32, 20), (5, 35), (7, 32), (14, 19), (2, 32), (3, 26), (20, 25), (8, 0), (13, 31), (8, 7), (21, 9), (31, 17), (16, 4), (18, 3), (29, 0), (31, 16), (20, 27), (12, 1), (21, 21), (31, 11), (2, 34), (20, 12), (27, 7), (31, 23), (6, 27), (15, 31), (8, 12), (15, 34), (9, 24), (0, 34), (21, 2), (15, 13), (28, 21), (10, 12), (14, 28), (20, 16), (26, 14), (3, 25), (10, 35), (12, 2), (1, 12), (12, 7), (9, 7), (28, 26), (29, 31), (24, 13), (17, 3), (17, 5), (23, 20), (9, 11), (20, 15), (22, 14), (26, 27), (23, 19), (12, 16), (2, 16), (21, 23), (1, 18), (7, 33), (6, 7), (8, 22), (5, 20), (11, 9), (9, 23), (8, 13), (27, 10), (6, 1), (4, 27), (12, 35), (32, 4), (23, 32), (9, 17), (12, 21), (4, 0), (10, 13), (4, 4), (22, 5), (6, 12), (1, 2), (32, 18), (17, 34), (27, 17), (13, 0), (17, 22), (13, 18), (22, 32), (15, 2), (25, 4), (0, 35), (2, 9), (6, 30), (7, 12), (14, 35), (19, 30), (24, 25), (25, 14), (4, 7), (19, 17), (25, 6), (4, 13), (15, 3), (25, 21), (11, 12), (3, 17), (18, 17), (3, 1), (31, 3), (23, 3), (10, 8), (8, 17), (15, 8), (4, 2), (27, 35), (2, 2), (4, 5), (1, 26), (0, 10), (17, 28), (11, 0), (11, 10), (24, 30), (18, 16), (32, 30), (15, 17), (31, 32), (18, 2), (10, 31), (27, 15), (21, 17), (14, 25), (30, 14), (0, 6), (15, 21), (18, 21), (28, 20), (3, 4), (25, 15), (4, 15), (20, 26), (19, 4), (10, 10), (5, 11), (2, 22), (18, 0), (7, 20), (32, 0), (3, 29), (3, 2), (10, 32), (1, 20), (31, 2), (25, 9), (20, 24), (22, 13), (9, 3), (6, 29), (30, 33), (6, 20), (0, 9), (30, 21), (16, 11), (30, 31), (1, 24), (7, 3), (26, 32), (4, 8), (21, 6), (21, 34), (24, 8), (30, 0), (26, 22), (3, 14), (18, 26), (16, 16), (2, 11), (19, 29), (27, 16), (18, 20), (18, 35), (12, 0), (26, 2), (1, 30), (29, 9), (22, 21), (27, 3), (12, 34), (11, 22), (4, 21), (21, 32), (6, 3), (1, 21), (5, 31), (28, 19), (23, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775170", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 32), (13, 33), (0, 26), (16, 25), (0, 28), (13, 11), (17, 2), (12, 13), (10, 2), (6, 15), (10, 36), (7, 8), (24, 9), (13, 26), (13, 16), (7, 20), (4, 35), (7, 22), (2, 32), (7, 29), (7, 13), (8, 24), (9, 19), (8, 32), (12, 16), (0, 3), (5, 35), (0, 20), (26, 37), (22, 0), (28, 6), (27, 24), (18, 26), (11, 25), (5, 31), (3, 6), (17, 30), (27, 34), (15, 21), (16, 19), (29, 23), (24, 4), (16, 0), (11, 13), (29, 10), (10, 20), (28, 29), (23, 17), (5, 14), (29, 26), (28, 21), (2, 11), (15, 8), (25, 21), (3, 20), (21, 20), (16, 5), (3, 29), (15, 12), (15, 24), (4, 0), (17, 6), (20, 5), (26, 4), (3, 27), (26, 26), (18, 29), (16, 15), (4, 32), (9, 11), (12, 6), (15, 16), (21, 26), (19, 14), (16, 2), (17, 23), (29, 9), (11, 28), (20, 31), (18, 13), (0, 11), (21, 1), (28, 16), (23, 1), (8, 27), (8, 28), (2, 13), (16, 35), (21, 5), (14, 37), (25, 19), (18, 37), (17, 4), (19, 24), (23, 3), (27, 31), (27, 20), (25, 12), (19, 0), (16, 3), (28, 13), (19, 7), (14, 15), (24, 25), (3, 32), (26, 23), (5, 37), (8, 10), (14, 29), (0, 19), (10, 34), (1, 8), (24, 20), (8, 11), (24, 28), (19, 1), (15, 36), (8, 18), (6, 6), (24, 15), (4, 18), (27, 7), (23, 8), (17, 36), (15, 33), (14, 8), (22, 11), (20, 17), (18, 10), (5, 13), (0, 29), (19, 18), (8, 1), (9, 5), (23, 24), (9, 23), (28, 28), (15, 1), (2, 24), (9, 6), (9, 21), (6, 28), (14, 17), (1, 36), (2, 9), (22, 22), (8, 14), (19, 16), (27, 0), (11, 14), (7, 23), (5, 28), (16, 14), (15, 7), (19, 26), (0, 4), (20, 35), (26, 27), (11, 8), (13, 32), (17, 18), (12, 35), (0, 34), (24, 1), (22, 21), (10, 8), (27, 9), (9, 28), (9, 3), (27, 1), (23, 9), (26, 8), (18, 24), (26, 18), (10, 4), (25, 3), (20, 37), (13, 13), (13, 14), (3, 24), (0, 17), (22, 6), (6, 32), (18, 21), (6, 10), (28, 3), (12, 4), (15, 11), (5, 9), (21, 34), (26, 19), (29, 4), (2, 16), (9, 27), (10, 30), (14, 32), (20, 11), (24, 36), (21, 7), (2, 8), (7, 18), (19, 21), (5, 16), (14, 3), (3, 30), (26, 28), (8, 4), (25, 5), (27, 33), (6, 29), (19, 34), (29, 24), (3, 8), (19, 20), (17, 12), (11, 29), (17, 5), (5, 0), (5, 22), (6, 9), (22, 7), (22, 9), (19, 36), (0, 30), (11, 0), (12, 28), (3, 10), (12, 34), (16, 11), (4, 16), (24, 34), (27, 32), (25, 16), (20, 7), (13, 24), (25, 9), (14, 1), (16, 1), (16, 22), (6, 34), (22, 30), (27, 4), (18, 36), (21, 31), (7, 35), (21, 10), (24, 6), (14, 14), (27, 30), (2, 1), (0, 18), (12, 14), (6, 36), (25, 10), (13, 29), (28, 17), (21, 27), (25, 17), (4, 37), (12, 26), (21, 17), (8, 34), (1, 37), (26, 34), (6, 14), (3, 9), (12, 2), (28, 8), (5, 1), (2, 36), (19, 19), (19, 32), (21, 36), (4, 24), (1, 2), (1, 18), (27, 3), (10, 23), (14, 33), (20, 25), (10, 0), (10, 15), (21, 28), (9, 36), (18, 31), (18, 8), (7, 32), (28, 32), (24, 16), (23, 23), (28, 23), (10, 7), (26, 22), (3, 28), (14, 19), (9, 16), (9, 34), (15, 9), (13, 22), (5, 25), (3, 12), (12, 10), (23, 30), (20, 3), (19, 22), (16, 20), (7, 6), (27, 29), (11, 31), (14, 0), (11, 2), (15, 18), (20, 33), (15, 14), (19, 23), (6, 31), (4, 36), (13, 17), (21, 12), (12, 11), (5, 34), (9, 25), (26, 33), (7, 24), (21, 35), (20, 30), (20, 28), (15, 35), (5, 21), (23, 5), (21, 24), (19, 2), (25, 15), (24, 29), (19, 8), (16, 24), (12, 12), (8, 5), (16, 37), (1, 24), (0, 36), (19, 37), (27, 27), (29, 12), (14, 36), (7, 12), (2, 18), (19, 4), (8, 21), (11, 5), (27, 23), (28, 7), (20, 9), (6, 30), (3, 26), (0, 35), (7, 5), (17, 34), (22, 28), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715392", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 34), (5, 0), (9, 1), (31, 24), (33, 11), (13, 31), (21, 13), (26, 24), (32, 16), (29, 10), (17, 25), (15, 28), (4, 14), (5, 20), (35, 31), (8, 21), (4, 35), (30, 11), (23, 28), (28, 14), (12, 15), (27, 36), (2, 29), (5, 35), (1, 5), (1, 3), (14, 15), (18, 19), (12, 14), (10, 34), (6, 0), (13, 33), (4, 28), (26, 29), (16, 11), (19, 9), (28, 11), (23, 18), (34, 15), (11, 23), (8, 34), (10, 17), (22, 35), (6, 3), (26, 21), (21, 29), (27, 0), (2, 30), (23, 8), (30, 8), (23, 30), (12, 5), (19, 8), (12, 29), (27, 15), (13, 10), (10, 11), (19, 19), (27, 6), (10, 9), (30, 12), (25, 1), (13, 3), (5, 11), (14, 4), (0, 24), (25, 25), (26, 3), (35, 28), (25, 8), (3, 4), (13, 28), (17, 35), (29, 13), (8, 12), (29, 2), (0, 4), (30, 17), (21, 26), (15, 20), (28, 8), (12, 28), (3, 9), (2, 2), (6, 11), (33, 29), (4, 24), (35, 5), (29, 25), (1, 21), (28, 22), (25, 34), (5, 3), (29, 29), (16, 9), (7, 32), (12, 26), (22, 10), (23, 4), (31, 0), (5, 26), (33, 33), (17, 34), (34, 17), (26, 31), (23, 15), (30, 21), (8, 10), (32, 10), (18, 24), (1, 1), (19, 5), (23, 35), (21, 15), (20, 23), (17, 1), (17, 11), (33, 17), (18, 16), (18, 23), (24, 33), (5, 4), (12, 34), (3, 5), (13, 36), (25, 22), (18, 9), (0, 34), (27, 11), (0, 10), (7, 23), (18, 14), (22, 29), (9, 5), (2, 31), (34, 25), (32, 18), (8, 18), (3, 18), (20, 24), (5, 5), (26, 34), (22, 24), (29, 18), (32, 17), (18, 20), (31, 7), (11, 31), (2, 36), (8, 1), (9, 6), (19, 6), (21, 18), (17, 19), (33, 1), (3, 8), (34, 12), (30, 1), (16, 23), (9, 12), (32, 7), (33, 21), (16, 6), (27, 13), (3, 15), (15, 16), (2, 15), (4, 9), (16, 27), (34, 14), (28, 20), (28, 15), (34, 1), (8, 31), (31, 22), (23, 16), (8, 4), (3, 12), (5, 32), (1, 36), (25, 27), (3, 26), (34, 5), (8, 33), (14, 27), (13, 0), (11, 30), (7, 12), (5, 36), (5, 24), (17, 33), (35, 0), (0, 28), (7, 18), (15, 30), (28, 19), (26, 5), (22, 19), (22, 28), (24, 6), (26, 18), (21, 33), (29, 14), (17, 10), (5, 2), (22, 8), (11, 2), (28, 21), (31, 17), (4, 31), (29, 30), (26, 22), (1, 16), (28, 17), (16, 35), (23, 34), (34, 34), (1, 22), (20, 18), (18, 17), (8, 32), (3, 20), (11, 25), (20, 26), (15, 34), (29, 33), (15, 22), (14, 20), (28, 7), (5, 15), (29, 4), (17, 27), (28, 2), (35, 26), (27, 21), (33, 23), (19, 32), (24, 23), (32, 33), (20, 15), (34, 16), (26, 13), (33, 9), (7, 35), (2, 9), (7, 17), (7, 36), (28, 25), (4, 22), (8, 11), (34, 26), (17, 18), (19, 1), (34, 9), (1, 15), (10, 21), (9, 23), (21, 22), (27, 23), (23, 17), (20, 2), (5, 29), (7, 2), (27, 14), (3, 21), (26, 15), (22, 15), (19, 30), (34, 32), (10, 19), (12, 4), (10, 20), (25, 29), (4, 7), (1, 19), (35, 24), (28, 36), (32, 26), (15, 35), (31, 25), (12, 9), (3, 28), (34, 18), (22, 3), (3, 17), (0, 2), (24, 19), (12, 25), (21, 32), (21, 12), (25, 11), (30, 27), (13, 15), (1, 11), (17, 20), (23, 26), (12, 22), (27, 22), (32, 14), (19, 17), (31, 1), (6, 13), (28, 32), (23, 2), (10, 28), (27, 1), (14, 0), (31, 23), (8, 0), (24, 18), (6, 21), (13, 20), (8, 30), (24, 32), (35, 20), (29, 5), (12, 11), (24, 35), (21, 20), (1, 12), (26, 36), (9, 19), (35, 34), (19, 21), (6, 1), (0, 26), (30, 26), (20, 17), (16, 8), (20, 14), (27, 31), (6, 28), (31, 34), (1, 9), (32, 32), (33, 30), (32, 21), (23, 13), (7, 6), (18, 26), (2, 12), (14, 25), (8, 6), (12, 35), (35, 12), (32, 36), (9, 3), (18, 15), (13, 16), (6, 23), (26, 2), (0, 15), (0, 36), (14, 3), (10, 32), (7, 3), (19, 10), (35, 13), (30, 0), (4, 19), (17, 8), (29, 24), (28, 35), (23, 5), (24, 12), (20, 7), (4, 23), (12, 0), (7, 26), (7, 14), (31, 4), (17, 24), (19, 29), (35, 22), (5, 16), (33, 28), (8, 2), (21, 3), (0, 30), (13, 14), (8, 8), (34, 2), (20, 34), (4, 17), (25, 4), (35, 25), (18, 6), (28, 10), (0, 14), (9, 17), (23, 25), (18, 13), (9, 22), (24, 21), (14, 9), (14, 28), (32, 24), (1, 24), (15, 32), (31, 5), (26, 14), (31, 33), (30, 3), (17, 2), (6, 10), (26, 16), (14, 6), (25, 26), (28, 28), (24, 5), (13, 13), (9, 11), (28, 31), (13, 23), (21, 21), (16, 28), (16, 31), (17, 16), (10, 36), (1, 2), (8, 23), (29, 27), (23, 1), (0, 32), (29, 35), (2, 6), (34, 27), (6, 22), (11, 28), (29, 26), (34, 7), (9, 34), (14, 32), (35, 2), (29, 0), (3, 19), (33, 22), (16, 18), (2, 24), (13, 19), (27, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706860", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 29), (26, 24), (10, 8), (23, 14), (4, 32), (11, 6), (31, 28), (23, 5), (29, 8), (6, 0), (21, 19), (10, 14), (31, 4), (7, 2), (11, 13), (22, 10), (5, 1), (28, 17), (24, 21), (4, 6), (16, 16), (6, 21), (20, 9), (0, 6), (24, 27), (12, 31), (15, 5), (26, 16), (29, 11), (28, 13), (19, 18), (14, 17), (29, 30), (18, 8), (12, 0), (25, 20), (1, 21), (4, 23), (11, 28), (3, 27), (1, 12), (32, 26), (31, 24), (7, 6), (33, 21), (10, 31), (32, 17), (20, 18), (1, 0), (6, 11), (18, 32), (0, 22), (19, 26), (4, 2), (30, 11), (31, 12), (15, 19), (25, 32), (10, 9), (32, 4), (14, 0), (5, 3), (8, 30), (29, 19), (20, 1), (3, 20), (23, 4), (5, 4), (14, 16), (21, 12), (3, 33), (31, 25), (5, 18), (17, 5), (17, 10), (27, 8), (22, 33), (3, 9), (11, 29), (11, 31), (15, 17), (3, 21), (26, 12), (7, 27), (22, 22), (28, 25), (18, 3), (11, 33), (29, 3), (18, 26), (15, 2), (22, 16), (9, 16), (13, 21), (20, 11), (25, 33), (26, 26), (18, 13), (27, 25), (3, 23), (31, 10), (28, 24), (20, 30), (17, 20), (23, 12), (14, 8), (5, 28), (26, 3), (27, 23), (0, 12), (2, 11), (10, 24), (10, 29), (7, 7), (14, 5), (21, 17), (35, 17), (30, 16), (33, 13), (31, 19), (10, 19), (1, 17), (7, 8), (20, 7), (11, 8), (1, 8), (23, 27), (29, 22), (34, 25), (31, 14), (27, 1), (28, 28), (20, 21), (11, 12), (19, 16), (18, 9), (13, 25), (25, 3), (1, 29), (10, 32), (29, 26), (19, 14), (22, 1), (25, 16), (15, 25), (29, 1), (30, 14), (0, 9), (26, 25), (3, 28), (35, 23), (4, 16), (10, 17), (22, 9), (0, 28), (13, 15), (23, 20), (2, 4), (27, 17), (30, 15), (29, 21), (14, 11), (10, 25), (34, 30), (21, 11), (3, 12), (33, 25), (20, 3), (17, 7), (17, 31), (23, 15), (5, 9), (33, 24), (0, 26), (31, 9), (28, 5), (12, 2), (23, 28), (1, 7), (16, 22), (33, 7), (1, 31), (23, 26), (8, 6), (26, 17), (8, 10), (25, 29), (18, 1), (30, 30), (2, 13), (31, 16), (29, 28), (32, 5), (4, 7), (3, 26), (23, 31), (32, 3), (4, 19), (10, 7), (32, 27), (23, 16), (23, 8), (24, 32), (27, 19), (12, 13), (18, 33), (23, 7), (9, 13), (7, 23), (35, 30), (20, 26), (34, 0), (30, 17), (1, 10), (20, 4), (12, 23), (34, 19), (12, 33), (17, 18), (29, 13), (19, 20), (12, 28), (2, 10), (23, 9), (29, 16), (4, 17), (15, 26), (13, 2), (15, 0), (35, 2), (35, 12), (16, 13), (33, 9), (31, 15), (23, 17), (32, 28), (35, 7), (32, 24), (5, 13), (14, 15), (2, 28), (35, 10), (32, 18), (6, 22), (15, 27), (11, 11), (29, 12), (26, 29), (2, 26), (21, 5), (13, 18), (15, 33), (16, 24), (32, 23), (15, 28), (29, 20), (32, 14), (6, 13), (13, 12), (23, 22), (28, 18), (5, 2), (27, 31), (32, 33), (22, 5), (2, 29), (9, 12), (24, 23), (29, 5), (19, 9), (33, 16), (25, 18), (2, 30), (8, 19), (24, 7), (21, 31), (22, 31), (30, 26), (16, 28), (9, 3), (14, 21), (14, 20), (9, 20), (2, 21), (10, 13), (0, 8), (25, 1), (7, 24), (33, 28), (27, 0), (3, 7), (19, 5), (18, 10), (29, 9), (27, 20), (0, 30), (5, 30), (3, 6), (23, 11), (34, 12), (10, 2), (7, 12), (21, 16), (6, 14), (29, 31), (25, 7), (4, 25), (6, 27), (16, 21), (8, 5), (2, 16), (1, 15), (33, 11), (16, 19), (12, 4), (14, 31), (27, 29), (6, 15), (28, 0), (6, 5), (15, 22), (7, 18), (14, 14), (10, 12), (18, 28), (33, 23), (13, 31), (25, 6), (3, 30), (12, 5), (27, 28), (13, 10), (9, 32), (12, 11), (13, 14), (3, 22), (6, 12), (7, 17), (9, 4), (24, 31), (34, 18), (26, 7), (19, 13), (6, 9), (7, 20), (33, 20), (22, 13), (25, 5), (8, 8), (32, 13), (25, 31), (14, 1), (19, 23), (24, 24), (17, 3), (25, 4), (35, 31), (14, 4), (17, 19), (24, 22), (19, 32), (15, 12), (4, 0), (2, 25), (14, 26), (29, 33), (35, 11), (26, 14), (30, 23), (18, 30), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "873600", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), 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), (29, 29), (32, 8), (15, 6), (30, 31), (34, 23), (20, 27), (32, 17), (37, 5), (16, 23), (32, 25), (12, 9), (30, 5), (14, 16), (26, 15), (37, 3), (8, 20), (26, 17), (18, 14), (18, 6), (12, 4), (29, 11), (2, 21), (16, 28), (32, 15), (7, 31), (19, 33), (4, 24), (31, 25), (36, 2), (13, 30), (7, 18), (16, 12), (14, 0), (24, 14), (14, 28), (6, 3), (1, 23), (21, 8), (4, 14), (22, 23), (2, 28), (21, 1), (18, 31), (17, 32), (35, 7), (5, 27), (13, 0), (13, 23), (20, 6), (35, 23), (34, 5), (5, 3), (16, 0), (30, 16), (7, 0), (10, 25), (1, 22), (28, 30), (22, 5), (25, 19), (12, 17), (18, 17), (5, 32), (30, 21), (3, 1), (30, 22), (27, 18), (26, 32), (31, 23), (26, 3), (18, 26), (19, 15), (16, 16), (18, 23), (7, 19), (13, 27), (15, 27), (35, 20), (30, 10), (35, 6), (25, 26), (26, 10), (16, 29), (30, 6), (29, 8), (13, 3), (7, 13), (20, 9), (38, 12), (0, 33), (14, 6), (17, 15), (17, 14), (30, 33), (21, 3), (18, 0), (2, 20), (26, 20), (34, 25), (14, 7), (33, 23), (32, 2), (27, 8), (29, 14), (29, 25), (13, 6), (11, 12), (5, 11), (25, 2), (27, 0), (5, 8), (23, 30), (32, 28), (9, 18), (29, 27), (32, 12), (33, 15), (30, 24), (17, 4), (33, 3), (11, 19), (23, 32), (17, 31), (17, 10), (35, 9), (15, 4), (22, 3), (29, 13), (15, 13), (16, 27), (13, 22), (32, 3), (18, 2), (2, 33), (23, 28), (6, 15), (15, 14), (24, 20), (9, 31), (6, 13), (3, 9), (11, 3), (23, 19), (16, 24), (20, 25), (8, 19), (20, 24), (4, 28), (3, 19), (31, 20), (5, 26), (25, 21), (8, 13), (21, 15), (15, 16), (28, 4), (10, 29), (2, 32), (11, 23), (35, 14), (4, 12), (28, 31), (17, 22), (4, 4), (14, 23), (31, 24), (5, 9), (20, 22), (17, 30), (14, 5), (36, 23), (9, 22), (17, 13), (1, 30), (5, 22), (9, 33), (0, 8), (35, 4), (28, 13), (17, 1), (27, 9), (19, 12), (38, 19), (38, 14), (18, 10), (4, 21), (33, 25), (25, 28), (11, 0), (30, 1), (1, 4), (0, 3), (27, 29), (6, 7), (38, 3), (21, 19), (17, 0), (21, 17), (28, 2), (24, 1), (25, 14), (17, 5), (38, 21), (9, 9), (31, 4), (9, 12), (18, 1), (21, 5), (1, 1), (19, 28), (33, 30), (16, 5), (17, 6), (19, 6), (38, 13), (36, 19), (9, 7), (38, 0), (19, 3), (34, 27), (30, 15), (29, 0), (34, 22), (27, 17), (16, 7), (28, 12), (13, 19), (28, 14), (7, 22), (28, 7), (0, 23), (16, 4), (12, 25), (21, 29), (38, 24), (36, 1), (33, 24), (18, 7), (37, 11), (5, 5), (0, 19), (18, 18), (6, 29), (35, 11), (24, 33), (1, 10), (24, 26), (4, 7), (7, 26), (7, 15), (24, 24), (25, 12), (15, 28), (20, 5), (10, 16), (8, 18), (23, 1), (36, 32), (23, 10), (35, 0), (26, 11), (29, 12), (6, 8), (20, 4), (9, 0), (21, 26), (0, 5), (12, 10), (8, 33), (6, 31), (38, 22), (30, 2), (4, 19), (1, 24), (19, 32), (2, 15), (23, 33), (19, 1), (32, 4), (19, 4), (4, 18), (9, 4), (29, 6), (35, 21), (23, 18), (23, 6), (16, 20), (37, 28), (23, 4), (21, 0), (5, 19), (20, 21), (2, 22), (26, 28), (25, 27), (17, 2), (31, 12), (26, 23), (28, 5), (29, 24), (24, 5), (10, 22), (26, 27), (18, 32), (27, 2), (21, 14), (3, 26), (34, 13), (22, 25), (29, 19), (0, 11), (28, 33), (21, 27), (28, 25), (32, 23), (8, 4), (3, 10), (15, 8), (32, 22), (38, 11), (8, 9), (16, 1), (34, 14), (37, 26), (21, 20), (15, 19), (5, 24), (6, 1), (21, 30), (0, 15), (22, 9), (13, 7), (24, 9), (22, 22), (26, 19), (37, 10), (11, 6), (34, 12), (9, 17), (37, 1), (8, 3), (37, 25), (10, 33), (36, 3), (20, 16), (0, 17), (2, 9), (1, 17), (32, 29), (6, 4), (11, 33), (22, 28), (8, 8), (19, 30), (24, 15), (22, 13), (38, 30), (22, 4), (32, 33), (22, 29), (0, 6), (31, 0), (34, 19), (18, 15), (3, 2), (15, 22), (38, 31), (3, 33), (1, 5), (17, 21), (1, 0), (17, 20), (29, 3), (15, 23), (19, 14), (15, 18), (27, 27), (1, 20), (7, 16), (12, 0), (8, 30), (8, 0), (25, 7), (12, 14), (33, 33), (10, 4), (8, 21), (6, 0), (36, 31), (25, 32), (20, 19), (36, 33), (34, 20), (0, 30), (7, 8), (10, 18), (13, 33), (35, 10), (33, 19), (29, 31), (14, 27), (2, 6), (21, 2), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726144", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), 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), (6, 29), (7, 14), (31, 17), (29, 19), (20, 21), (9, 8), (18, 4), (4, 24), (12, 15), (25, 21), (26, 5), (27, 21), (15, 3), (12, 14), (8, 26), (3, 26), (3, 1), (14, 3), (17, 21), (16, 14), (10, 16), (29, 29), (29, 22), (26, 21), (10, 26), (26, 11), (30, 16), (18, 13), (11, 10), (8, 5), (5, 11), (11, 12), (18, 18), (1, 0), (18, 6), (24, 17), (12, 11), (20, 7), (31, 6), (4, 23), (27, 11), (17, 16), (28, 11), (3, 12), (22, 4), (7, 2), (0, 13), (4, 9), (5, 3), (29, 12), (27, 2), (2, 27), (24, 8), (17, 24), (19, 9), (8, 25), (29, 14), (6, 12), (4, 17), (6, 28), (21, 1), (15, 11), (18, 16), (18, 14), (26, 23), (1, 19), (23, 0), (3, 20), (17, 5), (6, 3), (6, 6), (21, 12), (14, 2), (10, 13), (16, 7), (15, 6), (6, 2), (18, 19), (29, 16), (28, 0), (24, 1), (23, 30), (19, 18), (0, 28), (28, 5), (20, 27), (25, 10), (24, 11), (22, 14), (21, 21), (23, 16), (24, 2), (6, 7), (19, 0), (14, 20), (16, 13), (17, 0), (2, 24), (23, 29), (13, 10), (22, 26), (0, 4), (21, 17), (13, 28), (8, 16), (13, 19), (20, 0), (20, 23), (1, 6), (13, 22), (23, 24), (0, 2), (8, 12), (29, 0), (18, 22), (25, 11), (10, 10), (19, 11), (18, 25), (10, 5), (20, 1), (15, 21), (5, 18), (12, 18), (27, 4), (22, 0), (22, 28), (3, 29), (4, 0), (23, 19), (4, 26), (30, 9), (15, 23), (23, 14), (16, 15), (22, 21), (30, 7), (11, 22), (14, 18), (23, 7), (9, 17), (1, 24), (14, 30), (4, 8), (31, 25), (10, 3), (31, 29), (31, 28), (27, 20), (9, 9), (5, 10), (22, 18), (30, 23), (31, 14), (1, 4), (17, 22), (5, 5), (18, 30), (12, 17), (5, 9), (29, 24), (25, 25), (13, 21), (26, 1), (10, 14), (24, 13), (23, 4), (30, 24), (4, 25), (28, 18), (1, 10), (14, 23), (26, 30), (9, 26), (1, 25), (6, 10), (24, 19), (7, 10), (19, 19), (5, 12), (27, 16), (21, 29), (30, 1), (26, 2), (27, 30), (20, 8), (3, 30), (19, 2), (11, 23), (8, 6), (14, 28), (13, 2), (22, 20), (25, 4), (22, 29), (24, 22), (13, 18), (9, 1), (23, 27), (20, 19), (24, 15), (28, 14), (25, 2), (29, 13), (26, 17), (7, 5), (17, 29), (15, 17), (15, 18), (21, 2), (3, 0), (16, 0), (17, 19), (30, 25), (6, 13), (3, 4), (17, 6), (8, 0), (24, 9), (30, 14), (21, 0), (23, 10), (2, 5), (2, 7), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369432", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (4, 6), (8, 32), (36, 25), (13, 21), (20, 18), (24, 27), (30, 6), (18, 31), (27, 7), (22, 17), (9, 4), (14, 18), (18, 22), (8, 21), (6, 30), (16, 29), (31, 17), (6, 15), (22, 16), (19, 21), (21, 19), (25, 6), (21, 24), (28, 25), (32, 31), (23, 5), (31, 22), (2, 11), (11, 3), (37, 24), (31, 27), (14, 19), (34, 23), (31, 26), (22, 18), (11, 24), (16, 2), (1, 0), (17, 14), (31, 25), (24, 14), (22, 20), (5, 24), (13, 30), (5, 10), (27, 20), (19, 20), (26, 27), (30, 25), (1, 23), (15, 22), (1, 32), (10, 18), (20, 3), (34, 15), (10, 6), (19, 31), (17, 15), (5, 8), (13, 13), (13, 15), (19, 27), (10, 32), (35, 17), (8, 25), (24, 12), (32, 21), (19, 17), (2, 13), (20, 15), (16, 1), (1, 4), (17, 0), (14, 15), (22, 1), (15, 1), (17, 21), (21, 32), (5, 25), (22, 5), (37, 4), (30, 1), (12, 30), (34, 24), (0, 30), (14, 12), (1, 20), (16, 27), (6, 13), (33, 31), (32, 26), (13, 17), (15, 8), (10, 13), (34, 28), (18, 18), (14, 16), (12, 26), (4, 12), (36, 20), (9, 21), (4, 5), (29, 13), (9, 22), (31, 7), (12, 6), (14, 14), (24, 11), (28, 22), (23, 21), (28, 3), (37, 14), (28, 9), (6, 16), (17, 13), (22, 28), (9, 19), (13, 19), (6, 27), (0, 6), (34, 8), (8, 31), (37, 20), (36, 12), (27, 1), (25, 22), (0, 27), (14, 20), (31, 14), (26, 0), (28, 19), (4, 22), (35, 27), (30, 12), (11, 30), (0, 11), (24, 26), (18, 1), (6, 22), (19, 3), (26, 28), (11, 27), (9, 20), (20, 0), (24, 10), (9, 3), (29, 30), (29, 11), (32, 25), (4, 11), (27, 6), (3, 4), (6, 31), (3, 31), (6, 12), (2, 8), (4, 28), (15, 32), (30, 26), (32, 11), (1, 16), (8, 30), (37, 29), (3, 28), (12, 4), (3, 0), (32, 23), (3, 32), (22, 7), (20, 27), (33, 18), (21, 17), (10, 23), (33, 2), (7, 5), (8, 13), (34, 20), (12, 22), (16, 9), (23, 14), (15, 5), (26, 17), (3, 7), (18, 20), (9, 30), (1, 12), (8, 0), (18, 5), (14, 4), (15, 21), (36, 23), (31, 32), (23, 25), (11, 5), (26, 1), (33, 14), (32, 9), (35, 16), (14, 28), (11, 19), (31, 15), (29, 18), (29, 32), (23, 13), (28, 11), (22, 24), (25, 32), (26, 26), (18, 0), (27, 30), (21, 29), (27, 14), (14, 11), (32, 14), (23, 4), (16, 26), (27, 32), (36, 6), (15, 20), (17, 19), (12, 23), (15, 16), (27, 3), (21, 14), (34, 4), (32, 16), (23, 6), (27, 13), (4, 32), (1, 13), (23, 2), (2, 4), (26, 32), (8, 27), (12, 19), (34, 12), (28, 16), (28, 27), (13, 29), (20, 2), (10, 22), (13, 20), (15, 9), (24, 7), (10, 27), (8, 19), (9, 10), (7, 16), (12, 24), (1, 26), (15, 24), (5, 23), (9, 29), (22, 21), (11, 16), (6, 10), (30, 9), (37, 8), (21, 12), (36, 5), (21, 21), (35, 19), (33, 29), (17, 23), (3, 1), (25, 15), (2, 31), (14, 3), (22, 13), (9, 32), (17, 24), (28, 32), (32, 17), (0, 15), (27, 2), (7, 14), (21, 26), (15, 7), (15, 19), (13, 27), (23, 7), (12, 14), (28, 17), (26, 13), (10, 14), (6, 4), (7, 0), (37, 5), (7, 23), (32, 5), (37, 25), (11, 1), (18, 32), (35, 0), (27, 21), (20, 7), (7, 6), (28, 5), (24, 30), (13, 28), (19, 30), (14, 24), (14, 7), (11, 18), (9, 18), (14, 9), (12, 10), (2, 17), (9, 31), (15, 4), (21, 18), (9, 13), (2, 1), (15, 28), (4, 2), (35, 1), (26, 6), (5, 22), (36, 16), (34, 32), (20, 32), (0, 32), (1, 9), (21, 13), (19, 14), (12, 28), (4, 4), (35, 8), (5, 14), (33, 22), (16, 31), (21, 5), (34, 0), (25, 4), (33, 28), (24, 1), (30, 4), (10, 5), (33, 5), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "612360", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 0), (4, 15), (2, 13), (28, 9), (19, 19), (4, 18), (0, 30), (10, 29), (2, 28), (12, 7), (11, 10), (19, 3), (22, 29), (11, 1), (9, 16), (8, 31), (5, 35), (17, 25), (13, 12), (29, 6), (9, 17), (18, 23), (5, 19), (10, 21), (10, 27), (4, 14), (5, 12), (6, 28), (0, 10), (3, 24), (10, 17), (26, 27), (25, 2), (29, 22), (9, 26), (0, 4), (8, 24), (23, 28), (21, 10), (11, 24), (27, 29), (16, 30), (27, 10), (11, 18), (14, 5), (9, 6), (2, 1), (3, 17), (16, 19), (11, 30), (24, 24), (21, 4), (16, 28), (6, 27), (17, 34), (10, 33), (14, 0), (21, 16), (20, 14), (7, 24), (15, 4), (7, 26), (10, 9), (28, 15), (19, 6), (0, 35), (4, 1), (8, 34), (16, 3), (3, 34), (16, 6), (24, 22), (9, 3), (10, 28), (26, 20), (15, 2), (17, 20), (10, 24), (0, 7), (13, 7), (8, 0), (17, 24), (6, 34), (10, 26), (16, 8), (5, 34), (20, 29), (25, 27), (27, 18), (15, 0), (19, 33), (17, 35), (5, 25), (22, 22), (16, 2), (6, 32), (17, 2), (21, 20), (20, 24), (8, 6), (13, 13), (5, 17), (1, 1), (2, 3), (8, 21), (9, 25), (27, 17), (19, 0), (2, 8), (17, 0), (4, 23), (2, 24), (23, 25), (9, 8), (2, 23), (6, 22), (2, 31), (2, 0), (0, 26), (14, 35), (19, 9), (18, 17), (13, 26), (21, 19), (18, 10), (1, 27), (8, 9), (1, 7), (3, 26), (24, 33), (1, 9), (27, 14), (10, 15), (8, 17), (16, 0), (4, 32), (9, 32), (9, 34), (25, 15), (15, 22), (13, 34), (13, 3), (14, 11), (24, 16), (5, 0), (10, 22), (15, 7), (14, 12), (26, 13), (8, 35), (16, 9), (26, 19), (20, 15), (29, 23), (20, 12), (4, 21), (23, 27), (12, 9), (25, 12), (26, 28), (12, 15), (24, 5), (20, 23), (19, 32), (14, 7), (7, 18), (0, 19), (3, 30), (25, 21), (22, 17), (20, 3), (25, 6), (16, 16), (10, 0), (17, 8), (29, 1), (9, 27), (5, 8), (29, 3), (28, 20), (26, 32), (16, 12), (11, 13), (29, 4), (25, 10), (24, 26), (1, 21), (0, 17), (28, 27), (20, 28), (15, 35), (17, 32), (13, 20), (3, 1), (1, 30), (18, 29), (13, 10), (15, 8), (28, 13), (18, 16), (19, 34), (19, 23), (8, 2), (1, 28), (26, 5), (4, 4), (2, 26), (20, 18), (26, 25), (26, 21), (9, 9), (23, 14), (25, 1), (29, 28), (8, 7), (16, 27), (13, 2), (9, 1), (21, 5), (7, 17), (4, 11), (7, 35), (2, 17), (9, 30), (4, 5), (6, 21), (5, 22), (21, 15), (2, 7), (23, 0), (17, 19), (16, 4), (24, 21), (20, 8), (7, 2), (19, 31), (23, 35), (4, 25), (24, 9), (22, 7), (14, 13), (25, 24), (7, 21), (10, 16), (29, 14), (1, 2), (15, 32), (21, 30), (18, 7), (21, 21), (2, 25), (20, 2), (9, 7), (23, 8), (22, 19), (11, 34), (11, 19), (19, 7), (2, 16), (23, 10), (6, 29), (12, 34), (13, 4), (3, 27), (26, 16), (15, 5), (24, 25), (20, 0), (22, 31), (16, 1), (22, 23), (22, 30), (1, 26), (14, 22), (28, 21), (21, 11), (18, 12), (27, 1), (6, 30), (22, 28), (3, 5), (20, 27), (2, 5), (26, 17), (11, 26), (25, 3), (17, 31), (21, 27), (1, 29), (21, 12), (25, 34), (15, 27), (3, 22), (27, 22), (25, 23), (18, 25), (24, 29), (7, 15), (1, 15), (11, 0), (0, 8), (25, 22), (11, 28), (8, 32), (7, 33), (19, 12), (3, 14), (27, 21), (8, 28), (18, 31), (0, 18), (4, 8), (17, 14), (24, 23), (14, 8), (7, 6), (18, 13), (11, 25), (12, 21), (9, 5), (14, 19), (0, 29), (20, 5), (29, 26), (4, 30), (15, 33), (16, 23), (27, 8), (15, 1), (28, 10), (19, 1), (0, 25), (17, 27), (19, 10), (21, 9), (5, 3), (4, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "934416", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 13), (22, 11), (16, 38), (31, 28), (26, 17), (23, 18), (30, 28), (11, 37), (7, 12), (12, 35), (28, 29), (17, 18), (10, 38), (16, 32), (28, 2), (3, 18), (13, 25), (8, 1), (30, 38), (24, 22), (15, 12), (8, 27), (27, 7), (30, 4), (23, 1), (13, 17), (10, 5), (0, 26), (15, 18), (6, 18), (21, 13), (28, 28), (18, 9), (20, 28), (7, 4), (29, 32), (3, 11), (8, 28), (5, 36), (27, 22), (8, 22), (1, 29), (13, 33), (10, 26), (21, 14), (21, 22), (27, 2), (3, 34), (21, 26), (12, 10), (1, 10), (4, 21), (29, 28), (10, 34), (28, 24), (2, 0), (23, 21), (19, 36), (5, 12), (5, 29), (22, 12), (6, 32), (18, 19), (11, 38), (28, 6), (19, 14), (21, 29), (2, 25), (14, 30), (29, 6), (3, 7), (8, 26), (31, 13), (5, 28), (17, 0), (26, 8), (3, 37), (8, 37), (2, 33), (22, 29), (8, 13), (6, 7), (18, 1), (9, 8), (19, 15), (16, 9), (23, 0), (10, 13), (30, 25), (15, 26), (29, 24), (13, 23), (28, 27), (7, 37), (20, 13), (3, 9), (16, 17), (4, 33), (30, 1), (10, 14), (26, 3), (6, 15), (21, 35), (28, 34), (19, 26), (16, 30), (18, 3), (15, 28), (27, 37), (9, 24), (27, 33), (27, 4), (25, 20), (22, 36), (25, 34), (12, 18), (15, 0), (4, 30), (18, 8), (28, 10), (29, 31), (26, 29), (18, 23), (28, 13), (24, 36), (26, 5), (11, 4), (5, 18), (0, 13), (7, 31), (27, 9), (26, 35), (30, 18), (10, 6), (4, 37), (27, 12), (14, 5), (21, 19), (26, 36), (3, 24), (1, 23), (14, 38), (25, 18), (30, 37), (8, 10), (17, 4), (14, 16), (0, 31), (14, 31), (12, 15), (28, 8), (13, 22), (19, 17), (11, 23), (27, 8), (28, 30), (28, 0), (4, 18), (4, 28), (24, 24), (29, 25), (20, 21), (4, 1), (21, 17), (15, 5), (21, 37), (0, 37), (28, 16), (9, 0), (24, 31), (20, 5), (6, 14), (8, 3), (17, 13), (3, 21), (25, 19), (30, 11), (31, 24), (19, 0), (11, 30), (2, 12), (5, 34), (2, 24), (1, 16), (21, 20), (14, 23), (17, 31), (18, 2), (19, 24), (11, 31), (17, 25), (12, 9), (30, 13), (12, 30), (1, 7), (11, 33), (26, 20), (8, 2), (27, 10), (1, 25), (29, 38), (10, 11), (18, 13), (15, 30), (17, 35), (31, 25), (26, 31), (4, 29), (12, 25), (17, 19), (23, 2), (26, 34), (13, 34), (24, 8), (25, 35), (15, 9), (29, 29), (7, 33), (0, 7), (14, 37), (23, 24), (6, 10), (27, 29), (4, 8), (23, 16), (16, 25), (8, 19), (19, 13), (20, 15), (2, 17), (2, 2), (0, 4), (31, 9), (0, 1), (22, 25), (16, 1), (8, 15), (19, 6), (16, 34), (31, 31), (19, 25), (30, 2), (21, 36), (30, 9), (5, 11), (5, 0), (1, 27), (11, 20), (31, 23), (22, 17), (31, 7), (17, 23), (20, 11), (25, 32), (17, 32), (25, 17), (3, 15), (18, 11), (12, 11), (22, 18), (1, 19), (23, 20), (27, 21), (7, 7), (8, 34), (22, 15), (11, 3), (30, 34), (19, 3), (0, 30), (8, 29), (18, 34), (16, 15), (24, 34), (20, 9), (20, 8), (25, 14), (13, 15), (30, 35), (9, 21), (13, 16), (22, 38), (21, 32), (4, 12), (23, 6), (12, 19), (19, 2), (21, 16), (8, 18), (24, 4), (1, 35), (13, 37), (9, 30), (7, 22), (19, 11), (18, 15), (30, 24), (3, 19), (16, 18), (25, 1), (17, 7), (23, 30), (9, 7), (16, 10), (7, 3), (8, 7), (20, 26), (1, 17), (25, 33), (15, 2), (31, 30), (25, 37), (5, 35), (15, 38), (5, 31), (4, 0), (3, 30), (21, 24), (0, 6), (27, 32), (29, 4), (14, 12), (11, 28), (11, 8), (15, 22), (7, 13), (9, 29), (10, 18), (20, 3), (15, 1), (27, 26), (12, 33), (25, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "969000", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 2), (13, 1), (8, 5), (15, 12), (6, 21), (1, 26), (12, 9), (9, 11), (27, 19), (15, 28), (14, 14), (19, 27), (13, 24), (23, 12), (15, 29), (17, 26), (8, 16), (7, 2), (22, 19), (28, 13), (12, 10), (20, 15), (27, 5), (7, 7), (17, 18), (8, 6), (2, 16), (10, 10), (11, 5), (13, 23), (21, 20), (22, 14), (9, 1), (15, 27), (2, 10), (7, 14), (18, 9), (12, 20), (12, 3), (18, 0), (27, 23), (26, 4), (7, 21), (21, 1), (21, 16), (18, 23), (20, 13), (17, 2), (22, 8), (10, 19), (21, 24), (1, 11), (20, 29), (12, 29), (5, 1), (29, 3), (26, 23), (2, 24), (11, 1), (4, 9), (10, 8), (21, 12), (7, 17), (8, 1), (26, 14), (4, 5), (8, 7), (6, 9), (26, 18), (25, 11), (21, 6), (21, 5), (20, 25), (4, 6), (23, 29), (11, 28), (27, 25), (21, 10), (17, 6), (20, 2), (26, 13), (14, 28), (23, 5), (1, 12), (9, 2), (14, 21), (4, 19), (15, 9), (15, 16), (29, 15), (10, 26), (24, 25), (19, 2), (22, 6), (29, 4), (1, 10), (26, 21), (20, 24), (8, 0), (17, 11), (25, 15), (8, 20), (23, 13), (28, 17), (16, 20), (16, 1), (10, 28), (27, 8), (14, 20), (11, 10), (18, 26), (9, 27), (3, 16), (25, 19), (13, 15), (27, 18), (3, 23), (11, 3), (10, 22), (6, 11), (15, 5), (8, 2), (21, 4), (19, 0), (5, 0), (21, 18), (5, 7), (10, 2), (9, 29), (11, 8), (2, 15), (6, 4), (9, 19), (4, 4), (4, 29), (0, 28), (29, 0), (27, 9), (4, 14), (4, 15), (8, 9), (27, 20), (26, 27), (5, 6), (10, 16), (19, 12), (17, 5), (8, 21), (18, 15), (9, 14), (7, 6), (25, 4), (8, 15), (23, 10), (23, 15), (12, 26), (4, 20), (0, 29), (7, 20), (29, 24), (0, 8), (14, 27), (11, 18), (2, 21), (24, 20), (13, 28), (8, 29), (1, 21), (17, 3), (23, 6), (26, 29), (15, 19), (0, 5), (25, 8), (16, 17), (26, 0), (6, 3), (23, 26), (22, 18), (17, 13), (23, 28), (0, 22), (21, 14), (7, 25), (11, 12), (26, 6), (9, 17), (4, 10), (13, 8), (2, 6), (8, 26), (12, 25), (14, 26), (2, 18), (5, 27), (10, 24), (3, 14), (5, 21), (8, 27), (9, 28), (25, 26), (23, 3), (19, 11), (28, 19), (15, 2), (15, 18), (10, 5), (17, 10), (13, 0), (18, 16), (8, 4), (5, 28), (22, 21), (0, 17), (26, 2), (21, 19), (9, 26), (19, 25), (2, 26), (1, 4), (23, 9), (9, 23), (19, 14), (3, 29), (8, 11), (5, 13), (28, 0), (9, 18), (20, 7), (6, 15), (24, 21), (16, 24), (2, 2), (29, 12), (15, 15), (21, 8), (27, 26), (3, 4), (4, 8), (7, 3), (18, 10), (25, 9), (27, 6), (4, 12), (10, 4), (29, 6), (13, 25), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "589380", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 16), (28, 11), (9, 9), (3, 19), (4, 2), (7, 11), (11, 14), (2, 28), (9, 4), (14, 7), (12, 20), (15, 17), (29, 13), (26, 5), (23, 13), (11, 25), (16, 14), (1, 29), (26, 24), (14, 0), (21, 26), (6, 3), (7, 14), (19, 1), (10, 21), (28, 6), (13, 5), (2, 4), (17, 11), (24, 1), (6, 27), (7, 13), (21, 5), (7, 4), (10, 23), (10, 26), (5, 3), (26, 9), (23, 1), (2, 8), (25, 7), (18, 17), (13, 14), (23, 15), (20, 2), (2, 15), (20, 17), (24, 23), (19, 9), (21, 17), (7, 0), (15, 23), (22, 28), (11, 4), (1, 24), (15, 14), (19, 23), (21, 21), (20, 22), (14, 28), (0, 24), (4, 11), (5, 12), (8, 24), (7, 29), (13, 7), (9, 6), (22, 16), (4, 22), (11, 19), (9, 20), (14, 24), (29, 21), (0, 15), (5, 6), (9, 15), (2, 5), (0, 4), (4, 18), (22, 14), (14, 10), (5, 17), (7, 20), (2, 18), (17, 1), (17, 16), (23, 16), (10, 0), (27, 20), (28, 12), (3, 0), (26, 19), (18, 27), (3, 6), (11, 13), (7, 27), (24, 19), (27, 1), (3, 18), (17, 2), (23, 20), (3, 24), (13, 6), (24, 10), (9, 29), (21, 16), (1, 0), (18, 12), (19, 29), (20, 6), (14, 27), (1, 26), (14, 1), (20, 1), (20, 21), (12, 2), (22, 21), (12, 11), (10, 15), (16, 19), (18, 21), (27, 11), (19, 15), (2, 12), (6, 22), (11, 9), (23, 12), (19, 27), (24, 27), (21, 28), (17, 5), (20, 19), (2, 2), (11, 1), (6, 16), (2, 26), (12, 7), (1, 23), (17, 22), (17, 26), (20, 26), (7, 25), (26, 18), (3, 22), (28, 22), (6, 10), (29, 17), (28, 21), (8, 4), (4, 7), (17, 4), (14, 17), (8, 5), (13, 19), (21, 1), (0, 22), (22, 3), (8, 13), (11, 3), (8, 23), (0, 26), (18, 1), (3, 17), (20, 5), (1, 15), (1, 25), (0, 13), (14, 6), (18, 5), (18, 28), (11, 20), (22, 23), (12, 8), (25, 21), (23, 14), (0, 25), (15, 8), (25, 18), (5, 19), (1, 17), (3, 15), (19, 2), (4, 9), (17, 20), (10, 9), (29, 9), (22, 7), (17, 29), (0, 14), (22, 6), (18, 20), (9, 17), (23, 11), (19, 0), (5, 2), (29, 1), (26, 21), (14, 11), (25, 22), (11, 0), (8, 18), (7, 23), (5, 21), (5, 8), (16, 20), (12, 23), (21, 13), (12, 16), (0, 20), (15, 22), (29, 3), (5, 11), (21, 19), (13, 29), (24, 6), (16, 4), (7, 26), (5, 14), (18, 15), (28, 13), (9, 25), (6, 23), (10, 12), (0, 5), (1, 10), (15, 1), (27, 23), (27, 18), (13, 11), (26, 29), (3, 20), (6, 28), (13, 3), (13, 4), (25, 0), (24, 14), (9, 22), (3, 8), (25, 11), (1, 20), (26, 28), (12, 3), (29, 8), (26, 2), (1, 22), (21, 9), (27, 15), (26, 3), (15, 25), (17, 27), (26, 8), (28, 15), (22, 24), (8, 2), (9, 5), (5, 29), (24, 15), (3, 23), (13, 17), (29, 6), (17, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "642600", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 11), (2, 31), (20, 8), (18, 25), (33, 26), (14, 11), (27, 11), (16, 31), (21, 24), (23, 18), (5, 2), (17, 25), (4, 17), (31, 4), (25, 31), (16, 20), (9, 14), (6, 25), (14, 13), (15, 14), (14, 24), (14, 4), (15, 12), (31, 26), (19, 13), (19, 24), (23, 29), (30, 18), (2, 28), (12, 0), (22, 29), (25, 21), (13, 6), (2, 1), (21, 16), (8, 11), (6, 22), (1, 29), (30, 2), (16, 15), (17, 17), (20, 13), (20, 24), (26, 26), (33, 22), (10, 30), (2, 16), (33, 25), (19, 12), (5, 22), (6, 13), (31, 12), (12, 30), (14, 26), (18, 3), (25, 22), (20, 20), (25, 16), (14, 3), (6, 29), (11, 8), (16, 11), (18, 27), (7, 29), (21, 3), (17, 13), (3, 29), (7, 18), (29, 17), (30, 14), (25, 5), (27, 10), (27, 15), (28, 23), (16, 0), (2, 30), (15, 30), (16, 12), (31, 2), (18, 7), (27, 0), (30, 3), (4, 2), (30, 24), (18, 22), (25, 28), (16, 13), (19, 28), (9, 0), (9, 7), (2, 20), (18, 24), (29, 30), (8, 28), (0, 1), (1, 16), (19, 3), (23, 23), (12, 15), (32, 19), (18, 14), (16, 27), (28, 17), (9, 22), (5, 7), (29, 6), (17, 23), (7, 25), (15, 28), (11, 31), (17, 28), (25, 19), (30, 26), (11, 29), (2, 15), (28, 15), (22, 19), (24, 26), (33, 13), (16, 4), (21, 5), (30, 7), (32, 29), (30, 15), (28, 18), (13, 21), (10, 25), (1, 5), (27, 21), (20, 9), (25, 8), (20, 12), (17, 14), (11, 16), (16, 21), (22, 14), (12, 10), (19, 2), (33, 14), (17, 11), (1, 10), (27, 1), (7, 13), (12, 4), (10, 24), (14, 30), (19, 5), (33, 24), (1, 7), (17, 15), (13, 9), (0, 17), (5, 0), (3, 20), (19, 14), (14, 15), (0, 13), (15, 3), (4, 5), (12, 9), (5, 5), (31, 27), (21, 15), (11, 4), (9, 1), (24, 13), (24, 4), (26, 10), (6, 15), (3, 13), (2, 4), (1, 14), (24, 23), (23, 2), (21, 26), (11, 9), (8, 31), (26, 2), (13, 16), (29, 20), (30, 31), (26, 15), (11, 18), (14, 19), (12, 22), (8, 21), (3, 7), (9, 23), (14, 22), (25, 20), (28, 22), (1, 1), (30, 4), (4, 0), (33, 27), (32, 16), (22, 12), (2, 18), (1, 4), (24, 21), (11, 22), (10, 14), (11, 10), (30, 0), (10, 31), (28, 1), (21, 6), (24, 15), (30, 17), (5, 14), (9, 11), (27, 23), (7, 14), (9, 31), (0, 29), (20, 2), (8, 17), (1, 20), (19, 9), (26, 17), (17, 24), (9, 25), (24, 8), (16, 19), (30, 12), (31, 15), (31, 9), (6, 6), (20, 14), (29, 13), (0, 6), (12, 27), (29, 7), (4, 16), (17, 31), (31, 0), (2, 11), (33, 12), (29, 12), (25, 10), (0, 10), (29, 1), (20, 21), (1, 12), (15, 27), (32, 24), (19, 20), (9, 21), (33, 18), (23, 16), (21, 14), (10, 20), (12, 26), (26, 31), (13, 4), (25, 15), (18, 8), (7, 20), (18, 12), (26, 5), (0, 4), (30, 1), (22, 24), (3, 27), (32, 3), (23, 31), (3, 12), (3, 4), (5, 25), (17, 8), (16, 8), (1, 26), (2, 12), (25, 7), (14, 20), (22, 13), (32, 30), (19, 29), (19, 30), (22, 21), (3, 9), (23, 20), (26, 13), (6, 21), (26, 20), (24, 1), (18, 6), (5, 6), (2, 9), (4, 31), (12, 23), (16, 28), (8, 1), (13, 14), (0, 19), (28, 20), (10, 7), (25, 18), (22, 3), (12, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998738", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 3), (1, 5), (26, 29), (8, 27), (16, 29), (1, 23), (8, 26), (7, 1), (31, 24), (13, 3), (8, 30), (28, 7), (30, 30), (5, 6), (2, 16), (33, 9), (20, 5), (11, 27), (35, 6), (2, 6), (24, 22), (18, 17), (24, 24), (34, 21), (21, 24), (18, 18), (13, 33), (29, 4), (15, 24), (27, 34), (28, 22), (35, 15), (6, 26), (22, 11), (19, 18), (14, 9), (9, 29), (22, 13), (28, 23), (3, 22), (5, 22), (35, 21), (28, 29), (28, 31), (1, 26), (26, 31), (19, 20), (8, 29), (18, 27), (21, 25), (11, 14), (13, 12), (28, 28), (0, 29), (21, 11), (23, 20), (17, 12), (7, 2), (11, 28), (24, 3), (17, 5), (6, 7), (4, 9), (17, 24), (32, 4), (3, 4), (20, 8), (4, 5), (25, 18), (31, 31), (33, 6), (9, 23), (1, 16), (1, 24), (27, 24), (19, 5), (1, 18), (13, 27), (4, 0), (18, 29), (18, 25), (27, 32), (7, 20), (4, 33), (16, 32), (34, 25), (8, 2), (9, 18), (15, 8), (32, 29), (30, 24), (0, 7), (0, 13), (34, 1), (18, 15), (12, 30), (29, 33), (35, 28), (9, 17), (31, 22), (35, 31), (18, 26), (26, 2), (19, 26), (11, 5), (5, 28), (10, 33), (9, 22), (5, 14), (22, 2), (30, 21), (33, 24), (20, 25), (27, 1), (21, 19), (31, 18), (21, 2), (23, 12), (22, 30), (19, 19), (22, 23), (30, 6), (3, 21), (1, 31), (32, 14), (7, 5), (30, 10), (19, 0), (27, 14), (34, 11), (25, 16), (32, 1), (9, 26), (26, 22), (7, 23), (10, 5), (25, 3), (26, 32), (26, 0), (8, 6), (9, 31), (12, 18), (26, 19), (22, 1), (35, 7), (3, 33), (17, 15), (30, 1), (5, 0), (15, 11), (32, 16), (24, 31), (31, 0), (9, 30), (8, 3), (20, 0), (7, 22), (34, 34), (4, 24), (31, 1), (28, 15), (35, 22), (0, 21), (4, 23), (0, 9), (3, 8), (11, 34), (29, 28), (32, 2), (13, 30), (23, 24), (2, 14), (24, 21), (15, 18), (22, 20), (23, 2), (22, 5), (12, 31), (31, 21), (33, 16), (25, 21), (14, 1), (34, 22), (2, 9), (14, 3), (13, 4), (6, 10), (28, 30), (14, 6), (34, 29), (16, 21), (17, 33), (24, 19), (26, 27), (4, 20), (15, 4), (18, 1), (32, 15), (4, 32), (17, 19), (23, 17), (0, 33), (16, 22), (1, 20), (7, 31), (26, 14), (23, 21), (15, 23), (20, 16), (19, 28), (28, 20), (30, 12), (19, 27), (21, 31), (33, 19), (13, 23), (4, 27), (0, 14), (20, 20), (3, 23), (22, 32), (11, 32), (18, 13), (0, 23), (29, 15), (6, 11), (3, 7), (25, 29), (33, 13), (17, 16), (15, 15), (2, 26), (29, 34), (20, 27), (0, 20), (4, 1), (14, 12), (17, 11), (19, 10), (15, 30), (14, 14), (16, 3), (27, 17), (35, 20), (17, 0), (0, 11), (28, 19), (20, 21), (14, 10), (27, 26), (18, 8), (28, 14), (20, 24), (19, 4), (19, 24), (9, 9), (12, 22), (25, 15), (25, 1), (26, 7), (23, 8), (22, 27), (22, 8), (16, 20), (2, 4), (21, 4), (16, 8), (11, 7), (21, 15), (9, 1), (11, 18), (16, 9), (17, 1), (26, 25), (17, 32), (16, 10), (17, 18), (0, 27), (25, 4), (14, 15), (10, 32), (11, 9), (11, 11), (5, 27), (31, 8), (23, 7), (30, 5), (24, 13), (29, 1), (25, 33), (32, 10), (28, 3), (35, 17), (4, 3), (22, 22), (4, 22), (12, 0), (5, 16), (17, 26), (2, 12), (3, 15), (5, 12), (26, 21), (20, 28), (25, 13), (22, 34), (5, 9), (33, 3), (16, 18), (13, 22), (33, 14), (9, 28), (20, 7), (4, 29), (25, 7), (3, 12), (27, 15), (18, 10), (26, 28), (4, 13), (16, 23), (27, 22), (35, 2), (14, 27), (6, 19), (21, 18), (27, 25), (14, 33), (23, 32), (29, 13), (22, 18), (12, 13), (32, 25), (33, 15), (33, 21), (4, 26), (8, 21), (0, 18), (28, 34), (16, 2), (9, 20), (12, 15), (32, 13), (4, 4), (14, 8), (29, 32), (1, 22), (4, 18), (0, 32), (32, 22), (23, 15), (2, 32), (7, 14), (5, 8), (17, 20), (21, 13), (16, 15), (11, 10), (18, 19), (16, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "643200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), 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), (3, 20), (3, 4), (9, 13), (7, 12), (19, 6), (27, 5), (9, 15), (30, 17), (9, 28), (10, 3), (0, 25), (29, 33), (13, 38), (2, 13), (8, 21), (9, 21), (5, 10), (24, 15), (26, 11), (22, 27), (27, 0), (20, 18), (20, 4), (10, 8), (9, 33), (27, 30), (27, 21), (23, 29), (11, 12), (11, 28), (9, 22), (2, 17), (5, 15), (22, 7), (29, 28), (30, 34), (11, 33), (2, 19), (1, 21), (9, 23), (11, 10), (11, 24), (21, 14), (21, 22), (18, 35), (11, 20), (6, 35), (17, 38), (14, 32), (9, 27), (28, 23), (6, 38), (13, 4), (6, 37), (25, 1), (23, 25), (18, 27), (12, 20), (5, 1), (1, 16), (16, 7), (13, 10), (2, 33), (15, 26), (20, 26), (12, 36), (28, 21), (10, 9), (13, 9), (1, 8), (14, 9), (12, 28), (3, 23), (4, 38), (7, 33), (21, 19), (23, 9), (21, 18), (6, 15), (20, 1), (21, 35), (30, 21), (15, 11), (14, 34), (3, 16), (1, 38), (5, 19), (6, 30), (14, 22), (2, 25), (8, 6), (25, 11), (1, 11), (10, 33), (17, 8), (25, 7), (12, 33), (5, 30), (0, 10), (6, 11), (12, 3), (29, 24), (30, 32), (0, 35), (29, 37), (5, 3), (12, 2), (10, 4), (3, 27), (5, 23), (2, 28), (3, 17), (11, 37), (30, 20), (26, 35), (16, 21), (2, 10), (0, 24), (28, 15), (9, 10), (14, 8), (7, 19), (30, 23), (25, 34), (22, 18), (28, 32), (3, 31), (6, 5), (24, 6), (0, 17), (10, 36), (17, 29), (3, 35), (13, 31), (28, 10), (0, 38), (3, 19), (21, 38), (16, 5), (21, 27), (25, 15), (13, 30), (27, 23), (7, 1), (18, 19), (29, 30), (0, 36), (2, 16), (20, 6), (2, 34), (7, 25), (14, 5), (24, 19), (18, 8), (9, 37), (16, 1), (29, 35), (10, 38), (25, 6), (22, 33), (19, 7), (18, 29), (19, 19), (7, 11), (10, 29), (16, 2), (28, 8), (30, 37), (18, 21), (8, 37), (4, 13), (15, 14), (24, 30), (18, 13), (10, 30), (17, 10), (15, 18), (20, 34), (11, 30), (0, 34), (4, 22), (29, 15), (27, 1), (0, 30), (11, 26), (24, 29), (3, 14), (6, 27), (5, 32), (9, 1), (27, 33), (20, 12), (16, 27), (12, 23), (10, 17), (22, 28), (13, 19), (24, 32), (9, 34), (19, 31), (26, 19), (4, 20), (1, 31), (1, 1), (7, 21), (17, 17), (0, 4), (6, 0), (17, 14), (18, 3), (21, 12), (7, 13), (1, 34), (2, 26), (2, 38), (28, 11), (21, 30), (11, 2), (14, 16), (13, 14), (20, 25), (11, 16), (4, 36), (22, 14), (28, 29), (2, 31), (29, 13), (19, 12), (4, 29), (27, 29), (5, 25), (15, 17), (8, 36), (17, 7), (7, 29), (17, 33), (22, 4), (23, 0), (19, 34), (5, 28), (7, 20), (24, 24), (8, 23), (10, 24), (4, 10), (20, 17), (16, 14), (29, 10), (23, 13), (2, 23), (22, 0), (17, 22), (0, 13), (26, 8), (27, 7), (23, 31), (23, 15), (17, 18), (19, 14), (8, 34), (14, 10), (18, 0), (14, 37), (4, 11), (2, 6), (3, 18), (4, 8), (18, 5), (24, 4), (11, 27), (11, 15), (12, 10), (8, 26), (23, 32), (30, 1), (16, 18), (18, 15), (25, 22), (17, 26), (3, 38), (22, 37), (11, 17), (0, 32), (25, 13), (9, 24), (4, 3), (27, 20), (15, 32), (17, 4), (18, 18), (12, 4), (12, 25), (2, 2), (29, 32), (12, 24), (17, 19), (25, 12), (2, 9), (14, 3), (14, 19), (18, 1), (0, 33), (8, 12), (16, 9), (25, 2), (10, 22), (11, 23), (21, 23), (19, 4), (17, 5), (16, 8), (25, 26), (13, 2), (4, 26), (18, 22), (22, 9), (23, 11), (3, 3), (25, 37), (17, 34), (17, 11), (2, 37), (12, 26), (29, 18), (14, 14), (13, 12), (6, 24), (17, 28), (28, 9), (22, 25), (5, 12), (10, 37), (8, 20), (5, 26), (17, 13), (19, 24), (14, 26), (11, 29), (22, 31), (10, 27), (2, 20), (19, 15), (16, 32), (5, 9), (13, 16), (3, 10), (13, 36), (3, 9), (27, 2), (0, 26), (14, 4), (18, 23), (29, 23), (15, 2), (29, 3), (11, 18), (15, 21), (19, 17), (24, 12), (0, 21), (23, 22), (16, 24), (13, 29), (1, 29), (21, 11), (22, 23), (4, 6), (20, 30), (1, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "861840", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (18, 32), (25, 33), (33, 21), (32, 11), (5, 5), (18, 17), (31, 19), (32, 7), (22, 19), (1, 27), (10, 23), (15, 29), (32, 20), (12, 11), (12, 13), (11, 18), (7, 11), (5, 16), (20, 31), (16, 0), (1, 21), (33, 32), (13, 30), (6, 22), (14, 7), (8, 22), (21, 0), (25, 24), (13, 17), (11, 4), (2, 16), (25, 4), (2, 21), (28, 12), (17, 2), (27, 9), (10, 26), (29, 11), (3, 14), (0, 5), (10, 31), (0, 16), (2, 3), (19, 2), (0, 33), (5, 18), (28, 3), (6, 14), (28, 17), (29, 12), (17, 24), (9, 4), (12, 14), (26, 32), (10, 24), (32, 21), (0, 9), (3, 28), (10, 10), (9, 14), (30, 22), (27, 8), (14, 21), (26, 19), (20, 13), (28, 8), (19, 15), (22, 24), (19, 20), (0, 14), (20, 23), (22, 20), (11, 19), (33, 23), (21, 4), (1, 8), (30, 13), (14, 31), (2, 30), (13, 20), (32, 5), (13, 0), (26, 0), (23, 7), (20, 6), (0, 31), (33, 10), (24, 20), (6, 33), (21, 8), (15, 9), (6, 7), (24, 31), (13, 26), (25, 21), (15, 22), (15, 25), (10, 16), (7, 5), (27, 19), (4, 15), (23, 6), (25, 27), (24, 17), (14, 23), (17, 28), (25, 25), (9, 30), (25, 0), (22, 34), (11, 9), (21, 16), (8, 21), (28, 6), (33, 20), (12, 7), (26, 30), (19, 27), (23, 4), (14, 12), (27, 20), (16, 12), (24, 23), (6, 27), (1, 16), (29, 31), (21, 27), (29, 27), (12, 25), (21, 33), (17, 27), (5, 15), (5, 26), (26, 16), (18, 30), (12, 8), (6, 8), (7, 22), (8, 14), (32, 1), (13, 29), (0, 13), (14, 3), (7, 2), (31, 29), (15, 12), (0, 3), (3, 24), (29, 15), (17, 3), (29, 14), (30, 16), (25, 14), (12, 30), (26, 12), (32, 23), (4, 7), (29, 20), (10, 34), (2, 4), (12, 34), (30, 27), (27, 32), (6, 29), (25, 32), (28, 28), (2, 31), (33, 25), (18, 12), (3, 26), (17, 11), (16, 6), (12, 16), (4, 24), (32, 25), (2, 19), (8, 6), (19, 0), (18, 0), (18, 13), (13, 24), (25, 9), (13, 32), (17, 31), (32, 15), (13, 19), (4, 12), (7, 20), (27, 29), (27, 11), (23, 18), (16, 25), (0, 32), (8, 7), (13, 8), (10, 3), (28, 11), (18, 19), (9, 27), (8, 30), (15, 17), (6, 20), (26, 6), (24, 18), (8, 20), (28, 13), (19, 30), (10, 15), (6, 15), (14, 27), (13, 7), (15, 18), (14, 26), (15, 1), (28, 7), (25, 1), (18, 6), (23, 27), (21, 10), (29, 32), (24, 16), (30, 23), (21, 2), (10, 4), (7, 13), (29, 3), (22, 30), (18, 14), (24, 28), (17, 19), (32, 27), (12, 1), (9, 33), (5, 25), (31, 24), (23, 20), (3, 22), (6, 24), (13, 10), (15, 0), (24, 10), (26, 4), (6, 9), (4, 18), (3, 4), (13, 23), (19, 18), (5, 24), (32, 0), (5, 9), (27, 23), (19, 33), (1, 13), (12, 5), (16, 21), (18, 2), (30, 25), (14, 22), (8, 10), (11, 28), (25, 11), (11, 10), (24, 12), (14, 6), (11, 31), (26, 23), (28, 30), (0, 25), (20, 5), (10, 2), (32, 13), (1, 6), (17, 6), (16, 14), (20, 7), (9, 1), (16, 9), (28, 20), (26, 5), (15, 24), (0, 10), (17, 18), (33, 12), (6, 11), (21, 30), (30, 18), (24, 29), (28, 21), (11, 33), (11, 26), (9, 13), (8, 0), (6, 13), (21, 15), (17, 21), (7, 1), (32, 6), (27, 0), (0, 1), (0, 12), (21, 14), (7, 29), (2, 22), (8, 16), (25, 12), (24, 24), (9, 11), (31, 2), (33, 33), (21, 25), (16, 34), (33, 22), (24, 0), (15, 31), (9, 17), (14, 11), (33, 16), (33, 9), (33, 1), (31, 22), (22, 23), (6, 30), (8, 31), (18, 8), (1, 7), (4, 2), (21, 20), (5, 31), (17, 7), (15, 15), (20, 14), (26, 27), (20, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "593628", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 20), (1, 17), (20, 27), (11, 6), (14, 20), (22, 4), (12, 29), (11, 26), (2, 27), (18, 22), (4, 3), (8, 17), (19, 29), (29, 6), (21, 7), (18, 1), (29, 22), (28, 1), (0, 27), (13, 10), (10, 2), (5, 20), (16, 3), (32, 28), (21, 17), (15, 26), (12, 18), (22, 24), (22, 18), (24, 10), (21, 16), (14, 5), (6, 11), (25, 3), (29, 25), (33, 16), (11, 19), (1, 15), (10, 16), (18, 21), (28, 3), (1, 3), (6, 16), (11, 9), (0, 20), (19, 14), (2, 14), (23, 0), (17, 8), (0, 23), (27, 23), (32, 10), (7, 28), (9, 25), (4, 4), (6, 4), (5, 14), (8, 22), (3, 7), (4, 21), (8, 29), (33, 24), (15, 27), (20, 2), (23, 28), (2, 10), (18, 11), (26, 13), (3, 21), (14, 6), (4, 1), (28, 14), (13, 3), (29, 23), (26, 3), (3, 20), (9, 20), (26, 25), (21, 6), (29, 13), (10, 22), (0, 16), (6, 20), (27, 4), (7, 11), (12, 3), (16, 24), (26, 8), (2, 21), (27, 20), (2, 3), (27, 16), (0, 5), (25, 1), (29, 21), (24, 14), (12, 15), (5, 22), (11, 23), (28, 26), (8, 28), (19, 15), (23, 26), (1, 5), (4, 27), (21, 22), (18, 26), (1, 12), (28, 11), (12, 21), (18, 15), (6, 25), (18, 14), (16, 17), (3, 9), (12, 9), (2, 7), (12, 16), (10, 28), (15, 12), (0, 13), (5, 11), (20, 16), (25, 2), (30, 4), (28, 6), (32, 0), (23, 3), (16, 4), (26, 11), (20, 9), (26, 17), (20, 1), (2, 28), (29, 8), (31, 10), (23, 27), (33, 1), (7, 10), (18, 12), (0, 29), (1, 9), (8, 1), (17, 0), (17, 11), (16, 20), (31, 2), (33, 5), (28, 13), (28, 24), (24, 1), (9, 5), (20, 17), (3, 13), (6, 1), (23, 12), (32, 5), (2, 0), (9, 15), (28, 27), (5, 8), (30, 13), (22, 29), (27, 14), (21, 28), (21, 12), (28, 21), (19, 19), (24, 4), (24, 2), (21, 24), (12, 19), (21, 18), (5, 18), (21, 8), (28, 4), (22, 0), (24, 13), (32, 26), (18, 23), (8, 2), (12, 6), (5, 21), (18, 25), (22, 11), (21, 10), (31, 25), (33, 8), (25, 6), (2, 24), (4, 8), (8, 25), (25, 22), (15, 28), (19, 28), (32, 16), (14, 4), (3, 8), (21, 14), (28, 16), (28, 12), (15, 4), (13, 26), (0, 11), (4, 19), (23, 11), (17, 24), (10, 12), (18, 29), (15, 1), (25, 28), (16, 7), (20, 15), (8, 3), (23, 21), (6, 17), (9, 29), (11, 20), (6, 22), (2, 15), (28, 15), (7, 6), (7, 2), (18, 10), (9, 2), (30, 29), (17, 13), (24, 15), (22, 8), (18, 28), (27, 18), (2, 19), (24, 12), (16, 25), (7, 21), (7, 14), (31, 28), (22, 25), (23, 29), (28, 20), (9, 23), (9, 0), (22, 16), (20, 14), (12, 11), (16, 29), (6, 13), (21, 26), (17, 21), (10, 26), (4, 25), (28, 29), (28, 8), (15, 25), (4, 10), (25, 0), (22, 19), (16, 21), (27, 17), (30, 6), (32, 13), (3, 3), (24, 3), (8, 15), (5, 3), (14, 0), (31, 16), (25, 25), (20, 11), (17, 22), (5, 1), (3, 27), (1, 6), (15, 24), (17, 25), (8, 11), (1, 0), (13, 17), (30, 24), (17, 3), (15, 0), (24, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "568620", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), 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), (14, 38), (29, 26), (3, 32), (5, 19), (8, 4), (26, 24), (21, 1), (22, 18), (25, 28), (17, 29), (22, 38), (16, 12), (17, 7), (28, 1), (8, 37), (17, 16), (15, 35), (15, 10), (3, 2), (33, 25), (2, 6), (11, 0), (25, 35), (31, 0), (19, 5), (16, 11), (20, 7), (21, 9), (22, 12), (34, 4), (22, 3), (18, 11), (15, 6), (13, 15), (1, 25), (25, 23), (17, 26), (10, 1), (21, 12), (0, 5), (28, 8), (18, 1), (2, 13), (21, 3), (5, 14), (24, 10), (5, 16), (31, 18), (10, 37), (24, 37), (0, 28), (15, 12), (23, 6), (24, 8), (10, 19), (7, 18), (5, 20), (14, 9), (18, 2), (16, 38), (19, 6), (6, 2), (7, 23), (20, 32), (25, 8), (19, 35), (16, 18), (22, 25), (14, 17), (3, 29), (24, 0), (0, 25), (8, 21), (16, 35), (31, 34), (6, 35), (18, 37), (2, 37), (21, 24), (35, 22), (24, 19), (26, 8), (10, 16), (26, 2), (12, 38), (16, 10), (6, 25), (23, 7), (0, 31), (29, 21), (22, 10), (9, 17), (10, 6), (20, 21), (4, 25), (12, 23), (5, 17), (19, 10), (20, 37), (19, 24), (34, 22), (35, 18), (4, 6), (6, 9), (4, 35), (25, 15), (2, 25), (31, 19), (9, 8), (1, 3), (14, 1), (4, 12), (28, 12), (13, 1), (18, 4), (25, 3), (9, 24), (11, 28), (12, 5), (33, 23), (22, 20), (8, 31), (19, 12), (23, 13), (32, 9), (18, 14), (2, 36), (5, 3), (10, 30), (23, 34), (12, 9), (13, 8), (29, 13), (3, 4), (10, 9), (5, 15), (21, 33), (26, 16), (33, 21), (4, 21), (23, 1), (34, 6), (19, 17), (27, 4), (2, 19), (4, 24), (15, 8), (0, 16), (4, 19), (6, 18), (7, 31), (8, 19), (35, 8), (25, 26), (13, 36), (20, 20), (33, 16), (3, 0), (20, 15), (15, 25), (2, 32), (28, 5), (33, 30), (19, 38), (5, 6), (32, 35), (16, 23), (26, 27), (5, 12), (32, 38), (2, 1), (15, 23), (17, 3), (28, 25), (3, 10), (6, 15), (9, 5), (35, 17), (19, 22), (9, 31), (26, 7), (11, 14), (33, 31), (11, 18), (28, 35), (20, 29), (19, 2), (11, 12), (29, 6), (27, 15), (30, 0), (19, 16), (24, 2), (32, 36), (32, 18), (31, 6), (20, 28), (2, 15), (4, 20), (28, 10), (16, 19), (10, 32), (17, 9), (8, 6), (7, 34), (4, 0), (14, 27), (4, 1), (17, 12), (28, 30), (1, 32), (16, 21), (29, 24), (29, 27), (31, 5), (32, 6), (34, 25), (34, 10), (22, 30), (13, 34), (9, 14), (12, 18), (1, 11), (19, 4), (19, 1), (17, 24), (16, 33), (22, 35), (20, 36), (27, 9), (14, 21), (5, 2), (28, 29), (20, 25), (31, 11), (1, 12), (25, 5), (20, 33), (19, 3), (0, 18), (5, 1), (4, 29), (28, 17), (28, 16), (29, 23), (18, 28), (32, 11), (10, 4), (16, 36), (9, 25), (8, 20), (14, 26), (22, 2), (8, 24), (30, 8), (22, 29), (11, 2), (1, 17), (30, 30), (10, 18), (0, 37), (22, 34), (22, 0), (8, 14), (8, 22), (4, 28), (30, 11), (17, 17), (2, 16), (22, 32), (23, 30), (30, 34), (11, 25), (14, 36), (12, 28), (5, 8), (22, 4), (30, 1), (14, 13), (33, 15), (21, 14), (22, 14), (24, 16), (35, 37), (8, 10), (27, 5), (13, 14), (4, 15), (14, 18), (9, 4), (26, 14), (34, 27), (31, 26), (17, 11), (23, 21), (17, 20), (3, 8), (32, 30), (32, 0), (12, 32), (27, 10), (30, 10), (35, 6), (13, 12), (26, 1), (35, 10), (20, 13), (12, 36), (33, 11), (24, 33), (9, 22), (3, 5), (23, 19), (13, 27), (27, 37), (30, 9), (13, 32), (25, 32), (11, 8), (2, 20), (3, 19), (25, 38), (33, 9), (11, 13), (23, 8), (12, 17), (3, 38), (29, 22), (24, 35), (0, 4), (3, 35), (13, 13), (32, 17), (3, 23), (29, 15), (16, 31), (9, 36), (13, 30), (0, 29), (30, 5), (32, 20), (12, 34), (8, 13), (33, 37), (35, 24), (17, 10), (1, 8), (29, 20), (22, 15), (27, 24), (8, 28), (0, 19), (35, 9), (0, 10), (0, 33), (26, 11), (32, 23), (16, 28), (8, 8), (8, 17), (1, 36), (32, 37), (15, 22), (25, 20), (25, 27), (13, 11), (17, 33), (14, 11), (11, 15), (10, 10), (6, 5), (7, 38), (22, 27), (16, 13), (32, 15), (14, 34), (27, 16), (31, 23), (6, 38), (17, 34), (12, 19), (23, 3), (8, 12), (19, 21), (34, 8), (15, 36), (23, 4), (35, 27), (29, 35), (24, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "496176", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 33), (18, 31), (0, 28), (10, 4), (15, 10), (1, 31), (4, 15), (13, 29), (26, 28), (11, 34), (4, 32), (23, 13), (34, 11), (26, 25), (27, 22), (1, 20), (14, 16), (32, 18), (16, 15), (2, 19), (4, 7), (6, 7), (15, 14), (0, 5), (27, 26), (34, 7), (10, 37), (9, 16), (26, 8), (32, 16), (16, 31), (10, 35), (25, 6), (33, 31), (13, 33), (9, 32), (26, 17), (17, 12), (6, 8), (1, 35), (34, 19), (26, 15), (24, 17), (20, 13), (9, 11), (15, 35), (6, 37), (28, 27), (10, 2), (33, 0), (9, 18), (9, 8), (0, 15), (21, 27), (33, 33), (34, 8), (11, 17), (7, 32), (24, 9), (32, 7), (10, 14), (24, 23), (3, 9), (0, 36), (9, 9), (10, 21), (22, 36), (21, 18), (21, 19), (27, 1), (21, 1), (4, 22), (29, 7), (29, 27), (26, 32), (10, 25), (7, 6), (22, 7), (33, 4), (23, 28), (12, 5), (27, 11), (13, 27), (29, 32), (6, 24), (24, 12), (15, 18), (1, 29), (1, 4), (8, 1), (28, 11), (10, 19), (8, 27), (32, 3), (10, 7), (8, 37), (31, 15), (12, 7), (34, 4), (8, 12), (18, 26), (19, 18), (0, 18), (13, 7), (21, 24), (16, 1), (23, 30), (24, 32), (21, 8), (25, 27), (25, 18), (24, 0), (8, 13), (30, 34), (25, 7), (5, 8), (9, 10), (30, 35), (7, 11), (25, 0), (5, 7), (5, 20), (23, 27), (22, 31), (5, 21), (15, 33), (17, 11), (31, 8), (20, 2), (10, 11), (3, 29), (0, 8), (3, 24), (30, 31), (14, 1), (22, 11), (20, 31), (24, 22), (3, 1), (8, 30), (11, 31), (27, 23), (29, 37), (32, 28), (9, 1), (6, 12), (5, 1), (12, 11), (20, 29), (31, 11), (28, 22), (19, 20), (8, 19), (6, 13), (11, 33), (26, 36), (17, 2), (12, 12), (11, 29), (6, 0), (31, 22), (26, 34), (9, 37), (8, 15), (15, 27), (0, 17), (15, 26), (20, 34), (1, 1), (21, 5), (27, 13), (15, 16), (4, 33), (2, 7), (4, 6), (30, 24), (23, 35), (23, 8), (24, 37), (12, 14), (18, 21), (5, 0), (7, 30), (5, 23), (33, 3), (33, 22), (3, 37), (16, 22), (26, 3), (14, 26), (3, 17), (16, 35), (23, 29), (16, 26), (13, 21), (12, 27), (21, 20), (19, 27), (22, 20), (24, 20), (32, 2), (2, 16), (21, 2), (18, 20), (3, 27), (22, 6), (3, 16), (28, 2), (33, 24), (27, 10), (33, 1), (31, 23), (6, 15), (21, 23), (25, 19), (33, 18), (6, 26), (33, 16), (5, 14), (15, 31), (10, 16), (12, 35), (14, 20), (13, 1), (16, 16), (10, 12), (6, 29), (10, 5), (4, 31), (28, 20), (14, 12), (29, 26), (18, 34), (4, 35), (27, 16), (30, 15), (17, 37), (31, 0), (10, 33), (10, 18), (10, 31), (6, 16), (2, 30), (15, 37), (11, 24), (2, 23), (31, 5), (14, 23), (23, 32), (18, 30), (18, 11), (2, 26), (31, 26), (32, 12), (33, 28), (8, 10), (16, 19), (4, 1), (6, 11), (25, 30), (25, 9), (17, 16), (6, 36), (31, 10), (15, 19), (0, 12), (29, 10), (4, 18), (15, 17), (21, 7), (25, 10), (7, 37), (26, 26), (16, 9), (2, 4), (14, 19), (33, 15), (3, 25), (32, 0), (9, 24), (12, 16), (15, 6), (29, 25), (5, 4), (3, 32), (5, 36), (29, 13), (13, 16), (14, 27), (30, 10), (31, 33), (9, 29), (33, 10), (5, 9), (33, 8), (31, 14), (21, 36), (29, 14), (34, 35), (5, 6), (21, 14), (29, 19), (27, 30), (23, 0), (6, 2), (3, 34), (4, 27), (3, 15), (11, 16), (13, 35), (32, 25), (13, 17), (20, 25), (14, 36), (7, 36), (0, 14), (23, 9), (10, 27), (3, 22), (27, 31), (0, 34), (11, 11), (33, 25), (11, 8), (7, 9), (14, 4), (10, 1), (34, 30), (30, 0), (33, 37), (16, 24), (9, 13), (4, 19), (12, 2), (25, 5), (22, 12), (8, 7), (18, 15), (28, 28), (8, 9), (15, 3), (20, 19), (5, 29), (12, 25), (27, 34), (9, 20), (20, 32), (33, 19), (16, 0), (19, 22), (22, 17), (0, 21), (7, 29), (14, 8), (17, 25), (27, 5), (17, 5), (26, 0), (17, 7), (24, 8), (1, 27), (0, 2), (17, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853740", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 6), (5, 11), (29, 17), (27, 12), (13, 15), (2, 26), (6, 1), (24, 0), (4, 5), (1, 1), (33, 27), (20, 0), (8, 9), (31, 16), (24, 19), (24, 14), (1, 15), (10, 2), (8, 10), (4, 28), (11, 27), (16, 26), (33, 2), (11, 11), (25, 12), (14, 2), (6, 9), (33, 25), (21, 25), (28, 14), (24, 26), (11, 5), (26, 16), (13, 0), (29, 20), (4, 9), (1, 3), (0, 14), (19, 17), (26, 13), (29, 29), (24, 20), (32, 10), (25, 14), (18, 27), (4, 22), (20, 16), (12, 23), (22, 26), (18, 20), (33, 4), (29, 26), (8, 24), (24, 3), (31, 2), (8, 1), (29, 16), (32, 25), (22, 7), (27, 4), (5, 1), (17, 23), (25, 22), (15, 8), (18, 14), (33, 17), (25, 3), (4, 12), (17, 18), (25, 13), (12, 1), (0, 7), (18, 17), (32, 19), (12, 8), (25, 20), (4, 14), (4, 1), (10, 27), (10, 3), (32, 15), (29, 6), (0, 21), (10, 20), (15, 1), (13, 9), (13, 13), (21, 13), (31, 6), (10, 18), (0, 17), (17, 17), (26, 2), (5, 3), (31, 29), (11, 17), (15, 9), (17, 1), (2, 17), (25, 24), (22, 23), (9, 14), (23, 13), (30, 1), (13, 2), (12, 14), (1, 26), (19, 26), (7, 3), (2, 10), (19, 21), (23, 9), (15, 15), (20, 17), (32, 6), (28, 15), (2, 8), (22, 29), (4, 4), (18, 29), (3, 25), (31, 10), (5, 20), (29, 0), (4, 24), (12, 6), (19, 4), (12, 4), (32, 0), (33, 13), (17, 21), (33, 16), (22, 22), (2, 23), (17, 2), (28, 21), (14, 1), (30, 7), (0, 6), (25, 17), (31, 15), (0, 20), (32, 16), (20, 12), (32, 29), (22, 25), (16, 25), (9, 11), (7, 10), (24, 10), (30, 14), (26, 3), (11, 23), (33, 1), (14, 22), (20, 22), (20, 25), (27, 0), (1, 16), (12, 12), (26, 8), (11, 8), (5, 15), (4, 18), (29, 5), (8, 8), (0, 18), (4, 27), (6, 6), (32, 17), (14, 28), (27, 23), (14, 14), (19, 22), (15, 26), (6, 4), (22, 0), (1, 17), (3, 19), (2, 13), (6, 20), (18, 12), (6, 27), (25, 23), (5, 2), (21, 24), (31, 7), (4, 6), (20, 11), (23, 20), (12, 7), (9, 0), (25, 21), (9, 16), (30, 28), (2, 12), (28, 23), (5, 13), (18, 5), (3, 27), (5, 23), (13, 18), (13, 14), (0, 28), (12, 25), (26, 25), (10, 13), (9, 5), (2, 4), (8, 7), (26, 26), (26, 23), (1, 10), (29, 14), (23, 19), (10, 24), (12, 9), (1, 27), (29, 4), (24, 11), (21, 11), (22, 12), (27, 1), (19, 18), (14, 9), (2, 14), (5, 22), (15, 23), (3, 18), (9, 10), (19, 3), (6, 25), (24, 5), (7, 5), (6, 2), (5, 21), (18, 13), (22, 2), (9, 1), (16, 0), (11, 24), (32, 22), (16, 5), (19, 2), (28, 1), (16, 11), (23, 3), (8, 4), (8, 11), (28, 27), (22, 17), (20, 3), (7, 8), (13, 25), (7, 14), (22, 16), (1, 25), (26, 15), (21, 16), (7, 24), (30, 11), (7, 11), (32, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465248", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 2), (2, 28), (19, 26), (14, 32), (34, 33), (13, 20), (8, 27), (8, 32), (21, 11), (29, 21), (30, 7), (32, 5), (10, 28), (3, 12), (7, 3), (11, 9), (2, 11), (33, 16), (17, 33), (8, 13), (27, 3), (12, 18), (9, 18), (19, 13), (25, 3), (27, 10), (36, 9), (27, 9), (13, 25), (1, 16), (7, 15), (36, 17), (24, 16), (10, 12), (22, 0), (14, 3), (7, 8), (33, 11), (19, 12), (36, 22), (26, 18), (14, 15), (38, 25), (33, 30), (16, 15), (14, 5), (9, 14), (26, 21), (38, 13), (2, 10), (29, 20), (22, 14), (10, 6), (32, 14), (12, 23), (13, 16), (8, 22), (23, 20), (38, 10), (21, 27), (17, 10), (10, 31), (38, 17), (8, 28), (13, 11), (34, 31), (3, 18), (6, 21), (21, 10), (19, 10), (34, 20), (31, 24), (22, 20), (5, 18), (38, 8), (4, 21), (34, 24), (5, 8), (12, 1), (17, 14), (19, 29), (29, 32), (24, 9), (7, 17), (13, 8), (11, 31), (37, 18), (28, 20), (10, 18), (17, 18), (29, 13), (0, 29), (9, 5), (9, 9), (16, 2), (32, 20), (5, 0), (19, 0), (3, 9), (22, 23), (24, 14), (32, 4), (25, 19), (29, 5), (37, 6), (27, 18), (5, 4), (25, 0), (1, 31), (34, 28), (33, 6), (34, 5), (4, 15), (6, 9), (8, 29), (0, 13), (26, 2), (7, 5), (9, 12), (6, 18), (5, 26), (38, 14), (12, 2), (0, 27), (26, 6), (32, 23), (2, 2), (10, 16), (23, 5), (20, 29), (12, 3), (32, 19), (6, 5), (8, 4), (15, 27), (2, 24), (34, 25), (21, 16), (32, 17), (6, 28), (18, 16), (37, 10), (10, 0), (16, 32), (29, 31), (19, 30), (10, 22), (17, 4), (6, 25), (8, 33), (38, 21), (4, 6), (17, 12), (4, 29), (24, 21), (31, 31), (26, 23), (15, 24), (14, 11), (8, 31), (17, 28), (5, 10), (16, 14), (8, 0), (16, 26), (6, 1), (25, 22), (10, 32), (13, 23), (33, 13), (32, 7), (17, 11), (12, 27), (30, 14), (3, 33), (17, 24), (20, 11), (31, 29), (36, 18), (34, 14), (0, 24), (22, 11), (24, 32), (36, 29), (14, 9), (14, 33), (11, 12), (2, 8), (6, 3), (27, 15), (22, 24), (23, 10), (15, 22), (20, 8), (27, 23), (22, 17), (19, 11), (35, 25), (13, 28), (26, 27), (11, 19), (6, 11), (4, 3), (33, 25), (14, 12), (30, 32), (32, 18), (26, 12), (25, 18), (23, 1), (9, 10), (21, 23), (36, 15), (37, 26), (11, 2), (25, 1), (5, 27), (6, 13), (33, 9), (17, 3), (27, 33), (26, 7), (32, 28), (29, 29), (33, 29), (38, 5), (20, 7), (0, 3), (27, 32), (2, 9), (19, 8), (1, 29), (25, 23), (12, 22), (23, 24), (30, 19), (28, 33), (7, 26), (33, 26), (12, 25), (21, 33), (1, 33), (0, 10), (0, 14), (1, 4), (1, 28), (10, 15), (13, 14), (27, 11), (4, 28), (18, 5), (36, 10), (18, 22), (35, 20), (36, 27), (23, 33), (36, 31), (33, 4), (31, 22), (16, 31), (24, 20), (32, 3), (0, 9), (28, 23), (37, 32), (11, 27), (14, 18), (20, 13), (27, 28), (11, 24), (36, 12), (24, 29), (30, 22), (30, 5), (12, 26), (8, 14), (19, 16), (5, 33), (8, 30), (18, 6), (31, 33), (6, 8), (30, 23), (13, 6), (34, 23), (35, 3), (12, 6), (2, 33), (6, 30), (20, 1), (30, 3), (7, 0), (13, 19), (0, 23), (7, 7), (11, 22), (29, 2), (19, 17), (15, 10), (5, 22), (3, 25), (29, 3), (1, 23), (38, 11), (19, 28), (26, 15), (20, 26), (17, 13), (35, 11), (25, 28), (15, 18), (3, 31), (20, 0), (34, 6), (27, 17), (29, 18), (17, 32), (20, 33), (34, 15), (35, 10), (13, 9), (3, 20), (16, 16), (22, 10), (21, 29), (14, 10), (15, 31), (35, 27), (38, 16), (32, 6), (24, 5), (24, 1), (9, 4), (38, 2), (6, 15), (4, 22), (25, 33), (2, 0), (26, 1), (22, 21), (28, 4), (21, 22), (15, 15), (32, 13), (20, 23), (12, 11), (19, 3), (4, 0), (4, 25), (37, 12), (38, 18), (23, 0), (26, 31), (37, 11), (31, 5), (11, 21), (17, 5), (15, 6), (17, 16), (33, 12), (15, 1), (22, 13), (3, 5), (6, 2), (15, 3), (5, 31), (30, 11), (34, 9), (21, 9), (34, 21), (26, 8), (5, 19), (27, 19), (26, 19), (15, 29), (11, 1), (30, 21), (28, 21), (21, 2), (16, 33), (37, 1), (17, 2), (13, 5), (17, 19), (2, 13), (32, 33), (4, 20), (12, 21), (30, 10), (34, 4), (18, 31), (31, 19), (27, 0), (14, 22), (6, 19), (6, 4), (23, 27), (20, 19), (20, 9), (12, 13), (22, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900864", "dataset": "MATH"}
{"messages": [{"content": "In a 30x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 11), (19, 4), (14, 35), (16, 9), (28, 32), (22, 22), (8, 18), (18, 11), (3, 0), (29, 27), (14, 27), (15, 12), (10, 27), (27, 20), (7, 30), (28, 12), (17, 31), (7, 31), (27, 9), (29, 28), (0, 5), (21, 3), (15, 33), (26, 23), (7, 15), (28, 25), (0, 29), (21, 17), (29, 17), (25, 11), (11, 33), (14, 22), (17, 19), (28, 16), (11, 14), (7, 21), (10, 28), (28, 23), (5, 7), (10, 31), (29, 20), (17, 26), (22, 12), (28, 28), (16, 24), (3, 29), (28, 9), (12, 11), (3, 32), (19, 24), (12, 35), (1, 13), (6, 12), (22, 20), (14, 7), (1, 10), (24, 1), (5, 24), (24, 8), (12, 33), (6, 22), (16, 15), (14, 8), (16, 31), (11, 8), (21, 14), (10, 0), (26, 7), (21, 20), (13, 35), (22, 24), (12, 19), (23, 22), (29, 2), (1, 9), (4, 29), (28, 3), (0, 31), (11, 12), (26, 31), (13, 19), (6, 4), (23, 11), (10, 33), (9, 31), (14, 1), (3, 26), (5, 34), (4, 25), (5, 1), (3, 22), (29, 0), (8, 29), (8, 3), (23, 20), (27, 13), (29, 18), (17, 22), (28, 6), (7, 6), (23, 16), (14, 32), (16, 13), (12, 23), (21, 5), (16, 27), (8, 34), (10, 13), (7, 33), (25, 2), (18, 28), (12, 6), (19, 6), (22, 16), (28, 17), (20, 27), (4, 33), (9, 0), (2, 24), (9, 30), (9, 20), (22, 4), (10, 2), (24, 25), (14, 20), (1, 17), (20, 9), (20, 12), (23, 8), (3, 23), (25, 19), (27, 4), (9, 16), (6, 25), (22, 18), (29, 4), (27, 5), (19, 35), (15, 24), (1, 16), (19, 21), (6, 3), (4, 12), (15, 21), (13, 14), (27, 33), (6, 33), (18, 31), (3, 13), (2, 16), (2, 4), (11, 32), (18, 16), (25, 35), (5, 23), (2, 18), (26, 32), (0, 27), (25, 4), (12, 9), (8, 21), (15, 4), (3, 35), (4, 21), (23, 25), (12, 5), (27, 18), (28, 22), (0, 17), (20, 32), (14, 21), (24, 19), (13, 26), (6, 28), (16, 25), (15, 23), (20, 28), (7, 16), (3, 10), (5, 22), (24, 13), (21, 13), (26, 10), (1, 21), (0, 22), (23, 1), (0, 14), (13, 21), (25, 23), (25, 15), (15, 1), (7, 7), (5, 9), (5, 3), (10, 4), (21, 4), (22, 33), (25, 17), (16, 16), (2, 7), (12, 12), (1, 0), (6, 27), (6, 2), (13, 28), (20, 7), (29, 1), (23, 32), (16, 11), (22, 31), (11, 1), (27, 15), (13, 17), (2, 3), (12, 20), (11, 27), (8, 22), (5, 0), (7, 34), (24, 27), (29, 3), (6, 31), (17, 11), (18, 24), (20, 2), (18, 32), (3, 8), (0, 15), (24, 0), (27, 34), (4, 17), (7, 9), (2, 34), (17, 12), (24, 18), (17, 6), (11, 20), (22, 7), (21, 31), (9, 3), (12, 27), (12, 1), (11, 4), (15, 0), (28, 0), (26, 18), (25, 25), (27, 24), (5, 12), (25, 24), (26, 0), (19, 10), (8, 27), (22, 11), (13, 29), (14, 0), (19, 11), (3, 11), (17, 16), (13, 9), (2, 5), (15, 25), (7, 17), (25, 20), (24, 9), (29, 31), (24, 4), (27, 8), (16, 10), (11, 21), (7, 22), (17, 10), (29, 23), (18, 18), (27, 16), (8, 15), (14, 18), (9, 17), (27, 25), (17, 34), (11, 35), (3, 18), (14, 34), (29, 11), (4, 22), (26, 27), (13, 16), (17, 23), (26, 8), (18, 27), (17, 14), (24, 26), (5, 28), (27, 32), (9, 23), (24, 31), (15, 7), (18, 35), (19, 5), (25, 10), (20, 34), (2, 23), (11, 29), (15, 19), (17, 24), (8, 12), (25, 18), (7, 5), (12, 8), (24, 35), (23, 35), (23, 17), (13, 11), (18, 10), (26, 20), (23, 13), (2, 12), (12, 2), (24, 29), (8, 31), (21, 23), (21, 0), (21, 34), (14, 26), (3, 31), (2, 30), (26, 5), (0, 2), (25, 27), (9, 14), (11, 16), (19, 27), (20, 33), (9, 12), (8, 14), (1, 5), (21, 22), (19, 20), (17, 2), (17, 7), (8, 30), (22, 3), (6, 35), (26, 1), (21, 28), (4, 9), (26, 12), (6, 32), (2, 29), (13, 24), (26, 24), (22, 35), (23, 9), (5, 15), (1, 11), (6, 7), (0, 10), (28, 20), (16, 7), (0, 23), (27, 30), (6, 15), (0, 13), (15, 35), (24, 22), (12, 0), (6, 21), (8, 20), (9, 18), (0, 20), (7, 28), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "730800", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 23), (32, 3), (28, 16), (33, 6), (33, 0), (14, 15), (30, 3), (27, 17), (20, 9), (22, 28), (16, 3), (32, 11), (1, 31), (22, 1), (10, 10), (25, 30), (20, 15), (24, 11), (26, 31), (0, 16), (19, 21), (15, 1), (9, 2), (19, 12), (26, 29), (8, 21), (3, 25), (31, 15), (16, 29), (8, 25), (2, 5), (22, 0), (33, 25), (12, 26), (4, 22), (3, 22), (17, 20), (0, 28), (3, 2), (16, 5), (5, 1), (11, 8), (0, 18), (2, 20), (25, 2), (12, 7), (19, 6), (17, 24), (12, 8), (4, 6), (23, 20), (3, 14), (16, 11), (28, 22), (13, 26), (6, 17), (12, 29), (33, 2), (10, 12), (27, 32), (33, 9), (22, 19), (23, 29), (30, 31), (12, 11), (6, 2), (29, 22), (5, 19), (25, 11), (12, 25), (23, 4), (15, 17), (24, 27), (12, 24), (33, 12), (31, 1), (22, 13), (9, 3), (7, 23), (2, 1), (14, 16), (8, 4), (27, 2), (13, 16), (28, 31), (24, 24), (15, 20), (26, 22), (21, 22), (6, 13), (8, 2), (1, 11), (32, 25), (9, 12), (33, 1), (6, 1), (27, 27), (1, 29), (3, 27), (2, 30), (18, 10), (19, 31), (3, 19), (28, 24), (32, 20), (9, 7), (20, 4), (6, 26), (33, 8), (4, 10), (11, 13), (32, 8), (18, 20), (11, 12), (22, 8), (30, 32), (25, 15), (32, 22), (18, 0), (0, 6), (18, 2), (15, 18), (16, 13), (5, 12), (28, 13), (26, 5), (13, 4), (11, 2), (17, 16), (7, 17), (7, 15), (30, 5), (25, 27), (8, 11), (4, 23), (26, 21), (20, 32), (5, 3), (25, 12), (27, 22), (27, 1), (13, 1), (8, 28), (8, 15), (23, 16), (18, 9), (1, 30), (5, 17), (23, 1), (15, 24), (13, 32), (21, 24), (2, 26), (12, 28), (15, 12), (8, 16), (32, 30), (12, 32), (12, 9), (15, 6), (31, 8), (15, 25), (5, 2), (4, 1), (18, 1), (2, 12), (27, 0), (16, 31), (24, 18), (6, 19), (17, 12), (30, 0), (17, 29), (26, 1), (1, 19), (22, 10), (6, 0), (30, 28), (8, 27), (14, 10), (19, 26), (29, 19), (10, 19), (0, 10), (7, 13), (23, 13), (29, 8), (17, 3), (27, 29), (29, 12), (31, 3), (33, 5), (32, 26), (5, 10), (29, 10), (13, 18), (29, 9), (32, 32), (27, 4), (30, 6), (17, 19), (19, 16), (27, 30), (33, 10), (7, 31), (18, 8), (15, 21), (19, 17), (18, 21), (11, 17), (29, 13), (1, 9), (8, 19), (27, 9), (29, 20), (7, 32), (31, 7), (26, 24), (6, 12), (18, 23), (19, 29), (24, 5), (9, 10), (24, 23), (5, 24), (25, 0), (32, 24), (5, 18), (5, 14), (21, 9), (17, 7), (24, 20), (20, 19), (12, 30), (11, 4), (1, 22), (9, 11), (12, 14), (25, 14), (12, 12), (2, 11), (3, 0), (23, 5), (25, 7), (24, 7), (18, 31), (14, 17), (16, 9), (11, 1), (19, 7), (33, 22), (11, 11), (22, 23), (30, 22), (18, 16), (19, 2), (25, 31), (32, 16), (23, 18), (16, 26), (20, 18), (29, 15), (26, 15), (3, 24), (10, 17), (28, 21), (15, 14), (0, 26), (2, 29), (20, 29), (17, 27), (28, 14), (16, 0), (31, 17), (19, 28), (22, 27), (21, 10), (3, 31), (7, 30), (17, 28), (30, 14), (18, 24), (22, 20), (14, 27), (24, 9), (13, 22), (29, 26), (28, 19), (29, 7), (25, 23), (5, 8), (33, 13), (6, 24), (12, 16), (1, 0), (14, 14), (31, 16), (20, 7), (17, 11), (27, 23), (31, 26), (19, 15), (15, 13), (8, 18), (1, 32), (32, 15), (33, 27), (11, 31), (21, 15), (5, 25), (11, 27), (13, 31), (26, 30), (9, 9), (6, 31), (24, 13), (15, 16), (31, 6), (26, 8), (7, 12), (5, 26), (1, 18), (1, 20), (9, 14), (27, 14), (18, 29), (11, 16), (12, 4), (14, 7), (31, 9), (30, 21), (13, 30), (21, 28), (18, 13), (19, 30), (23, 31), (30, 11), (24, 16), (5, 5), (27, 24), (32, 9), (13, 25), (32, 2), (20, 22), (1, 16), (5, 21), (12, 21), (12, 3), (14, 3), (2, 16), (3, 32), (29, 30), (18, 11), (15, 3), (17, 4), (8, 3), (1, 13), (25, 3), (6, 14), (30, 19), (5, 23), (12, 18), (10, 28), (22, 15), (29, 17), (3, 23), (28, 3), (3, 16), (4, 31), (20, 2), (1, 25), (22, 5), (30, 26), (1, 24), (33, 11), (19, 13), (32, 1), (22, 32), (0, 22), (18, 5), (4, 32), (15, 29), (9, 1), (19, 27), (4, 28), (7, 10), (6, 9), (27, 12), (25, 18), (21, 26), (19, 32), (25, 13), (1, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "652680", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 33), (20, 19), (20, 17), (1, 6), (6, 16), (27, 15), (25, 17), (14, 21), (13, 28), (10, 17), (22, 13), (17, 22), (7, 23), (26, 21), (14, 3), (33, 27), (23, 14), (13, 10), (8, 29), (22, 14), (33, 14), (11, 19), (15, 2), (32, 18), (11, 24), (10, 8), (3, 8), (0, 25), (14, 34), (4, 23), (23, 5), (26, 10), (0, 9), (13, 16), (27, 32), (0, 23), (7, 1), (6, 2), (1, 25), (2, 23), (21, 22), (1, 10), (30, 14), (15, 21), (5, 30), (22, 2), (10, 31), (4, 29), (25, 28), (13, 14), (23, 15), (3, 30), (1, 15), (8, 4), (7, 4), (0, 7), (28, 1), (3, 3), (30, 0), (13, 32), (14, 8), (30, 16), (32, 31), (24, 24), (31, 23), (19, 28), (18, 33), (10, 23), (31, 16), (21, 35), (32, 25), (11, 21), (32, 32), (7, 14), (20, 8), (8, 5), (31, 14), (22, 25), (24, 5), (20, 25), (7, 35), (28, 3), (6, 30), (17, 20), (24, 23), (25, 33), (11, 14), (15, 5), (16, 7), (27, 19), (13, 33), (32, 16), (28, 21), (26, 0), (7, 7), (21, 4), (4, 26), (30, 9), (12, 1), (19, 10), (6, 21), (27, 16), (9, 18), (25, 20), (19, 25), (8, 25), (25, 7), (23, 23), (16, 17), (8, 30), (28, 34), (28, 5), (16, 11), (6, 15), (4, 1), (16, 18), (29, 11), (11, 26), (7, 0), (26, 11), (21, 11), (9, 4), (25, 34), (7, 12), (0, 28), (12, 11), (0, 12), (18, 17), (22, 21), (14, 27), (32, 0), (11, 34), (9, 16), (29, 1), (25, 27), (31, 33), (10, 16), (8, 32), (5, 18), (12, 35), (24, 25), (27, 24), (26, 14), (14, 1), (10, 11), (3, 4), (15, 26), (6, 0), (28, 4), (5, 32), (11, 29), (22, 22), (26, 1), (5, 17), (26, 17), (30, 33), (30, 19), (28, 14), (2, 3), (15, 11), (2, 1), (28, 24), (19, 9), (17, 6), (31, 24), (16, 8), (18, 23), (18, 11), (4, 7), (10, 29), (26, 19), (1, 28), (25, 15), (8, 31), (15, 25), (22, 8), (17, 13), (9, 17), (1, 1), (17, 1), (24, 7), (31, 1), (17, 4), (12, 12), (14, 23), (8, 8), (14, 31), (20, 13), (21, 17), (18, 27), (8, 20), (33, 1), (11, 10), (18, 24), (13, 12), (18, 1), (33, 6), (19, 19), (18, 15), (19, 1), (16, 26), (6, 25), (9, 19), (10, 32), (7, 16), (5, 5), (22, 35), (3, 11), (24, 0), (14, 13), (22, 7), (3, 13), (32, 19), (33, 22), (23, 16), (3, 31), (12, 27), (26, 26), (27, 30), (26, 13), (3, 26), (4, 34), (12, 4), (22, 0), (5, 22), (16, 22), (31, 21), (15, 34), (22, 17), (14, 14), (14, 24), (3, 35), (29, 29), (24, 32), (29, 25), (15, 7), (27, 21), (6, 28), (16, 21), (8, 7), (14, 35), (27, 35), (4, 25), (32, 13), (32, 24), (7, 17), (17, 25), (24, 13), (12, 20), (3, 23), (2, 32), (28, 10), (3, 32), (1, 18), (27, 3), (3, 20), (31, 6), (28, 30), (10, 2), (23, 2), (9, 35), (18, 14), (33, 15), (20, 35), (5, 1), (7, 24), (15, 9), (3, 14), (2, 17), (21, 18), (16, 32), (22, 15), (24, 33), (17, 33), (2, 30), (1, 31), (26, 27), (19, 24), (18, 19), (21, 28), (13, 27), (24, 34), (24, 30), (12, 31), (0, 2), (33, 21), (23, 34), (32, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "722960", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 6), (30, 24), (1, 35), (8, 32), (7, 10), (20, 26), (27, 26), (25, 34), (38, 17), (9, 22), (16, 10), (33, 7), (27, 8), (36, 21), (12, 25), (20, 19), (25, 19), (34, 12), (2, 35), (3, 25), (34, 3), (37, 30), (4, 6), (6, 17), (20, 31), (27, 19), (22, 3), (33, 4), (35, 8), (19, 9), (32, 15), (35, 2), (28, 30), (32, 13), (2, 33), (37, 3), (30, 18), (36, 28), (36, 33), (24, 35), (21, 35), (18, 1), (38, 26), (33, 21), (32, 11), (12, 19), (17, 7), (3, 10), (23, 21), (26, 25), (31, 33), (19, 33), (29, 28), (10, 18), (16, 4), (36, 37), (6, 23), (33, 29), (19, 30), (15, 7), (16, 28), (29, 30), (2, 5), (14, 0), (12, 18), (20, 21), (35, 16), (11, 22), (0, 18), (31, 15), (36, 4), (23, 24), (38, 1), (30, 22), (26, 3), (12, 14), (17, 16), (38, 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(15, 13), (35, 35), (0, 9), (10, 16), (6, 20), (12, 22), (24, 6), (27, 29), (15, 34), (31, 8), (14, 17), (34, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "596904", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), 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), (20, 1), (25, 16), (10, 5), (38, 20), (21, 4), (12, 24), (26, 0), (15, 7), (24, 18), (34, 2), (14, 25), (19, 8), (10, 11), (18, 18), (19, 21), (31, 19), (21, 30), (5, 26), (8, 18), (16, 1), (21, 7), (38, 9), (29, 27), (20, 2), (29, 23), (30, 19), (11, 8), (37, 14), (33, 29), (29, 17), (35, 31), (14, 10), (9, 25), (33, 4), (21, 14), (5, 14), (10, 21), (36, 21), (18, 7), (8, 6), (34, 24), (22, 4), (30, 26), (16, 22), (14, 5), (31, 16), (0, 26), (16, 28), (33, 18), (18, 11), (14, 19), (15, 27), (9, 1), (1, 23), (32, 4), (36, 27), (29, 31), (32, 21), (15, 17), (17, 28), (25, 13), (31, 24), (36, 13), (27, 21), (31, 27), (15, 18), (0, 7), (30, 4), (1, 29), (4, 26), (37, 0), (37, 19), (7, 21), (3, 15), (11, 12), (1, 17), (2, 29), (22, 12), (38, 28), (8, 16), (10, 19), (34, 21), (6, 2), (11, 28), (19, 10), (1, 16), (15, 29), (30, 30), (35, 27), (24, 11), (23, 5), (26, 11), (6, 0), (24, 30), (15, 16), (15, 8), (32, 19), (21, 16), (7, 4), (2, 23), (36, 12), (4, 1), (35, 16), (9, 6), (26, 27), (15, 1), (34, 31), (14, 2), (15, 11), (8, 31), (25, 0), (15, 0), (23, 27), (31, 23), (22, 14), (30, 12), (7, 25), (31, 1), (4, 16), (24, 21), (17, 11), (16, 15), (21, 10), (17, 9), (16, 7), (21, 9), (27, 16), (25, 31), (13, 7), (36, 26), (28, 24), (16, 25), (0, 24), (1, 31), (11, 25), (10, 16), (16, 12), (12, 6), (28, 18), (17, 31), (36, 24), (19, 24), (1, 6), (2, 5), (8, 0), (10, 6), (11, 19), (31, 22), (27, 14), (23, 26), (37, 9), (26, 14), (32, 6), (24, 1), (16, 26), (19, 13), (31, 20), (20, 9), (14, 23), (30, 20), (32, 7), (37, 7), (6, 19), (31, 11), (25, 11), (14, 6), (27, 18), (17, 14), (14, 20), (2, 26), (19, 15), (20, 8), (8, 8), (28, 16), (37, 15), (7, 9), (8, 10), (27, 29), (28, 26), (28, 30), (34, 19), (23, 0), (9, 30), (33, 14), (2, 6), (11, 5), (26, 28), (12, 9), (17, 10), (33, 21), (13, 5), (1, 15), (15, 24), (19, 1), (24, 2), (5, 25), (37, 24), (25, 12), (14, 9), (19, 11), (27, 10), (28, 28), (23, 24), (9, 24), (37, 12), (21, 6), (21, 23), (22, 22), (25, 28), (17, 19), (19, 22), (35, 26), (31, 5), (34, 6), (27, 28), (2, 16), (7, 2), (6, 16), (35, 14), (6, 26), (1, 7), (10, 20), (12, 17), (13, 31), (38, 29), (27, 20), (19, 29), (1, 22), (0, 15), (16, 16), (4, 29), (9, 29), (18, 0), (12, 15), (22, 27), (5, 3), (33, 19), (23, 28), (7, 27), (20, 29), (28, 0), (0, 27), (16, 3), (5, 29), (36, 11), (8, 9), (24, 22), (2, 1), (15, 15), (26, 9), (29, 7), (29, 19), (20, 3), (32, 8), (15, 14), (34, 26), (38, 12), (37, 4), (9, 13), (8, 3), (7, 0), (6, 17), (27, 30), (25, 26), (2, 0), (24, 24), (8, 17), (35, 25), (27, 6), (27, 26), (5, 9), (0, 29), (14, 1), (20, 5), (16, 27), (19, 16), (36, 22), (22, 17), (2, 10), (23, 8), (20, 18), (15, 21), (27, 4), (9, 31), (6, 5), (10, 15), (12, 20), (26, 18), (8, 1), (18, 25), (25, 30), (23, 13), (3, 2), (4, 8), (5, 20), (38, 26), (5, 11), (24, 23), (10, 31), (35, 10), (26, 1), (30, 16), (24, 16), (3, 20), (15, 31), (9, 0), (28, 2), (22, 5), (9, 21), (24, 19), (33, 8), (17, 2), (11, 1), (16, 5), (10, 26), (9, 22), (27, 22), (19, 0), (4, 2), (18, 30), (18, 2), (2, 30), (12, 1), (13, 1), (37, 29), (26, 2), (15, 22), (23, 10), (22, 24), (7, 23), (10, 27), (13, 6), (3, 18), (8, 21), (7, 28), (17, 17), (24, 7), (6, 22), (18, 9), (13, 25), (34, 1), (38, 15), (13, 26), (7, 18), (13, 19), (23, 1), (10, 9), (28, 21), (25, 22), (10, 12), (4, 24), (33, 31), (4, 28), (0, 17), (25, 24), (1, 5), (15, 6), (1, 14), (0, 13), (14, 4), (23, 31), (35, 8), (32, 11), (33, 17), (37, 31), (27, 1), (32, 20), (22, 30), (18, 28), (18, 8), (13, 8), (38, 23), (8, 5), (3, 22), (17, 29), (9, 20), (20, 6), (13, 29), (4, 4), (23, 2), (20, 12), (28, 15), (34, 17), (31, 15), (2, 31), (1, 25), (27, 11), (28, 11), (14, 7), (4, 9), (36, 17), (23, 16), (6, 8), (12, 27), (29, 15), (9, 17), (24, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776112", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (16, 26), (18, 18), (2, 26), (24, 15), (19, 1), (11, 33), (24, 4), (31, 15), (8, 22), (19, 9), (31, 22), (12, 12), (11, 11), (23, 10), (25, 17), (31, 12), (31, 14), (29, 25), (23, 16), (20, 35), (21, 12), (16, 20), (23, 3), (10, 10), (23, 34), (12, 14), (7, 9), (15, 8), (18, 14), (18, 15), (27, 15), (18, 13), (32, 4), (26, 32), (20, 0), (14, 0), (8, 30), (27, 19), (31, 9), (19, 18), (22, 26), (16, 35), (11, 13), (16, 10), (32, 12), (6, 23), (17, 8), (7, 10), (28, 8), (10, 20), (0, 15), (12, 5), (1, 18), (12, 10), (21, 1), (26, 25), (4, 5), (26, 20), (9, 29), (17, 22), (24, 30), (19, 14), (16, 5), (5, 15), (5, 7), (28, 34), (8, 6), (9, 18), (21, 25), (27, 16), (1, 13), (5, 30), (9, 30), (8, 34), (10, 31), (0, 12), (11, 19), (4, 26), (6, 35), (31, 1), (29, 3), (18, 11), (19, 26), (0, 17), (4, 31), (32, 3), (22, 11), (7, 11), (30, 34), (4, 28), (10, 1), (5, 24), (9, 2), (4, 35), (14, 28), (18, 27), (3, 17), (21, 9), (16, 15), (13, 12), (18, 31), (10, 17), (13, 32), (1, 35), (16, 16), (17, 6), (26, 29), (32, 31), (27, 2), (30, 31), (8, 26), (4, 8), (22, 0), (5, 9), (11, 10), (13, 28), (21, 24), (27, 31), (24, 29), (3, 32), (24, 33), (22, 21), (4, 7), (18, 19), (8, 25), (3, 5), (11, 15), (20, 15), (12, 18), (7, 16), (8, 9), (16, 18), (14, 25), (31, 21), (22, 17), (25, 7), (31, 27), (28, 13), (4, 25), (32, 7), (15, 25), (12, 11), (24, 35), (26, 34), (9, 17), (0, 9), (1, 26), (0, 23), (28, 26), (31, 20), (21, 32), (12, 34), (31, 26), (8, 13), (31, 7), (32, 0), (3, 8), (6, 8), (18, 1), (31, 11), (25, 18), (25, 21), (30, 14), (1, 24), (2, 6), (14, 15), (12, 4), (28, 11), (3, 33), (10, 11), (0, 34), (29, 10), (9, 32), (32, 21), (29, 0), (17, 23), (6, 24), (27, 17), (25, 5), (0, 3), (6, 16), (0, 30), (22, 23), (6, 13), (23, 19), (17, 14), (19, 31), (19, 8), (14, 13), (21, 34), (30, 23), (8, 2), (20, 20), (15, 20), (15, 34), (0, 5), (27, 27), (31, 0), (29, 15), (8, 28), (4, 2), (15, 9), (30, 12), (21, 29), (6, 1), (13, 27), (24, 32), (20, 30), (30, 19), (13, 26), (25, 25), (10, 30), (0, 24), (13, 0), (32, 22), (6, 30), (16, 24), (2, 25), (4, 21), (14, 30), (3, 21), (19, 0), (15, 14), (17, 5), (22, 14), (18, 32), (26, 35), (24, 8), (4, 32), (9, 8), (29, 30), (9, 4), (7, 0), (7, 33), (24, 17), (12, 7), (0, 21), (29, 31), (15, 27), (15, 0), (0, 2), (21, 2), (30, 17), (23, 9), (3, 3), (32, 16), (19, 6), (4, 6), (15, 7), (18, 29), (19, 21), (28, 18), (8, 31), (17, 17), (27, 10), (4, 1), (3, 24), (25, 15), (22, 31), (28, 28), (9, 33), (3, 20), (32, 18), (13, 13), (30, 7), (2, 31), (25, 24), (2, 13), (17, 13), (19, 30), (27, 25), (10, 22), (23, 22), (25, 33), (4, 23), (5, 8), (30, 4), (30, 32), (3, 29), (5, 21), (27, 20), (5, 26), (24, 18), (9, 25), (2, 8), (25, 28), (0, 29), (20, 14), (22, 1), (29, 27), (1, 21), (29, 16), (28, 2), (31, 33), (7, 26), (26, 11), (12, 8), (12, 13), (5, 25), (10, 4), (25, 23), (31, 32), (8, 4), (32, 13), (26, 8), (30, 10), (12, 32), (16, 33), (0, 10), (23, 28), (6, 6), (2, 1), (29, 24), (30, 6), (17, 18), (3, 11), (1, 4), (28, 12), (4, 11), (19, 24), (7, 1), (9, 20), (18, 0), (32, 9), (26, 4), (17, 3), (22, 22), (14, 18), (3, 1), (2, 15), (1, 3), (12, 31), (20, 22), (19, 23), (12, 28), (11, 14), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424872", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 29), (13, 28), (23, 0), (23, 17), (21, 4), (0, 8), (14, 24), (8, 28), (27, 12), (5, 22), (26, 21), (29, 25), (9, 0), (16, 27), (11, 22), (11, 21), (15, 19), (20, 17), (17, 28), (11, 20), (8, 25), (24, 0), (24, 30), (24, 15), (17, 19), (2, 18), (5, 27), (30, 18), (12, 8), (5, 0), (2, 27), (6, 5), (8, 13), (21, 29), (16, 24), (18, 14), (2, 13), (4, 13), (8, 15), (7, 2), (20, 3), (3, 26), (13, 2), (24, 18), (12, 22), (16, 6), (29, 24), (23, 11), (24, 23), (27, 24), (5, 30), (22, 5), (18, 8), (10, 7), (23, 23), (3, 21), (9, 3), (22, 27), (8, 10), (8, 20), (10, 13), (4, 5), (11, 8), (31, 10), (21, 22), (7, 15), (28, 27), (13, 30), (8, 4), (4, 16), (0, 30), (31, 25), (26, 0), (22, 18), (1, 5), (8, 0), (3, 29), (25, 3), (14, 4), (2, 9), (22, 10), (30, 3), (24, 9), (5, 20), (28, 2), (29, 4), (3, 27), (11, 28), (1, 29), (1, 9), (12, 3), (17, 8), (27, 4), (6, 10), (9, 11), (13, 26), (17, 15), (12, 20), (10, 20), (20, 19), (14, 18), (25, 4), (16, 30), (20, 18), (25, 14), (16, 23), (16, 11), (1, 16), (14, 3), (0, 9), (4, 20), (11, 25), (21, 28), (29, 21), (6, 1), (25, 23), (19, 22), (18, 29), (2, 15), (18, 16), (1, 15), (14, 11), (1, 19), (12, 25), (14, 12), (11, 15), (21, 20), (3, 9), (29, 7), (10, 30), (8, 11), (26, 5), (22, 15), (5, 5), (18, 23), (6, 29), (12, 15), (9, 20), (20, 21), (9, 18), (6, 18), (8, 16), (6, 16), (26, 24), (15, 10), (18, 25), (27, 17), (8, 1), (19, 20), (13, 1), (5, 24), (25, 15), (20, 22), (17, 23), (11, 30), (31, 1), (19, 24), (27, 13), (28, 23), (11, 17), (14, 1), (13, 17), (21, 15), (19, 0), (13, 6), (8, 21), (11, 2), (24, 21), (11, 19), (29, 10), (6, 6), (31, 13), (17, 18), (28, 22), (25, 20), (31, 17), (27, 22), (22, 7), (4, 6), (25, 29), (29, 8), (19, 25), (9, 26), (30, 16), (28, 19), (15, 13), (9, 14), (26, 28), (21, 16), (30, 2), (30, 29), (10, 21), (12, 14), (8, 8), (10, 12), (1, 10), (30, 23), (15, 11), (7, 18), (9, 23), (2, 23), (22, 25), (14, 14), (23, 7), (22, 23), (21, 17), (23, 18), (9, 6), (23, 1), (8, 3), (25, 13), (9, 13), (4, 19), (7, 30), (25, 10), (14, 25), (11, 14), (3, 11), (25, 6), (26, 2), (6, 25), (20, 11), (7, 24), (24, 7), (16, 21), (16, 16), (15, 1), (13, 4), (25, 18), (3, 14), (4, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338688", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 30), (3, 19), (10, 21), (27, 26), (36, 6), (5, 12), (2, 3), (4, 27), (29, 32), (28, 17), (10, 3), (12, 11), (30, 28), (21, 3), (18, 11), (17, 3), (17, 10), (33, 1), (11, 29), (8, 18), (21, 15), (34, 28), (28, 3), (6, 13), (29, 9), (7, 13), (13, 1), (35, 4), (10, 22), (4, 12), (0, 1), (25, 26), (31, 26), (4, 21), (1, 16), (35, 27), (0, 15), (13, 5), (7, 0), (11, 16), (12, 29), (9, 4), (24, 5), (21, 31), (16, 25), (29, 5), (23, 9), (5, 25), (10, 32), (35, 17), (12, 2), (20, 8), (31, 6), (36, 13), (28, 15), (21, 29), (26, 23), (9, 11), (28, 21), (18, 16), (25, 5), (16, 21), (14, 3), (9, 1), (6, 27), (2, 23), (21, 17), (32, 25), (3, 26), (31, 14), (17, 28), (17, 0), (17, 5), (25, 24), (20, 25), (11, 7), (28, 5), (5, 1), (33, 0), (35, 30), (0, 16), (29, 3), (16, 23), (15, 19), (12, 1), (4, 7), (29, 12), (36, 12), (27, 25), (23, 11), (20, 28), (18, 9), (37, 20), (22, 17), (32, 2), (3, 0), (31, 11), (1, 5), (10, 33), (31, 29), (22, 9), (2, 8), (20, 23), (5, 24), (3, 12), (3, 30), (32, 0), (11, 11), (6, 5), (15, 18), (33, 27), (31, 13), (15, 29), (5, 17), (33, 12), (13, 22), (31, 12), (2, 2), (30, 10), (21, 12), (19, 1), (35, 7), (20, 2), (2, 33), (11, 20), (23, 27), (29, 33), (6, 17), (6, 29), (2, 5), (4, 8), (8, 15), (32, 6), (22, 12), (24, 9), (26, 26), (5, 4), (22, 16), (21, 10), (27, 10), (1, 18), (12, 27), (16, 14), (6, 15), (4, 32), (17, 7), (10, 16), (37, 15), (29, 0), (37, 25), (15, 15), (5, 27), (29, 10), (26, 9), (20, 20), (20, 31), (26, 30), (1, 11), (16, 16), (25, 23), (30, 0), (0, 28), (15, 8), (36, 18), (37, 1), (16, 9), (9, 6), (17, 27), (0, 7), (34, 6), (12, 20), (30, 3), (31, 0), (5, 14), (0, 22), (34, 12), (5, 19), (24, 3), (26, 1), (27, 3), (3, 5), (25, 3), (19, 29), (37, 5), (25, 21), (24, 21), (32, 4), (34, 15), (2, 25), (26, 10), (36, 24), (10, 31), (28, 25), (35, 0), (3, 13), (18, 13), (14, 28), (18, 32), (9, 22), (35, 5), (12, 32), (23, 16), (11, 31), (11, 23), (21, 25), (2, 16), (33, 13), (26, 27), (10, 7), (3, 29), (8, 16), (15, 31), (15, 25), (35, 19), (15, 30), (34, 8), (1, 12), (20, 33), (31, 27), (29, 22), (16, 33), (8, 0), (22, 13), (24, 23), (0, 5), (26, 16), (10, 17), (23, 10), (37, 13), (1, 17), (32, 9), (28, 9), (33, 6), (9, 17), (36, 29), (36, 30), (4, 5), (7, 21), (14, 17), (13, 14), (3, 16), (35, 16), (15, 3), (10, 29), (11, 4), (17, 9), (9, 19), (24, 8), (13, 7), (21, 1), (0, 14), (27, 18), (22, 1), (14, 9), (8, 24), (6, 19), (22, 0), (37, 6), (27, 15), (30, 23), (23, 14), (32, 31), (18, 15), (7, 7), (25, 7), (36, 15), (10, 11), (10, 25), (35, 11), (15, 28), (21, 2), (28, 19), (22, 30), (12, 0), (7, 15), (29, 31), (9, 30), (10, 2), (1, 21), (9, 3), (24, 7), (14, 19), (15, 21), (6, 1), (26, 8), (0, 21), (24, 11), (5, 0), (36, 22), (36, 5), (25, 31), (36, 8), (33, 16), (16, 2), (27, 27), (27, 6), (4, 11), (7, 33), (5, 28), (34, 31), (36, 16), (11, 12), (30, 13), (28, 29), (24, 17), (23, 32), (3, 17), (21, 4), (12, 9), (22, 14), (23, 0), (8, 26), (10, 24), (12, 6), (14, 25), (30, 25), (24, 2), (26, 33), (20, 29), (13, 17), (29, 18), (20, 5), (20, 14), (12, 13), (8, 2), (26, 2), (36, 20), (17, 24), (22, 5), (16, 24), (11, 22), (11, 24), (35, 1), (32, 22), (24, 6), (12, 7), (1, 15), (21, 30), (35, 9), (30, 5), (31, 19), (34, 17), (0, 2), (17, 22), (24, 4), (13, 4), (7, 20), (2, 11), (9, 26), (18, 18), (19, 27), (37, 7), (21, 27), (9, 7), (6, 18), (19, 0), (4, 20), (21, 9), (12, 4), (14, 16), (0, 20), (37, 9), (37, 0), (8, 13), (4, 3), (13, 27), (7, 6), (16, 12), (33, 33), (37, 2), (13, 13), (14, 20), (22, 4), (34, 23), (23, 8), (33, 20), (31, 10), (11, 6), (28, 33), (21, 33), (35, 14), (25, 22), (0, 12), (4, 6), (23, 28), (5, 29), (35, 28), (30, 32), (30, 29), (8, 31), (1, 10), (6, 28), (25, 4), (25, 10), (27, 29), (32, 11), (14, 32), (12, 18), (7, 4), (29, 4), (15, 11), (29, 19), (11, 33), (5, 5), (27, 14), (16, 15), (25, 30), (31, 28), (35, 3), (21, 13), (36, 10), (32, 29), (5, 15), (34, 2), (28, 24), (18, 30), (3, 28), (23, 15), (22, 8), (10, 1), (23, 22), (30, 14), (19, 7), (27, 21), (19, 23), (11, 26), (34, 7), (29, 28), (30, 33), (33, 24), (26, 25), (3, 11), (26, 11), (31, 25), (1, 30), (2, 0), (7, 32), (18, 7), (9, 8), (33, 9), (20, 30), (16, 0), (19, 6), (23, 25), (30, 19), (14, 5), (2, 24), (1, 27), (25, 32), (2, 7), (31, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "742176", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (1, 7), (33, 15), (3, 16), (16, 30), (2, 20), (2, 18), (5, 18), (28, 22), (2, 27), (6, 12), (19, 6), (24, 24), (28, 23), (11, 7), (26, 0), (15, 14), (21, 8), (13, 13), (3, 15), (15, 0), (6, 26), (22, 27), (24, 30), (7, 8), (0, 13), (1, 31), (22, 13), (22, 31), (32, 22), (9, 18), (4, 5), (4, 28), (19, 7), (5, 10), (29, 17), (11, 12), (2, 14), (11, 1), (31, 16), (14, 21), (16, 15), (13, 20), (23, 28), (22, 4), (12, 18), (32, 8), (31, 13), (16, 19), (5, 11), (6, 22), (26, 5), (27, 13), (11, 19), (23, 1), (23, 30), (11, 13), (15, 18), (6, 10), (25, 24), (11, 27), (19, 22), (17, 20), (23, 8), (9, 20), (20, 2), (3, 28), (5, 16), (10, 28), (2, 26), (26, 26), (22, 2), (31, 4), (7, 15), (32, 21), (7, 3), (29, 1), (30, 1), (8, 30), (1, 23), (11, 29), (27, 22), (27, 7), (32, 25), (13, 10), (18, 9), (2, 17), (33, 27), (10, 6), (30, 3), (4, 3), (32, 20), (32, 17), (29, 23), (19, 20), (28, 20), (33, 24), (19, 13), (15, 13), (0, 9), (14, 29), (20, 17), (8, 22), (25, 2), (32, 9), (30, 24), (15, 21), (30, 2), (29, 31), (25, 16), (3, 25), (3, 18), (31, 27), (30, 18), (16, 1), (18, 4), (14, 26), (15, 15), (16, 4), (9, 4), (28, 5), (28, 4), (16, 23), (7, 16), (12, 10), (18, 30), (23, 13), (20, 8), (33, 16), (18, 17), (24, 15), (6, 25), (7, 22), (25, 21), (20, 11), (33, 4), (3, 26), (17, 16), (24, 4), (21, 16), (19, 17), (24, 25), (21, 21), (33, 10), (18, 25), (1, 10), (9, 7), (28, 7), (32, 29), (25, 26), (5, 0), (20, 23), (0, 22), (19, 19), (14, 28), (4, 17), (27, 9), (9, 22), (0, 26), (0, 19), (20, 1), (1, 3), (13, 2), (30, 27), (27, 26), (24, 27), (5, 9), (0, 28), (19, 25), (30, 22), (11, 4), (25, 13), (12, 25), (10, 16), (16, 14), (0, 17), (17, 0), (6, 4), (20, 4), (17, 5), (6, 29), (17, 30), (12, 22), (22, 0), (0, 24), (11, 26), (21, 14), (8, 28), (0, 5), (8, 29), (2, 1), (30, 21), (17, 28), (23, 16), (31, 26), (6, 2), (4, 27), (33, 29), (25, 22), (30, 10), (5, 14), (5, 6), (9, 14), (16, 0), (11, 22), (16, 2), (30, 30), (6, 7), (1, 0), (24, 14), (16, 17), (4, 10), (1, 28), (12, 12), (32, 10), (2, 5), (26, 16), (22, 5), (12, 9), (28, 16), (17, 1), (21, 31), (3, 14), (10, 13), (21, 10), (15, 6), (5, 27), (9, 31), (2, 2), (12, 21), (22, 28), (17, 2), (2, 16), (8, 11), (31, 19), (6, 20), (15, 25), (2, 31), (13, 30), (7, 28), (28, 2), (11, 20), (16, 24), (9, 25), (2, 0), (0, 10), (1, 8), (24, 21), (19, 9), (23, 22), (4, 25), (32, 2), (4, 2), (29, 12), (2, 15), (15, 31), (17, 3), (15, 23), (4, 26), (22, 20), (23, 6), (9, 29), (31, 12), (16, 5), (0, 11), (22, 18), (10, 9), (12, 30), (18, 23), (20, 25), (2, 30), (26, 14), (5, 24), (10, 31), (6, 9), (6, 3), (32, 30), (27, 5), (16, 29), (14, 23), (1, 16), (26, 24), (12, 11), (26, 11), (25, 19), (23, 25), (22, 17), (29, 6), (21, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895536", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 29), (18, 21), (28, 5), (30, 10), (32, 24), (29, 38), (28, 10), (9, 32), (14, 5), (32, 21), (4, 0), (20, 7), (8, 9), (20, 8), (1, 21), (19, 28), (25, 25), (5, 17), (16, 27), (32, 7), (15, 27), (2, 37), (16, 2), (22, 31), (7, 30), (14, 13), (6, 8), (28, 24), (15, 38), (1, 12), (15, 19), (8, 4), (9, 21), (26, 21), (4, 30), (25, 32), (20, 28), (4, 15), (27, 1), (13, 0), (7, 9), (2, 15), (24, 35), (9, 0), (16, 37), (30, 8), (10, 21), (29, 9), (30, 7), (24, 32), (13, 25), (24, 31), (4, 3), (7, 8), (26, 9), (23, 28), (3, 29), (28, 14), (10, 0), (3, 35), (24, 6), (24, 27), (11, 33), (7, 37), (15, 6), (4, 36), (25, 30), (5, 13), (24, 30), (30, 3), (32, 18), (17, 33), (18, 34), (0, 22), (15, 22), (26, 23), (22, 15), (22, 11), (28, 15), (28, 26), (6, 2), (24, 38), (28, 34), (31, 15), (19, 17), (12, 9), (14, 30), (27, 15), (13, 32), (23, 5), (14, 22), (23, 22), (0, 21), (3, 27), (12, 25), (1, 15), (28, 21), (29, 26), (23, 12), (9, 12), (15, 1), (9, 1), (9, 7), (25, 33), (14, 11), (6, 31), (27, 22), (29, 5), (21, 25), (29, 30), (7, 10), (31, 10), (20, 22), (26, 30), (22, 32), (5, 22), (17, 2), (9, 36), (24, 14), (10, 16), (2, 22), (1, 5), (13, 37), (16, 33), (18, 13), (28, 38), (9, 30), (8, 24), (11, 20), (22, 9), (25, 26), (18, 12), (23, 16), (29, 29), (6, 5), (23, 7), (2, 28), (19, 38), (23, 23), (7, 22), (2, 31), (21, 27), (16, 19), (17, 20), (19, 2), (19, 9), (9, 15), (9, 17), (17, 16), (26, 3), (25, 19), (26, 34), (28, 37), (1, 23), (29, 12), (10, 22), (7, 29), (27, 30), (15, 33), (16, 17), (29, 24), (7, 34), (13, 18), (17, 37), (25, 23), (20, 17), (7, 7), (11, 37), (16, 24), (13, 34), (19, 25), (21, 15), (12, 6), (0, 34), (7, 3), (21, 7), (2, 10), (27, 21), (3, 34), (18, 20), (11, 5), (26, 20), (3, 9), (5, 19), (22, 14), (10, 5), (28, 29), (17, 0), (30, 26), (1, 11), (21, 22), (14, 36), (18, 30), (11, 22), (22, 18), (32, 4), (29, 28), (32, 6), (18, 4), (18, 10), (10, 26), (4, 8), (14, 21), (15, 16), (1, 28), (6, 37), (15, 10), (13, 4), (29, 22), (32, 2), (1, 38), (24, 29), (13, 5), (23, 37), (7, 11), (30, 14), (22, 30), (32, 1), (5, 15), (18, 5), (0, 32), (3, 5), (1, 32), (11, 3), (14, 25), (3, 31), (28, 35), (25, 1), (12, 38), (21, 0), (10, 17), (19, 10), (5, 23), (22, 10), (21, 1), (2, 8), (4, 23), (2, 34), (27, 6), (28, 19), (8, 18), (2, 20), (19, 31), (24, 34), (25, 13), (31, 25), (21, 33), (3, 0), (8, 3), (24, 37), (23, 32), (25, 18), (22, 0), (28, 1), (18, 9), (22, 22), (0, 13), (0, 37), (1, 13), (29, 11), (31, 31), (16, 36), (0, 10), (32, 20), (21, 30), (11, 27), (21, 35), (0, 27), (28, 7), (20, 25), (15, 20), (4, 11), (5, 34), (2, 11), (16, 22), (1, 6), (17, 1), (21, 37), (14, 4), (20, 1), (8, 37), (3, 13), (25, 12), (11, 25), (32, 31), (26, 8), (3, 23), (7, 28), (4, 2), (20, 27), (30, 18), (1, 2), (31, 4), (23, 15), (20, 4), (12, 20), (0, 25), (3, 24), (3, 1), (7, 18), (29, 35), (19, 20), (16, 18), (17, 7), (18, 0), (13, 31), (29, 17), (30, 2), (27, 31), (5, 30), (12, 7), (30, 9), (13, 1), (20, 0), (0, 33), (30, 12), (4, 1), (14, 7), (2, 1), (8, 11), (11, 34), (8, 10), (2, 23), (30, 13), (3, 8), (16, 1), (31, 35), (5, 4), (5, 27), (2, 6), (28, 4), (26, 26), (17, 6), (25, 2), (11, 15), (1, 37), (21, 10), (30, 33), (17, 10), (1, 3), (24, 19), (22, 8), (24, 24), (28, 33), (32, 29), (28, 18), (3, 21), (6, 9), (28, 3), (25, 21), (32, 3), (1, 22), (6, 6), (30, 15), (11, 16), (19, 24), (7, 12), (6, 38), (30, 6), (18, 16), (29, 31), (7, 23), (32, 10), (6, 23), (15, 11), (15, 23), (11, 19), (13, 24), (24, 3), (26, 12), (7, 15), (16, 29), (32, 30), (4, 20), (12, 22), (28, 13), (19, 0), (18, 24), (5, 20), (13, 38), (23, 19), (15, 12), (18, 29), (21, 14), (22, 6), (0, 24), (29, 0), (32, 0), (21, 5), (8, 30), (13, 12), (10, 7), (10, 18), (20, 26), (6, 10), (31, 22), (8, 15), (16, 8), (26, 27), (20, 14), (25, 28), (18, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "701568", "dataset": "MATH"}
{"messages": [{"content": "In a 31x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 29), (15, 7), (21, 17), (16, 34), (14, 34), (10, 13), (1, 22), (5, 2), (15, 34), (12, 36), (10, 18), (16, 0), (10, 24), (14, 19), (14, 29), (19, 10), (8, 20), (2, 4), (24, 30), (0, 29), (4, 30), (3, 14), (24, 4), (23, 0), (8, 34), (26, 5), (23, 5), (7, 24), (3, 6), (17, 36), (7, 23), (21, 28), (28, 12), (21, 5), (8, 5), (15, 27), (30, 16), (8, 13), (30, 2), (8, 7), (12, 20), (15, 37), (9, 13), (6, 37), (9, 20), (25, 22), (9, 26), (28, 10), (23, 11), (25, 31), (23, 12), (4, 19), (4, 20), (20, 19), (12, 14), (15, 3), (14, 23), (7, 13), (5, 9), (10, 31), (9, 3), (24, 22), (6, 13), (2, 31), (14, 38), (12, 33), (20, 15), (16, 14), (2, 25), (25, 8), (7, 30), (16, 26), (19, 2), (0, 18), (22, 7), (5, 19), (11, 24), (0, 12), (21, 1), (6, 28), (11, 28), (26, 15), (22, 30), (2, 26), (3, 10), (15, 23), (18, 32), (28, 27), (27, 24), (19, 38), (7, 10), (20, 16), (22, 26), (24, 31), (5, 18), (26, 25), (7, 9), (21, 8), (17, 28), (13, 32), (3, 21), (28, 22), (22, 22), (6, 10), (29, 15), (18, 8), (6, 14), (30, 31), (4, 24), (2, 8), (23, 14), (17, 21), (25, 34), (7, 34), (0, 36), (25, 9), (14, 28), (28, 20), (4, 25), (1, 16), (14, 0), (8, 35), (29, 16), (13, 21), (0, 4), (0, 35), (0, 37), (1, 18), (17, 15), (9, 31), (1, 20), (26, 27), (26, 30), (20, 26), (18, 4), (15, 17), (30, 8), (2, 17), (4, 3), (6, 11), (15, 14), (5, 24), (13, 11), (5, 38), (2, 10), (8, 31), (23, 17), (14, 6), (4, 5), (11, 33), (6, 21), (30, 12), (7, 28), (10, 2), (12, 24), (4, 13), (13, 0), (8, 16), (4, 27), (5, 16), (1, 32), (10, 34), (22, 4), (26, 2), (1, 25), (23, 8), (2, 2), (5, 31), (11, 8), (25, 27), (3, 15), (26, 3), (9, 35), (13, 18), (18, 19), (24, 14), (10, 12), (6, 4), (16, 24), (25, 4), (15, 22), (5, 0), (14, 20), (8, 21), (25, 26), (29, 11), (22, 24), (23, 15), (19, 3), (30, 18), (21, 19), (29, 6), (13, 10), (6, 33), (13, 22), (22, 6), (3, 24), (13, 2), (5, 36), (14, 18), (30, 14), (13, 8), (0, 19), (25, 6), (24, 36), (20, 18), (1, 14), (23, 37), (20, 7), (21, 35), (0, 26), (5, 5), (1, 31), (22, 21), (25, 20), (2, 16), (4, 22), (30, 0), (5, 15), (26, 7), (7, 38), (24, 17), (17, 22), (21, 15), (24, 37), (10, 17), (5, 26), (1, 36), (14, 22), (15, 10), (15, 26), (30, 1), (27, 37), (6, 0), (26, 33), (17, 38), (17, 31), (25, 28), (26, 9), (30, 3), (10, 22), (30, 19), (30, 4), (9, 11), (17, 17), (27, 19), (30, 20), (24, 35), (9, 7), (19, 7), (22, 33), (3, 1), (16, 21), (29, 18), (29, 12), (29, 38), (7, 2), (1, 15), (4, 28), (3, 4), (15, 24), (27, 8), (24, 33), (21, 38), (21, 2), (14, 31), (21, 29), (29, 23), (24, 23), (20, 20), (24, 6), (27, 36), (15, 32), (2, 24), (16, 8), (1, 37), (20, 12), (25, 13), (11, 17), (28, 9), (12, 30), (23, 13), (25, 17), (21, 30), (2, 11), (23, 26), (7, 16), (30, 27), (9, 30), (9, 10), (18, 28), (30, 21), (20, 9), (1, 5), (16, 1), (24, 27), (7, 8), (27, 18), (10, 11), (0, 34), (26, 20), (8, 23), (29, 2), (2, 3), (28, 18), (2, 32), (11, 32), (21, 32), (12, 8), (28, 34), (28, 32), (3, 13), (20, 21), (11, 36), (24, 10), (28, 25), (9, 0), (11, 21), (10, 26), (20, 11), (6, 2), (5, 14), (10, 3), (0, 1), (4, 37), (18, 23), (17, 24), (8, 18), (17, 37), (24, 15), (7, 32), (24, 18), (13, 28), (26, 35), (25, 5), (20, 10), (23, 28), (24, 5), (17, 8), (18, 6), (6, 3), (15, 15), (22, 18), (11, 19), (6, 35), (16, 7), (30, 28), (28, 35), (23, 36), (19, 29), (22, 9), (24, 28), (16, 10), (3, 35), (29, 8), (9, 19), (3, 9), (29, 17), (29, 5), (14, 8), (4, 6), (5, 34), (5, 37), (7, 36), (13, 26), (10, 29), (29, 14), (11, 25), (2, 38), (12, 1), (5, 3), (1, 27), (28, 31), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "858048", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), 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), (33, 9), (31, 17), (0, 12), (29, 9), (26, 16), (6, 5), (8, 25), (32, 4), (26, 19), (3, 20), (31, 5), (21, 2), (12, 7), (14, 20), (21, 28), (3, 24), (12, 27), (23, 24), (0, 24), (25, 25), (17, 17), (10, 3), (15, 8), (16, 9), (30, 26), (4, 0), (34, 30), (34, 4), (31, 12), (24, 7), (9, 9), (20, 30), (36, 30), (24, 17), (32, 27), (21, 20), (0, 7), (14, 15), (22, 0), (5, 30), (4, 5), (31, 3), (19, 30), (20, 5), (28, 28), (22, 21), (35, 0), (22, 7), (1, 11), (20, 2), (24, 6), (7, 25), (5, 3), (14, 26), (28, 27), (0, 20), (10, 12), (26, 4), (32, 0), (5, 21), (33, 18), (29, 23), (25, 14), (21, 13), (30, 3), (1, 13), (31, 13), (12, 30), (31, 30), (18, 24), (31, 7), (13, 0), (27, 5), (6, 18), (29, 0), (9, 29), (20, 23), (7, 1), (15, 17), (29, 30), (11, 28), (9, 25), (37, 9), (5, 9), (0, 15), (5, 22), (9, 21), (14, 28), (33, 20), (2, 30), (1, 17), (3, 10), (37, 20), (21, 3), (7, 30), (16, 11), (36, 19), (30, 2), (18, 28), (8, 16), (36, 5), (10, 25), (13, 22), (3, 2), (37, 10), (21, 23), (10, 16), (2, 17), (18, 14), (11, 29), (9, 15), (23, 2), (11, 11), (36, 9), (11, 22), (13, 14), (1, 26), (23, 16), (2, 14), (3, 26), (28, 24), (28, 18), (30, 14), (33, 17), (28, 9), (26, 3), (9, 5), (14, 18), (35, 20), (19, 26), (24, 0), (27, 20), (15, 19), (31, 28), (18, 25), (11, 8), (13, 24), (30, 28), (19, 29), (5, 28), (10, 19), (36, 25), (7, 21), (0, 1), (11, 27), (8, 27), (29, 8), (5, 4), (23, 11), (20, 25), (25, 10), (6, 9), (15, 27), (4, 17), (27, 10), (37, 17), (24, 4), (14, 19), (33, 21), (11, 6), (10, 1), (1, 14), (33, 25), (26, 17), (17, 8), (17, 11), (29, 16), (15, 4), (8, 8), (13, 30), (23, 25), (15, 6), (10, 23), (0, 2), (1, 3), (21, 15), (7, 16), (37, 18), (1, 15), (8, 17), (3, 23), (27, 25), (5, 11), (28, 1), (37, 23), (24, 21), (13, 12), (31, 20), (22, 23), (17, 3), (15, 3), (28, 4), (32, 1), (18, 21), (9, 24), (28, 25), (17, 1), (37, 16), (17, 22), (22, 18), (30, 0), (22, 6), (12, 21), (6, 15), (25, 11), (19, 8), (6, 13), (25, 20), (12, 9), (10, 28), (0, 3), (5, 5), (14, 7), (7, 11), (32, 22), (27, 21), (1, 5), (13, 29), (21, 5), (25, 27), (9, 18), (11, 13), (15, 0), (6, 0), (28, 22), (30, 1), (10, 10), (4, 24), (21, 17), (22, 11), (21, 4), (18, 13), (21, 25), (27, 28), (16, 21), (19, 19), (21, 29), (7, 24), (3, 22), (6, 22), (16, 17), (23, 27), (25, 23), (12, 6), (25, 8), (31, 19), (19, 7), (32, 15), (27, 12), (36, 20), (19, 10), (11, 14), (15, 2), (7, 17), (2, 21), (29, 2), (18, 8), (28, 29), (25, 2), (36, 23), (26, 29), (25, 5), (18, 6), (25, 13), (33, 12), (33, 29), (28, 0), (4, 30), (0, 9), (21, 19), (24, 12), (35, 24), (1, 30), (33, 0), (37, 1), (22, 2), (37, 12), (29, 6), (16, 7), (16, 10), (20, 7), (30, 29), (0, 16), (32, 9), (9, 19), (0, 22), (14, 10), (7, 28), (5, 2), (18, 12), (33, 28), (5, 12), (19, 27), (21, 21), (18, 1), (32, 7), (13, 27), (11, 12), (8, 28), (22, 22), (34, 19), (36, 3), (29, 1), (16, 14), (4, 10), (37, 25), (27, 2), (14, 11), (7, 4), (1, 16), (1, 21), (14, 8), (8, 20), (19, 21), (29, 7), (6, 6), (33, 23), (34, 2), (17, 24), (35, 13), (0, 14), (3, 25), (18, 0), (29, 25), (34, 15), (5, 24), (36, 22), (16, 30), (23, 13), (2, 12), (26, 10), (2, 20), (11, 25), (2, 2), (13, 10), (17, 13), (11, 19), (4, 27), (20, 29), (9, 1), (13, 11), (36, 1), (19, 16), (32, 25), (16, 2), (28, 30), (4, 13), (17, 20), (15, 30), (22, 26), (34, 29), (25, 0), (32, 21), (9, 8), (18, 17), (10, 9), (8, 13), (13, 4), (31, 1), (0, 23), (32, 17), (30, 23), (22, 24), (14, 21), (32, 13), (18, 18), (8, 15), (17, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96750", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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), (23, 8), (7, 1), (18, 28), (9, 6), (15, 27), (3, 5), (23, 11), (22, 30), (6, 11), (20, 16), (11, 28), (27, 27), (6, 15), (6, 10), (18, 6), (26, 28), (21, 4), (23, 2), (10, 26), (17, 15), (28, 31), (26, 16), (2, 28), (16, 12), (2, 15), (27, 26), (9, 2), (15, 30), (11, 17), (4, 21), (12, 2), (12, 23), (17, 29), (2, 24), (8, 19), (19, 4), (29, 28), (13, 9), (5, 0), (28, 14), (27, 25), (9, 23), (9, 16), (12, 11), (16, 17), (8, 0), (22, 32), (10, 11), (5, 1), (15, 7), (27, 22), (18, 26), (0, 32), (21, 30), (22, 25), (0, 30), (14, 12), (1, 13), (15, 0), (8, 26), (20, 10), (13, 24), (11, 21), (17, 28), (12, 0), (26, 22), (17, 11), (17, 6), (12, 21), (28, 24), (21, 14), (25, 23), (19, 27), (12, 4), (29, 31), (6, 25), (6, 1), (19, 10), (2, 23), (28, 5), (10, 27), (7, 3), (20, 6), (21, 7), (21, 1), (26, 19), (22, 16), (21, 13), (4, 18), (8, 2), (17, 16), (28, 17), (8, 3), (22, 15), (19, 23), (14, 5), (21, 9), (13, 19), (15, 23), (9, 26), (15, 21), (8, 30), (11, 14), (4, 22), (9, 11), (25, 29), (20, 26), (3, 4), (14, 13), (17, 18), (13, 3), (17, 31), (7, 19), (16, 23), (13, 20), (8, 13), (25, 13), (12, 7), (18, 20), (27, 13), (15, 32), (26, 13), (14, 16), (21, 6), (18, 8), (4, 3), (14, 4), (0, 26), (5, 31), (12, 25), (16, 19), (21, 8), (0, 1), (12, 14), (15, 2), (13, 13), (27, 2), (26, 0), (7, 13), (13, 1), (9, 10), (2, 27), (10, 8), (18, 14), (8, 12), (12, 19), (0, 6), (9, 8), (3, 0), (20, 12), (11, 26), (0, 8), (23, 30), (20, 20), (20, 25), (18, 30), (22, 21), (1, 12), (10, 12), (7, 11), (0, 5), (10, 6), (26, 29), (26, 25), (25, 7), (29, 23), (5, 22), (9, 20), (25, 28), (11, 3), (4, 2), (28, 30), (8, 10), (29, 8), (17, 27), (0, 27), (6, 22), (20, 29), (16, 27), (22, 8), (18, 12), (27, 14), (3, 15), (20, 5), (12, 26), (25, 9), (10, 23), (15, 13), (3, 3), (4, 26), (7, 23), (23, 0), (17, 20), (25, 25), (13, 23), (21, 10), (22, 6), (19, 5), (4, 16), (4, 20), (2, 25), (20, 3), (16, 25), (9, 32), (29, 29), (3, 29), (28, 8), (11, 32), (29, 11), (1, 16), (25, 1), (27, 16), (14, 9), (19, 29), (0, 20), (18, 22), (21, 20), (0, 23), (1, 17), (9, 9), (8, 22), (20, 32), (18, 2), (10, 24), (3, 27), (11, 11), (20, 0), (5, 18), (6, 21), (23, 12), (9, 21), (13, 10), (0, 17), (27, 4), (29, 12), (18, 17), (26, 6), (7, 14), (24, 31), (2, 14), (21, 23), (11, 19), (11, 1), (18, 7), (3, 2), (27, 28), (10, 9), (17, 24), (5, 5), (26, 18), (15, 5), (8, 23), (4, 13), (21, 29), (6, 16), (21, 21), (23, 28), (10, 32), (14, 24), (5, 24), (28, 10), (22, 27), (26, 15), (2, 31), (20, 1), (16, 6), (2, 3), (15, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "855522", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 29), (25, 30), (31, 17), (23, 17), (11, 4), (26, 10), (7, 26), (29, 4), (10, 17), (23, 21), (32, 14), (5, 22), (21, 15), (9, 11), (2, 22), (1, 13), (31, 2), (19, 10), (5, 27), (28, 22), (0, 7), (0, 5), (13, 12), (29, 1), (5, 4), (14, 6), (25, 11), (33, 16), (32, 13), (23, 24), (30, 16), (7, 6), (29, 23), (24, 11), (8, 30), (33, 21), (34, 19), (24, 8), (18, 26), (33, 20), (29, 20), (30, 18), (17, 16), (14, 13), (16, 10), (19, 27), (23, 18), (20, 32), (11, 15), (27, 12), (8, 14), (22, 22), (4, 9), (1, 8), (23, 30), (22, 7), (21, 14), (0, 25), (26, 7), (32, 28), (4, 16), (20, 15), (33, 9), (5, 5), (29, 18), (9, 3), (3, 23), (10, 25), (8, 31), (28, 24), (0, 24), (2, 3), (29, 17), (3, 9), (25, 23), (5, 10), (21, 23), (3, 19), (22, 13), (14, 15), (23, 29), (9, 10), (29, 9), (31, 30), (19, 5), (33, 11), (7, 16), (8, 6), (6, 10), (5, 16), (19, 8), (12, 23), (23, 31), (21, 26), (5, 9), (21, 19), (26, 6), (7, 9), (18, 30), (3, 4), (27, 2), (1, 2), (24, 24), (10, 2), (18, 24), (34, 26), (33, 28), (17, 13), (1, 14), (19, 28), (20, 2), (1, 16), (12, 14), (35, 6), (33, 27), (10, 0), (3, 24), (24, 28), (7, 21), (8, 28), (9, 8), (34, 20), (3, 30), (5, 11), (23, 22), (27, 10), (16, 22), (10, 26), (30, 30), (9, 19), (12, 7), (33, 0), (27, 16), (12, 5), (23, 7), (6, 28), (28, 10), (0, 2), (35, 29), (26, 20), (28, 19), (26, 1), (13, 10), (5, 28), (25, 7), (3, 10), (12, 31), (28, 32), (10, 19), (34, 28), (28, 25), (15, 27), (18, 10), (32, 12), (0, 28), (18, 17), (29, 10), (10, 9), (13, 28), (29, 24), (24, 27), (1, 9), (6, 4), (16, 18), (27, 19), (9, 14), (4, 11), (11, 12), (14, 27), (18, 0), (21, 5), (20, 19), (9, 27), (26, 17), (31, 8), (9, 4), (10, 10), (4, 23), (4, 5), (28, 30), (27, 11), (15, 18), (28, 28), (27, 9), (4, 24), (21, 24), (24, 0), (4, 14), (0, 10), (5, 13), (26, 27), (18, 12), (25, 19), (16, 14), (2, 11), (8, 15), (28, 26), (17, 30), (19, 2), (20, 27), (32, 27), (7, 18), (15, 8), (21, 30), (27, 1), (14, 30), (19, 32), (15, 23), (34, 14), (2, 31), (19, 31), (11, 10), (11, 7), (32, 5), (15, 15), (4, 32), (29, 6), (18, 23), (12, 22), (4, 22), (33, 30), (14, 0), (2, 30), (6, 12), (16, 8), (23, 13), (6, 16), (34, 17), (19, 14), (35, 16), (6, 32), (20, 25), (28, 0), (5, 24), (15, 31), (11, 0), (4, 18), (16, 16), (12, 6), (29, 8), (24, 9), (19, 11), (35, 21), (30, 24), (16, 23), (18, 16), (26, 13), (30, 23), (17, 4), (1, 26), (27, 3), (3, 14), (15, 24), (30, 17), (1, 0), (31, 13), (9, 28), (28, 18), (0, 32), (32, 22), (2, 15), (20, 28), (7, 29), (21, 27), (8, 26), (14, 16), (34, 18), (16, 19), (18, 25), (10, 7), (35, 22), (2, 9), (20, 8), (3, 13), (34, 7), (15, 19), (16, 30), (21, 0), (5, 31), (22, 3), (15, 30), (0, 14), (31, 19), (20, 6), (10, 32), (5, 8), (34, 3), (4, 13), (26, 28), (18, 31), (23, 3), (14, 28), (18, 29), (16, 5), (34, 1), (27, 7), (13, 16), (28, 2), (34, 30), (9, 7), (3, 16), (26, 16), (33, 14), (2, 2), (22, 14), (25, 28), (9, 18), (25, 21), (33, 23), (25, 4), (28, 13), (3, 29), (2, 16), (17, 14), (9, 32), (18, 32), (1, 7), (3, 15), (30, 13), (25, 0), (8, 17), (4, 19), (17, 9), (30, 26), (34, 11), (7, 23), (25, 25), (18, 27), (31, 9), (6, 22), (18, 20), (23, 23), (28, 15), (3, 20), (14, 1), (34, 22), (28, 21), (2, 19), (13, 21), (16, 11), (23, 28), (20, 12), (6, 24), (31, 18), (15, 9), (21, 12), (32, 19), (18, 2), (32, 23), (22, 0), (29, 28), (24, 32), (32, 32), (28, 14), (12, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "347400", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), 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), (19, 11), (12, 8), (14, 14), (19, 6), (21, 7), (9, 0), (4, 3), (8, 10), (3, 32), (32, 10), (9, 36), (10, 30), (12, 13), (35, 12), (31, 18), (7, 21), (25, 0), (23, 12), (19, 23), (14, 25), (1, 28), (0, 15), (20, 30), (34, 17), (17, 23), (17, 34), (27, 23), (22, 13), (6, 7), (37, 6), (19, 7), (12, 23), (37, 18), (16, 28), (22, 27), (36, 3), (32, 1), (11, 28), (26, 30), (13, 1), (30, 4), (30, 6), (11, 7), (28, 25), (17, 36), (27, 2), (16, 11), (29, 21), (11, 4), (7, 9), (21, 28), (0, 29), (37, 5), (11, 30), (30, 11), (36, 20), (18, 33), (33, 23), (18, 32), (26, 16), (19, 2), (26, 19), (25, 18), (4, 27), (28, 15), (35, 17), (28, 14), (33, 2), (17, 28), (0, 17), (17, 3), (35, 9), (4, 14), (29, 10), (29, 29), (31, 36), (16, 15), (17, 5), (21, 33), (1, 12), (13, 31), (26, 21), (8, 36), (29, 26), (9, 33), (34, 33), (22, 35), (18, 23), (5, 32), (32, 28), (18, 9), (2, 25), (2, 4), (1, 18), (28, 29), (17, 17), (10, 14), (16, 25), (30, 20), (36, 17), (25, 6), (9, 15), (31, 9), (17, 27), (15, 16), (25, 13), (35, 24), (22, 18), (32, 3), (30, 35), (8, 21), (7, 20), (36, 18), (26, 14), (6, 12), (29, 15), (29, 8), (23, 30), (17, 37), (20, 12), (18, 36), (16, 21), (35, 37), (22, 32), (3, 18), (14, 20), (9, 27), (26, 22), (6, 20), (13, 14), (0, 21), (21, 31), (34, 12), (20, 8), (2, 26), (27, 30), (8, 32), (37, 34), (33, 19), (23, 27), (10, 10), (30, 1), (6, 0), (9, 19), (16, 10), (15, 14), (8, 25), (29, 2), (22, 28), (34, 31), (13, 22), (11, 8), (3, 14), (10, 12), (36, 14), (20, 7), (27, 26), (14, 31), (28, 3), (25, 16), (19, 26), (4, 19), (34, 21), (3, 33), (14, 32), (9, 17), (1, 30), (6, 14), (13, 9), (19, 5), (32, 36), (34, 35), (36, 0), (14, 27), (35, 31), (32, 24), (6, 16), (14, 16), (6, 31), (14, 12), (18, 16), (11, 35), (17, 24), (0, 20), (14, 35), (8, 22), (18, 20), (13, 7), (15, 2), (13, 21), (15, 30), (7, 18), (21, 17), (36, 11), (20, 17), (3, 2), (15, 24), (22, 1), (28, 35), (15, 36), (7, 17), (18, 21), (15, 11), (31, 2), (25, 8), (20, 16), (21, 35), (16, 37), (26, 23), (27, 0), (6, 35), (4, 24), (2, 5), (29, 4), (26, 5), (4, 15), (21, 8), (22, 15), (6, 19), (14, 36), (9, 9), (14, 30), (0, 14), (21, 25), (21, 3), (36, 24), (31, 6), (16, 20), (24, 2), (31, 12), (3, 0), (19, 16), (10, 32), (10, 19), (5, 30), (16, 6), (3, 25), (3, 30), (9, 7), (37, 2), (4, 9), (36, 35), (20, 6), (4, 5), (11, 16), (29, 9), (22, 7), (30, 12), (6, 21), (18, 14), (23, 1), (27, 12), (20, 15), (35, 5), (15, 32), (17, 14), (17, 25), (21, 9), (13, 12), (5, 1), (20, 13), (18, 8), (15, 1), (26, 6), (20, 35), (0, 11), (27, 24), (5, 2), (25, 10), (12, 32), (1, 23), (11, 22), (22, 9), (29, 13), (8, 1), (1, 14), (10, 25), (21, 13), (2, 31), (0, 6), (32, 37), (23, 18), (32, 25), (7, 34), (24, 21), (2, 33), (34, 24), (5, 33), (35, 25), (10, 9), (34, 5), (33, 16), (29, 36), (27, 25), (13, 29), (27, 27), (18, 35), (3, 17), (9, 31), (1, 29), (18, 22), (29, 34), (6, 15), (5, 7), (6, 34), (9, 29), (16, 33), (33, 30), (34, 34), (24, 22), (21, 6), (15, 23), (1, 3), (37, 26), (2, 0), (5, 25), (35, 32), (8, 14), (16, 1), (3, 4), (12, 19), (35, 28), (13, 24), (28, 7), (0, 36), (16, 26), (5, 23), (36, 5), (16, 9), (5, 21), (5, 37), (28, 34), (37, 27), (19, 19), (1, 26), (25, 30), (24, 28), (14, 0), (37, 33), (19, 34), (21, 12), (31, 5), (13, 6), (9, 26), (27, 17), (1, 33), (6, 10), (1, 2), (0, 24), (17, 2), (15, 19), (8, 29), (3, 7), (37, 36), (28, 33), (31, 0), (35, 14), (16, 24), (29, 16), (28, 8), (7, 14), (4, 17), (26, 20), (26, 7), (0, 25), (6, 8), (18, 26), (9, 11), (17, 20), (11, 6), (6, 30), (8, 26), (19, 20), (30, 7), (22, 22), (30, 33), (0, 18), (28, 31), (6, 18), (7, 26), (32, 19), (36, 28), (3, 23), (32, 34), (0, 12), (14, 9), (24, 13), (9, 24), (32, 7), (13, 19), (15, 34), (37, 11), (23, 2), (1, 24), (33, 10), (17, 1), (11, 10), (6, 5), (28, 17), (32, 15), (35, 6), (15, 33), (22, 19), (27, 36), (18, 13), (10, 37), (3, 24), (24, 35), (29, 1), (26, 28), (13, 33), (29, 14), (12, 27), (32, 8), (29, 7), (13, 2), (5, 13), (9, 21), (29, 33), (9, 16), (21, 36), (3, 29), (34, 23), (27, 10), (35, 21), (30, 16), (26, 24), (34, 14), (32, 30), (21, 10), (0, 7), (21, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "663840", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), 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), (26, 14), (18, 22), (9, 4), (30, 5), (27, 15), (11, 5), (19, 15), (16, 24), (12, 5), (7, 17), (25, 7), (31, 10), (1, 12), (22, 9), (1, 21), (21, 26), (0, 27), (4, 16), (22, 26), (33, 6), (26, 3), (31, 29), (32, 24), (26, 18), (24, 19), (3, 15), (6, 9), (12, 2), (7, 10), (12, 26), (34, 14), (19, 16), (16, 28), (10, 21), (13, 12), (27, 27), (13, 24), (16, 22), (31, 19), (30, 13), (36, 16), (34, 15), (20, 11), (17, 8), (18, 13), (20, 16), (36, 25), (29, 8), (24, 29), (22, 16), (4, 6), (3, 16), (14, 18), (17, 5), (27, 18), (15, 5), (24, 27), (35, 8), (35, 16), (18, 21), (23, 16), (16, 27), (13, 29), (31, 3), (36, 18), (4, 10), (36, 9), (26, 17), (26, 1), (24, 21), (12, 11), (34, 9), (24, 26), (7, 3), (5, 15), (30, 26), (4, 21), (35, 20), (30, 16), (25, 17), (10, 0), (34, 27), (19, 22), (0, 24), (9, 27), (27, 28), (12, 27), (15, 8), (23, 6), (33, 4), (21, 28), (22, 19), (24, 9), (34, 21), (34, 28), (26, 5), (1, 25), (22, 23), (33, 3), (20, 21), (22, 4), (17, 13), (12, 16), (9, 0), (29, 27), (27, 1), (15, 28), (22, 12), (23, 10), (19, 14), (17, 7), (32, 16), (0, 12), (9, 23), (13, 3), (2, 1), (3, 24), (12, 3), (21, 19), (6, 0), (12, 13), (7, 24), (35, 5), (23, 12), (4, 1), (9, 2), (35, 19), (7, 27), (15, 21), (26, 24), (26, 4), (19, 19), (3, 19), (25, 27), (5, 14), (32, 19), (8, 21), (0, 25), (8, 22), (18, 29), (8, 7), (21, 21), (24, 7), (9, 5), (34, 23), (13, 4), (12, 24), (32, 27), (28, 11), (25, 9), (14, 22), (15, 4), (12, 1), (16, 9), (11, 0), (21, 7), (22, 21), (13, 18), (12, 22), (29, 5), (23, 19), (13, 21), (13, 15), (10, 27), (28, 9), (30, 29), (15, 13), (2, 12), (21, 11), (0, 4), (9, 13), (30, 9), (8, 4), (32, 4), (25, 5), (35, 15), (18, 18), (36, 12), (30, 17), (1, 0), (29, 15), (32, 6), (3, 17), (14, 25), (27, 11), (21, 0), (19, 27), (33, 26), (32, 18), (19, 24), (11, 22), (16, 7), (6, 19), (20, 27), (3, 21), (16, 17), (7, 4), (35, 2), (8, 6), (19, 12), (24, 13), (33, 1), (16, 15), (26, 12), (17, 23), (25, 18), (17, 22), (18, 6), (1, 7), (17, 6), (26, 6), (21, 16), (28, 5), (7, 25), (13, 11), (14, 20), (12, 9), (20, 26), (22, 5), (14, 26), (13, 27), (8, 0), (4, 7), (7, 8), (26, 29), (34, 8), (1, 28), (32, 22), (32, 12), (10, 9), (36, 28), (22, 29), (25, 14), (30, 14), (2, 15), (27, 24), (22, 17), (11, 19), (25, 1), (1, 22), (19, 20), (25, 16), (4, 13), (16, 18), (34, 18), (35, 27), (22, 8), (0, 8), (31, 25), (28, 0), (15, 22), (31, 7), (30, 0), (25, 24), (11, 8), (6, 11), (31, 22), (28, 10), (16, 5), (1, 15), (19, 2), (12, 21), (1, 19), (31, 21), (25, 19), (21, 4), (13, 20), (5, 7), (14, 19), (36, 3), (32, 25), (27, 20), (15, 18), (29, 24), (33, 25), (0, 20), (11, 23), (1, 14), (2, 7), (18, 8), (14, 8), (23, 28), (12, 12), (29, 1), (33, 2), (14, 5), (36, 17), (29, 16), (10, 24), (9, 20), (31, 2), (25, 2), (5, 9), (15, 24), (36, 8), (33, 7), (18, 7), (17, 17), (36, 24), (7, 18), (0, 16), (29, 10), (10, 1), (1, 5), (14, 17), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "454800", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (13, 0), (3, 28), (25, 24), (28, 5), (18, 32), (21, 32), (24, 13), (18, 3), (17, 29), (14, 19), (25, 13), (22, 21), (1, 11), (17, 25), (21, 0), (2, 35), (13, 4), (13, 20), (9, 29), (15, 10), (26, 22), (17, 6), (7, 3), (20, 32), (0, 30), (29, 19), (16, 0), (2, 27), (18, 16), (30, 8), (1, 35), (31, 27), (2, 33), (16, 17), (9, 13), (21, 12), (20, 18), (23, 1), (27, 4), (14, 20), (6, 19), (19, 1), (14, 13), (24, 8), (26, 25), (13, 23), (12, 7), (18, 26), (15, 1), (20, 16), (1, 14), (10, 33), (26, 2), (2, 12), (16, 11), (30, 6), (10, 27), (16, 9), (5, 3), (3, 11), (4, 26), (14, 16), (30, 25), (11, 5), (15, 5), (6, 21), (25, 29), (25, 35), (28, 18), (8, 26), (3, 25), (23, 19), (18, 9), (24, 23), (4, 19), (10, 29), (27, 21), (30, 4), (9, 24), (28, 19), (23, 22), (8, 25), (6, 34), (9, 8), (2, 2), (25, 21), (5, 22), (16, 23), (22, 15), (8, 1), (13, 9), (28, 2), (6, 2), (2, 10), (13, 33), (30, 20), (32, 28), (28, 0), (18, 10), (6, 35), (27, 8), (6, 25), (18, 35), (4, 33), (0, 1), (9, 4), (18, 30), (31, 21), (14, 10), (24, 34), (13, 28), (32, 6), (10, 18), (15, 13), (2, 6), (15, 15), (18, 15), (24, 3), (15, 8), (17, 9), (32, 34), (29, 2), (5, 34), (7, 19), (17, 1), (19, 23), (10, 19), (29, 7), (4, 0), (24, 31), (22, 25), (12, 9), (0, 2), (18, 11), (30, 33), (10, 21), (5, 2), (11, 12), (0, 34), (3, 24), (4, 24), (12, 25), (10, 34), (22, 18), (20, 26), (17, 35), (16, 10), (22, 3), (10, 5), (2, 7), (27, 14), (18, 14), (7, 33), (32, 21), (19, 11), (23, 35), (15, 34), (6, 18), (18, 2), (25, 34), (5, 17), (16, 1), (12, 23), (4, 6), (5, 33), (14, 32), (0, 15), (7, 35), (31, 29), (10, 23), (9, 6), (1, 32), (4, 2), (23, 20), (20, 4), (27, 31), (4, 31), (0, 14), (32, 29), (2, 0), (22, 26), (23, 4), (16, 29), (0, 9), (23, 6), (4, 25), (11, 14), (13, 3), (16, 7), (1, 2), (28, 10), (19, 17), (12, 18), (12, 10), (10, 22), (12, 31), (13, 11), (13, 29), (31, 13), (14, 35), (7, 26), (17, 20), (11, 27), (16, 33), (20, 19), (12, 27), (8, 6), (19, 21), (23, 5), (31, 20), (6, 4), (18, 0), (25, 7), (20, 27), (10, 13), (32, 0), (11, 17), (8, 31), (3, 18), (25, 32), (32, 17), (28, 16), (21, 6), (32, 1), (0, 29), (25, 28), (18, 8), (19, 35), (5, 28), (29, 24), (20, 17), (17, 23), (8, 19), (26, 28), (7, 4), (1, 15), (2, 23), (31, 15), (9, 25), (8, 9), (2, 17), (24, 32), (30, 15), (25, 23), (6, 1), (16, 32), (9, 5), (6, 11), (10, 25), (9, 32), (16, 26), (19, 5), (27, 27), (29, 34), (7, 12), (20, 23), (22, 9), (19, 32), (23, 21), (7, 16), (21, 7), (20, 7), (23, 10), (21, 30), (2, 16), (26, 13), (2, 4), (2, 8), (32, 22), (0, 11), (4, 4), (18, 7), (22, 7), (3, 32), (18, 24), (6, 7), (3, 33), (2, 18), (5, 26), (13, 14), (29, 22), (32, 10), (32, 2), (6, 27), (11, 6), (1, 20), (8, 28), (4, 28), (6, 26), (19, 26), (16, 20), (3, 31), (15, 0), (6, 28), (9, 22), (16, 13), (24, 4), (23, 11), (31, 1), (12, 29), (32, 33), (29, 10), (10, 15), (7, 10), (17, 13), (7, 32), (24, 16), (25, 16), (9, 26), (3, 7), (27, 11), (16, 31), (28, 17), (31, 31), (3, 20), (32, 27), (26, 18), (31, 16), (6, 9), (24, 18), (10, 26), (30, 17), (23, 24), (14, 8), (22, 14), (5, 29), (32, 24), (17, 33), (9, 35), (15, 11), (16, 2), (10, 3), (24, 12), (9, 9), (3, 23), (8, 23), (5, 15), (1, 34), (9, 18), (7, 14), (11, 20), (9, 20), (29, 3), (11, 16), (3, 6), (2, 15), (11, 31), (19, 33), (19, 0), (7, 34), (16, 27), (19, 7), (14, 9), (26, 11), (15, 30), (14, 1), (16, 4), (12, 19), (10, 12), (31, 17), (4, 16), (7, 17), (31, 26), (17, 27), (20, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943380", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 31), (32, 20), (32, 9), (5, 29), (31, 5), (21, 20), (12, 28), (30, 5), (33, 31), (33, 6), (22, 13), (16, 26), (14, 25), (32, 5), (6, 33), (2, 18), (28, 16), (11, 32), (24, 20), (6, 29), (36, 27), (10, 15), (9, 32), (35, 0), (9, 29), (30, 25), (31, 18), (35, 9), (20, 14), (10, 7), (18, 11), (35, 10), (1, 9), (28, 1), (15, 33), (17, 24), (20, 33), (9, 13), (3, 12), (2, 11), (4, 28), (11, 9), (14, 15), (19, 28), (8, 25), (21, 15), (32, 30), (33, 28), (20, 25), (5, 23), (1, 6), (24, 33), (7, 10), (2, 10), (35, 21), (18, 16), (22, 28), (27, 4), (5, 27), (25, 11), (10, 16), (9, 22), (1, 22), (1, 30), (33, 12), (6, 9), (25, 6), (19, 18), (16, 14), (35, 22), (2, 16), (13, 28), (9, 24), (17, 17), (32, 31), (19, 33), (27, 31), (3, 15), (21, 8), (14, 23), (5, 7), (14, 0), (15, 11), (33, 14), (7, 15), (36, 29), (29, 4), (31, 11), (34, 27), (18, 23), (12, 19), (18, 22), (29, 30), (20, 30), (23, 13), (33, 1), (0, 26), (18, 15), (30, 8), (2, 13), (16, 30), (22, 34), (35, 14), (27, 3), (15, 17), (1, 2), (25, 21), (12, 27), (19, 23), (14, 24), (22, 6), (19, 8), (35, 13), (30, 24), (23, 32), (17, 33), (24, 28), (31, 9), (34, 10), (34, 16), (27, 1), (34, 17), (8, 10), (31, 0), (24, 27), (20, 9), (30, 16), (24, 26), (30, 27), (28, 7), (32, 23), (28, 26), (31, 20), (14, 16), (26, 15), (13, 23), (4, 29), (3, 10), (20, 27), (4, 21), (4, 8), (29, 16), (18, 5), (4, 0), (24, 31), (1, 4), (1, 29), (13, 32), (22, 0), (28, 8), (33, 5), (24, 13), (30, 4), (0, 3), (28, 23), (11, 21), (36, 21), (25, 7), (7, 32), (4, 5), (24, 14), (29, 33), (29, 26), (11, 25), (17, 20), (1, 0), (9, 34), (1, 26), (28, 10), (34, 1), (13, 1), (5, 16), (10, 30), (35, 1), (10, 14), (21, 13), (12, 30), (15, 2), (23, 2), (14, 33), (19, 25), (20, 12), (26, 24), (3, 20), (3, 27), (14, 29), (26, 6), (1, 31), (6, 24), (28, 21), (1, 18), (27, 6), (7, 30), (36, 17), (14, 32), (13, 20), (16, 19), (19, 29), (12, 9), (29, 34), (25, 3), (27, 0), (27, 8), (19, 20), (13, 19), (34, 22), (5, 5), (16, 4), (25, 16), (9, 25), (34, 28), (30, 23), (7, 9), (29, 0), (29, 24), (20, 22), (14, 3), (7, 21), (36, 26), (32, 6), (16, 21), (19, 30), (12, 15), (27, 27), (21, 26), (24, 34), (14, 17), (36, 12), (13, 24), (2, 6), (20, 18), (36, 16), (16, 34), (22, 14), (22, 32), (36, 0), (28, 28), (7, 8), (26, 17), (5, 20), (22, 1), (5, 19), (26, 25), (23, 34), (10, 23), (11, 1), (13, 9), (30, 31), (18, 19), (29, 1), (10, 6), (16, 22), (24, 24), (32, 29), (21, 28), (15, 19), (7, 25), (35, 19), (5, 11), (23, 23), (6, 12), (36, 1), (34, 25), (16, 23), (36, 25), (9, 2), (9, 18), (14, 27), (26, 19), (32, 3), (11, 33), (3, 4), (36, 20), (31, 26), (26, 16), (12, 17), (31, 4), (33, 26), (8, 24), (28, 3), (28, 17), (26, 20), (6, 2), (25, 24), (10, 29), (10, 9), (20, 21), (21, 29), (3, 28), (33, 33), (22, 25), (15, 1), (5, 26), (31, 6), (7, 19), (12, 8), (26, 30), (32, 33), (13, 16), (4, 31), (2, 19), (13, 25), (27, 20), (15, 14), (9, 11), (10, 21), (21, 24), (1, 21), (15, 25), (0, 29), (17, 31), (13, 3), (18, 30), (36, 13), (7, 34), (27, 32), (17, 11), (16, 11), (31, 19), (23, 3), (20, 3), (17, 8), (7, 4), (31, 17), (33, 9), (30, 26), (9, 12), (32, 32), (22, 24), (11, 14), (9, 27), (13, 14), (19, 21), (33, 25), (14, 12), (8, 3), (26, 31), (18, 28), (28, 34), (18, 32), (14, 31), (31, 2), (4, 6), (8, 6), (17, 5), (34, 18), (33, 10), (1, 7), (20, 16), (19, 9), (16, 6), (2, 20), (6, 19), (6, 1), (24, 19), (0, 11), (21, 3), (21, 19), (17, 0), (9, 0), (25, 13), (3, 0), (1, 14), (15, 5), (21, 16), (2, 25), (3, 21), (2, 23), (14, 18), (18, 20), (20, 4), (13, 4), (3, 22), (22, 17), (35, 32), (23, 7), (10, 19), (25, 1), (27, 5), (30, 17), (25, 30), (12, 10), (9, 15), (23, 8), (2, 28), (28, 15), (7, 27), (24, 7), (4, 12), (21, 30), (1, 10), (29, 20), (12, 22), (11, 23), (33, 22), (32, 17), (21, 4), (0, 13), (19, 12), (29, 8), (9, 14), (35, 15), (34, 4), (5, 12), (28, 25), (17, 6), (6, 11), (12, 13), (29, 28), (32, 26), (19, 26), (17, 25), (25, 12), (17, 34), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "650304", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), 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, 3), (13, 28), (2, 8), (5, 32), (10, 21), (27, 8), (22, 27), (21, 9), (6, 12), (11, 33), (4, 11), (10, 19), (26, 21), (24, 30), (7, 16), (26, 32), (4, 26), (7, 17), (9, 5), (7, 6), (17, 8), (28, 28), (23, 13), (11, 5), (6, 23), (4, 29), (17, 7), (26, 8), (17, 9), (17, 6), (15, 18), (22, 15), (0, 15), (7, 32), (24, 15), (6, 2), (17, 25), (6, 19), (23, 9), (19, 5), (2, 15), (8, 29), (9, 0), (19, 11), (22, 21), (2, 30), (22, 17), (14, 15), (2, 17), (17, 23), (14, 8), (10, 2), (14, 23), (6, 16), (16, 9), (22, 30), (3, 2), (13, 26), (26, 14), (24, 8), (1, 29), (24, 0), (18, 24), (29, 19), (2, 21), (9, 17), (11, 3), (11, 8), (18, 25), (14, 5), (11, 23), (1, 4), (9, 2), (29, 30), (6, 9), (24, 29), (15, 1), (28, 25), (24, 12), (13, 23), (6, 29), (11, 10), (10, 33), (28, 1), (24, 31), (11, 16), (9, 33), (12, 10), (26, 17), (25, 5), (10, 6), (5, 15), (19, 7), (3, 22), (11, 29), (22, 18), (4, 1), (2, 18), (16, 10), (25, 3), (12, 31), (4, 0), (28, 21), (6, 8), (4, 23), (25, 33), (10, 12), (20, 0), (28, 5), (5, 5), (5, 16), (24, 28), (25, 11), (12, 13), (20, 20), (5, 11), (23, 1), (9, 25), (26, 3), (1, 22), (0, 33), (9, 32), (12, 11), (8, 17), (8, 16), (9, 22), (5, 9), (7, 0), (23, 2), (16, 4), (25, 12), (19, 15), (13, 21), (22, 25), (9, 31), (15, 2), (7, 28), (9, 19), (7, 9), (14, 33), (8, 25), (12, 21), (3, 0), (10, 28), (8, 22), (8, 33), (8, 13), (29, 26), (26, 28), (2, 23), (0, 8), (9, 14), (20, 5), (2, 12), (0, 30), (17, 33), (4, 28), (2, 25), (28, 29), (16, 27), (25, 32), (25, 25), (24, 9), (5, 12), (13, 16), (5, 29), (21, 20), (1, 10), (26, 9), (19, 16), (13, 17), (15, 31), (21, 7), (8, 3), (6, 15), (10, 4), (9, 9), (4, 33), (5, 18), (4, 2), (1, 19), (14, 4), (16, 1), (12, 4), (9, 21), (28, 11), (4, 10), (0, 20), (2, 27), (17, 32), (0, 22), (18, 23), (17, 13), (6, 17), (25, 2), (3, 4), (15, 4), (13, 25), (16, 3), (15, 22), (0, 19), (14, 32), (13, 29), (23, 18), (8, 15), (0, 26), (12, 5), (15, 10), (18, 13), (25, 10), (15, 32), (2, 5), (0, 32), (1, 12), (7, 5), (28, 24), (1, 11), (28, 19), (15, 27), (11, 21), (15, 16), (9, 26), (5, 17), (22, 13), (1, 18), (3, 23), (15, 8), (4, 31), (8, 14), (21, 16), (22, 28), (23, 33), (7, 13), (20, 32), (29, 0), (1, 7), (22, 20), (3, 28), (29, 17), (20, 7), (3, 19), (27, 6), (25, 20), (22, 29), (0, 18), (15, 20), (16, 14), (10, 23), (29, 3), (7, 18), (7, 14), (23, 31), (21, 23), (23, 17), (28, 22), (23, 8), (10, 13), (17, 14), (10, 1), (26, 10), (2, 6), (12, 15), (5, 1), (21, 10), (15, 15), (4, 12), (24, 21), (0, 23), (6, 0), (13, 30), (28, 9), (14, 2), (19, 18), (2, 31), (22, 31), (29, 24), (16, 31), (6, 5), (16, 11), (3, 6), (12, 27), (28, 14), (18, 4), (12, 7), (15, 6), (1, 3), (25, 29), (14, 21), (25, 31), (27, 11), (0, 25), (8, 28), (25, 18), (23, 14), (0, 14), (26, 19), (19, 23), (27, 26), (22, 26), (0, 4), (7, 2), (11, 22), (18, 31), (23, 6), (13, 11), (19, 28), (12, 23), (7, 24), (20, 12), (16, 32), (23, 25), (18, 18), (22, 32), (23, 27), (28, 17), (29, 7), (14, 3), (3, 27), (29, 4), (16, 22), (20, 9), (4, 21), (7, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480168", "dataset": "MATH"}
{"messages": [{"content": "In a 33x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 29), 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), (21, 6), (30, 1), (4, 23), (3, 7), (24, 1), (21, 3), (17, 25), (5, 22), (22, 7), (17, 29), (10, 22), (23, 1), (14, 27), (27, 21), (9, 19), (2, 7), (24, 13), (7, 18), (15, 27), (19, 1), (32, 23), (6, 7), (10, 18), (16, 12), (30, 9), (8, 20), (1, 12), (25, 18), (7, 19), (13, 25), (28, 29), (18, 23), (5, 26), (24, 11), (24, 4), (23, 22), (23, 20), (29, 6), (24, 26), (5, 6), (21, 19), (6, 21), (24, 19), (11, 21), (7, 15), (27, 25), (20, 11), (3, 13), (19, 10), (11, 18), (13, 9), (11, 28), (9, 27), (8, 22), (28, 9), (16, 21), (30, 26), (21, 9), (21, 11), (9, 8), (4, 16), (12, 27), (3, 19), (13, 15), (17, 15), (32, 11), (32, 16), (26, 22), (0, 27), (16, 29), (24, 28), (22, 21), (21, 2), (11, 7), (5, 9), (15, 17), (0, 8), (14, 20), (28, 3), (16, 1), (15, 14), (19, 26), (20, 1), (15, 16), (12, 24), (18, 5), (11, 27), (20, 12), (15, 28), (20, 21), (26, 17), (32, 14), (4, 1), (27, 26), (29, 7), (30, 11), (30, 16), (1, 9), (9, 14), (30, 7), (27, 28), (25, 6), (8, 26), (2, 27), (4, 5), (24, 8), (12, 5), (12, 9), (11, 19), (8, 29), (0, 5), (29, 8), (24, 16), (19, 9), (3, 14), (12, 15), (6, 20), (7, 2), (20, 28), (4, 29), (6, 23), (24, 3), (23, 2), (23, 0), (26, 23), (13, 1), (9, 22), (23, 9), (19, 13), (29, 28), (10, 20), (16, 2), (23, 17), (13, 22), (20, 27), (23, 10), (31, 25), (32, 22), (18, 17), (32, 17), (25, 19), (3, 6), (26, 4), (11, 2), (18, 7), (15, 6), (6, 16), (14, 16), (13, 6), (16, 17), (26, 10), (28, 11), (3, 17), (22, 18), (17, 11), (2, 12), (21, 25), (7, 12), (31, 20), (15, 24), (8, 15), (13, 7), (19, 6), (25, 7), (3, 23), (21, 28), (4, 10), (15, 22), (14, 28), (9, 23), (12, 7), (29, 23), (24, 25), (12, 3), (7, 16), (22, 15), (17, 20), (25, 25), (1, 7), (3, 21), (7, 26), (30, 0), (17, 13), (12, 11), (13, 3), (4, 22), (15, 25), (25, 16), (31, 19), (15, 11), (19, 8), (13, 13), (16, 11), (7, 8), (30, 17), (3, 20), (11, 15), (19, 14), (24, 7), (30, 13), (11, 4), (5, 3), (16, 10), (6, 1), (7, 1), (22, 11), (1, 19), (0, 9), (22, 22), (28, 4), (2, 25), (8, 4), (12, 14), (9, 28), (23, 15), (21, 4), (6, 10), (12, 16), (21, 5), (2, 15), (19, 7), (30, 23), (6, 27), (3, 27), (23, 28), (16, 16), (16, 23), (3, 0), (9, 5), (21, 20), (27, 24), (5, 28), (14, 3), (21, 0), (3, 1), (12, 2), (13, 20), (13, 16), (21, 7), (19, 25), (9, 7), (8, 3), (16, 0), (4, 21), (23, 18), (19, 27), (17, 14), (11, 6), (12, 17), (24, 6), (20, 14), (14, 29), (5, 8), (31, 18), (1, 14), (16, 25), (8, 5), (17, 26), (25, 13), (13, 21), (9, 11), (30, 28), (18, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "514998", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), 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), (29, 16), (11, 9), (12, 12), (30, 13), (9, 6), (31, 8), (19, 28), (27, 21), (10, 17), (17, 7), (25, 27), (33, 30), (10, 7), (2, 23), (8, 33), (11, 20), (12, 13), (16, 9), (0, 8), (14, 14), (33, 9), (11, 10), (15, 20), (33, 16), (33, 21), (0, 24), (4, 11), (19, 5), (13, 0), (19, 1), (31, 22), (26, 7), (26, 0), (0, 19), (18, 10), (20, 20), (32, 22), (3, 20), (26, 2), (19, 31), (11, 14), (28, 32), (23, 12), (6, 18), (21, 27), (31, 10), (6, 3), (16, 17), (27, 0), (1, 29), (26, 5), (11, 25), (8, 16), (9, 8), (2, 17), (23, 21), (0, 2), (33, 32), (12, 16), (28, 20), (28, 3), (1, 7), (18, 28), (5, 0), (4, 28), (19, 6), (10, 32), (32, 11), (31, 17), (3, 13), (19, 13), (7, 18), (14, 0), (14, 29), (7, 0), (15, 11), (15, 17), (3, 2), (1, 33), (23, 18), (32, 7), (25, 1), (11, 33), (28, 5), (8, 11), (26, 14), (18, 5), (25, 21), (16, 0), (18, 13), (8, 22), (32, 29), (28, 24), (4, 9), (3, 26), (26, 10), (7, 20), (28, 2), (4, 14), (20, 15), (31, 26), (29, 25), (2, 24), (17, 14), (19, 11), (0, 16), (28, 25), (33, 19), (9, 32), (21, 20), (2, 21), (29, 22), (24, 6), (10, 33), (8, 32), (22, 21), (30, 19), (9, 14), (31, 11), (8, 12), (19, 3), (18, 6), (16, 24), (21, 11), (18, 23), (18, 16), (31, 15), (12, 1), (20, 12), (30, 26), (33, 11), (26, 22), (5, 14), (18, 7), (12, 0), (11, 1), (23, 11), (4, 5), (8, 18), (2, 22), (20, 28), (5, 21), (8, 13), (17, 31), (15, 6), (12, 30), (3, 21), (1, 22), (31, 13), (18, 25), (27, 3), (32, 14), (0, 14), (0, 10), (30, 12), (25, 26), (1, 0), (6, 0), (23, 25), (20, 9), (3, 18), (6, 9), (33, 15), (20, 1), (19, 16), (16, 1), (14, 11), (27, 10), (0, 32), (5, 25), (26, 28), (32, 18), (31, 16), (2, 31), (5, 20), (16, 4), (22, 24), (29, 5), (23, 15), (20, 18), (22, 29), (14, 3), (22, 10), (3, 0), (29, 20), (12, 25), (14, 32), (32, 17), (25, 7), (4, 1), (16, 27), (0, 20), (17, 20), (12, 2), (32, 10), (5, 17), (18, 2), (3, 23), (26, 20), (4, 22), (11, 32), (4, 25), (7, 30), (30, 18), (4, 19), (28, 14), (25, 3), (26, 15), (3, 25), (17, 2), (32, 3), (5, 8), (3, 24), (3, 15), (15, 29), (15, 18), (26, 3), (19, 24), (28, 11), (17, 22), (14, 16), (6, 33), (16, 13), (21, 3), (24, 4), (29, 30), (15, 7), (16, 23), (16, 26), (16, 18), (20, 30), (25, 20), (7, 3), (20, 24), (1, 14), (6, 27), (32, 1), (21, 4), (29, 24), (3, 5), (12, 31), (6, 12), (24, 8), (3, 3), (23, 8), (15, 31), (1, 27), (17, 21), (2, 5), (21, 18), (4, 4), (33, 25), (13, 33), (7, 13), (24, 32), (26, 25), (29, 21), (6, 30), (12, 20), (32, 15), (18, 19), (33, 22), (5, 30), (23, 3), (27, 7), (7, 15), (23, 16), (3, 8), (27, 23), (2, 32), (11, 31), (7, 19), (2, 11), (11, 29), (30, 3), (9, 9), (7, 33), (4, 30), (29, 2), (1, 32), (0, 30), (23, 32), (19, 9), (18, 4), (32, 19), (8, 20), (14, 28), (28, 31), (12, 23), (31, 0), (5, 12), (3, 9), (33, 28), (29, 27), (15, 30), (22, 22), (23, 6), (7, 7), (7, 27), (29, 28), (30, 24), (12, 26), (6, 16), (10, 30), (8, 25), (32, 13), (28, 33), (14, 31), (29, 17), (14, 24), (8, 31), (10, 10), (10, 15), (26, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902118", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 30), (32, 11), (10, 24), (24, 6), (14, 18), (13, 12), (11, 11), (10, 28), (17, 27), (26, 13), (1, 7), (16, 28), (22, 7), (25, 1), (2, 10), (31, 11), (8, 5), (32, 21), (17, 24), (20, 11), (29, 11), (19, 27), (34, 16), (7, 11), (28, 16), (29, 17), (24, 9), (32, 10), (29, 26), (15, 9), (13, 22), (16, 29), (19, 24), (15, 0), (22, 19), (4, 1), (35, 15), (32, 22), (0, 27), (35, 17), (12, 6), (3, 29), (13, 1), (1, 19), (28, 6), (2, 24), (16, 17), (10, 5), (25, 29), (27, 10), (30, 10), (19, 5), (16, 20), (30, 29), (29, 13), (25, 6), (34, 3), (20, 4), (5, 11), (2, 14), (11, 19), (31, 0), (25, 21), (4, 15), (31, 18), (14, 25), (22, 24), (20, 17), (0, 15), (2, 30), (3, 13), (0, 3), (6, 9), (6, 27), (27, 27), (17, 3), (18, 28), (3, 12), (21, 13), (28, 17), (32, 17), (31, 19), (22, 26), (13, 21), (24, 27), (32, 9), (1, 2), (29, 29), (18, 7), (26, 8), (4, 2), (33, 15), (3, 22), (29, 20), (20, 29), (14, 16), (28, 22), (11, 3), (8, 29), (20, 18), (8, 28), (21, 3), (20, 7), (7, 0), (4, 10), (29, 8), (34, 12), (35, 11), (23, 7), (17, 10), (20, 3), (0, 6), (8, 30), (34, 26), (22, 25), (27, 23), (32, 28), (26, 16), (12, 10), (27, 29), (34, 14), (9, 28), (31, 5), (0, 23), (13, 19), (18, 6), (8, 14), (23, 14), (1, 30), (15, 27), (3, 6), (31, 20), (16, 8), (34, 18), (12, 1), (33, 6), (18, 21), (32, 6), (13, 26), (13, 16), (1, 9), (6, 10), (7, 22), (25, 27), (24, 2), (8, 12), (1, 17), (17, 21), (0, 9), (12, 19), (25, 26), (17, 19), (0, 14), (8, 21), (32, 20), (26, 20), (30, 5), (24, 22), (30, 17), (1, 20), (22, 29), (13, 13), (9, 7), (13, 15), (30, 28), (12, 8), (19, 1), (28, 0), (14, 11), (7, 27), (21, 10), (27, 21), (27, 4), (15, 2), (23, 1), (19, 6), (6, 3), (3, 21), (26, 1), (26, 28), (9, 8), (3, 3), (29, 1), (21, 19), (4, 8), (6, 28), (7, 10), (34, 10), (29, 16), (29, 14), (27, 20), (23, 30), (9, 5), (7, 23), (18, 29), (17, 6), (11, 6), (19, 12), (18, 20), (24, 23), (32, 5), (26, 0), (27, 6), (3, 25), (22, 18), (6, 17), (2, 27), (12, 2), (35, 12), (15, 8), (25, 20), (24, 10), (26, 6), (3, 0), (15, 24), (27, 8), (4, 5), (15, 22), (20, 24), (15, 4), (11, 18), (8, 4), (14, 1), (17, 16), (4, 23), (9, 20), (7, 15), (12, 13), (17, 17), (21, 23), (9, 18), (0, 13), (19, 15), (12, 11), (8, 26), (5, 14), (30, 20), (9, 0), (5, 23), (1, 14), (19, 0), (29, 15), (15, 29), (28, 20), (22, 21), (21, 9), (21, 6), (11, 2), (16, 1), (33, 7), (35, 24), (6, 23), (33, 28), (11, 15), (19, 10), (7, 13), (21, 14), (25, 13), (20, 1), (13, 20), (13, 8), (33, 1), (5, 27), (0, 21), (10, 14), (10, 11), (24, 21), (30, 6), (2, 12), (20, 0), (5, 4), (12, 15), (30, 0), (21, 7), (34, 28), (17, 22), (31, 21), (18, 13), (20, 30), (13, 23), (10, 21), (24, 20), (33, 5), (1, 25), (16, 2), (30, 8), (34, 11), (8, 16), (30, 7), (35, 16), (19, 9), (35, 19), (12, 27), (4, 22), (17, 1), (27, 9), (24, 29), (25, 5), (0, 25), (3, 30), (25, 16), (26, 26), (26, 2), (22, 4), (32, 14), (17, 13), (12, 17), (13, 29), (6, 18), (6, 26), (9, 3), (18, 26), (15, 10), (9, 29), (16, 22), (15, 17), (7, 19), (31, 3), (19, 19), (34, 20), (4, 21), (26, 11), (12, 28), (25, 15), (18, 5), (24, 17), (30, 23), (27, 17), (19, 8), (20, 2), (31, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "889056", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 4), (2, 17), (1, 13), (8, 14), (27, 18), (1, 5), (14, 15), (20, 23), (7, 16), (7, 34), (18, 21), (6, 36), (9, 17), (18, 19), (5, 1), (26, 5), (25, 5), (10, 23), (16, 0), (9, 25), (14, 25), (6, 19), (26, 19), (17, 24), (22, 12), (22, 24), (6, 33), (24, 24), (7, 14), (20, 37), (28, 22), (22, 8), (2, 24), (1, 16), (11, 1), (13, 32), (22, 32), (15, 28), (2, 9), (1, 3), (4, 35), (13, 34), (24, 28), (16, 8), (9, 20), (21, 14), (7, 8), (22, 28), (28, 28), (18, 0), (22, 5), (11, 34), (18, 9), (20, 33), (11, 26), (28, 13), (15, 24), (23, 13), (1, 19), (9, 7), (25, 10), (9, 3), (25, 7), (11, 3), (19, 36), (30, 36), (27, 30), (20, 0), (7, 18), (18, 33), (4, 33), (23, 20), (26, 10), (29, 14), (15, 15), (23, 10), (11, 8), (1, 17), (13, 5), (22, 20), (20, 28), (21, 31), (21, 17), (1, 14), (5, 2), (13, 6), (20, 26), (14, 27), (20, 17), (28, 6), (13, 27), (9, 14), (3, 5), (29, 22), (9, 12), (4, 34), (21, 20), (7, 13), (0, 3), (30, 10), (30, 26), (7, 29), (23, 37), (28, 32), (16, 3), (21, 22), (26, 26), (11, 23), (3, 24), (17, 32), (29, 28), (10, 3), (27, 6), (8, 24), (10, 11), (28, 21), (5, 13), (22, 27), (15, 5), (17, 10), (16, 27), (23, 18), (20, 30), (1, 12), (3, 31), (6, 29), (21, 33), (29, 4), (24, 10), (22, 11), (0, 22), (0, 35), (25, 19), (13, 4), (20, 16), (14, 6), (22, 0), (17, 3), (12, 0), (27, 24), (20, 18), (19, 2), (2, 2), (16, 34), (26, 30), (6, 34), (2, 3), (1, 20), (24, 23), (21, 24), (16, 29), (21, 27), (26, 33), (12, 13), (19, 37), (26, 23), (18, 2), (22, 34), (5, 33), (21, 30), (22, 13), (29, 32), (21, 11), (26, 1), (10, 35), (8, 25), (5, 4), (28, 31), (8, 37), (25, 15), (24, 15), (4, 28), (0, 20), (3, 17), (17, 13), (21, 0), (25, 30), (7, 17), (22, 21), (0, 10), (17, 28), (17, 34), (3, 36), (17, 17), (19, 21), (14, 22), (22, 2), (6, 18), (26, 35), (4, 3), (22, 25), (7, 36), (9, 5), (25, 33), (8, 0), (6, 4), (20, 10), (7, 0), (1, 6), (25, 21), (9, 27), (3, 1), (14, 10), (25, 2), (21, 21), (9, 26), (9, 10), (24, 25), (11, 4), (8, 9), (19, 19), (4, 5), (29, 8), (20, 25), (29, 6), (12, 1), (25, 1), (19, 33), (8, 16), (23, 9), (19, 25), (15, 8), (3, 9), (2, 36), (29, 36), (5, 24), (8, 30), (0, 13), (17, 36), (10, 34), (18, 10), (8, 20), (11, 9), (14, 29), (12, 29), (2, 5), (6, 6), (20, 9), (9, 11), (20, 31), (13, 21), (6, 13), (27, 4), (18, 8), (3, 4), (18, 27), (18, 20), (18, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172260", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), 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), (5, 19), (0, 28), (17, 4), (9, 11), (27, 12), (2, 20), (33, 6), (10, 1), (24, 23), (8, 2), (13, 10), (13, 14), (25, 26), (33, 17), (21, 8), (21, 13), (16, 11), (20, 29), (28, 24), (9, 12), (22, 1), (27, 19), (0, 21), (4, 27), (27, 31), (31, 29), (22, 18), (14, 6), (3, 27), (10, 20), (32, 4), (26, 16), (18, 22), (10, 11), (33, 1), (9, 5), (5, 4), (26, 1), (9, 19), (9, 16), (31, 19), (22, 15), (16, 21), (23, 24), (6, 21), (12, 4), (3, 0), (11, 16), (8, 19), (23, 2), (13, 21), (9, 29), (22, 9), (12, 9), (2, 10), (30, 2), (0, 16), (14, 17), (3, 31), (15, 15), (21, 31), (13, 29), (24, 13), (25, 11), (29, 29), (24, 0), (27, 15), (29, 8), (30, 9), (25, 9), (27, 29), (14, 9), (30, 13), (26, 6), (13, 17), (28, 9), (0, 17), (23, 28), (9, 18), (1, 16), (30, 29), (32, 29), (6, 11), (16, 14), (28, 29), (14, 26), (9, 2), (27, 18), (28, 27), (3, 15), (28, 0), (16, 12), (1, 9), (29, 21), (0, 9), (12, 3), (13, 1), (12, 11), (33, 14), (32, 10), (29, 10), (15, 3), (8, 26), (11, 24), (23, 25), (12, 23), (18, 18), (28, 20), (27, 9), (17, 0), (3, 23), (1, 7), (0, 19), (31, 5), (18, 25), (19, 4), (31, 0), (15, 9), (2, 25), (32, 19), (22, 29), (14, 19), (6, 31), (29, 22), (8, 25), (1, 21), (30, 16), (27, 4), (8, 9), (31, 2), (14, 16), (12, 12), (17, 24), (16, 31), (29, 15), (7, 23), (0, 23), (21, 15), (22, 20), (14, 29), (10, 6), (29, 13), (24, 26), (14, 11), (11, 31), (28, 17), (30, 12), (10, 3), (26, 13), (15, 17), (13, 30), (26, 5), (22, 11), (32, 24), (21, 1), (6, 16), (24, 17), (28, 18), (19, 24), (30, 3), (27, 27), (14, 21), (33, 28), (19, 26), (31, 1), (1, 24), (25, 7), (4, 14), (16, 7), (23, 19), (9, 8), (10, 14), (23, 20), (14, 14), (6, 3), (0, 31), (13, 18), (21, 3), (26, 8), (0, 6), (32, 25), (20, 21), (22, 4), (16, 22), (33, 4), (33, 2), (7, 24), (32, 2), (20, 28), (15, 26), (33, 5), (15, 4), (11, 7), (33, 22), (17, 21), (27, 16), (29, 20), (16, 26), (10, 2), (21, 14), (29, 4), (20, 14), (27, 24), (9, 15), (22, 24), (33, 30), (15, 14), (10, 13), (8, 28), (12, 10), (11, 25), (29, 28), (18, 9), (30, 4), (4, 19), (15, 6), (13, 12), (3, 16), (30, 10), (14, 15), (31, 4), (2, 15), (32, 5), (2, 8), (2, 14), (2, 24), (17, 14), (5, 24), (7, 11), (9, 7), (0, 20), (3, 3), (16, 4), (10, 27), (29, 17), (28, 16), (20, 17), (23, 4), (18, 12), (19, 11), (23, 6), (18, 29), (1, 26), (0, 11), (25, 16), (5, 9), (7, 15), (13, 3), (26, 4), (4, 20), (4, 6), (5, 22), (16, 15), (22, 22), (20, 7), (28, 23), (19, 25), (33, 29), (16, 3), (7, 12), (18, 31), (27, 10), (18, 17), (32, 6), (1, 27), (17, 22), (6, 19), (6, 22), (17, 13), (23, 1), (10, 23), (5, 16), (6, 13), (12, 16), (18, 21), (7, 29), (20, 23), (1, 29), (2, 27), (33, 7), (4, 22), (22, 30), (29, 14), (9, 21), (32, 27), (33, 26), (27, 8), (26, 26), (0, 1), (6, 29), (14, 27), (8, 12), (7, 25), (22, 31), (8, 30), (6, 0), (0, 15), (14, 4), (7, 5), (5, 27), (5, 31), (12, 26), (8, 5), (14, 30), (23, 26), (1, 1), (9, 22), (14, 23), (27, 0), (14, 2), (26, 23), (29, 26), (3, 19), (2, 17), (2, 21), (18, 24), (17, 5), (15, 30), (11, 15), (8, 3), (32, 14), (15, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), 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), (23, 17), (19, 8), (29, 23), (3, 20), (1, 23), (4, 28), (29, 26), (19, 24), (8, 10), (28, 32), (20, 28), (11, 2), (16, 16), (1, 7), (18, 12), (24, 22), (8, 7), (28, 33), (14, 32), (11, 23), (30, 22), (26, 31), (19, 32), (6, 32), (22, 33), (7, 4), (27, 9), (22, 13), (8, 23), (16, 25), (15, 22), (11, 9), (5, 20), (9, 8), (2, 12), (18, 31), (5, 24), (17, 0), (6, 7), (15, 3), (24, 9), (22, 27), (2, 4), (25, 15), (0, 11), (12, 23), (15, 27), (7, 8), (22, 3), (22, 10), (6, 27), (28, 6), (29, 32), (28, 0), (25, 32), (12, 7), (23, 0), (25, 17), (10, 23), (23, 23), (9, 15), (3, 12), (19, 0), (29, 22), (7, 2), (7, 28), (30, 18), (22, 25), (12, 13), (0, 24), (12, 21), (19, 23), (2, 11), (11, 31), (5, 30), (25, 29), (10, 0), (16, 6), (22, 32), (19, 20), (1, 14), (0, 6), (12, 16), (12, 26), (30, 10), (13, 24), (0, 22), (20, 14), (28, 27), (7, 3), (18, 28), (9, 32), (30, 11), (6, 6), (25, 1), (14, 1), (9, 17), (8, 9), (25, 11), (0, 2), (15, 21), (17, 4), (1, 8), (14, 15), (21, 9), (23, 32), (9, 33), (20, 2), (13, 4), (10, 18), (13, 16), (5, 8), (7, 23), (9, 3), (16, 19), (12, 0), (2, 33), (24, 19), (22, 16), (24, 14), (16, 28), (4, 33), (28, 11), (7, 10), (10, 11), (5, 3), (12, 25), (0, 5), (27, 20), (30, 6), (18, 10), (25, 26), (6, 2), (1, 9), (4, 19), (10, 28), (17, 32), (30, 9), (14, 7), (15, 1), (17, 29), (8, 20), (13, 25), (5, 17), (11, 13), (1, 22), (25, 20), (3, 11), (3, 24), (25, 0), (15, 2), (13, 12), (17, 5), (5, 9), (18, 1), (3, 19), (3, 7), (19, 13), (16, 27), (24, 32), (20, 33), (11, 33), (3, 9), (0, 25), (17, 19), (3, 10), (30, 1), (24, 3), (10, 2), (19, 30), (8, 11), (29, 5), (28, 7), (17, 11), (16, 9), (21, 27), (9, 4), (2, 21), (20, 30), (2, 2), (26, 24), (6, 11), (17, 28), (14, 23), (30, 16), (16, 12), (27, 30), (28, 1), (10, 27), (23, 3), (22, 8), (20, 11), (16, 7), (20, 22), (11, 5), (29, 28), (15, 19), (2, 24), (12, 18), (21, 32), (13, 32), (18, 20), (6, 4), (2, 16), (21, 25), (7, 9), (18, 23), (29, 19), (21, 28), (27, 0), (5, 13), (11, 8), (22, 21), (2, 9), (28, 14), (2, 14), (3, 23), (26, 21), (28, 26), (29, 20), (17, 33), (12, 3), (26, 16), (19, 28), (26, 23), (27, 13), (5, 18), (14, 21), (29, 6), (12, 31), (4, 0), (13, 20), (14, 29), (18, 16), (16, 33), (16, 20), (26, 8), (9, 13), (17, 27), (23, 31), (27, 25), (0, 3), (3, 21), (27, 5), (5, 11), (22, 30), (14, 2), (0, 14), (11, 25), (15, 10), (8, 21), (18, 4), (11, 3), (29, 25), (23, 10), (19, 1), (11, 22), (27, 31), (7, 25), (11, 7), (5, 33), (13, 30), (27, 6), (11, 28), (24, 13), (29, 27), (11, 17), (24, 0), (24, 23), (12, 15), (27, 1), (26, 18), (0, 10), (14, 27), (19, 33), (26, 20), (6, 21), (25, 27), (9, 20), (30, 13), (30, 29), (4, 5), (1, 20), (6, 25), (17, 18), (5, 5), (3, 25), (16, 13), (4, 11), (19, 25), (28, 24), (25, 25), (17, 13), (0, 9), (14, 19), (12, 24), (17, 15), (9, 10), (24, 26), (7, 24), (5, 19), (9, 1), (6, 23), (29, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667008", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 8), (8, 20), (28, 27), (24, 7), (2, 18), (29, 28), (17, 6), (14, 7), (1, 26), (9, 18), (35, 11), (30, 10), (19, 29), (19, 0), (14, 5), (17, 26), (19, 26), (27, 19), (8, 28), (36, 14), (27, 27), (23, 10), (2, 8), (14, 10), (22, 23), (18, 9), (38, 7), (20, 18), (11, 14), (16, 18), (28, 23), (32, 26), (2, 22), (19, 10), (24, 2), (5, 15), (34, 27), (18, 22), (7, 11), (33, 23), (28, 3), (38, 25), (19, 18), (19, 13), (34, 26), (13, 8), (4, 25), (35, 28), (2, 1), (27, 25), (7, 5), (22, 25), (21, 0), (14, 6), (35, 17), (36, 1), (20, 29), (30, 9), (31, 12), (38, 8), (34, 5), (36, 28), (34, 24), (25, 11), (37, 20), (20, 27), (24, 3), (16, 4), (4, 5), (29, 15), (23, 2), (28, 2), (24, 12), (23, 3), (8, 17), (6, 12), (27, 15), (9, 11), (33, 28), (34, 11), (6, 13), (27, 20), (25, 1), (19, 14), (8, 19), (32, 18), (6, 26), (30, 23), (28, 29), (16, 21), (3, 20), (9, 23), (30, 8), (17, 29), (37, 22), (23, 9), (20, 5), (10, 8), (38, 9), (36, 24), (1, 19), (0, 21), (11, 25), (16, 20), (36, 12), (34, 7), (6, 19), (26, 12), (6, 1), (10, 7), (16, 10), (7, 23), (23, 7), (6, 25), (12, 8), (21, 19), (5, 18), (1, 22), (13, 9), (12, 4), (21, 26), (24, 18), (27, 3), (0, 13), (26, 21), (2, 4), (3, 22), (1, 13), (35, 15), (30, 3), (0, 28), (29, 21), (8, 10), (29, 22), (20, 10), (24, 16), (20, 22), (5, 9), (3, 17), (10, 29), (12, 15), (34, 22), (37, 7), (24, 28), (37, 11), (9, 25), (9, 9), (8, 21), (11, 28), (17, 16), (20, 24), (37, 3), (27, 17), (6, 9), (23, 24), (19, 15), (1, 11), (38, 18), (28, 17), (34, 18), (31, 13), (30, 1), (32, 25), (25, 25), (34, 19), (17, 1), (24, 20), (14, 17), (15, 18), (35, 1), (33, 25), (36, 22), (37, 12), (6, 16), (11, 21), (26, 28), (14, 20), (37, 24), (34, 20), (25, 19), (3, 16), (8, 15), (6, 5), (9, 28), (37, 23), (15, 3), (13, 21), (14, 8), (3, 4), (32, 0), (38, 15), (26, 9), (26, 16), (3, 13), (24, 26), (27, 14), (9, 4), (35, 6), (12, 7), (9, 0), (22, 20), (8, 7), (17, 5), (10, 27), (38, 16), (35, 3), (1, 7), (33, 8), (28, 22), (19, 12), (26, 20), (0, 9), (22, 1), (5, 0), (14, 13), (16, 24), (14, 15), (12, 19), (26, 15), (27, 23), (13, 19), (4, 26), (32, 14), (35, 18), (37, 10), (12, 21), (22, 6), (21, 29), (12, 22), (7, 14), (13, 17), (13, 26), (24, 1), (8, 25), (17, 23), (36, 10), (0, 3), (35, 25), (0, 26), (29, 4), (4, 17), (1, 24), (17, 15), (20, 16), (31, 29), (22, 8), (17, 0), (21, 22), (5, 1), (6, 3), (29, 24), (37, 13), (1, 8), (9, 14), (29, 8), (31, 11), (7, 9), (1, 15), (36, 16), (29, 3), (25, 26), (18, 12), (30, 12), (2, 0), (36, 11), (33, 3), (24, 5), (26, 10), (38, 20), (5, 28), (22, 12), (26, 29), (0, 14), (32, 6), (27, 1), (3, 12), (18, 6), (38, 13), (35, 5), (13, 15), (27, 4), (31, 0), (11, 15), (4, 24), (37, 19), (8, 22), (37, 0), (16, 11), (16, 19), (8, 23), (16, 25), (2, 28), (22, 26), (20, 26), (34, 21), (27, 6), (16, 15), (5, 3), (38, 23), (28, 6), (18, 11), (11, 9), (4, 16), (11, 5), (11, 11), (5, 11), (22, 3), (23, 16), (9, 16), (16, 1), (12, 27), (15, 13), (5, 10), (37, 2), (30, 15), (36, 23), (5, 6), (10, 26), (15, 11), (5, 20), (7, 18), (32, 8), (25, 15), (25, 10), (30, 4), (26, 6), (9, 12), (23, 25), (15, 19), (13, 24), (2, 25), (30, 16), (19, 4), (34, 28), (17, 22), (6, 20), (25, 5), (34, 8), (0, 24), (3, 27), (11, 18), (3, 14), (0, 1), (31, 16), (21, 12), (36, 5), (14, 12), (0, 8), (11, 16), (7, 21), (36, 2), (0, 20), (3, 24), (18, 13), (13, 25), (16, 5), (23, 23), (35, 0), (14, 28), (34, 13), (9, 24), (18, 8), (12, 28), (19, 28), (36, 0), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "678726", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 6), (13, 1), (23, 23), (29, 13), (18, 18), (13, 13), (11, 9), (21, 21), (5, 23), (22, 29), (11, 0), (6, 6), (5, 6), (17, 19), (9, 22), (26, 3), (11, 24), (34, 18), (15, 31), (15, 10), (20, 10), (27, 4), (5, 22), (34, 8), (14, 26), (27, 32), (25, 13), (15, 27), (4, 14), (2, 18), (5, 2), (2, 16), (8, 6), (4, 19), (32, 3), (6, 25), (3, 2), (13, 12), (21, 16), (29, 16), (22, 7), (21, 10), (10, 1), (31, 0), (12, 28), (28, 23), (6, 21), (20, 28), (30, 22), (17, 29), (15, 30), (3, 14), (26, 27), (26, 32), (21, 6), (25, 17), (22, 0), (12, 31), (23, 3), (32, 10), (25, 16), (29, 12), (8, 16), (16, 14), (30, 1), (10, 11), (6, 18), (12, 17), (32, 16), (2, 22), (4, 30), (18, 4), (32, 5), (5, 26), (15, 1), (16, 0), (9, 31), (34, 30), (20, 23), (22, 5), (11, 2), (26, 21), (27, 27), (9, 18), (31, 18), (25, 1), (0, 19), (10, 16), (8, 25), (13, 2), (4, 1), (1, 28), (27, 10), (1, 0), (18, 9), (19, 27), (5, 31), (26, 22), (2, 21), (7, 18), (31, 10), (18, 15), (32, 23), (18, 30), (8, 13), (2, 13), (10, 18), (23, 12), (20, 0), (30, 6), (1, 7), (3, 20), (8, 18), (27, 15), (31, 22), (30, 30), (35, 24), (12, 32), (24, 11), (22, 30), (4, 9), (12, 19), (10, 23), (32, 12), (7, 8), (25, 0), (24, 28), (13, 6), (12, 20), (23, 15), (32, 22), (23, 2), (29, 23), (12, 24), (5, 8), (26, 5), (2, 27), (13, 23), (14, 22), (14, 24), (22, 22), (10, 7), (32, 18), (19, 11), (33, 25), (7, 12), (16, 7), (21, 25), (35, 0), (18, 7), (11, 15), (3, 28), (19, 24), (18, 20), (7, 31), (24, 22), (13, 15), (16, 6), (17, 3), (15, 29), (15, 3), (17, 23), (20, 4), (29, 28), (13, 14), (25, 25), (21, 28), (14, 30), (0, 25), (34, 28), (13, 18), (26, 24), (14, 14), (10, 30), (19, 8), (21, 31), (24, 12), (22, 20), (12, 0), (35, 22), (22, 21), (18, 1), (33, 2), (0, 2), (3, 26), (2, 29), (28, 8), (18, 11), (6, 10), (21, 14), (20, 13), (20, 26), (34, 13), (20, 18), (6, 30), (30, 3), (33, 22), (13, 0), (1, 30), (3, 9), (6, 26), (23, 10), (19, 13), (24, 5), (33, 21), (2, 8), (2, 19), (11, 8), (11, 23), (25, 10), (25, 21), (10, 3), (13, 32), (15, 18), (8, 12), (5, 16), (23, 5), (34, 19), (25, 24), (11, 20), (34, 29), (4, 28), (6, 12), (27, 0), (5, 17), (1, 31), (35, 17), (34, 14), (6, 27), (15, 7), (29, 4), (21, 26), (13, 29), (8, 29), (33, 10), (13, 20), (34, 17), (4, 23), (24, 4), (0, 28), (30, 23), (1, 22), (23, 13), (18, 28), (14, 20), (9, 21), (22, 28), (22, 2), (20, 32), (2, 7), (19, 22), (12, 6), (21, 15), (30, 24), (28, 25), (11, 19), (33, 27), (16, 15), (10, 10), (29, 29), (12, 14), (8, 11), (28, 28), (29, 10), (22, 13), (11, 5), (5, 1), (23, 24), (16, 22), (6, 8), (18, 12), (22, 24), (9, 17), (10, 21), (3, 30), (26, 31), (32, 24), (32, 13), (9, 3), (30, 20), (23, 1), (6, 4), (34, 32), (0, 4), (8, 17), (21, 20), (15, 20), (16, 3), (23, 20), (25, 19), (0, 15), (20, 29), (3, 22), (4, 27), (16, 18), (26, 9), (0, 7), (30, 21), (30, 13), (17, 17), (17, 9), (11, 7), (14, 32), (23, 22), (27, 26), (7, 22), (27, 6), (26, 7), (7, 5), (33, 16), (31, 6), (15, 19), (32, 9), (32, 2), (8, 31), (9, 0), (6, 14), (16, 20), (28, 19), (10, 8), (12, 27), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58968", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 33), (10, 14), (22, 6), (16, 31), (19, 8), (26, 17), (22, 35), (28, 1), (9, 20), (30, 36), (29, 3), (6, 15), (2, 14), (10, 31), (8, 29), (16, 12), (31, 25), (27, 22), (13, 10), (15, 9), (32, 3), (27, 14), (17, 9), (13, 33), (8, 16), (5, 20), (8, 18), (10, 8), (21, 26), (17, 2), (4, 10), (20, 26), (6, 22), (5, 5), (1, 34), (1, 18), (4, 3), (5, 13), (2, 34), (17, 35), (31, 26), (29, 34), (27, 35), (12, 9), (11, 4), (14, 12), (5, 23), (29, 21), (22, 2), (5, 0), (9, 15), (19, 24), (29, 30), (10, 27), (11, 23), (0, 11), (22, 11), (3, 25), (27, 2), (9, 13), (17, 33), (27, 17), (9, 8), (22, 24), (12, 16), (7, 27), (1, 24), (20, 6), (3, 16), (0, 13), (13, 23), (2, 13), (3, 18), (16, 30), (17, 0), (15, 3), (29, 17), (0, 21), (20, 29), (11, 30), (25, 29), (7, 0), (28, 14), (21, 11), (21, 27), (16, 28), (4, 25), (24, 3), (18, 31), (3, 35), (10, 29), (18, 16), (4, 8), (29, 19), (3, 33), (22, 22), (9, 10), (8, 23), (0, 36), (19, 26), (17, 10), (5, 32), (30, 12), (13, 5), (22, 9), (31, 28), (24, 21), (12, 8), (30, 0), (18, 0), (21, 4), (16, 5), (15, 10), (15, 30), (23, 1), (21, 9), (30, 19), (25, 14), (30, 20), (12, 25), (31, 27), (18, 9), (12, 27), (13, 26), (27, 6), (20, 3), (1, 6), (6, 5), (24, 18), (17, 12), (13, 12), (10, 22), (25, 28), (4, 16), (28, 11), (22, 13), (2, 30), (28, 5), (30, 25), (19, 4), (25, 18), (18, 22), (19, 22), (1, 9), (30, 9), (16, 33), (8, 6), (7, 25), (26, 12), (23, 34), (5, 25), (27, 11), (14, 5), (13, 6), (32, 24), (16, 9), (12, 17), (9, 24), (17, 31), (4, 24), (3, 9), (29, 8), (10, 32), (29, 10), (17, 19), (26, 8), (25, 15), (25, 4), (31, 31), (17, 13), (3, 28), (21, 33), (1, 16), (22, 34), (10, 9), (2, 16), (21, 25), (32, 23), (3, 17), (8, 8), (29, 27), (25, 11), (22, 7), (30, 18), (11, 29), (10, 24), (23, 16), (8, 27), (8, 19), (4, 2), (24, 2), (16, 17), (15, 16), (9, 5), (25, 10), (22, 36), (17, 14), (25, 8), (19, 27), (26, 9), (16, 6), (24, 5), (2, 7), (16, 14), (4, 21), (11, 1), (2, 1), (26, 31), (31, 2), (0, 16), (26, 6), (7, 17), (0, 24), (7, 35), (13, 13), (9, 12), (9, 31), (23, 23), (23, 29), (0, 5), (14, 18), (14, 28), (31, 29), (9, 1), (12, 0), (13, 14), (8, 20), (27, 28), (0, 30), (28, 36), (30, 33), (6, 10), (23, 31), (27, 9), (6, 32), (8, 35), (7, 9), (16, 25), (18, 15), (24, 29), (24, 34), (17, 1), (18, 11), (23, 10), (28, 20), (23, 17), (31, 20), (26, 4), (20, 17), (18, 28), (3, 8), (23, 12), (1, 15), (9, 11), (26, 1), (28, 23), (9, 23), (22, 27), (1, 10), (23, 27), (1, 5), (10, 6), (18, 7), (20, 8), (6, 3), (10, 34), (21, 6), (11, 24), (30, 2), (4, 9), (15, 27), (24, 14), (26, 24), (18, 21), (3, 30), (1, 0), (31, 36), (23, 33), (11, 14), (23, 30), (7, 18), (32, 12), (3, 0), (28, 35), (5, 11), (23, 6), (8, 21), (26, 14), (1, 1), (1, 28), (4, 1), (8, 22), (0, 22), (12, 34), (17, 30), (2, 15), (11, 22), (0, 6), (24, 10), (28, 28), (25, 20), (0, 23), (31, 4), (23, 19), (15, 15), (25, 3), (21, 7), (10, 4), (14, 32), (1, 14), (25, 26), (32, 6), (12, 22), (14, 21), (27, 18), (18, 24), (14, 6), (2, 23), (0, 7), (14, 8), (2, 8), (26, 22), (20, 30), (7, 13), (19, 0), (11, 18), (1, 19), (18, 10), (6, 8), (1, 17), (19, 23), (8, 14), (2, 35), (17, 36), (18, 30), (21, 23), (14, 7), (7, 10), (25, 34), (27, 30), (23, 32), (28, 2), (11, 11), (16, 13), (14, 2), (24, 12), (12, 32), (1, 2), (21, 30), (26, 20), (32, 32), (31, 6), (11, 31), (3, 4), (5, 24), (32, 29), (8, 26), (4, 33), (14, 27), (25, 31), (10, 11), (4, 11), (8, 28), (4, 32), (15, 2), (26, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "747936", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 1), (17, 16), (28, 29), (5, 11), (13, 32), (3, 24), (21, 17), (17, 35), (22, 1), (25, 4), (23, 11), (15, 25), (17, 25), (15, 1), (7, 0), (3, 0), (0, 18), (16, 22), (6, 18), (28, 30), (2, 32), (15, 33), (19, 1), (7, 25), (16, 11), (3, 7), (27, 22), (30, 1), (13, 26), (11, 15), (0, 4), (0, 21), (12, 33), (4, 33), (9, 31), (11, 22), (5, 13), (6, 32), (13, 27), (14, 24), (14, 14), (8, 1), (25, 8), (0, 27), (14, 17), (9, 24), (8, 4), (26, 5), (7, 6), (13, 14), (15, 17), (28, 17), (25, 11), (23, 4), (30, 36), (8, 23), (17, 34), (21, 1), (24, 7), (21, 20), (16, 27), (22, 29), (30, 17), (16, 35), (12, 8), (22, 32), (20, 7), (3, 26), (31, 34), (23, 31), (4, 30), (26, 3), (24, 32), (17, 36), (30, 4), (12, 25), (1, 22), (27, 3), (8, 11), (27, 32), (27, 1), (16, 30), (20, 14), (24, 6), (6, 1), (15, 2), (24, 2), (4, 24), (29, 0), (2, 24), (11, 36), (14, 29), (10, 33), (30, 14), (26, 34), (2, 23), (28, 11), (18, 12), (3, 21), (23, 25), (31, 19), (21, 30), (21, 24), (4, 10), (23, 27), (24, 18), (16, 25), (13, 16), (30, 7), (24, 17), (14, 35), (10, 30), (1, 18), (25, 32), (18, 33), (26, 25), (19, 10), (1, 14), (18, 1), (27, 31), (5, 10), (3, 6), (22, 17), (29, 13), (3, 22), (25, 36), (9, 28), (1, 11), (0, 2), (7, 29), (8, 19), (27, 25), (28, 36), (8, 17), (18, 15), (8, 13), (24, 31), (19, 24), (12, 16), (2, 12), (9, 19), (14, 11), (1, 29), (12, 14), (19, 14), (12, 5), (9, 8), (8, 24), (15, 11), (13, 5), (25, 34), (15, 28), (3, 23), (3, 36), (12, 20), (16, 8), (17, 5), (17, 28), (26, 14), (20, 29), (28, 21), (1, 36), (0, 16), (29, 8), (31, 6), (31, 2), (2, 26), (12, 2), (2, 13), (21, 12), (11, 23), (2, 4), (24, 8), (18, 6), (17, 15), (9, 35), (16, 20), (29, 18), (20, 26), (12, 17), (23, 1), (26, 30), (0, 29), (29, 29), (30, 15), (3, 30), (2, 11), (4, 6), (23, 32), (4, 0), (22, 26), (2, 15), (16, 10), (7, 3), (6, 16), (0, 20), (22, 5), (25, 18), (31, 20), (5, 12), (5, 9), (22, 8), (21, 15), (25, 29), (12, 30), (24, 14), (17, 3), (7, 19), (23, 12), (6, 17), (7, 20), (29, 19), (22, 33), (0, 35), (0, 26), (11, 9), (2, 35), (21, 5), (2, 10), (22, 3), (21, 25), (11, 6), (16, 7), (28, 33), (9, 5), (6, 36), (16, 4), (3, 35), (26, 31), (5, 33), (5, 1), (0, 23), (13, 19), (7, 4), (11, 0), (16, 14), (14, 9), (12, 31), (29, 25), (21, 28), (25, 20), (3, 18), (11, 19), (8, 21), (19, 17), (20, 27), (10, 36), (29, 16), (28, 28), (27, 18), (15, 32), (7, 35), (20, 9), (17, 20), (19, 9), (5, 6), (10, 25), (4, 2), (6, 27), (8, 3), (9, 4), (19, 5), (4, 26), (2, 29), (23, 9), (14, 7), (1, 10), (13, 13), (15, 9), (16, 28), (9, 18), (16, 18), (9, 10), (24, 34), (7, 36), (20, 0), (11, 28), (29, 15), (31, 3), (2, 0), (10, 20), (20, 25), (18, 16), (10, 2), (6, 24), (19, 30), (28, 4), (23, 13), (18, 14), (16, 1), (23, 33), (28, 23), (21, 8), (8, 0), (0, 28), (12, 18), (3, 16), (15, 18), (12, 32), (26, 27), (14, 31), (25, 23), (8, 30), (17, 14), (28, 13), (8, 15), (23, 14), (15, 16), (23, 34), (23, 28), (4, 17), (18, 21), (2, 9), (6, 13), (14, 32), (21, 23), (26, 10), (8, 10), (16, 15), (16, 2), (31, 11), (29, 6), (1, 7), (20, 23), (1, 6), (12, 15), (9, 1), (26, 32), (8, 34), (29, 32), (1, 12), (27, 21), (3, 8), (1, 30), (10, 1), (15, 23), (18, 29), (12, 21), (25, 30), (21, 27), (17, 32), (17, 21), (30, 3), (11, 17), (26, 13), (4, 28), (1, 24), (3, 4), (30, 0), (7, 16), (22, 22), (10, 14), (17, 9), (27, 13), (14, 18), (31, 10), (19, 3), (30, 10), (4, 11), (15, 26), (1, 25), (6, 28), (17, 2), (11, 33), (20, 1), (15, 36), (31, 23), (25, 7), (17, 24), (15, 10), (0, 10), (19, 33), (31, 4), (4, 3), (27, 7), (25, 28), (22, 28), (7, 1), (10, 17), (17, 22), (14, 21), (6, 29), (21, 33), (26, 1), (19, 29), (9, 2), (24, 5), (26, 15), (4, 20), (0, 22), (28, 9), (26, 33), (10, 18), (14, 36), (20, 12), (27, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "771840", "dataset": "MATH"}
{"messages": [{"content": "In a 34x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 30), 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), (0, 24), (21, 24), (23, 14), (27, 18), (8, 27), (33, 26), (26, 9), (14, 28), (27, 2), (32, 2), (2, 10), (6, 15), (14, 2), (3, 9), (9, 0), (9, 12), (1, 25), (4, 22), (2, 27), (24, 15), (33, 22), (10, 13), (14, 17), (28, 29), (14, 0), (32, 29), (5, 25), (7, 11), (6, 1), (3, 23), (30, 13), (10, 24), (21, 20), (11, 28), (11, 19), (13, 14), (13, 9), (32, 18), (1, 20), (27, 21), (29, 12), (1, 4), (28, 17), (14, 6), (21, 16), (13, 18), (31, 11), (10, 16), (18, 13), (33, 15), (15, 17), (22, 11), (7, 7), (0, 26), (3, 18), (25, 11), (28, 30), (16, 20), (15, 21), (3, 2), (27, 20), (18, 12), (23, 16), (13, 5), (26, 2), (22, 28), (3, 19), (7, 19), (4, 20), (33, 10), (33, 25), (27, 27), (12, 22), (11, 22), (2, 28), (16, 11), (32, 26), (22, 1), (28, 4), (4, 27), (32, 17), (24, 16), (14, 16), (5, 8), (0, 2), (5, 15), (4, 10), (19, 29), (24, 8), (8, 5), (5, 26), (24, 30), (32, 3), (21, 0), (5, 11), (33, 4), (22, 10), (4, 17), (14, 22), (32, 16), (3, 12), (11, 25), (29, 11), (20, 7), (13, 23), (5, 21), (20, 8), (5, 6), (12, 1), (31, 15), (8, 2), (15, 11), (27, 23), (4, 1), (1, 2), (2, 1), (9, 10), (10, 20), (0, 23), (31, 2), (12, 17), (26, 28), (12, 23), (15, 18), (4, 15), (16, 8), (14, 5), (27, 8), (24, 4), (14, 26), (26, 30), (3, 3), (30, 21), (8, 10), (1, 23), (13, 11), (0, 1), (7, 24), (13, 25), (16, 26), (17, 3), (23, 21), (12, 27), (6, 3), (30, 28), (31, 12), (6, 24), (16, 21), (21, 15), (13, 30), (0, 9), (26, 20), (5, 4), (12, 19), (26, 19), (21, 30), (6, 29), (31, 3), (20, 11), (21, 26), (24, 6), (29, 1), (28, 18), (26, 15), (16, 27), (3, 25), (8, 15), (23, 25), (8, 12), (20, 12), (22, 9), (2, 6), (30, 30), (1, 9), (14, 15), (18, 0), (23, 17), (33, 3), (1, 1), (5, 18), (6, 14), (26, 27), (18, 8), (8, 23), (29, 24), (4, 7), (26, 6), (1, 19), (3, 15), (19, 8), (22, 29), (11, 10), (7, 26), (17, 12), (0, 17), (18, 1), (2, 19), (18, 10), (12, 8), (19, 5), (6, 23), (28, 21), (12, 4), (30, 16), (18, 4), (24, 28), (30, 22), (17, 4), (31, 18), (10, 4), (33, 16), (28, 10), (18, 21), (25, 13), (32, 14), (30, 1), (0, 16), (5, 7), (0, 18), (23, 19), (17, 25), (11, 4), (17, 20), (19, 2), (13, 10), (13, 19), (29, 13), (31, 4), (27, 22), (24, 22), (19, 0), (27, 11), (11, 9), (31, 17), (6, 30), (7, 5), (10, 27), (27, 14), (27, 0), (33, 27), (22, 18), (2, 30), (18, 30), (27, 29), (21, 5), (26, 12), (15, 12), (2, 8), (19, 13), (0, 29), (2, 13), (19, 28), (4, 26), (15, 16), (11, 21), (22, 25), (26, 29), (26, 17), (29, 20), (19, 25), (21, 9), (6, 21), (28, 25), (13, 15), (0, 27), (12, 7), (5, 27), (30, 2), (33, 8), (3, 7), (27, 13), (4, 28), (10, 0), (32, 13), (11, 17), (21, 8), (26, 0), (4, 30), (23, 18), (7, 1), (25, 30), (32, 27), (7, 27), (17, 19), (7, 18), (10, 8), (13, 3), (7, 0), (0, 15), (6, 22), (26, 16), (15, 2), (7, 6), (9, 9), (0, 6), (8, 16), (7, 30), (16, 5), (29, 29), (19, 10), (19, 21), (3, 14), (7, 22), (28, 22), (12, 5), (7, 13), (24, 23), (8, 7), (21, 13), (25, 3), (17, 13), (13, 21), (4, 2), (25, 1), (12, 12), (10, 7), (28, 2), (3, 24), (17, 30), (18, 29), (25, 4), (15, 24), (4, 5), (16, 18), (17, 0), (19, 16), (6, 11), (11, 27), (16, 24), (11, 1), (6, 26), (6, 4), (12, 0), (31, 0), (11, 26), (15, 10), (8, 30), (24, 9), (9, 7), (29, 18), (25, 25), (32, 24), (30, 11), (11, 2), (32, 4), (18, 5), (7, 23), (24, 5), (0, 7), (11, 16), (25, 9), (14, 3), (4, 18), (27, 19), (3, 1), (25, 21), (32, 9), (9, 17), (21, 29), (18, 6), (1, 24), (0, 22), (24, 19), (4, 11), (4, 6), (3, 5), (32, 30), (16, 17), (13, 28), (5, 28), (3, 21), (22, 17), (3, 30), (6, 5), (0, 3), (8, 9), (28, 11), (4, 14), (0, 13), (31, 9), (1, 3), (10, 12), (19, 3), (0, 4), (9, 27), (2, 22), (21, 2), (15, 22), (3, 8), (32, 19), (17, 23), (30, 18), (25, 7), (29, 28), (17, 5), (12, 30), (0, 21), (2, 11), (19, 4), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "589248", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), 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), (23, 4), (10, 7), (28, 20), (20, 32), (8, 11), (8, 24), (18, 30), (8, 16), (7, 26), (31, 16), (9, 17), (33, 8), (28, 5), (31, 13), (21, 5), (16, 33), (14, 0), (25, 19), (1, 19), (16, 20), (35, 11), (28, 2), (30, 8), (11, 33), (24, 9), (1, 0), (3, 24), (1, 20), (7, 5), (26, 26), (25, 20), (34, 22), (31, 32), (22, 10), (29, 6), (12, 15), (35, 26), (20, 9), (24, 28), (19, 26), (8, 22), (17, 2), (22, 32), (32, 12), (19, 1), (10, 0), (16, 25), (22, 31), (4, 2), (19, 17), (36, 18), (32, 4), (3, 30), (4, 25), (0, 12), (21, 12), (33, 29), (20, 5), (26, 22), (13, 27), (20, 29), (31, 14), (1, 30), (10, 27), (7, 18), (6, 27), (31, 18), (8, 10), (1, 17), (20, 25), (10, 17), (27, 4), (29, 19), (18, 18), (12, 25), (14, 7), (34, 19), (7, 24), (27, 33), (2, 22), (0, 4), (26, 9), (3, 15), (30, 7), (8, 28), (11, 32), (21, 25), (31, 33), (24, 13), (23, 17), (25, 24), (23, 15), (24, 19), (10, 25), (4, 4), (26, 15), (4, 19), (14, 30), (2, 27), (22, 0), (1, 5), (10, 30), (34, 30), (22, 24), (8, 30), (14, 2), (29, 3), (16, 13), (18, 6), (35, 2), (22, 9), (34, 11), (9, 24), (35, 16), (1, 8), (3, 9), (6, 30), (25, 28), (4, 16), (19, 7), (1, 22), (2, 4), (18, 7), (29, 25), (31, 31), (13, 1), (17, 18), (25, 27), (9, 26), (24, 33), (17, 20), (32, 8), (34, 31), (6, 31), (15, 3), (5, 9), (28, 29), (12, 10), (3, 19), (31, 22), (26, 19), (35, 4), (6, 0), (25, 0), (29, 27), (36, 3), (25, 21), (1, 11), (5, 1), (6, 6), (19, 6), (15, 6), (0, 33), (27, 6), (18, 9), (14, 13), (19, 21), (7, 23), (4, 18), (12, 1), (10, 16), (14, 6), (29, 2), (8, 29), (9, 23), (17, 8), (36, 7), (11, 26), (15, 5), (11, 22), (10, 29), (19, 4), (21, 29), (18, 25), (4, 22), (35, 13), (16, 7), (15, 29), (34, 7), (1, 13), (4, 27), (12, 22), (27, 29), (10, 28), (13, 5), (16, 32), (34, 29), (17, 31), (31, 23), (25, 3), (22, 15), (6, 4), (33, 12), (11, 8), (12, 27), (7, 21), (30, 1), (5, 25), (22, 28), (29, 28), (28, 11), (23, 16), (29, 26), (13, 16), (23, 25), (21, 26), (24, 25), (31, 9), (28, 24), (35, 32), (27, 25), (24, 22), (27, 21), (21, 21), (13, 24), (24, 8), (11, 5), (10, 1), (1, 14), (32, 21), (17, 0), (27, 7), (26, 14), (21, 15), (36, 6), (5, 7), (5, 5), (31, 0), (33, 32), (11, 15), (5, 26), (0, 17), (25, 10), (27, 31), (17, 33), (9, 4), (18, 28), (9, 3), (1, 6), (29, 14), (29, 4), (27, 23), (36, 24), (10, 14), (24, 17), (16, 22), (31, 7), (20, 30), (17, 29), (26, 17), (21, 1), (31, 28), (10, 15), (33, 24), (0, 8), (14, 4), (28, 16), (1, 18), (23, 9), (0, 15), (11, 6), (26, 32), (14, 27), (19, 10), (0, 29), (23, 6), (5, 23), (17, 6), (15, 17), (12, 4), (34, 16), (19, 23), (24, 27), (26, 0), (24, 5), (2, 12), (11, 19), (0, 7), (24, 1), (27, 12), (7, 30), (3, 7), (28, 7), (28, 10), (17, 16), (9, 28), (2, 2), (22, 21), (0, 14), (18, 21), (25, 4), (14, 25), (8, 13), (5, 32), (17, 21), (32, 14), (33, 2), (18, 15), (33, 13), (7, 20), (20, 7), (29, 11), (34, 33), (32, 9), (21, 6), (29, 31), (5, 33), (0, 26), (23, 3), (7, 1), (7, 11), (11, 9), (27, 16), (16, 30), (22, 22), (26, 12), (18, 0), (2, 9), (1, 32), (26, 25), (16, 2), (12, 29), (26, 31), (22, 16), (27, 28), (22, 13), (2, 10), (0, 22), (33, 10), (26, 5), (4, 17), (1, 28), (36, 30), (30, 27), (22, 12), (28, 14), (32, 23), (15, 25), (25, 8), (11, 3), (1, 2), (14, 16), (24, 24), (4, 23), (13, 4), (8, 15), (1, 12), (17, 10), (4, 28), (31, 30), (1, 7), (15, 12), (24, 16), (8, 7), (15, 14), (29, 33), (5, 21), (6, 28), (21, 14), (28, 1), (16, 6), (21, 31), (23, 23), (5, 12), (24, 11), (18, 12), (34, 32), (33, 19), (11, 23), (7, 33), (10, 19), (19, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912384", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 21), (34, 13), (34, 19), (19, 29), (10, 35), (9, 21), (33, 3), (35, 33), (34, 27), (27, 23), (17, 7), (23, 1), (17, 2), (30, 14), (7, 29), (16, 2), (35, 32), (22, 9), (29, 19), (2, 35), (28, 35), (24, 26), (26, 12), (11, 10), (2, 14), (0, 6), (22, 28), (31, 28), (35, 16), (35, 9), (20, 16), (16, 24), (11, 4), (29, 35), (21, 10), (16, 19), (1, 13), (16, 8), (16, 22), (17, 33), (19, 35), (5, 10), (19, 25), (9, 31), (19, 17), (12, 14), (31, 27), (14, 29), (28, 12), (35, 12), (27, 2), (32, 21), (0, 35), (22, 16), (14, 22), (14, 25), (24, 11), (33, 25), (22, 30), (12, 26), (4, 3), (23, 5), (5, 26), (5, 7), (19, 18), (30, 28), (14, 27), (19, 26), (0, 12), (16, 33), (28, 30), (9, 23), (35, 26), (5, 13), (10, 9), (20, 26), (18, 16), (32, 28), (11, 11), (11, 22), (9, 33), (19, 33), (22, 6), (8, 17), (31, 20), (8, 19), (20, 29), (19, 11), (17, 30), (30, 11), (9, 32), (35, 4), (15, 0), (9, 6), (32, 18), (24, 3), (2, 29), (2, 27), (15, 27), (5, 24), (34, 28), (29, 26), (33, 1), (27, 28), (16, 18), (10, 15), (23, 2), (28, 6), (3, 2), (17, 17), (23, 4), (35, 24), (13, 21), (4, 18), (35, 30), (31, 12), (10, 34), (14, 6), (15, 24), (8, 13), (4, 28), (21, 21), (25, 23), (12, 23), (21, 23), (31, 21), (7, 7), (21, 29), (32, 25), (26, 0), (2, 22), (23, 30), (10, 18), (5, 19), (11, 34), (4, 12), (22, 15), (2, 3), (17, 0), (18, 31), (11, 20), (6, 15), (36, 0), (26, 28), (30, 12), (9, 2), (3, 17), (28, 7), (26, 13), (14, 10), (0, 24), (24, 20), (35, 31), (35, 29), (9, 27), (28, 13), (17, 3), (7, 13), (18, 27), (14, 12), (35, 25), (34, 18), (32, 4), (26, 2), (0, 13), (9, 30), (1, 12), (3, 4), (31, 13), (1, 7), (8, 10), (28, 9), (2, 4), (19, 19), (35, 14), (2, 13), (27, 12), (20, 20), (20, 19), (6, 32), (36, 5), (29, 3), (34, 11), (34, 6), (33, 18), (12, 21), (31, 25), (35, 17), (4, 6), (32, 3), (9, 29), (10, 24), (3, 24), (25, 32), (22, 21), (34, 0), (5, 35), (27, 35), (8, 24), (28, 32), (36, 10), (13, 27), (20, 10), (33, 14), (11, 18), (4, 7), (24, 22), (27, 19), (19, 16), (21, 27), (30, 20), (0, 10), (17, 4), (13, 1), (25, 25), (5, 34), (8, 23), (1, 6), (22, 10), (3, 21), (31, 34), (6, 4), (32, 13), (24, 16), (22, 4), (12, 7), (10, 19), (32, 19), (28, 33), (27, 22), (28, 11), (19, 5), (6, 6), (18, 0), (31, 9), (30, 21), (5, 12), (32, 16), (34, 17), (30, 16), (35, 8), (11, 26), (32, 33), (7, 28), (20, 12), (33, 35), (22, 34), (28, 1), (28, 5), (20, 3), (17, 34), (3, 0), (34, 24), (26, 10), (31, 17), (34, 7), (27, 18), (7, 1), (1, 18), (8, 31), (1, 23), (1, 9), (16, 20), (8, 27), (7, 3), (31, 1), (3, 31), (30, 24), (2, 7), (1, 19), (3, 12), (5, 29), (3, 10), (11, 29), (27, 25), (6, 25), (33, 23), (25, 11), (28, 10), (6, 5), (25, 29), (24, 27), (9, 20), (28, 18), (8, 4), (10, 30), (17, 24), (16, 25), (15, 20), (3, 13), (19, 24), (10, 10), (0, 30), (25, 5), (30, 2), (32, 34), (32, 23), (21, 22), (3, 18), (29, 8), (28, 19), (14, 31), (33, 24), (18, 22), (30, 34), (36, 9), (4, 4), (30, 15), (29, 14), (9, 8), (9, 18), (31, 19), (15, 31), (36, 20), (14, 19), (29, 9), (14, 20), (14, 14), (3, 3), (15, 16), (33, 20), (25, 19), (1, 24), (0, 2), (23, 23), (19, 10), (14, 1), (4, 20), (0, 28), (32, 11), (12, 9), (28, 21), (13, 11), (6, 1), (30, 29), (15, 22), (1, 35), (4, 5), (25, 21), (13, 20), (10, 5), (5, 5), (16, 32), (14, 18), (2, 30), (24, 13), (33, 11), (12, 17), (5, 1), (12, 16), (16, 35), (13, 33), (1, 32), (3, 27), (16, 30), (28, 31), (24, 17), (32, 2), (14, 32), (30, 7), (36, 15), (24, 19), (6, 16), (22, 23), (31, 22), (16, 16), (6, 35), (18, 24), (36, 24), (4, 22), (9, 9), (10, 21), (29, 0), (6, 0), (17, 22), (6, 30), (32, 0), (3, 30), (25, 4), (29, 27), (25, 35), (23, 20), (34, 12), (29, 24), (25, 26), (4, 25), (20, 21), (13, 30), (18, 13), (1, 20), (15, 9), (21, 33), (13, 29), (36, 13), (3, 6), (32, 9), (8, 14), (35, 18), (27, 21), (17, 32), (29, 31), (34, 9), (7, 22), (19, 14), (13, 6), (8, 8), (23, 24), (6, 21), (8, 6), (12, 31), (20, 15), (26, 7), (7, 6), (33, 12), (26, 1), (9, 19), (20, 30), (23, 3), (22, 29), (22, 1), (11, 35), (7, 26), (1, 30), (24, 31), (20, 2), (36, 7), (25, 10), (34, 4), (20, 32), (10, 0), (26, 35), (5, 20), (20, 14), (13, 25), (21, 8), (9, 14), (8, 18), (10, 17), (26, 31), (21, 25), (17, 13), (15, 5), (23, 17), (31, 23), (25, 9), (19, 32), (23, 25), (7, 8), (19, 3), (29, 28), (36, 12), (20, 17), (25, 20), (10, 12), (12, 28), (32, 14), (20, 23), (27, 8), (15, 3), (23, 21), (2, 26), (1, 27), (27, 1), (8, 34), (6, 31), (34, 32), (18, 17), (22, 19), (32, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "539460", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), 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), (10, 8), (33, 3), (27, 13), (17, 14), (0, 33), (26, 23), (33, 29), (10, 18), (2, 25), (20, 10), (25, 24), (2, 9), (0, 15), (24, 30), (26, 14), (25, 17), (25, 32), (13, 5), (35, 10), (15, 36), (9, 11), (25, 23), (31, 18), (13, 29), (25, 18), (14, 5), (5, 28), (26, 7), (12, 17), (15, 21), (24, 21), (17, 5), (11, 13), (33, 25), (16, 30), (4, 3), (8, 29), (5, 8), (20, 17), (26, 25), (8, 35), (0, 18), (17, 0), (19, 19), (34, 34), (3, 19), (7, 16), (19, 18), (22, 4), (14, 1), (34, 18), (35, 18), (6, 29), (7, 30), (1, 7), (33, 34), (21, 28), (27, 11), (13, 23), (4, 15), (15, 27), (0, 24), (13, 27), (0, 7), (29, 18), (34, 8), (6, 21), (13, 3), (14, 19), (15, 32), (23, 7), (8, 12), (11, 14), (29, 29), (14, 22), (9, 1), (25, 25), (13, 22), (30, 4), (21, 12), (14, 29), (22, 2), (15, 3), (19, 7), (8, 24), (15, 9), (14, 21), (21, 35), (27, 20), (22, 34), (28, 24), (16, 22), (30, 34), (32, 13), (5, 25), (18, 21), (21, 19), (17, 20), (8, 9), (31, 14), (17, 35), (5, 5), (14, 24), (24, 18), (0, 5), (4, 19), (30, 9), (8, 13), (22, 26), (5, 3), (1, 18), (27, 23), (22, 18), (1, 15), (8, 26), (29, 26), (0, 23), (31, 17), (21, 21), (35, 9), (23, 29), (8, 11), (12, 34), (32, 16), (22, 7), (20, 25), (17, 25), (11, 28), (11, 2), (1, 22), (9, 6), (12, 13), (22, 15), (28, 15), (15, 17), (17, 29), (31, 19), (34, 25), (18, 20), (10, 16), (22, 14), (7, 32), (31, 7), (8, 5), (4, 31), (32, 31), (23, 5), (29, 8), (30, 30), (20, 4), (35, 3), (11, 35), (20, 18), (11, 30), (33, 6), (7, 1), (3, 29), (6, 10), (2, 26), (17, 8), (27, 29), (20, 29), (31, 12), (22, 22), (21, 14), (18, 2), (12, 28), (7, 7), (30, 25), (20, 22), (14, 14), (5, 24), (3, 34), (16, 24), (14, 10), (0, 9), (17, 34), (15, 5), (5, 17), (5, 30), (5, 14), (28, 13), (29, 5), (7, 26), (0, 17), (9, 12), (14, 2), (2, 29), (1, 24), (16, 12), (35, 31), (27, 18), (19, 15), (29, 14), (1, 21), (1, 34), (30, 32), (3, 18), (34, 36), (22, 27), (11, 8), (34, 3), (17, 1), (33, 4), (23, 27), (35, 4), (16, 26), (7, 21), (6, 8), (19, 13), (29, 34), (19, 34), (7, 35), (29, 3), (7, 0), (1, 16), (30, 23), (31, 2), (31, 35), (33, 1), (15, 11), (15, 10), (33, 28), (9, 10), (14, 26), (35, 19), (30, 24), (14, 6), (21, 4), (27, 32), (13, 26), (3, 0), (9, 13), (4, 26), (5, 23), (33, 32), (24, 14), (10, 22), (9, 8), (11, 7), (20, 15), (13, 18), (13, 9), (9, 0), (11, 25), (16, 16), (33, 20), (19, 11), (8, 15), (25, 0), (17, 32), (24, 5), (0, 19), (11, 18), (16, 19), (27, 24), (12, 20), (3, 23), (9, 31), (4, 1), (30, 19), (10, 4), (9, 35), (29, 1), (12, 23), (11, 32), (19, 30), (22, 10), (11, 22), (26, 15), (26, 31), (4, 6), (22, 12), (1, 19), (25, 21), (32, 29), (31, 1), (23, 3), (2, 1), (6, 9), (3, 10), (19, 32), (1, 23), (17, 6), (24, 22), (23, 31), (26, 18), (17, 9), (33, 13), (1, 20), (4, 2), (24, 35), (15, 29), (11, 9), (31, 11), (17, 36), (18, 16), (32, 11), (16, 36), (10, 7), (10, 21), (12, 35), (3, 22), (21, 18), (31, 31), (5, 33), (29, 35), (6, 20), (33, 22), (27, 12), (22, 35), (22, 21), (26, 33), (34, 33), (34, 29), (6, 17), (28, 6), (7, 24), (1, 3), (6, 19), (11, 16), (12, 5), (18, 35), (27, 31), (28, 19), (3, 32), (22, 11), (35, 23), (22, 32), (35, 29), (21, 20), (28, 30), (11, 33), (5, 12), (25, 16), (17, 19), (17, 10), (29, 13), (21, 24), (2, 31), (12, 27), (14, 9), (21, 7), (1, 31), (33, 18), (5, 9), (19, 0), (7, 25), (20, 21), (12, 31), (23, 24), (22, 16), (28, 32), (16, 9), (3, 28), (28, 26), (4, 16), (12, 9), (30, 20), (19, 28), (4, 21), (12, 2), (19, 6), (31, 13), (34, 17), (30, 21), (23, 36), (32, 35), (23, 0), (31, 21), (25, 15), (27, 21), (0, 20), (2, 0), (15, 4), (5, 31), (27, 4), (2, 24), (0, 11), (32, 0), (25, 13), (30, 1), (34, 35), (23, 32), (22, 31), (32, 36), (32, 21), (9, 3), (24, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2240", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 5), (24, 19), (17, 14), (16, 34), (31, 19), (12, 29), (22, 34), (14, 25), (19, 1), (28, 33), (10, 5), (25, 19), (8, 28), (7, 15), (5, 28), (25, 32), (31, 11), (23, 0), (34, 19), (17, 1), (28, 17), (14, 10), (20, 29), (29, 19), (6, 25), (33, 1), (9, 30), (11, 14), (6, 27), (30, 32), (2, 11), (23, 33), (8, 33), (1, 15), (2, 33), (2, 30), (13, 13), (25, 28), (2, 12), (25, 6), (5, 21), (22, 26), (22, 24), (8, 3), (11, 15), (21, 19), (2, 10), (18, 21), (24, 28), (2, 35), (1, 35), (30, 24), (21, 29), (15, 11), (19, 24), (5, 27), (24, 11), (31, 27), (16, 21), (22, 3), (30, 11), (22, 16), (26, 21), (14, 6), (28, 2), (30, 23), (3, 35), (30, 15), (8, 16), (28, 22), (18, 22), (19, 15), (30, 8), (9, 19), (3, 14), (16, 1), (13, 17), (25, 25), (15, 29), (16, 0), (34, 22), (29, 15), (35, 16), (27, 17), (5, 32), (24, 3), (10, 34), (4, 21), (19, 35), (18, 24), (2, 13), (33, 8), (25, 18), (23, 22), (1, 16), (32, 23), (10, 18), (22, 8), (15, 28), (9, 32), (24, 16), (35, 9), (3, 24), (21, 15), (9, 10), (7, 22), (32, 19), (33, 32), (9, 4), (3, 19), (24, 15), (17, 5), (25, 7), (11, 17), (29, 8), (29, 28), (35, 7), (5, 9), (19, 6), (14, 16), (32, 14), (33, 28), (18, 32), (7, 28), (4, 14), (0, 22), (9, 2), (5, 6), (25, 23), (23, 21), (13, 15), (30, 7), (1, 4), (22, 28), (22, 19), (19, 13), (28, 4), (24, 31), (14, 8), (19, 9), (6, 0), (22, 2), (13, 18), (24, 5), (6, 7), (17, 26), (25, 9), (14, 33), (27, 29), (9, 17), (0, 34), (26, 18), (13, 22), (11, 22), (9, 22), (33, 19), (12, 2), (8, 27), (23, 15), (5, 18), (0, 12), (13, 26), (35, 27), (17, 27), (5, 25), (4, 13), (1, 26), (30, 2), (16, 19), (34, 21), (16, 25), (20, 0), (14, 22), (27, 34), (14, 27), (6, 18), (28, 9), (25, 14), (29, 23), (11, 4), (2, 29), (19, 21), (30, 27), (22, 21), (2, 18), (7, 12), (0, 14), (12, 28), (27, 11), (16, 6), (24, 29), (24, 33), (34, 23), (20, 31), (17, 31), (24, 17), (12, 18), (24, 1), (7, 2), (21, 18), (16, 8), (22, 12), (9, 9), (20, 6), (24, 27), (4, 0), (30, 20), (31, 32), (22, 11), (14, 3), (26, 4), (15, 15), (14, 21), (0, 2), (13, 2), (12, 26), (33, 10), (4, 10), (28, 0), (18, 6), (25, 31), (5, 11), (17, 7), (18, 28), (34, 4), (0, 31), (11, 26), (34, 25), (25, 4), (32, 13), (25, 1), (15, 34), (33, 4), (16, 35), (14, 0), (10, 2), (5, 4), (8, 18), (9, 11), (35, 12), (16, 27), (28, 16), (29, 21), (23, 26), (26, 25), (19, 29), (7, 24), (2, 19), (7, 1), (3, 12), (19, 25), (33, 16), (32, 1), (7, 4), (10, 22), (11, 1), (31, 22), (19, 5), (20, 18), (10, 21), (32, 26), (13, 30), (18, 12), (28, 7), (0, 15), (6, 31), (26, 8), (35, 13), (16, 16), (22, 27), (4, 3), (2, 3), (32, 28), (19, 27), (8, 6), (0, 16), (16, 13), (3, 23), (22, 35), (23, 19), (15, 1), (24, 23), (35, 31), (6, 15), (1, 18), (20, 35), (0, 21), (33, 12), (11, 35), (10, 31), (33, 25), (24, 30), (6, 13), (15, 21), (10, 0), (14, 12), (32, 6), (4, 29), (29, 22), (31, 25), (1, 7), (18, 18), (28, 21), (35, 20), (31, 4), (34, 10), (15, 27), (19, 14), (18, 2), (2, 16), (14, 35), (26, 32), (11, 21), (32, 16), (3, 11), (26, 1), (0, 24), (27, 12), (18, 34), (4, 26), (15, 13), (21, 24), (15, 2), (2, 25), (32, 34), (18, 4), (31, 8), (28, 8), (34, 14), (5, 23), (21, 4), (2, 8), (20, 5), (35, 28), (34, 33), (14, 24), (20, 30), (14, 4), (15, 23), (28, 15), (12, 35), (28, 5), (5, 2), (17, 2), (13, 8), (34, 9), (23, 31), (26, 33), (3, 27), (30, 17), (13, 24), (15, 24), (31, 20), (31, 16), (22, 5), (27, 1), (17, 30), (18, 1), (3, 7), (13, 35), (3, 18), (1, 29), (16, 24), (12, 16), (1, 21), (35, 32), (29, 16), (26, 26), (20, 32), (0, 18), (30, 33), (25, 2), (26, 20), (4, 30), (30, 0), (21, 32), (31, 3), (3, 22), (31, 6), (25, 29), (20, 26), (31, 24), (6, 5), (25, 27), (9, 26), (23, 2), (3, 32), (4, 8), (21, 12), (19, 2), (10, 6), (28, 19), (5, 17), (26, 2), (24, 32), (1, 8), (33, 18), (28, 13), (28, 35), (34, 1), (23, 14), (21, 31), (6, 20), (17, 28), (12, 8), (35, 25), (5, 20), (24, 20), (19, 26), (6, 28), (16, 22), (9, 27), (26, 11), (6, 4), (1, 20), (16, 14), (17, 32), (29, 14), (16, 30), (13, 21), (22, 4), (23, 3), (7, 20), (35, 5), (9, 5), (34, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793800", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 31), (10, 21), (8, 13), (21, 26), (20, 3), (10, 1), (13, 18), (10, 30), (29, 13), (28, 10), (16, 8), (10, 18), (11, 12), (0, 32), (7, 22), (19, 8), (1, 13), (17, 26), (6, 30), (11, 4), (7, 8), (5, 17), (28, 13), (17, 29), (24, 30), (28, 27), (24, 8), (23, 14), (24, 18), (1, 15), (17, 20), (29, 11), (18, 31), (17, 27), (14, 15), (9, 29), (7, 31), (18, 16), (2, 2), (23, 15), (19, 18), (8, 29), (16, 3), (12, 2), (9, 32), (28, 18), (26, 3), (28, 6), (14, 28), (5, 15), (17, 22), (22, 11), (0, 22), (24, 1), (26, 10), (17, 24), (24, 31), (22, 27), (6, 26), (6, 14), (20, 27), (10, 7), (25, 21), (20, 32), (0, 15), (9, 12), (14, 19), (2, 18), (21, 20), (25, 25), (25, 20), (27, 19), (24, 33), (26, 26), (6, 20), (16, 14), (16, 13), (1, 18), (5, 33), (17, 17), (6, 4), (1, 28), (4, 27), (13, 17), (12, 29), (3, 11), (23, 10), (24, 22), (23, 23), (10, 33), (6, 7), (5, 16), (19, 17), (19, 0), (25, 1), (18, 7), (0, 14), (5, 18), (1, 22), (10, 19), (20, 30), (10, 3), (29, 32), (4, 18), (23, 12), (22, 30), (16, 28), (13, 12), (13, 30), (28, 29), (8, 6), (5, 24), (21, 6), (20, 31), (22, 16), (7, 27), (12, 11), (24, 13), (9, 30), (21, 15), (17, 32), (21, 24), (18, 3), (18, 1), (11, 22), (2, 24), (9, 13), (16, 19), (23, 33), (0, 26), (15, 24), (25, 12), (13, 32), (0, 30), (18, 5), (17, 0), (1, 7), (4, 13), (10, 31), (1, 12), (5, 6), (9, 31), (25, 29), (27, 3), (15, 0), (2, 9), (10, 22), (4, 31), (14, 31), (4, 28), (22, 23), (2, 28), (5, 13), (0, 20), (14, 32), (1, 26), (10, 14), (23, 9), (25, 4), (2, 14), (6, 28), (23, 0), (17, 14), (25, 6), (12, 22), (1, 32), (8, 1), (11, 7), (19, 28), (19, 13), (10, 12), (25, 19), (8, 5), (29, 18), (7, 21), (23, 17), (9, 10), (27, 13), (22, 19), (16, 10), (7, 10), (7, 6), (26, 31), (15, 4), (19, 27), (21, 12), (7, 20), (5, 29), (29, 27), (19, 32), (17, 15), (14, 26), (23, 8), (19, 22), (8, 22), (25, 15), (4, 11), (5, 11), (5, 7), (12, 19), (5, 30), (3, 9), (20, 13), (23, 11), (2, 16), (12, 12), (27, 4), (26, 2), (12, 1), (28, 24), (20, 20), (22, 7), (4, 0), (23, 3), (1, 8), (8, 23), (3, 14), (0, 11), (7, 14), (11, 11), (21, 29), (29, 22), (9, 7), (6, 19), (20, 24), (11, 19), (6, 2), (25, 16), (1, 20), (28, 26), (14, 21), (28, 30), (20, 26), (22, 32), (11, 32), (11, 30), (21, 23), (3, 12), (3, 0), (24, 19), (9, 6), (16, 24), (17, 31), (28, 0), (4, 5), (9, 11), (4, 14), (24, 28), (16, 25), (28, 28), (2, 19), (18, 2), (23, 29), (26, 15), (18, 4), (3, 25), (20, 15), (26, 9), (13, 0), (5, 20), (0, 27), (26, 12), (6, 23), (9, 0), (9, 9), (20, 8), (3, 21), (28, 21), (17, 23), (24, 26), (28, 11), (27, 2), (17, 30), (15, 18), (5, 19), (7, 0), (11, 33), (4, 20), (8, 8), (16, 32), (6, 0), (23, 22), (10, 4), (29, 20), (8, 0), (4, 24), (20, 7), (27, 28), (7, 2), (27, 20), (8, 14), (2, 17), (14, 25), (11, 16), (11, 21), (8, 24), (5, 2), (28, 4), (29, 29), (28, 32), (21, 8), (20, 33), (20, 4), (12, 14), (2, 33), (3, 23), (29, 3), (24, 6), (0, 21), (17, 16), (1, 5), (13, 10), (6, 1), (21, 4), (24, 25), (16, 29), (24, 20), (4, 4), (28, 31), (6, 25), (3, 15), (1, 11), (8, 18), (18, 29), (1, 25), (16, 9), (17, 7), (13, 27), (13, 29), (6, 6), (2, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432000", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 23), (15, 23), (13, 35), (33, 14), (9, 7), (34, 25), (28, 35), (18, 15), (23, 6), (33, 29), (18, 36), (22, 12), (5, 8), (31, 18), (33, 3), (16, 36), (2, 6), (2, 15), (1, 32), (20, 11), (31, 21), (10, 31), (18, 30), (27, 6), (31, 12), (15, 11), (1, 5), (9, 10), (34, 7), (1, 31), (1, 12), (4, 36), (28, 8), (19, 7), (14, 8), (1, 16), (20, 12), (6, 27), (0, 29), (16, 30), (27, 9), (16, 4), (30, 31), (21, 21), (10, 4), (21, 2), (13, 10), (28, 24), (8, 30), (26, 33), (7, 9), (9, 32), (18, 18), (8, 29), (23, 35), (1, 17), (24, 15), (31, 4), (0, 9), (20, 32), (10, 36), (29, 16), (0, 18), (15, 1), (0, 15), (30, 29), (22, 23), (0, 11), (5, 35), (34, 1), (14, 4), (28, 21), (30, 37), (23, 13), (7, 37), (8, 14), (26, 26), (34, 31), (0, 30), (18, 10), (19, 34), (11, 15), (23, 12), (13, 28), (23, 8), (10, 16), (20, 36), (30, 17), (10, 0), (8, 36), (14, 15), (19, 22), (21, 30), (24, 6), (34, 18), (17, 27), (10, 29), (21, 26), (12, 11), (9, 26), (29, 13), (8, 32), (16, 25), (4, 15), (29, 8), (12, 5), (15, 29), (5, 26), (15, 34), (3, 12), (19, 29), (0, 4), (30, 24), (17, 4), (29, 33), (8, 13), (4, 2), (2, 34), (5, 24), (13, 15), (16, 12), (2, 0), (15, 15), (30, 28), (29, 15), (27, 27), (33, 5), (29, 11), (7, 7), (21, 33), (30, 11), (31, 28), (17, 31), (1, 26), (7, 11), (12, 8), (34, 15), (15, 30), (11, 8), (14, 19), (16, 13), (4, 23), (16, 3), (27, 26), (25, 37), (32, 33), (19, 2), (31, 9), (26, 12), (12, 36), (33, 35), (32, 7), (11, 24), (6, 32), (28, 14), (21, 31), (0, 12), (12, 1), (29, 0), (27, 28), (22, 19), (23, 3), (23, 21), (26, 14), (31, 33), (31, 0), (10, 20), (20, 14), (7, 8), (26, 16), (24, 29), (22, 17), (25, 7), (1, 33), (12, 31), (3, 6), (28, 4), (18, 9), (21, 16), (2, 10), (34, 4), (25, 10), (31, 23), (18, 33), (26, 15), (29, 14), (1, 7), (29, 30), (11, 7), (32, 35), (13, 13), (20, 7), (25, 15), (4, 10), (9, 17), (23, 29), (10, 32), (26, 0), (22, 8), (9, 15), (34, 36), (17, 16), (1, 24), (3, 5), (32, 6), (20, 18), (22, 22), (33, 0), (17, 13), (23, 20), (24, 14), (34, 28), (33, 15), (12, 30), (10, 37), (11, 29), (18, 17), (17, 30), (5, 28), (1, 10), (34, 6), (20, 29), (10, 7), (1, 20), (13, 33), (27, 37), (11, 9), (28, 31), (3, 1), (12, 37), (27, 18), (31, 34), (8, 7), (30, 16), (23, 1), (28, 3), (9, 6), (9, 21), (17, 37), (31, 7), (8, 25), (20, 8), (13, 37), (14, 27), (1, 9), (15, 27), (3, 31), (22, 2), (21, 14), (24, 8), (8, 26), (14, 26), (4, 0), (18, 2), (33, 24), (18, 19), (10, 6), (23, 16), (29, 34), (11, 37), (23, 26), (27, 33), (2, 12), (15, 26), (13, 25), (11, 5), (34, 35), (1, 19), (19, 6), (0, 8), (16, 0), (6, 11), (16, 26), (13, 21), (11, 22), (4, 28), (18, 32), (8, 23), (16, 7), (12, 17), (22, 11), (32, 22), (8, 33), (9, 24), (34, 16), (33, 21), (4, 37), (6, 15), (12, 3), (27, 11), (32, 4), (4, 35), (8, 6), (34, 27), (31, 20), (24, 34), (3, 16), (11, 35), (27, 0), (11, 20), (10, 14), (14, 35), (9, 19), (16, 24), (14, 13), (27, 4), (29, 26), (20, 21), (2, 28), (34, 17), (2, 31), (7, 0), (9, 23), (6, 13), (11, 14), (13, 9), (14, 20), (7, 24), (2, 22), (2, 27), (8, 12), (6, 35), (21, 28), (20, 28), (22, 1), (21, 22), (18, 27), (4, 18), (34, 0), (4, 5), (18, 28), (3, 17), (27, 3), (26, 25), (13, 8), (26, 23), (5, 14), (28, 7), (28, 20), (34, 11), (31, 1), (25, 27), (34, 20), (4, 25), (11, 16), (5, 34), (4, 9), (17, 24), (23, 24), (12, 35), (19, 8), (13, 6), (5, 16), (34, 24), (30, 5), (7, 21), (0, 3), (14, 14), (3, 35), (28, 6), (10, 10), (0, 36), (29, 23), (4, 1), (21, 24), (20, 30), (34, 30), (15, 12), (22, 7), (17, 20), (8, 16), (34, 9), (22, 21), (1, 22), (26, 24), (16, 1), (6, 23), (17, 21), (11, 19), (29, 28), (32, 20), (24, 18), (10, 23), (9, 29), (6, 4), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863226", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 35), (8, 22), (1, 16), (5, 7), (14, 12), (18, 5), (12, 23), (14, 11), (4, 20), (2, 37), (35, 22), (12, 19), (10, 27), (22, 9), (19, 3), (5, 22), (23, 9), (6, 21), (4, 37), (27, 14), (20, 25), (0, 30), (6, 6), (30, 35), (29, 15), (26, 29), (35, 4), (10, 17), (26, 28), (13, 18), (3, 28), (19, 8), (6, 11), (35, 23), (33, 29), (10, 36), (7, 3), (11, 21), (19, 35), (17, 16), (23, 24), (30, 18), (24, 32), (6, 0), (11, 26), (0, 17), (5, 30), (31, 20), (35, 30), (2, 24), (14, 29), (18, 1), (13, 31), (9, 23), (23, 0), (20, 5), (34, 12), (17, 36), (14, 2), (7, 7), (34, 14), (14, 7), (33, 19), (24, 11), (18, 19), (17, 17), (23, 25), (18, 3), (11, 31), (19, 20), (29, 25), (25, 17), (9, 17), (33, 36), (8, 27), (18, 33), (25, 24), (20, 14), (15, 32), (15, 19), (15, 21), (15, 10), (14, 35), (7, 5), (26, 11), (30, 27), (34, 20), (19, 36), (29, 37), (16, 37), (4, 36), (16, 22), (26, 10), (10, 16), (32, 22), (4, 7), (35, 27), (22, 24), (21, 24), (2, 3), (10, 33), (11, 17), (25, 13), (28, 34), (24, 36), (18, 30), (33, 0), (35, 25), (17, 19), (23, 21), (28, 24), (23, 14), (19, 12), (22, 31), (28, 2), (27, 1), (32, 3), (23, 13), (5, 15), (31, 33), (9, 26), (10, 37), (20, 21), (18, 7), (30, 33), (17, 4), (15, 28), (27, 22), (20, 36), (15, 26), (12, 36), (31, 8), (4, 34), (17, 33), (30, 2), (28, 28), (8, 14), (4, 14), (23, 33), (12, 34), (7, 18), (16, 34), (35, 9), (20, 1), (24, 3), (21, 12), (23, 8), (32, 11), (14, 4), (10, 5), (32, 8), (21, 29), (2, 12), (28, 31), (0, 13), (32, 20), (1, 2), (8, 3), (17, 15), (32, 4), (25, 30), (14, 10), (19, 23), (25, 8), (13, 35), (23, 37), (12, 37), (21, 23), (5, 34), (1, 21), (5, 35), (12, 0), (24, 4), (1, 20), (13, 12), (24, 21), (35, 8), (14, 28), (0, 14), (22, 30), (23, 29), (25, 0), (34, 30), (7, 1), (17, 28), (5, 36), (7, 21), (0, 6), (7, 32), (18, 28), (7, 29), (0, 36), (24, 2), (16, 14), (20, 37), (11, 0), (35, 3), (30, 12), (11, 32), (8, 15), (13, 9), (27, 37), (9, 11), (14, 19), (10, 29), (33, 11), (25, 20), (14, 0), (29, 6), (2, 7), (10, 24), (20, 29), (11, 20), (21, 20), (15, 27), (17, 10), (29, 20), (27, 23), (12, 6), (11, 14), (8, 21), (3, 11), (14, 1), (12, 27), (26, 23), (29, 35), (29, 2), (30, 6), (17, 7), (5, 12), (27, 8), (7, 19), (11, 30), (0, 20), (0, 18), (35, 20), (6, 33), (17, 18), (22, 33), (31, 37), (22, 27), (14, 6), (24, 31), (33, 26), (10, 6), (11, 10), (8, 19), (34, 19), (34, 4), (34, 28), (27, 9), (4, 24), (8, 17), (22, 2), (16, 21), (34, 10), (0, 37), (7, 26), (9, 28), (24, 37), (16, 11), (27, 29), (2, 32), (3, 3), (34, 17), (6, 29), (29, 3), (25, 27), (32, 34), (25, 16), (11, 6), (8, 37), (35, 17), (33, 2), (31, 0), (1, 28), (0, 4), (18, 23), (10, 28), (11, 12), (18, 31), (3, 34), (29, 5), (2, 6), (13, 23), (27, 16), (0, 28), (29, 19), (34, 15), (35, 0), (31, 14), (32, 5), (24, 18), (30, 7), (28, 27), (15, 3), (18, 34), (2, 2), (29, 33), (25, 18), (0, 35), (5, 18), (27, 12), (23, 15), (6, 15), (24, 10), (2, 10), (35, 31), (9, 31), (0, 19), (18, 12), (21, 10), (15, 29), (31, 32), (10, 0), (29, 30), (9, 0), (16, 9), (31, 34), (23, 27), (14, 31), (31, 2), (16, 13), (16, 35), (11, 34), (35, 33), (1, 36), (3, 6), (13, 19), (6, 37), (16, 33), (20, 19), (32, 24), (33, 1), (22, 19), (25, 1), (19, 21), (28, 4), (25, 3), (3, 30), (16, 20), (11, 7), (16, 17), (7, 36), (3, 0), (21, 11), (23, 35), (5, 4), (1, 7), (1, 9), (21, 4), (9, 32), (15, 18), (24, 13), (30, 13), (6, 7), (30, 22), (3, 4), (5, 28), (24, 0), (8, 25), (10, 31), (19, 10), (7, 33), (18, 25), (35, 2), (28, 13), (35, 24), (19, 30), (28, 10), (17, 11), (7, 0), (19, 11), (30, 29), (31, 27), (0, 34), (31, 1), (22, 26), (33, 31), (4, 21), (29, 10), (19, 26), (30, 31), (22, 16), (31, 22), (33, 13), (2, 5), (33, 17), (17, 34), (8, 1), (16, 0), (12, 7), (23, 20), (35, 19), (31, 23), (4, 11), (14, 5), (22, 21), (24, 34), (32, 21), (9, 22), (17, 3), (4, 1), (15, 12), (2, 16), (34, 2), (12, 12), (5, 1), (6, 28), (30, 30), (1, 32), (10, 12), (13, 32), (10, 32), (24, 5), (4, 0), (16, 10), (35, 28), (18, 17), (18, 15), (17, 35), (1, 30), (17, 14), (4, 32), (23, 10), (30, 37), (5, 31), (21, 34), (1, 22), (20, 16), (13, 29), (21, 18), (35, 15), (7, 4), (15, 7), (32, 19), (31, 12), (7, 27), (22, 6), (6, 35), (33, 5), (21, 25), (19, 19), (27, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "926640", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 25), (14, 15), (14, 21), (18, 5), (20, 26), (12, 8), (27, 33), (24, 23), (28, 27), (8, 21), (16, 0), (16, 15), (18, 33), (21, 6), (9, 12), (29, 11), (18, 6), (19, 21), (30, 3), (31, 21), (9, 26), (27, 31), (19, 8), (7, 18), (22, 15), (21, 9), (13, 34), (15, 11), (3, 22), (17, 19), (5, 20), (8, 25), (29, 10), (12, 4), (18, 0), (18, 4), (0, 10), (21, 14), (27, 1), (4, 14), (0, 34), (25, 10), (18, 29), (22, 34), (3, 3), (4, 22), (8, 22), (3, 34), (5, 5), (25, 0), (1, 7), (3, 12), (12, 31), (25, 32), (24, 17), (9, 15), (3, 5), (8, 20), (21, 23), (11, 23), (13, 14), (19, 27), (27, 15), (7, 17), (25, 5), (9, 11), (7, 30), (22, 9), (19, 5), (8, 1), (26, 9), (19, 28), (15, 16), (30, 2), (22, 5), (11, 30), (2, 0), (23, 12), (14, 10), (24, 8), (28, 11), (5, 22), (21, 31), (9, 0), (0, 25), (25, 23), (27, 18), (8, 16), (15, 20), (24, 5), (28, 16), (13, 22), (16, 20), (5, 34), (31, 26), (16, 1), (20, 4), (31, 17), (23, 16), (29, 29), (12, 33), (14, 24), (11, 20), (7, 14), (17, 16), (27, 5), (13, 5), (22, 16), (21, 20), (19, 33), (22, 22), (20, 11), (5, 33), (7, 28), (2, 27), (7, 20), (16, 23), (24, 7), (13, 18), (14, 6), (15, 31), (8, 32), (16, 6), (10, 29), (28, 33), (20, 6), (13, 27), (11, 12), (26, 5), (14, 19), (0, 19), (16, 14), (6, 31), (26, 11), (22, 30), (11, 18), (8, 28), (14, 11), (3, 31), (25, 19), (15, 12), (6, 4), (30, 30), (12, 9), (27, 13), (21, 28), (12, 27), (21, 0), (5, 13), (30, 15), (21, 34), (8, 33), (19, 20), (18, 13), (1, 0), (12, 18), (21, 15), (25, 11), (6, 6), (3, 24), (26, 18), (1, 3), (14, 23), (27, 30), (19, 10), (31, 23), (17, 32), (16, 10), (1, 14), (4, 0), (6, 24), (31, 6), (22, 28), (8, 2), (10, 13), (7, 0), (19, 31), (28, 21), (6, 32), (8, 19), (13, 4), (7, 29), (3, 32), (12, 21), (25, 24), (18, 3), (16, 24), (11, 27), (23, 8), (12, 20), (11, 21), (31, 32), (6, 26), (20, 27), (29, 3), (4, 7), (12, 19), (27, 11), (1, 26), (4, 29), (2, 18), (27, 4), (23, 31), (18, 18), (11, 2), (25, 30), (5, 8), (7, 19), (26, 32), (11, 1), (13, 25), (26, 1), (12, 32), (25, 17), (15, 13), (4, 9), (30, 29), (31, 24), (30, 31), (1, 2), (9, 6), (29, 1), (15, 7), (24, 25), (23, 23), (16, 26), (29, 23), (20, 33), (19, 2), (24, 31), (7, 21), (9, 13), (6, 5), (10, 22), (14, 0), (3, 18), (19, 14), (19, 23), (8, 23), (29, 27), (30, 0), (16, 21), (10, 0), (0, 32), (7, 16), (25, 18), (1, 19), (25, 29), (8, 17), (9, 16), (30, 19), (3, 28), (29, 0), (1, 34), (17, 27), (16, 8), (4, 33), (4, 34), (15, 32), (9, 17), (1, 30), (10, 18), (7, 2), (5, 32), (2, 19), (20, 24), (24, 20), (22, 25), (20, 20), (8, 29), (31, 22), (3, 10), (11, 10), (16, 7), (14, 14), (8, 24), (16, 33), (4, 16), (1, 27), (22, 21), (10, 25), (21, 12), (16, 4), (14, 17), (4, 15), (19, 24), (17, 4), (22, 33), (15, 5), (26, 13), (30, 10), (25, 34), (30, 12), (28, 1), (16, 9), (23, 5), (12, 24), (6, 12), (21, 33), (29, 32), (4, 4), (22, 8), (8, 34), (7, 33), (28, 6), (0, 16), (20, 5), (10, 24), (1, 32), (20, 34), (4, 31), (28, 18), (2, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226240", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 26), (2, 8), (3, 22), (21, 30), (31, 34), (13, 20), (26, 9), (6, 34), (3, 9), (10, 30), (29, 2), (10, 20), (17, 25), (28, 2), (1, 2), (31, 24), (4, 9), (0, 24), (25, 3), (18, 27), (16, 24), (20, 11), (30, 17), (5, 22), (1, 23), (13, 8), (3, 33), (14, 0), (19, 28), (6, 25), (21, 19), (6, 24), (24, 24), (27, 14), (13, 25), (20, 18), (15, 5), (28, 12), (24, 30), (17, 28), (29, 19), (20, 10), (7, 3), (19, 4), (22, 16), (24, 21), (26, 7), (30, 34), (5, 20), (4, 25), (26, 11), (2, 27), (2, 28), (27, 23), (23, 18), (15, 0), (7, 19), (12, 33), (18, 5), (30, 16), (1, 28), (24, 32), (15, 22), (18, 15), (6, 28), (23, 27), (13, 16), (28, 33), (23, 7), (16, 7), (18, 12), (9, 20), (29, 14), (0, 33), (11, 15), (10, 18), (5, 27), (29, 16), (22, 34), (4, 22), (0, 2), (15, 18), (12, 31), (24, 0), (8, 2), (27, 20), (28, 31), (7, 31), (0, 21), (0, 15), (31, 1), (17, 14), (25, 35), (11, 29), (7, 22), (1, 11), (10, 3), (7, 20), (15, 24), (18, 21), (18, 18), (19, 1), (12, 13), (23, 33), (2, 14), (2, 2), (21, 32), (3, 35), (15, 16), (9, 3), (13, 35), (15, 15), (23, 23), (13, 22), (24, 20), (21, 12), (19, 30), (18, 31), (2, 16), (13, 9), (27, 7), (0, 11), (6, 17), (25, 14), (27, 26), (3, 2), (26, 5), (23, 26), (14, 9), (15, 6), (31, 18), (9, 6), (19, 34), (28, 34), (6, 11), (30, 15), (18, 13), (14, 7), (30, 11), (5, 5), (15, 29), (30, 3), (13, 32), (19, 2), (25, 24), (25, 19), (25, 22), (0, 18), (20, 32), (18, 35), (11, 1), (11, 26), (26, 33), (16, 0), (2, 30), (12, 29), (5, 18), (13, 18), (27, 31), (24, 11), (6, 8), (20, 15), (13, 6), (12, 21), (8, 5), (25, 16), (3, 25), (16, 32), (12, 24), (16, 23), (4, 34), (5, 24), (19, 20), (15, 4), (28, 5), (15, 8), (29, 29), (23, 17), (1, 17), (12, 19), (11, 34), (1, 35), (13, 5), (25, 33), (29, 28), (27, 1), (22, 33), (12, 23), (28, 10), (24, 15), (5, 34), (7, 18), (31, 8), (13, 13), (5, 25), (26, 24), (20, 6), (30, 22), (10, 23), (22, 32), (14, 19), (11, 24), (19, 15), (2, 31), (14, 2), (10, 21), (31, 14), (18, 28), (4, 33), (25, 6), (16, 25), (30, 24), (31, 21), (28, 27), (24, 4), (22, 4), (31, 3), (15, 17), (10, 17), (18, 17), (14, 11), (24, 12), (4, 29), (0, 4), (2, 7), (16, 12), (0, 8), (10, 34), (21, 29), (28, 1), (5, 8), (3, 26), (22, 29), (5, 7), (20, 33), (28, 26), (25, 25), (19, 10), (26, 31), (26, 6), (6, 0), (8, 24), (24, 9), (8, 8), (23, 6), (21, 15), (11, 4), (27, 18), (23, 31), (6, 14), (31, 25), (3, 1), (5, 16), (12, 14), (1, 27), (7, 8), (6, 18), (20, 9), (22, 28), (7, 2), (15, 2), (28, 24), (7, 4), (27, 0), (16, 19), (9, 35), (11, 20), (26, 14), (10, 33), (31, 32), (3, 5), (22, 8), (17, 6), (10, 12), (2, 12), (28, 25), (24, 7), (26, 26), (7, 33), (2, 20), (30, 8), (17, 7), (23, 19), (9, 5), (24, 14), (3, 32), (9, 2), (0, 26), (29, 13), (4, 35), (23, 13), (3, 13), (22, 3), (20, 3), (11, 19), (13, 17), (30, 13), (0, 12), (9, 17), (7, 6), (21, 5), (31, 7), (21, 6), (13, 7), (24, 35), (28, 3), (22, 23), (26, 16), (29, 24), (9, 27), (17, 35), (23, 15), (8, 7), (24, 29), (6, 20), (1, 1), (27, 16), (17, 2), (3, 17), (9, 26), (17, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117504", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 0), (20, 16), (24, 11), (23, 16), (18, 0), (11, 24), (22, 29), (28, 26), (25, 7), (20, 17), (21, 11), (17, 16), (11, 15), (30, 25), (1, 8), (13, 29), (35, 24), (13, 25), (26, 13), (8, 29), (3, 13), (17, 24), (28, 14), (27, 26), (23, 29), (16, 29), (16, 23), (8, 19), (12, 29), (8, 22), (2, 20), (22, 24), (35, 9), (22, 3), (0, 14), (31, 2), (17, 29), (7, 17), (20, 11), (15, 4), (4, 3), (33, 13), (10, 24), (35, 3), (2, 23), (15, 11), (13, 28), (21, 22), (22, 0), (29, 5), (5, 13), (10, 25), (23, 8), (28, 23), (13, 10), (14, 21), (12, 23), (29, 29), (3, 22), (23, 0), (15, 2), (7, 29), (9, 16), (12, 8), (13, 16), (5, 4), (19, 19), (34, 18), (19, 18), (10, 7), (27, 3), (0, 19), (5, 5), (2, 2), (21, 6), (4, 23), (21, 13), (2, 14), (14, 0), (31, 9), (13, 3), (0, 1), (0, 4), (35, 19), (6, 10), (9, 17), (14, 1), (19, 5), (22, 28), (4, 7), (13, 9), (0, 20), (11, 10), (31, 22), (24, 18), (11, 13), (16, 7), (1, 6), (30, 15), (26, 2), (27, 17), (25, 26), (1, 9), (11, 3), (35, 4), (22, 4), (26, 22), (12, 16), (10, 0), (9, 26), (20, 20), (16, 13), (35, 5), (32, 18), (0, 15), (11, 23), (22, 21), (7, 9), (8, 13), (22, 16), (10, 18), (19, 1), (10, 27), (10, 14), (7, 2), (23, 1), (1, 24), (20, 27), (4, 24), (14, 20), (15, 26), (11, 17), (28, 6), (10, 26), (32, 20), (18, 20), (15, 5), (31, 0), (19, 29), (9, 20), (0, 29), (17, 23), (16, 3), (30, 3), (6, 28), (15, 15), (14, 7), (24, 17), (5, 20), (4, 6), (32, 7), (34, 3), (34, 27), (3, 1), (29, 10), (6, 25), (12, 15), (10, 16), (8, 0), (21, 9), (26, 29), (24, 22), (17, 17), (9, 15), (1, 15), (34, 22), (3, 7), (32, 25), (12, 19), (12, 5), (19, 24), (11, 6), (15, 23), (8, 8), (5, 11), (18, 16), (2, 9), (35, 23), (33, 14), (15, 25), (35, 26), (18, 6), (24, 21), (1, 2), (16, 17), (3, 19), (8, 2), (26, 14), (35, 27), (5, 16), (2, 21), (29, 11), (17, 20), (8, 16), (12, 22), (16, 21), (26, 19), (6, 22), (10, 23), (26, 5), (22, 8), (23, 25), (23, 17), (12, 20), (11, 8), (18, 22), (17, 6), (9, 19), (5, 17), (32, 9), (13, 24), (23, 2), (34, 26), (0, 2), (33, 17), (10, 9), (25, 0), (18, 12), (16, 28), (30, 24), (12, 4), (29, 16), (35, 10), (17, 15), (23, 9), (7, 25), (33, 12), (6, 26), (20, 8), (20, 5), (25, 16), (10, 2), (16, 10), (29, 3), (1, 26), (29, 15), (19, 23), (13, 13), (0, 16), (18, 26), (10, 28), (16, 24), (6, 4), (7, 22), (26, 17), (25, 12), (11, 28), (8, 7), (7, 8), (23, 10), (13, 2), (12, 12), (18, 24), (6, 13), (17, 7), (18, 8), (8, 6), (35, 17), (23, 18), (28, 0), (14, 10), (4, 2), (19, 4), (34, 11), (23, 20), (35, 12), (22, 18), (28, 1), (14, 2), (21, 26), (7, 3), (1, 5), (3, 11), (29, 2), (35, 1), (16, 16), (2, 11), (22, 2), (27, 23), (21, 21), (8, 24), (19, 20), (5, 7), (31, 24), (7, 19), (35, 16), (16, 27), (21, 8), (29, 13), (6, 21), (21, 2), (19, 28), (23, 5), (21, 14), (28, 8), (21, 27), (28, 22), (32, 15), (9, 13), (4, 8), (12, 9), (5, 12), (35, 6), (24, 6), (13, 14), (27, 0), (28, 9), (34, 5), (32, 6), (35, 21), (26, 27), (25, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "619776", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 34), (15, 8), (31, 18), (16, 13), (18, 17), (8, 9), (6, 34), (32, 2), (7, 35), (20, 0), (32, 27), (21, 30), (23, 25), (31, 35), (24, 9), (25, 24), (11, 10), (27, 16), (31, 5), (34, 13), (4, 1), (29, 25), (24, 18), (17, 6), (15, 21), (34, 25), (28, 5), (3, 13), (12, 2), (22, 10), (27, 27), (34, 8), (23, 32), (9, 30), (9, 15), (3, 8), (5, 33), (15, 12), (19, 11), (3, 29), (34, 7), (12, 20), (8, 35), (23, 3), (34, 17), (10, 29), (21, 22), (15, 9), (5, 11), (34, 21), (4, 6), (16, 20), (21, 23), (13, 30), (3, 31), (0, 33), (26, 3), (27, 7), (19, 31), (4, 30), (12, 7), (18, 30), (1, 29), (4, 9), (11, 18), (6, 26), (19, 10), (1, 27), (13, 1), (34, 5), (26, 7), (7, 23), (14, 2), (17, 16), (19, 8), (12, 4), (4, 7), (30, 5), (31, 20), (7, 26), (0, 3), (7, 16), (10, 10), (28, 0), (11, 32), (13, 19), (34, 11), (34, 2), (15, 33), (32, 26), (15, 13), (31, 17), (25, 8), (14, 6), (15, 23), (31, 28), (11, 0), (5, 2), (34, 27), (32, 12), (32, 6), (30, 8), (29, 3), (1, 9), (14, 24), (21, 11), (11, 26), (13, 8), (34, 34), (3, 34), (2, 9), (24, 16), (29, 33), (33, 0), (27, 13), (10, 18), (1, 24), (32, 24), (12, 3), (24, 23), (26, 5), (25, 9), (15, 34), (8, 36), (26, 6), (20, 1), (8, 0), (20, 3), (13, 35), (34, 3), (12, 33), (1, 1), (31, 19), (32, 15), (4, 8), (2, 15), (7, 32), (32, 8), (30, 31), (17, 3), (12, 25), (5, 25), (9, 28), (29, 28), (21, 29), (7, 7), (31, 16), (5, 28), (27, 10), (26, 26), (25, 5), (13, 31), (34, 24), (16, 14), (14, 36), (3, 28), (6, 24), (31, 25), (32, 10), (29, 12), (25, 12), (26, 21), (27, 35), (25, 4), (17, 15), (18, 5), (14, 7), (15, 10), (25, 32), (32, 16), (2, 10), (28, 2), (1, 3), (20, 11), (13, 13), (7, 0), (24, 10), (11, 27), (34, 0), (17, 8), (32, 3), (1, 26), (13, 34), (3, 0), (5, 5), (8, 23), (25, 20), (5, 30), (18, 1), (16, 0), (10, 9), (8, 13), (16, 30), (8, 31), (1, 6), (17, 4), (14, 5), (16, 9), (30, 25), (22, 14), (12, 35), (26, 34), (29, 14), (7, 27), (24, 36), (26, 20), (21, 8), (11, 11), (2, 18), (7, 18), (16, 17), (4, 11), (8, 14), (22, 29), (5, 14), (19, 15), (7, 22), (29, 18), (21, 14), (16, 12), (6, 13), (24, 26), (29, 9), (6, 0), (31, 4), (17, 23), (3, 14), (23, 8), (10, 5), (28, 17), (1, 22), (22, 30), (16, 18), (33, 5), (15, 26), (7, 33), (32, 11), (6, 19), (18, 0), (16, 16), (22, 36), (33, 13), (24, 4), (10, 2), (24, 21), (14, 22), (9, 32), (7, 30), (19, 27), (10, 36), (9, 21), (16, 32), (30, 22), (17, 33), (8, 27), (30, 28), (16, 25), (32, 22), (16, 26), (22, 33), (32, 25), (17, 27), (8, 6), (31, 22), (16, 4), (10, 26), (4, 19), (11, 22), (0, 6), (15, 20), (32, 9), (6, 25), (5, 9), (22, 4), (4, 18), (8, 29), (10, 11), (26, 13), (28, 9), (4, 15), (9, 33), (24, 12), (30, 19), (1, 20), (2, 5), (0, 22), (34, 10), (28, 3), (14, 15), (19, 18), (21, 26), (9, 18), (23, 12), (0, 1), (16, 29), (27, 25), (34, 18), (18, 4), (19, 19), (30, 26), (2, 35), (6, 23), (0, 32), (27, 11), (11, 33), (1, 31), (10, 34), (20, 33), (5, 26), (13, 16), (30, 18), (23, 21), (28, 28), (15, 6), (31, 11), (10, 8), (34, 30), (33, 20), (34, 35), (5, 27), (18, 10), (20, 10), (29, 10), (20, 31), (22, 15), (10, 16), (23, 18), (27, 0), (16, 22), (14, 30), (30, 4), (12, 16), (31, 6), (25, 27), (13, 25), (21, 5), (19, 0), (31, 10), (10, 14), (4, 35), (30, 11), (21, 13), (33, 26), (20, 13), (18, 11), (8, 5), (24, 22), (11, 28), (21, 21), (1, 36), (25, 31), (6, 22), (5, 19), (28, 20), (7, 9), (31, 8), (19, 5), (1, 10), (5, 13), (23, 11), (33, 4), (22, 13), (7, 13), (20, 4), (4, 31), (28, 34), (32, 14), (19, 36), (19, 23), (27, 17), (3, 18), (19, 4), (33, 31), (21, 20), (24, 7), (13, 5), (28, 4), (3, 25), (18, 16), (13, 17), (2, 25), (25, 14), (19, 14), (34, 31), (2, 24), (23, 35), (14, 35), (13, 15), (28, 13), (0, 31), (11, 17), (24, 3), (33, 3), (1, 4), (10, 4), (27, 28), (5, 1), (25, 16), (31, 12), (2, 3), (6, 17), (5, 7), (28, 19), (7, 4), (1, 30), (23, 20), (29, 36), (34, 6), (3, 12), (22, 25), (19, 2), (25, 15), (27, 36), (9, 34), (0, 7), (9, 11), (22, 27), (25, 19), (20, 6), (19, 20), (7, 19), (19, 6), (27, 34), (25, 22), (27, 2), (31, 9), (18, 6), (19, 29), (23, 36), (16, 2), (5, 12), (30, 21), (20, 25), (31, 14), (17, 2), (26, 19), (14, 33), (9, 22), (12, 31), (15, 5), (0, 8), (15, 30), (25, 35), (19, 33), (19, 26), (26, 33), (0, 5), (25, 34), (15, 25), (29, 20), (17, 14), (29, 13), (7, 29), (24, 6), (30, 33), (27, 29), (3, 9), (4, 14), (22, 18), (2, 21), (9, 3), (30, 20), (22, 23), (13, 23), (23, 33), (20, 19), (26, 12), (2, 13), (28, 30), (23, 2), (7, 10), (30, 30), (30, 14), (6, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "887040", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), 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), (15, 12), (25, 2), (35, 31), (22, 4), (12, 17), (3, 11), (17, 12), (34, 14), (37, 28), (30, 8), (4, 29), (20, 16), (7, 28), (22, 6), (29, 16), (18, 24), (31, 27), (6, 9), (8, 28), (16, 31), (33, 15), (0, 3), (20, 9), (21, 16), (38, 14), (15, 31), (26, 8), (19, 29), (24, 8), (34, 4), (10, 3), (7, 25), (36, 8), (25, 8), (37, 7), (35, 18), (2, 3), (27, 23), (7, 16), (25, 9), (18, 8), (12, 4), (10, 15), (15, 11), (17, 18), (26, 22), (32, 5), (9, 6), (8, 22), (1, 23), (20, 3), (29, 17), (35, 19), (25, 31), (25, 26), (15, 18), (25, 0), (19, 15), (11, 31), (17, 8), (28, 9), (12, 15), (11, 25), (1, 0), (28, 3), (18, 29), (27, 15), (28, 1), (33, 14), (11, 26), (19, 25), (30, 1), (16, 2), (34, 27), (24, 10), (27, 17), (23, 28), (13, 28), (2, 4), (26, 2), (32, 4), (37, 18), (17, 26), (8, 1), (10, 20), (19, 22), (28, 27), (10, 1), (13, 20), (33, 12), (22, 19), (36, 5), (33, 26), (17, 6), (3, 3), (35, 4), (33, 19), (37, 1), (7, 26), (26, 1), (28, 25), (18, 2), (25, 24), (28, 16), (7, 2), (36, 23), (2, 8), (6, 27), (24, 5), (33, 27), (18, 11), (24, 31), (19, 6), (6, 23), (32, 14), (25, 29), (0, 2), (29, 6), (3, 28), (15, 28), (30, 5), (13, 4), (6, 28), (2, 30), (8, 12), (9, 10), (20, 28), (33, 31), (10, 14), (25, 1), (5, 17), (2, 29), (28, 28), (23, 31), (34, 9), (7, 7), (20, 6), (0, 29), (3, 27), (29, 19), (7, 10), (14, 8), (22, 30), (3, 23), (8, 10), (32, 21), (9, 28), (35, 10), (18, 31), (15, 21), (17, 13), (36, 24), (12, 2), (8, 8), (5, 21), (38, 12), (14, 13), (8, 11), (32, 10), (26, 24), (9, 20), (31, 12), (14, 4), (1, 16), (30, 12), (27, 27), (37, 6), (22, 11), (18, 3), (33, 11), (29, 12), (2, 11), (9, 26), (29, 4), (10, 27), (31, 25), (10, 30), (5, 2), (14, 5), (36, 26), (30, 23), (35, 27), (27, 28), (7, 31), (10, 25), (31, 2), (33, 3), (13, 18), (23, 10), (5, 4), (24, 20), (5, 6), (24, 29), (17, 19), (19, 28), (29, 22), (12, 27), (8, 25), (18, 10), (23, 0), (3, 8), (33, 13), (16, 14), (21, 28), (4, 9), (13, 14), (17, 11), (37, 16), (3, 12), (16, 0), (7, 22), (2, 1), (19, 7), (11, 10), (14, 3), (38, 7), (16, 1), (10, 28), (36, 20), (38, 28), (10, 13), (3, 17), (2, 5), (1, 24), (23, 4), (16, 6), (17, 3), (14, 6), (17, 21), (35, 20), (19, 3), (18, 12), (7, 11), (34, 17), (31, 10), (28, 11), (19, 17), (37, 13), (16, 21), (34, 3), (4, 24), (8, 23), (6, 29), (1, 21), (23, 26), (28, 0), (24, 11), (16, 12), (6, 5), (13, 8), (12, 24), (29, 20), (5, 23), (6, 15), (13, 17), (8, 19), (31, 3), (34, 28), (31, 21), (32, 20), (3, 10), (15, 17), (33, 28), (8, 5), (35, 11), (2, 19), (25, 14), (22, 26), (27, 31), (31, 15), (27, 9), (32, 28), (2, 20), (8, 16), (12, 29), (12, 12), (16, 29), (27, 7), (14, 30), (5, 11), (5, 10), (21, 9), (35, 17), (15, 0), (10, 19), (13, 26), (26, 25), (9, 1), (19, 2), (8, 3), (15, 13), (17, 31), (11, 20), (24, 3), (11, 18), (24, 0), (26, 17), (22, 13), (20, 20), (11, 19), (22, 27), (26, 4), (34, 16), (22, 25), (38, 8), (27, 1), (34, 12), (26, 3), (23, 2), (35, 9), (23, 16), (11, 7), (22, 18), (34, 29), (13, 27), (23, 22), (24, 26), (24, 7), (27, 29), (9, 7), (14, 14), (30, 17), (10, 21), (14, 27), (6, 22), (38, 25), (31, 26), (30, 6), (28, 26), (5, 31), (1, 20), (0, 22), (38, 23), (34, 13), (10, 24), (6, 16), (10, 6), (26, 29), (34, 18), (37, 31), (32, 8), (24, 23), (23, 29), (8, 21), (21, 14), (1, 13), (34, 2), (9, 27), (23, 1), (25, 5), (9, 0), (0, 23), (13, 5), (5, 15), (4, 21), (8, 13), (31, 28), (18, 20), (24, 14), (34, 6), (28, 14), (28, 30), (38, 16), (7, 18), (20, 11), (37, 15), (16, 17), (27, 30), (14, 29), (1, 11), (29, 13), (28, 19), (34, 24), (15, 22), (18, 18), (12, 19), (30, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960300", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 30), (21, 3), (26, 29), (6, 25), (30, 22), (28, 15), (25, 7), (27, 9), (10, 11), (25, 3), (13, 32), (16, 25), (10, 15), (27, 15), (10, 28), (20, 6), (23, 0), (4, 6), (0, 21), (0, 24), (1, 6), (14, 32), (24, 31), (4, 0), (10, 14), (16, 15), (16, 23), (29, 8), (13, 24), (15, 32), (11, 13), (16, 26), (7, 0), (18, 27), (0, 16), (30, 20), (12, 29), (29, 32), (7, 15), (22, 5), (13, 5), (8, 26), (16, 7), (16, 8), (18, 26), (28, 26), (0, 29), (5, 10), (10, 29), (9, 25), (7, 34), (29, 28), (24, 18), (6, 21), (1, 27), (3, 17), (3, 11), (4, 27), (8, 21), (13, 12), (5, 22), (3, 9), (5, 20), (18, 25), (19, 28), (6, 17), (3, 34), (27, 18), (31, 17), (19, 24), (14, 28), (16, 13), (15, 11), (19, 18), (15, 30), (27, 11), (9, 34), (17, 33), (21, 30), (29, 5), (1, 5), (20, 22), (9, 18), (20, 16), (23, 10), (15, 8), (3, 28), (29, 14), (19, 13), (23, 8), (5, 30), (9, 1), (8, 17), (14, 21), (29, 15), (6, 1), (3, 20), (22, 21), (22, 32), (26, 0), (14, 19), (21, 24), (12, 11), (7, 3), (20, 18), (8, 20), (29, 3), (26, 12), (15, 15), (22, 7), (31, 29), (5, 31), (30, 0), (8, 14), (0, 12), (11, 6), (24, 9), (13, 4), (25, 22), (0, 23), (10, 30), (15, 27), (15, 10), (9, 21), (13, 7), (14, 6), (17, 24), (0, 5), (21, 32), (15, 22), (7, 10), (1, 30), (22, 33), (5, 0), (9, 8), (0, 10), (28, 16), (18, 0), (23, 23), (20, 32), (19, 16), (0, 8), (27, 13), (7, 30), (19, 11), (3, 14), (7, 25), (1, 28), (10, 3), (11, 20), (28, 11), (4, 8), (23, 11), (2, 30), (19, 15), (18, 16), (8, 19), (13, 27), (30, 24), (2, 24), (6, 2), (26, 16), (10, 19), (7, 17), (3, 27), (29, 2), (8, 9), (9, 29), (4, 3), (19, 21), (0, 22), (3, 22), (27, 20), (19, 22), (11, 14), (26, 11), (18, 11), (3, 24), (13, 31), (4, 13), (24, 3), (15, 17), (29, 18), (28, 23), (17, 0), (29, 12), (21, 8), (5, 5), (31, 18), (1, 3), (10, 6), (22, 4), (18, 33), (26, 1), (1, 12), (4, 17), (20, 11), (16, 21), (11, 3), (0, 11), (28, 28), (21, 15), (18, 34), (22, 16), (8, 33), (19, 32), (11, 32), (26, 34), (3, 5), (17, 20), (6, 14), (21, 29), (11, 16), (6, 20), (11, 15), (8, 2), (28, 17), (19, 33), (13, 16), (18, 6), (24, 8), (25, 4), (11, 11), (14, 20), (16, 30), (5, 34), (2, 31), (25, 19), (6, 12), (11, 21), (26, 22), (8, 7), (19, 17), (11, 2), (1, 26), (4, 28), (10, 17), (20, 21), (9, 32), (16, 10), (16, 6), (16, 5), (23, 14), (14, 3), (27, 30), (20, 27), (12, 18), (30, 15), (8, 13), (30, 26), (1, 16), (2, 18), (30, 8), (24, 29), (24, 23), (21, 22), (12, 25), (8, 10), (18, 30), (25, 11), (17, 18), (19, 4), (19, 10), (8, 6), (15, 13), (10, 26), (11, 23), (14, 17), (28, 13), (3, 31), (30, 30), (7, 7), (2, 34), (3, 3), (9, 27), (27, 32), (18, 29), (1, 13), (31, 4), (15, 9), (3, 13), (14, 11), (20, 15), (7, 24), (30, 2), (8, 1), (0, 2), (27, 14), (7, 28), (8, 8), (26, 18), (28, 3), (25, 20), (1, 21), (21, 27), (3, 7), (23, 1), (29, 6), (30, 1), (16, 2), (23, 16), (30, 23), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 16), (22, 5), (17, 35), (32, 23), (16, 4), (30, 11), (24, 8), (1, 21), (1, 31), (31, 25), (9, 19), (30, 15), (32, 12), (27, 33), (27, 15), (24, 1), (12, 3), (27, 18), (8, 34), (8, 35), (12, 10), (29, 37), (13, 33), (18, 5), (28, 10), (21, 1), (25, 7), (15, 22), (14, 15), (5, 15), (30, 36), (6, 32), (3, 34), (24, 31), (6, 10), (19, 0), (22, 32), (3, 16), (29, 26), (21, 37), (10, 15), (20, 37), (1, 0), (15, 3), (1, 3), (4, 7), (24, 0), (13, 27), (9, 15), (30, 26), (29, 19), (1, 8), (9, 2), (10, 4), (6, 36), (27, 28), (11, 23), (26, 14), (1, 35), (7, 3), (33, 22), (22, 29), (22, 28), (23, 6), (28, 21), (13, 14), (30, 12), (23, 13), (17, 7), (16, 7), (1, 14), (25, 10), (2, 12), (25, 1), (1, 5), (3, 8), (1, 33), (8, 7), (11, 3), (27, 1), (32, 17), (28, 11), (15, 13), (17, 14), (8, 1), (27, 12), (22, 22), (25, 13), (24, 13), (31, 11), (10, 13), (27, 27), (5, 30), (19, 14), (21, 6), (14, 26), (0, 20), (13, 5), (7, 21), (24, 2), (15, 15), (29, 30), (13, 4), (7, 1), (27, 9), (22, 16), (5, 5), (10, 18), (26, 18), (15, 20), (13, 25), (31, 16), (21, 21), (8, 37), (19, 30), (31, 36), (19, 15), (6, 30), (2, 34), (25, 33), (8, 27), (23, 28), (27, 21), (21, 32), (22, 15), (28, 4), (19, 37), (10, 27), (23, 29), (2, 29), (11, 8), (20, 30), (31, 33), (3, 11), (32, 20), (6, 6), (31, 10), (12, 22), (9, 16), (6, 35), (13, 12), (28, 23), (31, 15), (17, 16), (2, 32), (23, 7), (14, 12), (19, 32), (1, 23), (27, 11), (16, 6), (27, 13), (2, 22), (17, 30), (7, 29), (17, 5), (19, 24), (20, 29), (8, 25), (6, 7), (12, 29), (18, 7), (11, 5), (7, 23), (0, 9), (25, 23), (3, 6), (15, 34), (7, 16), (13, 0), (29, 6), (25, 37), (4, 18), (26, 3), (24, 23), (23, 16), (30, 17), (2, 8), (10, 34), (3, 37), (5, 4), (1, 26), (23, 23), (18, 2), (13, 13), (32, 25), (28, 37), (1, 6), (8, 2), (21, 4), (29, 0), (13, 7), (27, 19), (17, 24), (23, 4), (28, 5), (25, 30), (7, 5), (14, 31), (23, 37), (24, 18), (9, 27), (17, 2), (14, 35), (26, 16), (24, 35), (13, 1), (13, 24), (17, 8), (12, 27), (14, 14), (26, 28), (5, 10), (11, 19), (7, 31), (4, 37), (3, 22), (6, 31), (5, 17), (0, 15), (14, 17), (22, 11), (26, 2), (16, 25), (13, 30), (27, 7), (18, 21), (22, 18), (22, 27), (27, 29), (26, 26), (4, 35), (19, 10), (3, 12), (31, 31), (9, 35), (18, 14), (16, 37), (8, 5), (5, 22), (14, 0), (27, 8), (32, 32), (11, 0), (9, 1), (2, 7), (30, 18), (24, 7), (20, 5), (32, 2), (22, 30), (4, 31), (8, 18), (23, 14), (7, 6), (14, 32), (14, 22), (29, 5), (11, 37), (5, 3), (22, 3), (27, 3), (26, 10), (19, 1), (5, 11), (7, 25), (6, 15), (18, 8), (18, 34), (28, 19), (20, 24), (5, 19), (17, 28), (31, 6), (17, 34), (9, 24), (27, 36), (10, 21), (17, 26), (27, 2), (33, 9), (15, 19), (20, 26), (7, 18), (12, 16), (16, 19), (21, 26), (8, 19), (6, 26), (11, 17), (7, 20), (25, 15), (0, 34), (32, 10), (0, 30), (28, 32), (16, 23), (29, 27), (7, 17), (15, 37), (14, 13), (8, 8), (32, 13), (5, 20), (3, 29), (24, 30), (31, 12), (16, 13), (29, 2), (24, 28), (17, 37), (30, 1), (10, 9), (20, 13), (3, 1), (14, 25), (11, 24), (31, 20), (2, 1), (18, 20), (15, 31), (19, 3), (24, 10), (20, 6), (33, 33), (1, 17), (1, 36), (32, 16), (1, 10), (31, 3), (25, 18), (30, 32), (5, 35), (0, 5), (11, 34), (13, 37), (25, 34), (33, 23), (17, 31), (22, 24), (24, 27), (1, 28), (4, 13), (29, 4), (15, 36), (28, 31), (13, 18), (29, 22), (4, 28), (13, 26), (19, 23), (11, 7), (23, 17), (8, 33), (19, 27), (23, 25), (24, 20), (26, 22), (4, 27), (32, 1), (21, 25), (13, 6), (20, 21), (8, 26), (19, 26), (22, 10), (1, 29), (4, 4), (23, 8), (33, 10), (15, 33), (11, 18), (26, 1), (15, 18), (9, 29), (25, 14), (21, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "950048", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), 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), (26, 7), (12, 23), (24, 17), (4, 6), (23, 13), (28, 24), (4, 12), (0, 4), (37, 1), (20, 4), (35, 16), (23, 14), (34, 34), (29, 4), (13, 12), (16, 19), (30, 21), (21, 6), (23, 18), (7, 14), (26, 13), (0, 11), (24, 26), (18, 17), (27, 20), (33, 1), (9, 6), (10, 19), (29, 23), (12, 8), (35, 15), (9, 27), (6, 27), (28, 1), (12, 26), (6, 14), (33, 26), (5, 26), (37, 31), (36, 26), (33, 0), (22, 27), (5, 31), (4, 25), (21, 18), (31, 32), (26, 6), (16, 6), (29, 3), (7, 11), (13, 34), (36, 32), (8, 28), (36, 31), (14, 27), (6, 4), (14, 2), (35, 18), (19, 24), (27, 23), (34, 28), (3, 33), (36, 30), (24, 0), (13, 27), (2, 11), (7, 16), (37, 22), (6, 29), (16, 26), (23, 3), (35, 29), (0, 26), (14, 12), (9, 11), (1, 31), (2, 22), (33, 8), (13, 33), (32, 26), (3, 5), (18, 11), (1, 6), (26, 24), (5, 23), (17, 10), (6, 5), (36, 23), (6, 11), (27, 19), (3, 19), (16, 10), (19, 3), (5, 33), (12, 33), (22, 21), (30, 12), (26, 4), (23, 17), (18, 34), (12, 7), (0, 27), (9, 15), (4, 16), (16, 16), (36, 17), (19, 18), (15, 5), (11, 12), (31, 31), (24, 3), (14, 1), (32, 6), (7, 29), (28, 19), (11, 6), (21, 28), (35, 24), (0, 28), (13, 19), (15, 24), (17, 6), (11, 16), (29, 28), (8, 18), (21, 8), (23, 12), (22, 9), (19, 29), (30, 19), (23, 2), (27, 30), (34, 33), (15, 23), (8, 10), (7, 4), (7, 20), (6, 25), (0, 1), (31, 34), (17, 12), (20, 34), (21, 26), (33, 30), (5, 2), (12, 15), (32, 2), (17, 7), (37, 30), (2, 18), (28, 2), (30, 16), (0, 5), (5, 20), (18, 33), (29, 19), (3, 11), (8, 21), (13, 18), (24, 27), (34, 8), (2, 7), (2, 28), (5, 24), (0, 19), (26, 10), (5, 10), (31, 6), (5, 5), (20, 30), (17, 27), (3, 25), (17, 20), (21, 33), (7, 22), (19, 16), (22, 3), (21, 24), (30, 25), (2, 3), (7, 33), (12, 34), (25, 28), (13, 23), (2, 25), (33, 33), (35, 3), (34, 7), (16, 33), (32, 3), (31, 25), (7, 28), (24, 30), (31, 15), (30, 18), (7, 23), (37, 33), (30, 29), (20, 19), (30, 7), (19, 34), (21, 7), (8, 4), (24, 23), (20, 33), (23, 21), (7, 26), (27, 33), (32, 8), (19, 32), (9, 31), (17, 34), (37, 23), (35, 12), (32, 22), (21, 1), (24, 8), (8, 3), (20, 9), (9, 34), (7, 21), (34, 1), (12, 14), (33, 10), (36, 21), (2, 13), (24, 7), (8, 20), (18, 21), (4, 31), (22, 24), (34, 5), (4, 17), (15, 7), (18, 22), (30, 17), (27, 24), (12, 9), (10, 7), (29, 5), (19, 5), (31, 21), (35, 6), (12, 13), (33, 34), (21, 30), (27, 15), (12, 3), (28, 20), (5, 12), (8, 0), (16, 11), (22, 28), (11, 9), (12, 5), (14, 26), (32, 27), (21, 4), (3, 29), (32, 7), (18, 13), (36, 5), (12, 28), (16, 27), (9, 28), (35, 20), (30, 11), (30, 4), (2, 30), (0, 7), (16, 9), (21, 22), (0, 17), (11, 27), (37, 9), (29, 9), (10, 2), (26, 0), (23, 22), (1, 20), (31, 8), (21, 21), (20, 29), (17, 16), (10, 21), (33, 22), (34, 31), (20, 0), (24, 28), (12, 18), (5, 32), (4, 1), (30, 28), (37, 25), (28, 23), (20, 18), (12, 17), (34, 19), (15, 33), (29, 14), (36, 12), (29, 18), (23, 10), (9, 3), (14, 33), (19, 33), (2, 2), (25, 11), (4, 2), (20, 1), (16, 25), (13, 16), (32, 29), (34, 20), (18, 30), (30, 31), (31, 1), (29, 24), (18, 26), (5, 28), (34, 23), (6, 20), (9, 1), (0, 13), (31, 3), (14, 24), (23, 9), (10, 34), (19, 13), (11, 7), (20, 6), (21, 34), (20, 28), (25, 12), (22, 31), (4, 7), (21, 5), (21, 19), (12, 25), (6, 16), (21, 25), (9, 25), (0, 32), (13, 22), (3, 20), (7, 19), (30, 8), (24, 6), (29, 27), (4, 10), (8, 1), (6, 9), (28, 30), (25, 6), (9, 0), (34, 27), (13, 28), (4, 0), (22, 13), (22, 17), (18, 24), (7, 32), (13, 29), (16, 3), (32, 15), (9, 20), (33, 16), (3, 18), (18, 6), (9, 24), (18, 5), (0, 2), (16, 21), (5, 29), (17, 31), (10, 13), (13, 4), (33, 15), (12, 24), (10, 0), (25, 1), (16, 2), (25, 26), (18, 7), (4, 29), (12, 19), (5, 1), (29, 32), (14, 0), (17, 1), (29, 7), (18, 19), (33, 11), (32, 11), (33, 20), (36, 14), (3, 16), (22, 7), (0, 22), (25, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55104", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 27), (13, 13), (1, 38), (17, 37), (22, 16), (9, 7), (10, 38), (33, 31), (13, 5), (24, 9), (7, 2), (36, 15), (30, 3), (24, 22), (15, 19), (30, 19), (0, 17), (35, 23), (36, 5), (23, 26), (11, 8), (4, 3), (12, 16), (6, 21), (33, 15), (6, 16), (0, 26), (4, 5), (8, 37), (2, 26), (21, 13), (26, 14), (16, 1), (2, 27), (35, 17), (2, 35), (14, 31), (36, 23), (14, 24), (21, 23), (8, 17), (11, 1), (34, 3), (21, 12), (8, 12), (3, 9), (16, 21), (20, 18), (23, 13), (5, 35), (18, 11), (26, 11), (17, 18), (8, 4), (16, 6), (26, 27), (19, 15), (27, 21), (30, 37), (16, 11), (29, 13), (13, 28), (17, 26), (31, 37), (15, 27), (1, 23), (28, 34), (22, 24), (13, 6), (26, 20), (35, 3), (16, 26), (31, 7), (7, 17), (15, 36), (12, 19), (11, 10), (1, 8), (4, 35), (4, 2), (27, 7), (27, 20), (12, 30), (16, 33), (26, 4), (0, 7), (25, 32), (16, 22), (13, 34), (22, 13), (17, 5), (5, 7), (1, 13), (22, 33), (20, 25), (6, 3), (34, 7), (25, 4), (25, 12), (21, 35), (33, 19), (13, 12), (15, 16), (0, 36), (15, 14), (33, 26), (20, 17), (14, 18), (36, 35), (16, 3), (34, 37), (0, 28), (5, 9), (7, 23), (18, 1), (16, 16), (5, 15), (10, 22), (36, 28), (6, 20), (24, 1), (23, 6), (0, 25), (31, 4), (2, 25), (33, 5), (23, 0), (19, 7), (9, 4), (18, 12), (10, 15), (9, 6), (29, 30), (3, 7), (9, 15), (24, 6), (14, 21), (36, 11), (13, 26), (19, 3), (18, 20), (29, 14), (30, 30), (5, 13), (24, 11), (32, 34), (14, 27), (4, 15), (20, 34), (17, 25), (36, 8), (17, 13), (12, 21), (15, 26), (13, 0), (23, 18), (4, 17), (19, 36), (35, 24), (1, 21), (8, 2), (33, 0), (28, 9), (31, 36), (20, 11), (2, 15), (20, 9), (6, 9), (15, 21), (19, 4), (22, 7), (18, 21), (18, 29), (26, 37), (31, 13), (20, 32), (14, 13), (29, 35), (36, 22), (10, 29), (34, 0), (24, 36), (30, 18), (27, 32), (18, 25), (9, 35), (0, 12), (9, 3), (14, 34), (2, 14), (35, 7), (2, 0), (5, 36), (4, 24), (19, 19), (8, 13), (21, 3), (14, 0), (2, 24), (12, 25), (24, 18), (6, 35), (32, 29), (15, 5), (33, 33), (27, 33), (21, 8), (17, 31), (30, 13), (13, 24), (19, 13), (10, 10), (26, 24), (30, 2), (21, 33), (9, 31), (10, 16), (34, 24), (15, 28), (7, 21), (32, 13), (1, 4), (16, 34), (18, 10), (23, 20), (32, 36), (36, 6), (3, 31), (5, 30), (3, 18), (34, 11), (29, 23), (4, 37), (11, 21), (34, 19), (12, 23), (25, 13), (34, 12), (35, 36), (8, 28), (35, 26), (17, 19), (18, 35), (29, 31), (18, 8), (1, 27), (20, 24), (16, 4), (22, 1), (8, 35), (16, 9), (6, 32), (27, 37), (17, 10), (11, 16), (21, 20), (29, 9), (28, 11), (18, 6), (29, 19), (3, 21), (30, 21), (12, 17), (14, 4), (19, 27), (11, 4), (33, 9), (34, 17), (5, 24), (2, 11), (3, 35), (7, 5), (18, 17), (31, 24), (3, 4), (13, 19), (16, 30), (12, 26), (28, 28), (22, 0), (25, 22), (13, 38), (34, 18), (10, 8), (26, 8), (25, 14), (30, 28), (25, 31), (12, 9), (11, 18), (1, 36), (36, 19), (31, 10), (19, 22), (5, 37), (33, 27), (30, 6), (14, 28), (26, 1), (19, 1), (14, 20), (34, 1), (25, 23), (14, 8), (25, 15), (8, 7), (9, 5), (13, 17), (22, 31), (35, 35), (22, 6), (35, 13), (6, 30), (7, 20), (13, 35), (2, 32), (25, 8), (2, 12), (8, 31), (10, 19), (11, 30), (32, 2), (20, 12), (13, 31), (29, 16), (27, 0), (24, 8), (29, 11), (15, 37), (31, 18), (25, 28), (0, 23), (19, 16), (4, 30), (17, 4), (4, 18), (31, 14), (27, 17), (32, 35), (31, 22), (0, 32), (13, 22), (8, 8), (16, 19), (21, 22), (0, 15), (10, 23), (36, 3), (10, 1), (19, 35), (14, 1), (21, 31), (27, 35), (18, 31), (19, 17), (30, 0), (28, 30), (27, 13), (9, 8), (22, 11), (26, 16), (29, 3), (25, 30), (14, 32), (4, 32), (2, 21), (11, 20), (9, 24), (33, 12), (21, 38), (15, 10), (28, 24), (29, 27), (29, 21), (36, 20), (11, 9), (22, 2), (15, 9), (23, 32), (36, 10), (21, 1), (31, 1), (8, 30), (21, 30), (32, 19), (36, 21), (1, 22), (12, 32), (26, 2), (5, 34), (29, 10), (29, 6), (5, 6), (0, 6), (11, 35), (31, 27), (0, 4), (16, 12), (35, 2), (34, 16), (34, 5), (3, 19), (27, 6), (11, 38), (30, 33), (33, 34), (32, 25), (2, 38), (9, 9), (20, 16), (18, 32), (22, 12), (19, 25), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168912", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 15), (14, 22), (24, 22), (7, 1), (18, 26), (16, 18), (20, 1), (13, 24), (13, 11), (11, 7), (3, 11), (0, 6), (9, 21), (2, 3), (10, 29), (4, 7), (5, 8), (30, 2), (28, 7), (10, 24), (25, 8), (5, 32), (5, 11), (28, 12), (3, 14), (10, 12), (6, 25), (24, 10), (11, 30), (20, 25), (21, 24), (28, 33), (13, 3), (27, 15), (7, 25), (7, 14), (3, 27), (5, 29), (15, 16), (21, 14), (14, 0), (25, 14), (13, 34), (24, 3), (22, 16), (33, 4), (20, 10), (13, 5), (2, 33), (1, 5), (25, 19), (25, 32), (19, 11), (5, 22), (20, 22), (15, 15), (19, 14), (27, 36), (16, 4), (22, 19), (23, 1), (19, 29), (22, 29), (33, 2), (19, 22), (26, 14), (11, 34), (15, 9), (15, 20), (2, 0), (3, 9), (8, 34), (9, 0), (17, 20), (9, 28), (17, 6), (17, 0), (11, 16), (3, 20), (13, 20), (32, 2), (19, 16), (15, 23), (1, 15), (0, 14), (27, 31), (1, 17), (2, 25), (3, 17), (29, 5), (9, 31), (2, 13), (15, 17), (3, 6), (31, 20), (0, 36), (19, 9), (15, 18), (25, 3), (2, 22), (29, 34), (11, 33), (20, 4), (21, 19), (29, 4), (32, 25), (3, 18), (33, 8), (20, 20), (5, 35), (17, 3), (31, 30), (6, 19), (6, 31), (15, 1), (0, 5), (25, 31), (17, 33), (32, 17), (20, 14), (30, 16), (32, 21), (3, 7), (9, 6), (23, 27), (3, 4), (18, 4), (2, 14), (3, 34), (20, 32), (22, 22), (6, 1), (21, 17), (21, 0), (6, 4), (15, 0), (2, 30), (26, 23), (0, 17), (11, 29), (15, 14), (22, 2), (19, 8), (10, 11), (8, 31), (27, 9), (12, 1), (15, 8), (23, 32), (5, 23), (6, 12), (25, 5), (17, 29), (17, 19), (16, 32), (28, 27), (25, 28), (22, 6), (33, 5), (10, 16), (2, 28), (27, 2), (23, 12), (31, 35), (17, 2), (24, 32), (6, 32), (28, 20), (31, 1), (24, 12), (27, 24), (22, 3), (22, 25), (24, 28), (30, 9), (27, 35), (27, 13), (25, 35), (24, 9), (3, 8), (7, 32), (32, 19), (28, 9), (22, 1), (15, 32), (14, 16), (26, 16), (14, 18), (12, 26), (5, 26), (20, 2), (30, 27), (23, 22), (10, 21), (21, 6), (5, 10), (28, 5), (7, 33), (25, 15), (11, 27), (24, 1), (12, 35), (28, 10), (6, 26), (33, 0), (32, 12), (2, 4), (20, 11), (33, 18), (32, 11), (2, 34), (32, 33), (4, 36), (28, 14), (11, 15), (1, 25), (0, 23), (21, 10), (29, 7), (12, 29), (1, 29), (33, 24), (15, 35), (4, 2), (11, 24), (26, 0), (31, 31), (13, 10), (3, 36), (1, 34), (23, 3), (14, 28), (3, 29), (5, 7), (14, 26), (13, 18), (16, 34), (28, 31), (22, 9), (18, 13), (25, 33), (16, 25), (16, 0), (32, 3), (17, 23), (0, 21), (16, 27), (4, 5), (27, 26), (3, 32), (12, 13), (11, 17), (27, 17), (7, 15), (20, 15), (33, 16), (7, 35), (9, 1), (14, 34), (21, 36), (26, 6), (0, 25), (6, 27), (18, 28), (28, 28), (12, 7), (33, 10), (21, 31), (13, 36), (26, 32), (13, 23), (15, 31), (4, 17), (10, 14), (19, 0), (4, 21), (20, 13), (10, 27), (10, 22), (1, 7), (1, 24), (31, 13), (3, 21), (9, 22), (11, 20), (8, 12), (23, 5), (29, 21), (2, 8), (14, 12), (23, 15), (24, 4), (16, 36), (23, 17), (29, 22), (7, 23), (30, 3), (16, 30), (2, 15), (1, 12), (20, 3), (3, 24), (19, 7), (18, 31), (9, 7), (10, 28), (25, 16), (16, 1), (26, 34), (12, 8), (9, 18), (7, 19), (33, 27), (33, 3), (31, 10), (16, 12), (15, 6), (24, 25), (29, 26), (18, 5), (21, 34), (30, 22), (18, 36), (23, 26), (9, 12), (3, 35), (12, 25), (26, 27), (4, 6), (33, 30), (31, 12), (9, 25), (6, 21), (33, 25), (2, 26), (4, 16), (29, 14), (20, 7), (24, 19), (8, 7), (19, 26), (31, 2), (30, 35), (9, 11), (9, 9), (4, 24), (20, 9), (8, 0), (21, 27), (28, 26), (15, 22), (5, 17), (4, 8), (24, 16), (7, 4), (26, 26), (23, 11), (21, 15), (21, 12), (15, 3), (10, 17), (8, 22), (11, 14), (5, 21), (26, 5), (33, 20), (5, 12), (14, 5), (1, 35), (20, 21), (10, 13), (23, 18), (0, 19), (18, 12), (2, 31), (6, 0), (2, 17), (2, 16), (12, 15), (1, 19), (21, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464256", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 7), (5, 9), (22, 8), (22, 10), (1, 4), (31, 1), (12, 22), (32, 14), (36, 3), (31, 19), (34, 19), (1, 7), (12, 26), (9, 18), (5, 31), (37, 20), (26, 4), (37, 17), (11, 3), (18, 15), (11, 32), (29, 21), (28, 0), (12, 3), (29, 30), (27, 11), (25, 14), (30, 14), (2, 15), (12, 0), (22, 32), (20, 0), (22, 23), (25, 15), (17, 9), (24, 9), (22, 30), (17, 11), (29, 10), (5, 16), (34, 20), (33, 1), (13, 14), (15, 9), (9, 30), (11, 18), (17, 20), (8, 24), (30, 3), (15, 21), (2, 14), (2, 22), (0, 28), (4, 16), (17, 25), (17, 22), (27, 9), (32, 3), (11, 14), (24, 25), (7, 10), (14, 22), (5, 4), (0, 9), (11, 16), (23, 8), (17, 33), (5, 0), (12, 6), (10, 25), (33, 8), (36, 27), (26, 31), (11, 1), (19, 32), (6, 4), (35, 19), (12, 17), (20, 7), (23, 18), (24, 3), (26, 29), (3, 0), (37, 19), (3, 13), (8, 6), (20, 8), (30, 29), (10, 33), (31, 33), (9, 12), (11, 0), (18, 1), (23, 24), (12, 13), (27, 6), (30, 21), (18, 23), (12, 11), (29, 17), (17, 23), (18, 29), (20, 25), (29, 5), (22, 22), (22, 18), (2, 0), (15, 24), (0, 23), (1, 12), (25, 16), (26, 0), (17, 17), (37, 31), (21, 2), (30, 1), (19, 28), (1, 10), (17, 8), (5, 7), (6, 30), (6, 3), (4, 1), (30, 23), (5, 17), (31, 7), (0, 4), (23, 30), (6, 19), (11, 5), (30, 22), (37, 1), (0, 14), (20, 26), (4, 22), (33, 33), (10, 24), (0, 25), (25, 3), (15, 26), (7, 25), (10, 0), (12, 9), (21, 5), (34, 25), (8, 28), (1, 15), (37, 18), (10, 22), (33, 31), (36, 19), (8, 21), (27, 10), (23, 25), (11, 12), (4, 8), (0, 29), (19, 12), (11, 11), (36, 11), (27, 2), (25, 29), (34, 29), (14, 24), (15, 19), (3, 23), (27, 12), (11, 27), (7, 16), (20, 33), (27, 27), (26, 11), (28, 1), (3, 10), (25, 33), (12, 24), (16, 1), (29, 7), (9, 9), (34, 11), (1, 31), (1, 5), (6, 16), (32, 5), (1, 14), (3, 28), (24, 7), (7, 5), (27, 31), (15, 13), (9, 25), (8, 11), (34, 14), (11, 28), (17, 5), (37, 25), (34, 7), (33, 22), (13, 7), (35, 22), (36, 18), (10, 8), (15, 16), (16, 17), (23, 5), (7, 21), (29, 33), (34, 13), (21, 0), (19, 15), (1, 9), (35, 8), (33, 0), (5, 32), (32, 9), (37, 13), (16, 14), (30, 27), (27, 28), (28, 20), (27, 7), (28, 13), (15, 3), (25, 4), (28, 5), (8, 15), (18, 6), (18, 32), (32, 19), (36, 24), (14, 9), (17, 30), (22, 25), (6, 8), (33, 6), (35, 6), (28, 19), (4, 15), (9, 28), (35, 27), (24, 15), (29, 29), (33, 11), (22, 19), (5, 15), (2, 3), (6, 6), (4, 10), (26, 7), (1, 26), (34, 8), (10, 10), (18, 16), (30, 16), (18, 24), (12, 4), (30, 7), (10, 5), (5, 28), (20, 22), (11, 23), (31, 21), (3, 11), (26, 32), (4, 32), (16, 21), (36, 22), (15, 12), (27, 22), (27, 14), (13, 18), (33, 13), (19, 0), (20, 9), (23, 6), (32, 7), (23, 22), (16, 20), (10, 15), (36, 25), (4, 28), (35, 32), (33, 21), (26, 22), (9, 32), (8, 0), (16, 9), (4, 27), (14, 21), (26, 24), (10, 30), (28, 22), (35, 7), (29, 25), (7, 31), (30, 15), (17, 4), (24, 18), (30, 17), (33, 15), (6, 26), (18, 27), (4, 7), (34, 4), (0, 6), (1, 27), (28, 8), (12, 21), (5, 33), (34, 16), (13, 13), (13, 26), (21, 16), (2, 11), (7, 13), (4, 12), (28, 25), (30, 9), (3, 33), (10, 11), (6, 11), (25, 1), (4, 30), (14, 30), (13, 32), (1, 32), (4, 0), (34, 28), (20, 10), (37, 24), (18, 9), (36, 17), (17, 0), (0, 1), (28, 16), (33, 12), (35, 9), (8, 33), (3, 7), (19, 20), (33, 4), (6, 13), (19, 25), (26, 27), (6, 9), (36, 29), (0, 16), (29, 9), (27, 3), (20, 19), (24, 10), (32, 33), (6, 7), (32, 13), (30, 12), (19, 18), (8, 3), (29, 2), (21, 18), (32, 6), (25, 19), (28, 17), (34, 22), (8, 22), (21, 1), (37, 16), (35, 3), (28, 27), (30, 4), (12, 30), (26, 18), (20, 4), (36, 28), (33, 23), (25, 17), (13, 28), (26, 8), (32, 12), (18, 20), (9, 23), (7, 9), (16, 30), (16, 7), (23, 19), (3, 25), (22, 5), (8, 23), (37, 11), (21, 32), (16, 6), (18, 17), (35, 18), (27, 0), (27, 4), (8, 8), (19, 5), (3, 31), (10, 32), (17, 28), (14, 26), (34, 1), (36, 6), (7, 20), (31, 26), (35, 10), (18, 28), (21, 6), (36, 15), (11, 13), (13, 6), (10, 14), (32, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "683802", "dataset": "MATH"}
{"messages": [{"content": "In a 30x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 27), (6, 22), (0, 23), (11, 14), (28, 14), (4, 20), (20, 29), (20, 17), (21, 12), (24, 27), (20, 15), (20, 5), (10, 4), (18, 10), (20, 28), (4, 21), (15, 8), (0, 21), (23, 4), (19, 2), (10, 13), (26, 12), (22, 7), (18, 29), (1, 2), (24, 14), (25, 10), (9, 12), (16, 21), (19, 21), (11, 11), (24, 21), (12, 28), (22, 3), (22, 10), (12, 27), (23, 13), (9, 20), (17, 11), (19, 5), (16, 12), (4, 22), (19, 14), (18, 18), (25, 21), (3, 0), (24, 4), (24, 6), (1, 23), (8, 21), (14, 12), (15, 24), (3, 10), (11, 18), (20, 26), (25, 20), (14, 29), (8, 20), (27, 28), (9, 0), (19, 4), (3, 13), (9, 4), (13, 10), (14, 11), (9, 27), (26, 20), (21, 4), (3, 12), (13, 4), (24, 7), (11, 27), (29, 7), (21, 13), (18, 3), (6, 7), (29, 6), (3, 16), (3, 5), (7, 6), (26, 25), (13, 20), (27, 16), (24, 16), (16, 16), (29, 11), (6, 0), (26, 27), (17, 27), (4, 9), (23, 12), (13, 25), (23, 7), (7, 14), (15, 12), (0, 8), (26, 16), (6, 11), (29, 5), (22, 16), (7, 18), (18, 12), (13, 16), (1, 4), (4, 26), (23, 2), (14, 22), (11, 13), (21, 16), (24, 17), (11, 25), (3, 28), (15, 19), (9, 16), (28, 20), (8, 29), (25, 17), (3, 15), (4, 18), (23, 1), (3, 1), (27, 26), (21, 29), (10, 6), (19, 13), (22, 5), (20, 19), (23, 6), (25, 16), (27, 3), (18, 17), (0, 6), (14, 17), (1, 25), (29, 8), (0, 19), (0, 24), (26, 29), (12, 3), (25, 13), (8, 9), (25, 2), (26, 13), (4, 27), (4, 28), (4, 23), (26, 0), (27, 19), (16, 3), (18, 19), (15, 11), (17, 13), (23, 20), (3, 20), (22, 27), (5, 19), (1, 24), (0, 17), (8, 19), (25, 7), (8, 15), (15, 18), (16, 11), (17, 2), (4, 10), (10, 10), (21, 5), (28, 24), (2, 1), (6, 24), (7, 7), (8, 3), (7, 20), (22, 12), (17, 3), (20, 25), (28, 6), (17, 22), (14, 23), (24, 3), (11, 4), (2, 19), (11, 15), (2, 23), (6, 18), (12, 20), (5, 20), (26, 18), (8, 8), (8, 0), (2, 15), (13, 23), (12, 16), (21, 10), (29, 23), (23, 18), (9, 7), (29, 22), (26, 6), (24, 18), (13, 6), (26, 15), (8, 6), (7, 17), (14, 0), (15, 16), (14, 7), (26, 21), (17, 4), (18, 13), (8, 26), (14, 26), (22, 21), (15, 26), (0, 12), (26, 1), (26, 23), (14, 27), (4, 14), (19, 9), (13, 27), (19, 29), (6, 19), (23, 9), (18, 28), (2, 22), (17, 8), (3, 7), (29, 3), (11, 5), (12, 19), (29, 1), (7, 25), (23, 26), (28, 7), (28, 1), (17, 0), (18, 6), (23, 29), (23, 0), (2, 26), (9, 19), (6, 4), (27, 12), (4, 17), (26, 14), (8, 5), (1, 29), (14, 3), (28, 26), (1, 0), (27, 17), (2, 3), (3, 29), (20, 12), (16, 1), (10, 22), (17, 26), (13, 15), (26, 10), (10, 11), (9, 21), (10, 27), (14, 4), (23, 28), (8, 11), (17, 14), (12, 13), (8, 28), (9, 24), (13, 13), (27, 11), (23, 25), (5, 25), (3, 19), (3, 9), (5, 26), (19, 24), (24, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346158", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 32), (17, 12), (12, 0), (29, 13), (21, 27), (26, 22), (12, 12), (18, 29), (9, 15), (11, 8), (7, 18), (25, 29), (23, 37), (17, 31), (31, 13), (19, 6), (11, 22), (20, 6), (31, 3), (29, 10), (8, 17), (26, 23), (18, 7), (20, 38), (15, 35), (27, 37), (18, 16), (33, 26), (28, 18), (17, 37), (10, 11), (27, 20), (20, 22), (12, 20), (33, 29), (27, 5), (33, 17), (34, 8), (32, 3), (15, 25), (10, 18), (16, 13), (20, 37), (35, 32), (13, 36), (16, 36), (21, 29), (15, 20), (14, 23), (19, 2), (14, 37), (27, 2), (9, 35), (4, 33), (5, 5), (5, 33), (2, 34), (9, 28), (26, 7), (30, 3), (5, 9), (6, 36), (22, 10), (26, 18), (25, 33), (16, 12), (24, 21), (8, 3), (33, 34), (8, 11), (16, 6), (7, 35), (0, 21), (33, 15), (14, 15), (19, 31), (23, 18), (32, 6), (9, 0), (15, 32), (2, 28), (19, 27), (24, 2), (23, 14), (28, 5), (8, 24), (25, 17), (26, 27), (7, 14), (17, 21), (18, 34), (30, 25), (2, 1), (32, 16), (12, 18), (19, 25), (13, 23), (0, 36), (25, 6), (31, 12), (19, 7), (16, 15), (28, 13), (0, 32), (34, 38), (35, 18), (14, 38), (23, 10), (3, 24), (28, 33), (11, 38), (13, 32), (16, 4), (12, 34), (11, 14), (34, 34), (23, 28), (13, 33), (12, 4), (1, 18), (18, 33), (33, 22), (1, 25), (4, 20), (17, 35), (27, 15), (20, 31), (6, 37), (20, 11), (23, 25), (17, 0), (24, 14), (4, 17), (6, 4), (34, 19), (22, 26), (14, 33), (25, 19), (0, 28), (35, 36), (25, 38), (16, 24), (21, 15), (19, 16), (32, 14), (29, 5), (30, 16), (19, 30), (7, 34), (27, 30), (29, 6), (2, 35), (17, 20), (18, 12), (13, 28), (9, 22), (16, 14), (1, 21), (35, 13), (13, 7), (33, 9), (20, 21), (3, 36), (14, 6), (31, 17), (18, 26), (13, 11), (28, 16), (22, 2), (7, 6), (1, 11), (32, 38), (35, 8), (28, 30), (4, 38), (28, 34), (18, 31), (25, 35), (23, 24), (34, 9), (34, 36), (32, 0), (7, 1), (9, 7), (9, 21), (2, 27), (11, 11), (6, 2), (27, 36), (7, 24), (2, 10), (21, 2), (14, 17), (24, 13), (35, 16), (30, 26), (35, 15), (14, 4), (28, 0), (20, 25), (18, 20), (17, 3), (24, 24), (0, 17), (7, 28), (34, 30), (23, 3), (24, 18), (18, 22), (26, 16), (7, 4), (5, 38), (9, 10), (31, 7), (32, 18), (30, 5), (8, 35), (32, 8), (5, 28), (20, 14), (9, 23), (26, 14), (33, 5), (6, 11), (28, 26), (31, 6), (16, 38), (7, 33), (2, 22), (33, 33), (24, 28), (24, 35), (17, 30), (6, 28), (12, 27), (14, 19), (23, 31), (12, 23), (20, 34), (10, 1), (22, 12), (16, 25), (6, 9), (19, 9), (2, 3), (21, 4), (19, 36), (34, 10), (19, 29), (16, 35), (22, 11), (6, 12), (33, 27), (9, 18), (11, 23), (15, 21), (3, 33), (30, 35), (9, 8), (32, 37), (26, 19), (31, 25), (33, 2), (4, 11), (6, 20), (30, 36), (22, 13), (23, 36), (23, 11), (6, 24), (0, 14), (19, 5), (10, 24), (26, 21), (33, 0), (20, 2), (4, 7), (17, 33), (11, 21), (11, 20), (30, 33), (11, 13), (24, 10), (22, 14), (23, 23), (3, 3), (23, 19), (22, 1), (16, 30), (27, 7), (4, 29), (5, 23), (33, 1), (8, 37), (31, 38), (32, 15), (14, 9), (1, 5), (24, 6), (25, 31), (8, 32), (17, 5), (12, 38), (13, 5), (30, 11), (19, 23), (10, 3), (18, 18), (31, 21), (8, 18), (33, 18), (9, 36), (12, 32), (29, 37), (23, 13), (14, 34), (6, 8), (22, 3), (17, 34), (15, 36), (12, 1), (29, 22), (35, 26), (31, 33), (3, 7), (32, 4), (13, 21), (3, 28), (1, 22), (13, 29), (25, 27), (30, 7), (33, 6), (18, 13), (17, 1), (4, 0), (4, 18), (17, 6), (23, 22), (6, 21), (16, 8), (28, 7), (5, 11), (23, 2), (23, 20), (15, 10), (27, 13), (27, 34), (21, 19), (18, 25), (4, 31), (16, 0), (4, 14), (28, 2), (6, 1), (19, 12), (6, 29), (5, 12), (8, 4), (21, 1), (8, 6), (22, 38), (4, 32), (19, 1), (13, 38), (6, 32), (10, 10), (21, 6), (6, 34), (7, 25), (0, 33), (18, 1), (6, 15), (14, 14), (10, 35), (11, 32), (10, 7), (4, 30), (32, 17), (12, 36), (9, 30), (24, 4), (4, 6), (20, 29), (19, 14), (35, 12), (5, 35), (1, 38), (29, 36), (13, 6), (11, 25), (18, 9), (24, 29), (0, 9), (28, 11), (23, 4), (27, 8), (12, 2), (31, 14), (14, 11), (22, 19), (14, 1), (15, 34), (0, 3), (10, 21), (34, 26), (5, 4), (23, 32), (3, 20), (10, 23), (17, 2), (25, 5), (8, 15), (3, 15), (1, 30), (31, 18), (10, 30), (34, 31), (35, 24), (8, 26), (10, 6), (12, 25), (8, 8), (13, 2), (5, 18), (32, 30), (27, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787080", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (1, 22), (17, 20), (32, 18), (5, 29), (26, 8), (5, 7), (27, 18), (31, 35), (28, 27), (3, 33), (5, 26), (30, 9), (24, 27), (3, 28), (0, 10), (23, 9), (20, 2), (30, 22), (15, 34), (8, 22), (32, 7), (1, 11), (1, 20), (4, 34), (1, 5), (31, 34), (5, 15), (31, 32), (7, 25), (32, 25), (14, 0), (6, 10), (21, 35), (19, 14), (19, 7), (28, 4), (9, 2), (19, 10), (21, 14), (14, 34), (22, 13), (30, 31), (1, 8), (9, 35), (7, 16), (31, 3), (30, 5), (25, 16), (25, 13), (17, 32), (25, 32), (22, 33), (22, 11), (6, 24), (2, 14), (20, 11), (10, 1), (13, 9), (30, 10), (17, 8), (28, 15), (22, 25), (5, 20), (13, 16), (8, 4), (22, 29), (22, 22), (11, 20), (30, 21), (26, 31), (17, 29), (2, 5), (22, 5), (29, 0), (2, 27), (2, 20), (19, 26), (25, 25), (3, 34), (2, 12), (6, 25), (16, 32), (30, 13), (28, 29), (13, 8), (14, 8), (28, 6), (17, 5), (31, 17), (14, 26), (12, 12), (23, 25), (6, 5), (12, 6), (1, 35), (10, 35), (8, 7), (26, 10), (11, 28), (9, 27), (16, 15), (20, 26), (29, 16), (27, 32), (0, 23), (6, 12), (17, 9), (22, 28), (32, 6), (30, 24), (1, 30), (25, 27), (3, 1), (23, 14), (11, 3), (14, 21), (16, 24), (17, 28), (21, 5), (11, 14), (19, 25), (10, 8), (10, 31), (25, 22), (1, 16), (2, 19), (7, 13), (4, 19), (10, 20), (29, 4), (21, 20), (27, 1), (2, 22), (6, 28), (20, 1), (10, 10), (4, 30), (3, 18), (9, 20), (27, 10), (6, 30), (16, 1), (28, 13), (32, 10), (14, 17), (29, 22), (6, 0), (2, 26), (20, 20), (0, 6), (4, 33), (5, 16), (16, 8), (12, 3), (8, 16), (15, 9), (20, 4), (26, 25), (20, 25), (8, 6), (20, 29), (17, 30), (31, 5), (14, 35), (16, 7), (22, 0), (19, 8), (0, 7), (6, 13), (19, 23), (21, 21), (24, 11), (26, 2), (0, 8), (13, 14), (32, 29), (23, 4), (31, 12), (15, 20), (14, 27), (12, 11), (25, 11), (28, 30), (14, 2), (2, 11), (4, 11), (17, 35), (9, 9), (6, 26), (16, 27), (9, 8), (27, 23), (1, 33), (28, 18), (24, 22), (0, 16), (6, 22), (8, 29), (32, 32), (11, 4), (29, 3), (27, 29), (11, 16), (7, 11), (15, 27), (11, 18), (11, 35), (15, 7), (16, 17), (23, 7), (22, 18), (28, 17), (4, 3), (1, 7), (29, 32), (17, 27), (30, 23), (1, 6), (0, 29), (3, 14), (28, 24), (17, 0), (18, 16), (3, 31), (18, 29), (19, 31), (22, 26), (10, 16), (24, 14), (3, 13), (0, 27), (1, 25), (25, 29), (31, 14), (19, 17), (21, 25), (14, 11), (8, 0), (16, 31), (5, 32), (21, 13), (11, 6), (20, 32), (24, 23), (16, 19), (10, 17), (29, 13), (3, 9), (1, 1), (4, 6), (21, 17), (6, 31), (22, 21), (25, 17), (23, 33), (19, 35), (30, 1), (29, 25), (20, 9), (24, 29), (4, 17), (21, 10), (11, 0), (3, 12), (5, 0), (12, 15), (30, 8), (32, 19), (14, 30), (9, 15), (10, 26), (29, 21), (14, 13), (19, 15), (31, 7), (22, 15), (5, 17), (6, 34), (31, 26), (8, 31), (4, 32), (3, 32), (16, 21), (19, 9), (18, 15), (14, 14), (26, 9), (24, 21), (13, 30), (21, 15), (24, 0), (8, 21), (11, 15), (9, 23), (10, 30), (22, 30), (1, 23), (11, 5), (6, 27), (3, 2), (6, 4), (19, 33), (5, 4), (6, 16), (1, 21), (30, 7), (17, 33), (23, 10), (1, 12), (8, 24), (16, 10), (9, 17), (13, 2), (10, 21), (14, 22), (25, 30), (8, 33), (3, 24), (10, 32), (24, 30), (9, 34), (22, 17), (16, 22), (0, 19), (23, 29), (4, 18), (27, 34), (1, 32), (30, 19), (11, 12), (4, 26), (31, 25), (6, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791520", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 19), (20, 22), (20, 13), (9, 25), (26, 20), (26, 13), (33, 24), (32, 8), (9, 24), (1, 0), (30, 19), (25, 11), (21, 4), (32, 1), (22, 20), (34, 10), (35, 21), (33, 22), (24, 11), (4, 5), (22, 18), (5, 11), (29, 20), (23, 10), (4, 7), (29, 29), (36, 6), (27, 11), (13, 3), (22, 25), (9, 17), (0, 26), (37, 20), (22, 8), (21, 8), (18, 28), (22, 13), (38, 23), (24, 2), (1, 16), (19, 18), (5, 29), (19, 3), (27, 30), (13, 14), (29, 31), (36, 22), (28, 0), (14, 12), (14, 23), (14, 8), (34, 23), (10, 6), (20, 15), (1, 6), (36, 13), (30, 13), (18, 31), (23, 3), (6, 25), (20, 5), (32, 15), (26, 24), (20, 8), (25, 28), (27, 16), (3, 23), (5, 30), (9, 9), (37, 7), (17, 6), (8, 22), (32, 9), (36, 15), (29, 6), (22, 11), (30, 3), (10, 0), (2, 10), (31, 24), (12, 16), (16, 9), (24, 14), (33, 13), (7, 13), (25, 1), (29, 8), (38, 17), (13, 4), (22, 6), (19, 24), (4, 14), (17, 0), (5, 0), (28, 4), (21, 25), (1, 19), (32, 19), (17, 23), (12, 5), (36, 30), (31, 27), (0, 23), (32, 10), (25, 31), (30, 21), (22, 12), (15, 2), (26, 18), (6, 14), (29, 11), (28, 30), (10, 18), (20, 19), (36, 31), (12, 2), (24, 0), (1, 1), (22, 24), (0, 16), (32, 28), (25, 26), (12, 4), (29, 24), (16, 7), (30, 18), (0, 3), (18, 15), (10, 1), (1, 14), (12, 18), (25, 12), (20, 4), (29, 10), (24, 17), (12, 9), (10, 25), (30, 7), (19, 20), (31, 0), (16, 3), (20, 26), (35, 20), (12, 26), (5, 20), (29, 18), (1, 15), (16, 2), (23, 6), (31, 6), (5, 27), (20, 3), (8, 4), (8, 18), (21, 29), (0, 10), (0, 25), (8, 0), (11, 7), (11, 27), (18, 3), (23, 24), (13, 6), (34, 29), (13, 27), (18, 12), (27, 18), (11, 29), (18, 6), (32, 18), (19, 31), (6, 22), (37, 15), (24, 6), (32, 0), (35, 3), (31, 21), (31, 31), (25, 30), (38, 12), (26, 1), (17, 28), (0, 30), (6, 27), (22, 31), (37, 12), (7, 31), (34, 6), (11, 17), (19, 11), (21, 0), (1, 23), (10, 13), (17, 20), (4, 31), (35, 13), (14, 30), (9, 23), (2, 23), (19, 7), (10, 15), (32, 22), (31, 5), (37, 6), (29, 3), (4, 4), (34, 15), (15, 29), (1, 12), (19, 15), (5, 4), (25, 4), (8, 20), (10, 29), (8, 17), (27, 8), (10, 24), (0, 27), (8, 30), (31, 17), (19, 14), (4, 17), (7, 26), (0, 17), (5, 18), (21, 18), (25, 24), (2, 27), (26, 23), (13, 25), (16, 28), (26, 30), (7, 19), (36, 2), (17, 16), (34, 11), (28, 8), (9, 1), (21, 5), (20, 2), (38, 25), (2, 19), (5, 1), (26, 0), (5, 22), (5, 15), (27, 7), (5, 24), (8, 25), (34, 30), (12, 17), (25, 21), (37, 19), (4, 21), (19, 16), (38, 6), (36, 18), (20, 6), (0, 13), (8, 2), (28, 31), (25, 8), (10, 17), (23, 16), (9, 31), (37, 1), (21, 31), (2, 12), (25, 16), (16, 18), (6, 21), (1, 29), (23, 23), (28, 27), (18, 9), (37, 11), (6, 6), (2, 6), (31, 4), (36, 27), (1, 5), (35, 15), (2, 7), (9, 10), (15, 25), (30, 10), (12, 11), (9, 18), (2, 16), (8, 8), (35, 2), (15, 22), (5, 5), (3, 26), (24, 29), (14, 25), (19, 22), (19, 4), (2, 5), (35, 12), (38, 10), (2, 8), (20, 23), (29, 14), (14, 13), (14, 31), (31, 22), (35, 25), (26, 4), (31, 16), (38, 8), (16, 26), (21, 3), (27, 22), (19, 19), (37, 10), (32, 29), (31, 28), (8, 26), (37, 5), (10, 31), (20, 7), (17, 10), (37, 0), (20, 11), (25, 23), (17, 2), (38, 22), (21, 22), (22, 28), (24, 25), (29, 25), (18, 30), (15, 11), (14, 16), (2, 20), (15, 5), (17, 24), (0, 5), (10, 11), (37, 27), (37, 16), (29, 12), (20, 1), (26, 27), (31, 9), (26, 22), (16, 15), (25, 14), (8, 3), (18, 25), (38, 5), (31, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971565", "dataset": "MATH"}
{"messages": [{"content": "In a 36x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 33), 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), (19, 8), (6, 24), (5, 29), (17, 0), (5, 1), (34, 30), (10, 10), (32, 15), (8, 30), (12, 21), (21, 4), (13, 28), (20, 31), (25, 17), (32, 13), (8, 3), (5, 25), (1, 6), (32, 26), (11, 18), (27, 2), (3, 0), (16, 28), (1, 8), (23, 10), (19, 2), (28, 21), (9, 1), (24, 16), (29, 30), (9, 6), (20, 1), (12, 17), (27, 15), (4, 13), (16, 8), (35, 2), (28, 9), (28, 14), (30, 13), (3, 25), (10, 16), (23, 31), (11, 13), (28, 19), (15, 18), (1, 12), (12, 25), (23, 14), (7, 27), (13, 14), (25, 14), (25, 30), (26, 32), (16, 21), (15, 5), (22, 29), (15, 25), (35, 25), (19, 22), (20, 17), (7, 1), (14, 33), (10, 24), (32, 7), (9, 12), (5, 13), (20, 11), (32, 8), (34, 0), (33, 4), (19, 13), (15, 29), (30, 1), (35, 12), (33, 32), (24, 29), (2, 26), (28, 5), (15, 8), (1, 24), (4, 32), (25, 2), (9, 10), (9, 15), (21, 25), (32, 1), (13, 1), (7, 21), (32, 4), (0, 27), (27, 33), (7, 28), (33, 8), (20, 29), (5, 8), (6, 17), (7, 8), (17, 26), (27, 10), (7, 13), (31, 30), (0, 7), (8, 17), (15, 13), (31, 15), (7, 23), (20, 30), (7, 32), (31, 24), (2, 27), (9, 2), (14, 18), (16, 26), (5, 10), (27, 8), (23, 32), (33, 30), (12, 1), (2, 31), (16, 6), (18, 29), (4, 27), (28, 24), (0, 3), (8, 26), (26, 30), (35, 0), (32, 18), (26, 27), (7, 6), (28, 12), (14, 17), (6, 6), (23, 5), (29, 27), (22, 30), (27, 32), (35, 21), (31, 14), (31, 18), (30, 0), (18, 28), (27, 18), (18, 6), (28, 29), (27, 29), (2, 14), (22, 5), (16, 14), (2, 6), (6, 1), (30, 9), (32, 5), (8, 8), (27, 25), (21, 17), (11, 11), (2, 20), (1, 11), (32, 14), (8, 22), (33, 14), (3, 5), (28, 0), (19, 24), (19, 1), (2, 10), (31, 17), (31, 21), (30, 18), (16, 13), (10, 8), (25, 3), (21, 8), (4, 17), (30, 3), (29, 8), (26, 15), (25, 26), (23, 25), (22, 7), (34, 17), (26, 22), (10, 27), (4, 23), (22, 22), (24, 30), (19, 6), (24, 23), (16, 1), (33, 0), (24, 0), (29, 21), (6, 12), (24, 25), (16, 4), (22, 2), (17, 20), (12, 3), (16, 25), (30, 31), (10, 2), (9, 9), (7, 18), (17, 15), (13, 4), (11, 14), (31, 12), (25, 27), (31, 27), (13, 10), (23, 6), (6, 14), (1, 31), (21, 6), (16, 2), (18, 19), (32, 17), (4, 21), (12, 18), (22, 9), (34, 23), (21, 12), (33, 1), (15, 30), (6, 10), (17, 11), (17, 30), (19, 26), (8, 11), (9, 22), (7, 4), (23, 18), (35, 23), (15, 12), (12, 22), (0, 16), (33, 25), (10, 30), (19, 17), (18, 20), (19, 15), (11, 25), (23, 12), (32, 25), (13, 21), (23, 19), (19, 4), (30, 4), (18, 9), (14, 24), (20, 24), (20, 16), (0, 30), (2, 7), (23, 26), (21, 7), (29, 11), (14, 27), (11, 27), (28, 25), (5, 24), (11, 4), (35, 14), (20, 25), (4, 7), (17, 14), (15, 2), (9, 17), (6, 33), (3, 6), (12, 10), (20, 23), (23, 17), (11, 32), (6, 18), (4, 6), (13, 30), (32, 3), (22, 32), (0, 13), (28, 30), (15, 33), (24, 14), (5, 2), (25, 8), (33, 7), (31, 0), (4, 14), (10, 25), (18, 0), (4, 18), (19, 23), (14, 29), (10, 23), (16, 0), (19, 31), (28, 33), (14, 0), (0, 31), (13, 7), (23, 8), (35, 13), (6, 2), (14, 1), (28, 17), (33, 13), (21, 31), (21, 5), (3, 15), (18, 12), (24, 21), (15, 4), (14, 32), (2, 2), (26, 25), (4, 5), (23, 13), (6, 28), (8, 29), (32, 9), (3, 14), (25, 31), (2, 23), (15, 14), (34, 18), (29, 14), (20, 10), (17, 29), (12, 31), (30, 21), (31, 32), (0, 5), (6, 11), (23, 28), (31, 10), (5, 31), (19, 19), (33, 24), (11, 7), (3, 12), (19, 33), (20, 27), (35, 8), (18, 32), (22, 19), (29, 19), (11, 21), (9, 5), (30, 10), (35, 17), (0, 15), (6, 25), (15, 3), (0, 10), (22, 15), (7, 30), (26, 6), (31, 11), (4, 28), (14, 16), (27, 26), (29, 1), (27, 24), (33, 18), (1, 32), (21, 23), (34, 12), (28, 26), (30, 12), (25, 19), (27, 13), (11, 5), (21, 18), (5, 9), (13, 27), (22, 25), (3, 3), (28, 3), (7, 16), (3, 8), (24, 28), (29, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87480", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (25, 31), (17, 0), (0, 16), (11, 26), (14, 19), (13, 36), (1, 5), (23, 27), (31, 25), (10, 36), (31, 14), (22, 19), (19, 16), (12, 10), (6, 16), (9, 36), (13, 25), (3, 22), (22, 10), (25, 12), (19, 13), (22, 5), (0, 27), (27, 17), (2, 16), (29, 11), (12, 29), (21, 6), (32, 8), (13, 35), (29, 29), (20, 20), (14, 10), (16, 5), (21, 26), (33, 30), (28, 23), (18, 33), (5, 20), (29, 5), (17, 25), (19, 18), (20, 1), (15, 30), (21, 2), (24, 33), (15, 32), (7, 27), (15, 6), (10, 18), (33, 15), (17, 9), (6, 22), (28, 10), (20, 18), (21, 28), (5, 27), (11, 32), (10, 35), (10, 12), (29, 1), (26, 4), (19, 25), (23, 35), (30, 12), (28, 33), (22, 31), (3, 5), (19, 14), (30, 18), (4, 2), (16, 28), (1, 35), (0, 7), (9, 9), (4, 8), (32, 22), (18, 27), (19, 17), (27, 22), (21, 21), (28, 0), (16, 22), (3, 3), (20, 13), (4, 35), (23, 26), (23, 14), (21, 16), (23, 30), (22, 28), (32, 20), (20, 16), (1, 19), (11, 11), (23, 33), (23, 20), (33, 22), (32, 27), (17, 16), (33, 9), (4, 34), (32, 21), (18, 14), (12, 1), (18, 2), (15, 26), (9, 20), (8, 16), (31, 7), (27, 26), (9, 10), (20, 32), (27, 33), (22, 34), (2, 1), (15, 21), (19, 19), (1, 13), (30, 19), (30, 22), (19, 21), (30, 34), (27, 3), (29, 12), (5, 23), (33, 12), (9, 30), (31, 20), (31, 10), (27, 21), (9, 18), (21, 34), (27, 5), (31, 35), (30, 27), (8, 29), (14, 4), (10, 15), (25, 2), (15, 10), (12, 19), (6, 1), (9, 19), (26, 19), (12, 35), (3, 1), (22, 20), (3, 12), (19, 27), (30, 29), (17, 10), (33, 2), (4, 36), (16, 0), (29, 15), (6, 21), (16, 20), (27, 10), (30, 13), (28, 6), (8, 2), (22, 14), (2, 27), (6, 34), (26, 13), (30, 14), (16, 27), (17, 15), (17, 23), (26, 25), (12, 28), (30, 25), (18, 7), (26, 29), (5, 16), (27, 32), (2, 18), (22, 1), (3, 6), (1, 4), (26, 36), (20, 29), (6, 3), (7, 28), (13, 20), (15, 11), (9, 27), (29, 32), (0, 26), (19, 2), (2, 28), (33, 33), (5, 8), (3, 36), (27, 13), (25, 23), (19, 32), (18, 13), (23, 31), (5, 9), (6, 6), (33, 17), (2, 2), (11, 29), (14, 20), (12, 18), (3, 11), (0, 14), (15, 13), (12, 23), (19, 28), (20, 23), (1, 20), (23, 18), (16, 6), (19, 24), (7, 15), (8, 34), (26, 16), (14, 27), (0, 13), (29, 14), (1, 0), (13, 19), (23, 0), (8, 32), (32, 14), (13, 31), (17, 1), (9, 0), (7, 30), (17, 27), (1, 18), (3, 29), (15, 14), (10, 28), (22, 7), (14, 16), (25, 29), (2, 20), (12, 26), (25, 25), (2, 34), (4, 24), (33, 35), (10, 31), (14, 9), (4, 22), (2, 9), (30, 11), (25, 15), (23, 22), (23, 34), (23, 36), (0, 34), (8, 21), (10, 26), (26, 17), (29, 23), (15, 4), (29, 30), (17, 7), (7, 32), (15, 24), (12, 16), (29, 8), (0, 20), (2, 11), (21, 31), (12, 12), (4, 14), (3, 34), (1, 36), (12, 0), (15, 2), (4, 21), (28, 32), (19, 1), (8, 33), (6, 35), (32, 10), (15, 23), (3, 8), (22, 21), (26, 28), (11, 12), (23, 6), (29, 26), (13, 34), (7, 33), (18, 9), (0, 2), (32, 28), (12, 9), (25, 21), (18, 30), (3, 14), (22, 36), (7, 26), (19, 36), (13, 16), (3, 32), (27, 25), (17, 6), (26, 7), (25, 35), (13, 22), (7, 11), (18, 32), (23, 12), (26, 22), (6, 33), (27, 19), (10, 34), (2, 5), (21, 18), (33, 1), (18, 29), (20, 27), (12, 21), (9, 23), (6, 11), (33, 14), (11, 17), (14, 12), (24, 27), (4, 17), (5, 3), (30, 30), (15, 35), (20, 34), (31, 23), (10, 23), (5, 12), (11, 1), (26, 14), (11, 19), (3, 18), (25, 7), (3, 10), (26, 31), (12, 11), (33, 32), (33, 20), (8, 3), (1, 30), (12, 30), (10, 27), (17, 17), (15, 36), (24, 23), (11, 24), (26, 33), (20, 4), (31, 5), (13, 9), (29, 27), (32, 5), (5, 10), (29, 34), (24, 25), (13, 26), (33, 19), (16, 10), (22, 23), (4, 26), (18, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "508950", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 29), (7, 33), (22, 1), (18, 10), (28, 17), (12, 1), (19, 20), (21, 30), (21, 19), (20, 11), (28, 27), (11, 15), (3, 8), (23, 12), (14, 18), (12, 33), (13, 18), (14, 13), (4, 0), (25, 17), (3, 12), (28, 9), (22, 14), (24, 14), (8, 32), (23, 11), (20, 18), (1, 29), (1, 9), (10, 23), (28, 7), (16, 33), (11, 27), (3, 21), (10, 20), (24, 5), (1, 27), (17, 8), (9, 6), (26, 1), (22, 9), (25, 6), (19, 4), (7, 5), (7, 28), (25, 28), (29, 27), (24, 19), (0, 16), (4, 29), (14, 10), (2, 19), (3, 20), (5, 4), (13, 6), (8, 22), (27, 12), (18, 25), (20, 32), (15, 1), (20, 31), (15, 26), (17, 4), (26, 28), (24, 24), (10, 10), (16, 11), (1, 32), (1, 18), (19, 32), (17, 28), (1, 10), (10, 5), (27, 11), (14, 17), (14, 26), (0, 18), (26, 6), (4, 33), (5, 23), (26, 0), (16, 0), (21, 24), (25, 19), (12, 16), (24, 8), (22, 25), (8, 23), (0, 8), (13, 26), (2, 32), (4, 7), (17, 2), (14, 11), (29, 13), (9, 4), (13, 15), (4, 10), (24, 12), (14, 4), (3, 15), (13, 32), (27, 9), (24, 27), (29, 11), (28, 10), (8, 12), (25, 27), (3, 19), (7, 12), (1, 7), (8, 17), (4, 5), (20, 28), (9, 7), (22, 6), (25, 2), (23, 31), (16, 7), (6, 23), (24, 17), (25, 1), (9, 12), (11, 14), (0, 26), (12, 6), (9, 18), (15, 25), (21, 9), (25, 24), (10, 3), (22, 24), (15, 22), (27, 30), (7, 2), (22, 12), (1, 6), (20, 13), (9, 30), (0, 30), (13, 2), (14, 25), (0, 22), (1, 22), (3, 11), (27, 24), (4, 11), (21, 18), (6, 9), (3, 10), (11, 8), (18, 29), (23, 23), (13, 16), (28, 1), (9, 24), (0, 27), (13, 4), (23, 22), (19, 33), (0, 19), (2, 2), (20, 27), (8, 7), (16, 17), (3, 25), (8, 28), (26, 33), (16, 4), (22, 32), (1, 2), (25, 4), (29, 4), (11, 21), (25, 30), (11, 28), (0, 9), (3, 32), (17, 11), (3, 31), (10, 21), (19, 28), (2, 21), (29, 23), (13, 19), (21, 17), (9, 22), (17, 3), (24, 32), (14, 24), (22, 22), (9, 26), (11, 20), (4, 8), (24, 28), (29, 26), (23, 1), (25, 31), (20, 1), (7, 32), (2, 23), (23, 15), (19, 30), (21, 6), (12, 28), (7, 30), (8, 2), (13, 5), (12, 0), (27, 0), (6, 3), (0, 12), (19, 27), (2, 24), (8, 11), (24, 6), (17, 12), (21, 21), (13, 27), (29, 0), (17, 13), (11, 0), (1, 26), (27, 2), (26, 16), (29, 1), (19, 31), (4, 31), (16, 21), (13, 24), (6, 24), (16, 19), (0, 13), (3, 33), (3, 0), (22, 7), (11, 24), (21, 27), (17, 14), (25, 25), (2, 1), (22, 8), (13, 11), (0, 33), (28, 8), (23, 24), (16, 24), (26, 25), (4, 9), (28, 5), (29, 20), (14, 32), (10, 31), (10, 8), (5, 3), (8, 13), (15, 5), (27, 14), (18, 22), (16, 14), (2, 0), (19, 23), (15, 29), (6, 12), (8, 30), (26, 11), (24, 4), (18, 28), (6, 19), (23, 6), (14, 28), (17, 26), (27, 16), (14, 7), (15, 3), (10, 24), (2, 6), (24, 31), (7, 24), (8, 15), (20, 23), (21, 25), (9, 17), (21, 16), (18, 5), (6, 16), (29, 15), (12, 31), (21, 20), (19, 12), (25, 20), (12, 24), (2, 9), (23, 4), (23, 19), (27, 20), (12, 25), (9, 11), (16, 22), (27, 28), (12, 22), (25, 13), (0, 5), (7, 6), (0, 23), (27, 21), (0, 20), (4, 14), (20, 3), (20, 20), (24, 10), (13, 17), (7, 27), (8, 19), (14, 19), (4, 13), (10, 15), (9, 9), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "653184", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 32), (22, 6), (4, 7), (8, 6), (21, 4), (13, 12), (10, 23), (23, 17), (17, 27), (4, 2), (16, 8), (13, 20), (19, 5), (21, 29), (0, 18), (19, 16), (6, 23), (14, 24), (4, 16), (33, 25), (18, 25), (17, 21), (20, 6), (4, 17), (0, 23), (25, 17), (7, 5), (21, 1), (8, 14), (24, 1), (17, 19), (20, 29), (38, 10), (8, 29), (26, 5), (35, 5), (12, 4), (27, 14), (27, 33), (28, 30), (4, 10), (5, 8), (10, 24), (20, 23), (28, 8), (38, 20), (34, 23), (37, 16), (29, 26), (0, 8), (1, 31), (37, 9), (7, 20), (6, 27), (23, 21), (9, 5), (21, 32), (1, 12), (28, 7), (19, 12), (17, 0), (0, 33), (25, 33), (9, 1), (13, 23), (26, 10), (37, 21), (14, 4), (5, 23), (16, 7), (37, 29), (7, 0), (10, 28), (38, 23), (0, 26), (8, 25), (21, 23), (1, 17), (13, 10), (34, 10), (29, 4), (17, 25), (34, 1), (35, 25), (3, 13), (30, 21), (30, 19), (17, 5), (35, 26), (1, 9), (30, 1), (14, 3), (3, 8), (24, 13), (27, 32), (3, 20), (26, 16), (0, 14), (32, 16), (1, 8), (4, 9), (28, 27), (12, 14), (32, 4), (29, 13), (14, 20), (17, 22), (23, 29), (10, 26), (28, 28), (8, 33), (34, 17), (27, 11), (30, 0), (13, 13), (24, 30), (10, 6), (28, 0), (16, 20), (12, 10), (18, 0), (22, 12), (1, 24), (10, 21), (27, 1), (12, 32), (2, 20), (23, 10), (32, 20), (33, 16), (8, 5), (25, 16), (20, 2), (9, 9), (14, 22), (29, 31), (27, 29), (6, 5), (28, 5), (16, 17), (0, 32), (1, 20), (32, 10), (31, 11), (28, 23), (18, 21), (15, 10), (18, 15), (17, 28), (24, 21), (15, 5), (17, 4), (38, 2), (5, 21), (18, 24), (32, 29), (32, 18), (34, 31), (21, 30), (20, 4), (14, 19), (35, 2), (18, 12), (28, 13), (18, 10), (26, 1), (34, 29), (18, 3), (11, 14), (37, 23), (33, 19), (28, 20), (35, 12), (14, 32), (35, 6), (1, 14), (17, 11), (19, 6), (8, 30), (8, 8), (24, 29), (20, 27), (33, 17), (6, 1), (22, 13), (13, 0), (0, 9), (27, 27), (32, 21), (16, 30), (15, 6), (18, 8), (30, 25), (38, 26), (33, 1), (11, 31), (4, 22), (30, 18), (20, 19), (32, 12), (9, 14), (24, 7), (3, 30), (4, 26), (11, 2), (10, 4), (14, 18), (10, 14), (24, 27), (8, 23), (19, 28), (17, 17), (0, 12), (17, 30), (38, 24), (7, 19), (24, 12), (21, 8), (1, 11), (3, 4), (12, 5), (18, 6), (17, 10), (26, 6), (38, 11), (26, 3), (2, 24), (20, 3), (4, 28), (17, 12), (33, 23), (15, 30), (36, 21), (22, 5), (13, 15), (24, 33), (29, 12), (23, 15), (22, 17), (35, 13), (36, 18), (38, 30), (13, 25), (3, 33), (11, 1), (9, 22), (11, 0), (20, 15), (14, 16), (36, 7), (15, 21), (12, 16), (0, 11), (28, 6), (18, 14), (16, 2), (21, 13), (28, 3), (2, 8), (32, 11), (18, 26), (26, 8), (18, 13), (32, 17), (16, 18), (16, 21), (14, 30), (37, 1), (33, 11), (12, 12), (16, 27), (29, 5), (19, 32), (25, 14), (1, 0), (20, 20), (12, 22), (12, 2), (18, 16), (19, 29), (21, 33), (38, 29), (11, 15), (21, 19), (27, 23), (14, 9), (34, 18), (1, 19), (14, 0), (7, 25), (9, 8), (31, 0), (5, 33), (3, 3), (19, 33), (15, 23), (6, 19), (24, 2), (10, 31), (12, 7), (26, 18), (29, 32), (13, 1), (18, 22), (13, 2), (15, 7), (35, 1), (3, 12), (27, 25), (22, 25), (28, 21), (35, 32), (37, 14), (27, 22), (22, 15), (35, 30), (29, 7), (27, 17), (16, 24), (19, 7), (38, 21), (22, 26), (4, 23), (25, 9), (12, 18), (35, 7), (15, 0), (28, 2), (0, 29), (33, 28), (4, 6), (16, 5), (32, 7), (0, 3), (30, 29), (33, 7), (31, 17), (34, 33), (37, 11), (28, 29), (14, 23), (1, 22), (32, 22), (18, 20), (32, 32), (8, 1), (26, 27), (10, 27), (31, 12), (9, 7), (17, 32), (3, 21), (19, 15), (13, 29), (35, 3), (36, 20), (36, 19), (30, 32), (23, 19), (7, 31), (27, 0), (27, 3), (30, 27), (35, 27), (21, 6), (9, 2), (12, 24), (23, 0), (20, 12), (23, 8), (31, 21), (22, 14), (28, 16), (38, 19), (28, 24), (19, 1), (31, 1), (37, 6), (8, 24), (33, 14), (24, 11), (20, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "724896", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (33, 12), (8, 30), (18, 14), (7, 13), (33, 8), (20, 29), (0, 9), (1, 21), (18, 12), (32, 3), (1, 16), (21, 24), (9, 7), (12, 23), (24, 22), (21, 9), (7, 7), (5, 15), (8, 4), (4, 20), (13, 7), (11, 22), (4, 5), (21, 22), (34, 2), (33, 23), (21, 14), (14, 9), (18, 23), (14, 7), (33, 11), (30, 18), (4, 21), (29, 3), (22, 28), (18, 31), (23, 22), (26, 24), (17, 4), (14, 14), (5, 21), (13, 6), (11, 31), (6, 23), (17, 19), (7, 22), (31, 12), (35, 0), (20, 25), (35, 24), (12, 16), (26, 18), (25, 19), (7, 12), (21, 20), (7, 17), (8, 12), (18, 22), (14, 11), (28, 12), (24, 20), (11, 0), (1, 3), (16, 20), (33, 24), (7, 29), (13, 10), (19, 12), (31, 14), (10, 22), (24, 5), (13, 22), (5, 1), (35, 30), (3, 19), (30, 15), (2, 19), (14, 18), (17, 7), (27, 4), (30, 14), (33, 1), (8, 24), (30, 24), (7, 16), (26, 16), (20, 4), (29, 31), (31, 26), (15, 25), (3, 16), (17, 18), (3, 24), (33, 6), (26, 25), (31, 10), (17, 1), (34, 27), (11, 8), (12, 10), (30, 5), (0, 12), (12, 15), (35, 3), (4, 30), (10, 8), (4, 9), (28, 21), (1, 28), (30, 16), (6, 15), (31, 19), (2, 18), (34, 14), (22, 23), (14, 24), (22, 13), (11, 25), (17, 29), (32, 31), (34, 4), (0, 6), (2, 26), (5, 12), (22, 14), (9, 3), (6, 4), (0, 10), (25, 12), (9, 20), (22, 15), (12, 31), (8, 18), (31, 2), (1, 18), (1, 26), (25, 10), (12, 7), (33, 14), (20, 3), (32, 20), (23, 26), (22, 4), (7, 9), (20, 8), (29, 6), (9, 2), (9, 6), (20, 0), (16, 2), (7, 28), (35, 1), (17, 25), (31, 30), (31, 4), (9, 25), (13, 3), (14, 2), (4, 8), (12, 14), (19, 14), (4, 28), (26, 9), (12, 12), (4, 22), (24, 21), (11, 7), (19, 11), (1, 12), (33, 4), (35, 6), (31, 13), (4, 6), (26, 7), (8, 19), (4, 19), (31, 16), (18, 11), (33, 20), (16, 25), (12, 21), (27, 20), (19, 23), (30, 30), (20, 1), (15, 10), (3, 13), (10, 10), (20, 28), (25, 0), (26, 22), (34, 28), (2, 20), (0, 3), (23, 29), (8, 31), (27, 19), (31, 20), (10, 9), (7, 6), (8, 11), (29, 5), (13, 17), (10, 4), (14, 22), (21, 21), (30, 8), (17, 10), (12, 19), (6, 25), (6, 2), (17, 16), (7, 2), (24, 27), (17, 2), (18, 20), (26, 10), (11, 12), (6, 7), (5, 19), (32, 24), (9, 16), (24, 14), (35, 20), (6, 17), (29, 16), (20, 26), (1, 23), (25, 7), (27, 2), (16, 5), (33, 16), (14, 0), (13, 27), (8, 16), (10, 1), (19, 21), (1, 14), (35, 17), (8, 9), (22, 18), (2, 13), (16, 10), (9, 0), (6, 5), (28, 14), (15, 27), (35, 21), (29, 1), (2, 4), (14, 21), (1, 25), (24, 8), (32, 26), (14, 27), (25, 26), (3, 5), (14, 28), (11, 24), (20, 14), (32, 1), (24, 16), (23, 19), (18, 5), (15, 21), (0, 8), (27, 12), (18, 8), (5, 31), (10, 18), (35, 4), (34, 23), (29, 24), (18, 15), (16, 14), (34, 7), (33, 13), (20, 9), (10, 29), (11, 4), (32, 18), (15, 0), (5, 2), (13, 23), (17, 13), (24, 7), (2, 0), (16, 3), (5, 10), (9, 5), (17, 0), (10, 30), (6, 30), (17, 20), (11, 1), (31, 15), (22, 29), (12, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770796", "dataset": "MATH"}
{"messages": [{"content": "In a 33x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 8), (11, 7), (20, 20), (32, 17), (0, 22), (0, 15), (28, 4), (24, 14), (6, 12), (29, 11), (14, 25), (15, 11), (18, 13), (26, 17), (29, 7), (14, 26), (22, 6), (8, 21), (10, 21), (26, 11), (21, 3), (22, 4), (2, 10), (4, 15), (9, 24), (6, 13), (31, 9), (8, 4), (30, 25), (32, 6), (16, 21), (21, 29), (29, 23), (26, 0), (2, 6), (20, 15), (12, 20), (25, 17), (26, 20), (32, 22), (10, 22), (26, 15), (14, 9), (16, 0), (25, 14), (30, 24), (29, 15), (19, 19), (9, 8), (22, 2), (12, 29), (21, 2), (29, 21), (18, 20), (2, 8), (17, 20), (7, 22), (13, 0), (27, 25), (15, 10), (0, 17), (21, 23), (13, 19), (14, 17), (2, 0), (19, 25), (15, 2), (30, 0), (14, 18), (24, 20), (17, 19), (11, 9), (31, 19), (10, 1), (18, 6), (9, 29), (17, 18), (5, 12), (2, 14), (31, 3), (11, 2), (1, 5), (25, 5), (23, 24), (21, 15), (11, 29), (13, 24), (30, 5), (9, 19), (1, 29), (20, 11), (29, 29), (25, 28), (22, 19), (3, 28), (21, 16), (13, 10), (25, 15), (6, 2), (2, 5), (29, 27), (23, 4), (14, 6), (5, 7), (0, 29), (21, 25), (26, 12), (5, 17), (19, 24), (4, 10), (1, 3), (3, 3), (7, 8), (28, 10), (23, 11), (23, 26), (18, 21), (9, 10), (32, 14), (23, 17), (32, 20), (6, 25), (31, 18), (3, 6), (14, 21), (15, 14), (10, 29), (14, 2), (8, 0), (2, 3), (26, 9), (31, 0), (29, 25), (20, 21), (30, 3), (27, 0), (20, 17), (5, 3), (1, 28), (21, 28), (4, 27), (26, 5), (16, 16), (23, 3), (13, 3), (29, 12), (3, 26), (6, 29), (23, 23), (30, 21), (3, 5), (28, 7), (11, 15), (12, 18), (32, 4), (28, 9), (28, 28), (28, 15), (26, 19), (5, 25), (27, 21), (4, 7), (20, 26), (13, 2), (4, 16), (22, 5), (23, 2), (17, 27), (24, 11), (16, 12), (10, 28), (19, 12), (29, 6), (11, 19), (16, 7), (28, 13), (32, 24), (23, 9), (28, 19), (9, 2), (23, 22), (5, 28), (28, 5), (6, 20), (14, 10), (1, 12), (2, 22), (8, 9), (13, 13), (30, 12), (7, 1), (19, 26), (24, 24), (16, 27), (20, 16), (22, 7), (13, 5), (25, 1), (17, 5), (18, 9), (21, 18), (7, 21), (16, 17), (30, 1), (28, 25), (16, 10), (5, 26), (26, 25), (4, 3), (15, 7), (11, 18), (24, 17), (4, 14), (9, 17), (4, 20), (3, 29), (7, 14), (30, 6), (8, 26), (0, 11), (14, 29), (2, 28), (25, 23), (8, 8), (32, 9), (10, 10), (8, 23), (15, 29), (25, 3), (20, 2), (29, 8), (24, 19), (26, 6), (1, 10), (2, 15), (18, 27), (0, 23), (13, 16), (8, 5), (6, 9), (10, 20), (20, 22), (1, 24), (16, 25), (30, 8), (16, 2), (12, 26), (8, 3), (17, 1), (31, 27), (13, 15), (30, 29), (22, 8), (8, 19), (18, 8), (8, 11), (11, 11), (0, 9), (6, 8), (18, 12), (0, 18), (9, 21), (18, 1), (22, 26), (27, 20), (27, 14), (8, 7), (23, 15), (20, 6), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358340", "dataset": "MATH"}
{"messages": [{"content": "In a 31x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 32), (26, 19), (8, 2), (30, 19), (7, 18), (19, 12), (4, 18), (4, 32), (1, 12), (20, 28), (2, 25), (28, 11), (23, 28), (16, 19), (7, 13), (4, 19), (20, 34), (11, 18), (16, 20), (16, 16), (29, 32), (20, 23), (7, 19), (14, 6), (29, 9), (13, 33), (20, 32), (0, 32), (8, 1), (2, 3), (3, 21), (20, 31), (24, 21), (18, 21), (3, 22), (16, 27), (19, 24), (18, 0), (18, 10), (25, 17), (22, 11), (8, 18), (6, 29), (18, 27), (24, 14), (6, 4), (13, 1), (1, 33), (26, 17), (23, 6), (30, 21), (6, 5), (26, 22), (14, 32), (9, 10), (22, 26), (12, 18), (0, 1), (24, 32), (27, 13), (0, 24), (2, 8), (1, 29), (7, 12), (7, 8), (20, 22), (22, 28), (11, 14), (2, 33), (1, 24), (19, 16), (29, 19), (20, 19), (16, 8), (7, 24), (16, 3), (20, 5), (21, 5), (30, 25), (10, 4), (5, 23), (11, 28), (7, 30), (1, 32), (16, 21), (14, 20), (17, 1), (5, 9), (4, 34), (10, 3), (1, 4), (0, 30), (28, 12), (3, 19), (16, 0), (15, 31), (15, 16), (24, 12), (9, 1), (22, 29), (0, 2), (17, 21), (30, 0), (27, 18), (6, 19), (24, 27), (19, 7), (18, 25), (16, 5), (8, 27), (21, 2), (0, 25), (19, 8), (4, 8), (20, 14), (9, 25), (17, 15), (29, 4), (3, 1), (24, 3), (1, 2), (21, 34), (12, 27), (10, 21), (15, 4), (24, 31), (30, 10), (22, 24), (21, 10), (25, 12), (13, 34), (17, 3), (25, 13), (29, 2), (14, 17), (25, 9), (24, 34), (29, 20), (22, 2), (9, 11), (22, 15), (22, 22), (7, 7), (8, 26), (3, 13), (19, 10), (19, 2), (17, 11), (23, 7), (9, 28), (18, 18), (25, 24), (12, 34), (29, 31), (3, 15), (18, 17), (30, 33), (19, 0), (8, 0), (16, 32), (7, 21), (7, 11), (13, 16), (9, 15), (9, 14), (10, 0), (29, 25), (21, 12), (14, 30), (23, 22), (23, 16), (26, 28), (2, 28), (7, 34), (10, 25), (3, 5), (15, 21), (17, 4), (29, 26), (22, 3), (26, 20), (21, 18), (1, 8), (24, 15), (7, 29), (19, 31), (28, 19), (29, 15), (22, 19), (0, 14), (13, 2), (27, 19), (13, 32), (10, 5), (30, 20), (16, 14), (11, 1), (21, 1), (18, 30), (17, 2), (2, 24), (14, 31), (2, 13), (26, 14), (28, 34), (23, 31), (5, 1), (12, 25), (5, 11), (6, 3), (7, 17), (5, 0), (3, 29), (1, 6), (13, 19), (26, 34), (26, 7), (23, 20), (10, 24), (2, 4), (29, 16), (0, 3), (20, 16), (15, 30), (22, 18), (15, 32), (2, 0), (17, 17), (4, 5), (18, 26), (15, 15), (25, 23), (12, 6), (3, 32), (2, 15), (1, 3), (8, 4), (15, 5), (24, 1), (15, 24), (30, 28), (16, 13), (24, 24), (30, 2), (27, 23), (11, 26), (13, 30), (2, 5), (0, 8), (11, 24), (27, 4), (17, 29), (18, 5), (27, 26), (5, 7), (7, 10), (21, 25), (14, 2), (13, 21), (12, 7), (10, 32), (25, 22), (17, 16), (13, 11), (26, 31), (21, 28), (25, 4), (24, 10), (8, 22), (6, 10), (24, 5), (13, 22), (11, 21), (8, 30), (27, 34), (12, 8), (11, 29), (2, 14), (29, 10), (24, 17), (4, 26), (22, 34), (1, 26), (3, 30), (6, 24), (7, 9), (29, 6), (4, 0), (28, 18), (16, 23), (8, 20), (9, 34), (10, 33), (5, 25), (20, 10), (10, 16), (13, 13), (28, 16), (16, 30), (4, 10), (16, 17), (13, 9), (27, 32), (9, 18), (15, 13), (14, 19), (17, 12), (25, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874800", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (30, 12), (11, 8), (32, 25), (17, 27), (12, 2), (3, 31), (26, 28), (17, 34), (24, 30), (27, 8), (18, 7), (3, 5), (6, 29), (1, 8), (6, 18), (7, 0), (14, 10), (5, 22), (8, 34), (30, 14), (25, 11), (3, 22), (28, 10), (29, 22), (28, 11), (23, 13), (4, 30), (17, 21), (4, 15), (5, 0), (14, 30), (18, 33), (1, 15), (27, 26), (25, 14), (1, 6), (23, 0), (23, 14), (13, 8), (25, 12), (1, 13), (15, 3), (12, 20), (2, 20), (15, 20), (2, 35), (20, 30), (15, 17), (18, 16), (23, 35), (29, 28), (9, 24), (6, 10), (20, 34), (32, 16), (7, 31), (4, 16), (32, 14), (22, 26), (9, 25), (4, 10), (13, 27), (18, 9), (22, 28), (29, 12), (14, 1), (8, 16), (32, 34), (18, 22), (9, 6), (5, 5), (21, 19), (25, 16), (17, 31), (1, 17), (26, 2), (9, 31), (9, 21), (17, 23), (5, 13), (22, 27), (13, 15), (13, 4), (21, 8), (27, 27), (18, 15), (2, 16), (11, 14), (25, 34), (11, 35), (22, 12), (9, 11), (17, 25), (4, 23), (15, 16), (32, 32), (6, 6), (8, 19), (30, 0), (18, 10), (4, 6), (32, 28), (21, 5), (15, 18), (21, 7), (9, 18), (31, 0), (32, 2), (19, 25), (10, 31), (18, 4), (30, 10), (18, 35), (8, 30), (32, 1), (14, 28), (29, 9), (13, 24), (13, 7), (21, 23), (0, 5), (16, 30), (14, 4), (2, 6), (18, 18), (30, 13), (9, 17), (25, 0), (24, 3), (31, 15), (28, 6), (13, 26), (16, 7), (9, 13), (7, 14), (17, 20), (11, 27), (14, 26), (12, 8), (22, 21), (23, 11), (29, 11), (27, 10), (3, 19), (22, 31), (26, 25), (8, 21), (28, 9), (24, 0), (5, 6), (30, 2), (24, 29), (26, 18), (8, 23), (29, 17), (24, 9), (2, 3), (28, 2), (26, 9), (5, 23), (2, 19), (26, 23), (31, 7), (32, 17), (30, 19), (14, 33), (8, 1), (12, 32), (23, 30), (4, 11), (17, 3), (7, 22), (28, 3), (30, 21), (27, 1), (18, 25), (2, 11), (6, 16), (24, 4), (22, 25), (16, 22), (3, 34), (28, 0), (21, 2), (29, 15), (22, 8), (17, 11), (19, 20), (4, 34), (2, 22), (16, 20), (26, 5), (1, 29), (29, 16), (32, 30), (7, 30), (1, 22), (6, 9), (31, 5), (0, 26), (30, 15), (11, 26), (4, 0), (21, 1), (28, 26), (9, 30), (18, 17), (17, 28), (9, 3), (9, 28), (4, 19), (16, 9), (7, 21), (24, 5), (26, 31), (12, 19), (14, 18), (5, 4), (13, 29), (12, 7), (31, 21), (15, 22), (17, 33), (6, 3), (25, 26), (20, 31), (27, 13), (13, 28), (14, 31), (26, 4), (18, 5), (11, 2), (16, 11), (6, 32), (8, 20), (14, 20), (7, 13), (29, 34), (13, 13), (22, 9), (19, 21), (25, 32), (10, 1), (6, 34), (20, 14), (2, 7), (8, 27), (31, 17), (1, 23), (28, 4), (3, 35), (15, 1), (7, 28), (30, 7), (26, 24), (0, 15), (29, 19), (11, 9), (26, 26), (3, 12), (21, 33), (29, 5), (23, 10), (11, 31), (8, 28), (31, 20), (32, 10), (9, 34), (27, 33), (0, 20), (15, 29), (18, 26), (23, 29), (12, 24), (8, 10), (12, 17), (0, 8), (31, 28), (11, 22), (29, 31), (21, 11), (30, 32), (16, 8), (25, 18), (25, 13), (32, 21), (14, 19), (19, 32), (14, 3), (27, 2), (29, 6), (18, 31), (14, 7), (29, 18), (19, 30), (5, 32), (18, 2), (16, 29), (3, 1), (7, 10), (0, 19), (1, 35), (19, 2), (21, 13), (30, 24), (3, 21), (20, 25), (6, 26), (10, 24), (9, 10), (9, 29), (19, 27), (32, 12), (4, 35), (29, 3), (30, 16), (7, 34), (8, 17), (9, 5), (8, 15), (6, 31), (27, 32), (10, 32), (2, 30), (24, 6), (25, 15), (10, 26), (32, 33), (16, 19), (21, 31), (14, 29), (9, 23), (10, 11), (31, 12), (16, 27), (2, 34), (6, 8), (27, 15), (32, 11), (15, 35), (31, 27), (3, 25), (3, 30), (0, 1), (30, 23), (19, 35), (4, 8), (1, 12), (15, 23), (8, 6), (20, 17), (28, 25), (25, 4), (20, 35), (7, 20), (28, 15), (24, 20), (7, 7), (5, 12), (15, 7), (32, 0), (22, 18), (17, 18), (10, 9), (14, 5), (32, 27), (28, 8), (31, 3), (19, 4), (29, 24), (0, 30), (13, 34), (24, 16), (6, 33), (31, 29), (20, 2), (7, 35), (3, 0), (24, 21), (4, 25), (8, 32), (12, 15), (12, 21), (7, 27), (2, 33), (9, 9), (0, 31), (15, 10), (12, 12), (18, 8), (6, 24), (9, 2), (13, 33), (4, 21), (27, 16), (4, 28), (22, 5), (15, 21), (3, 7), (16, 25), (11, 21), (17, 32), (26, 32), (27, 23), (7, 1), (12, 3), (23, 1), (4, 32), (1, 19), (12, 33), (6, 27), (29, 0), (6, 21), (19, 29), (10, 6), (10, 27), (14, 15), (19, 1), (15, 31), (14, 27), (13, 9), (29, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "544464", "dataset": "MATH"}
{"messages": [{"content": "In a 30x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 31), 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), (11, 6), (5, 13), (16, 16), (22, 17), (1, 30), (22, 31), (14, 8), (11, 2), (2, 8), (6, 21), (3, 23), (4, 2), (19, 16), (17, 12), (7, 4), (3, 1), (27, 7), (24, 28), (29, 28), (8, 5), (18, 13), (29, 8), (1, 20), (4, 7), (27, 9), (6, 31), (9, 4), (17, 9), (18, 5), (21, 13), (14, 26), (9, 16), (1, 28), (9, 11), (11, 12), (25, 24), (16, 4), (7, 22), (3, 11), (26, 0), (17, 30), (18, 4), (0, 9), (24, 31), (18, 29), (14, 1), (1, 3), (28, 29), (29, 9), (11, 14), (15, 4), (6, 28), (14, 19), (22, 3), (29, 29), (29, 18), (21, 3), (10, 25), (24, 22), (8, 1), (25, 26), (5, 25), (5, 17), (5, 24), (17, 23), (10, 7), (2, 1), (25, 8), (16, 6), (29, 21), (11, 28), (3, 22), (19, 13), (25, 12), (27, 28), (18, 12), (10, 19), (23, 19), (10, 21), (23, 17), (20, 23), (9, 3), (27, 15), (22, 1), (16, 19), (5, 26), (3, 20), (25, 11), (10, 31), (18, 2), (27, 18), (28, 16), (19, 0), (23, 14), (15, 21), (14, 14), (24, 7), (12, 6), (11, 20), (21, 7), (13, 10), (24, 15), (19, 28), (19, 10), (0, 10), (0, 5), (0, 22), (14, 22), (8, 24), (2, 13), (5, 18), (29, 24), (4, 19), (29, 27), (21, 12), (11, 16), (7, 19), (7, 16), (9, 15), (27, 22), (6, 1), (12, 10), (13, 2), (5, 22), (13, 29), (23, 8), (24, 26), (8, 21), (4, 14), (10, 17), (5, 7), (8, 17), (14, 12), (27, 0), (1, 12), (24, 14), (8, 23), (9, 29), (5, 20), (3, 13), (28, 8), (21, 27), (29, 14), (14, 18), (22, 15), (0, 14), (21, 11), (14, 0), (28, 13), (18, 6), (13, 24), (3, 26), (8, 19), (4, 5), (5, 4), (20, 30), (2, 23), (0, 25), (18, 28), (13, 14), (13, 25), (22, 28), (15, 11), (18, 25), (10, 30), (11, 24), (2, 30), (8, 31), (0, 21), (23, 29), (20, 7), (1, 0), (1, 9), (28, 5), (22, 14), (20, 13), (21, 18), (3, 2), (18, 15), (16, 7), (7, 1), (11, 4), (5, 15), (28, 4), (0, 4), (20, 18), (14, 15), (14, 7), (21, 4), (23, 13), (5, 21), (11, 18), (12, 25), (11, 3), (0, 6), (17, 7), (6, 30), (12, 29), (6, 2), (21, 25), (0, 8), (7, 5), (12, 21), (21, 8), (26, 4), (4, 26), (8, 6), (22, 26), (25, 23), (19, 8), (14, 23), (21, 22), (0, 29), (18, 24), (23, 16), (28, 30), (26, 14), (17, 1), (19, 11), (24, 4), (29, 3), (14, 9), (12, 31), (22, 23), (8, 8), (22, 6), (19, 18), (16, 23), (27, 11), (21, 30), (6, 22), (26, 21), (28, 3), (27, 16), (22, 22), (2, 12), (14, 24), (4, 12), (25, 19), (27, 19), (21, 15), (23, 24), (17, 20), (19, 7), (7, 25), (15, 7), (5, 5), (24, 23), (14, 25), (21, 2), (15, 14), (17, 10), (16, 25), (3, 9), (9, 27), (25, 18), (6, 19), (26, 10), (7, 30), (15, 18), (26, 12), (20, 4), (12, 28), (14, 13), (3, 29), (26, 20), (17, 19), (20, 16), (12, 24), (15, 30), (21, 14), (11, 8), (10, 4), (13, 6), (1, 1), (13, 31), (3, 5), (9, 7), (14, 3), (0, 31), (21, 16), (6, 4), (8, 28), (5, 2), (9, 25), (17, 0), (10, 26), (28, 14), (6, 12), (17, 28), (29, 7), (14, 10), (28, 17), (1, 23), (1, 11), (17, 21), (2, 31), (1, 16), (15, 3), (16, 31), (20, 24), (26, 24), (19, 21), (21, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "659016", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), 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), (18, 20), (25, 12), (15, 10), (28, 6), (8, 29), (4, 0), (16, 8), (19, 29), (15, 6), (28, 24), (26, 9), (18, 30), (16, 7), (10, 1), (19, 9), (10, 2), (18, 4), (16, 17), (22, 2), (10, 11), (4, 27), (15, 15), (27, 4), (24, 25), (5, 24), (21, 27), (22, 10), (28, 1), (19, 10), (7, 10), (12, 30), (18, 3), (18, 27), (27, 13), (9, 24), (17, 3), (20, 19), (2, 2), (22, 30), (1, 11), (4, 26), (23, 4), (22, 28), (23, 19), (1, 19), (25, 9), (25, 21), (5, 17), (6, 1), (21, 20), (13, 16), (2, 25), (24, 14), (22, 23), (11, 10), (3, 2), (2, 27), (14, 22), (16, 23), (21, 6), (25, 10), (13, 3), (28, 7), (8, 22), (25, 5), (6, 30), (21, 23), (23, 14), (24, 8), (18, 14), (29, 25), (18, 0), (22, 4), (4, 3), (19, 27), (9, 0), (15, 16), (6, 14), (24, 3), (17, 5), (27, 12), (17, 4), (13, 18), (6, 6), (28, 17), (5, 20), (15, 9), (25, 2), (12, 8), (4, 13), (27, 6), (14, 0), (4, 17), (0, 28), (12, 24), (13, 23), (21, 29), (17, 14), (21, 0), (5, 18), (29, 13), (25, 11), (13, 15), (19, 2), (26, 6), (3, 24), (8, 1), (13, 7), (2, 30), (29, 3), (26, 23), (11, 7), (2, 12), (13, 10), (27, 23), (0, 21), (16, 11), (15, 26), (12, 13), (5, 2), (11, 2), (7, 7), (12, 27), (0, 11), (4, 8), (16, 19), (5, 27), (11, 19), (23, 23), (25, 14), (20, 12), (5, 9), (9, 7), (19, 3), (23, 20), (11, 22), (8, 19), (21, 14), (16, 9), (15, 0), (4, 10), (17, 21), (19, 7), (17, 30), (0, 4), (13, 1), (6, 26), (14, 24), (14, 2), (11, 1), (2, 8), (12, 19), (14, 20), (18, 8), (28, 9), (24, 5), (18, 13), (27, 14), (7, 16), (3, 28), (25, 0), (10, 15), (15, 11), (7, 28), (16, 28), (3, 18), (13, 14), (9, 6), (11, 12), (24, 9), (29, 14), (17, 13), (14, 30), (7, 15), (4, 22), (5, 7), (9, 1), (17, 22), (0, 23), (12, 2), (2, 28), (21, 17), (27, 8), (10, 27), (2, 11), (20, 8), (7, 12), (1, 1), (21, 16), (16, 29), (16, 24), (12, 5), (23, 27), (0, 12), (27, 25), (8, 30), (13, 4), (3, 3), (2, 9), (15, 27), (21, 18), (25, 19), (5, 3), (11, 26), (24, 26), (6, 24), (18, 23), (0, 13), (2, 17), (28, 3), (27, 18), (14, 3), (6, 2), (3, 10), (21, 25), (13, 20), (3, 14), (19, 25), (21, 21), (11, 16), (7, 27), (2, 13), (22, 13), (13, 24), (22, 18), (9, 29), (25, 15), (22, 25), (23, 7), (28, 28), (20, 26), (26, 3), (11, 9), (26, 12), (13, 22), (10, 25), (11, 29), (7, 3), (26, 25), (10, 12), (18, 19), (14, 4), (5, 15), (27, 3), (28, 11), (3, 17), (19, 30), (18, 26), (8, 5), (7, 26), (17, 24), (12, 26), (4, 23), (15, 13), (7, 9), (21, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840800", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 33), (1, 0), (30, 14), (26, 9), (27, 29), (7, 15), (3, 19), (13, 18), (21, 29), (27, 23), (3, 11), (27, 27), (10, 9), (22, 8), (3, 6), (17, 24), (14, 31), (19, 0), (30, 23), (24, 19), (16, 20), (11, 7), (5, 12), (14, 9), (25, 2), (0, 7), (19, 32), (27, 26), (17, 26), (29, 24), (20, 24), (2, 24), (30, 24), (30, 16), (21, 33), (17, 28), (14, 24), (30, 13), (11, 22), (19, 22), (0, 3), (2, 26), (8, 0), (25, 0), (13, 19), (8, 23), (26, 32), (25, 33), (4, 15), (18, 15), (21, 8), (15, 9), (8, 30), (28, 19), (15, 2), (14, 3), (15, 1), (26, 6), (16, 11), (24, 31), (1, 25), (8, 10), (15, 23), (24, 7), (20, 2), (22, 25), (2, 18), (29, 28), (14, 7), (10, 0), (21, 18), (21, 14), (23, 15), (28, 24), (3, 10), (11, 30), (29, 2), (13, 1), (15, 12), (1, 20), (30, 2), (6, 25), (8, 9), (10, 5), (23, 4), (24, 29), (21, 31), (26, 18), (6, 21), (26, 5), (9, 21), (24, 6), (14, 28), (16, 21), (17, 20), (4, 21), (25, 15), (13, 15), (19, 4), (1, 33), (15, 25), (24, 18), (26, 29), (2, 14), (2, 27), (20, 18), (4, 17), (15, 21), (28, 3), (4, 32), (28, 32), (27, 12), (15, 14), (24, 25), (13, 5), (13, 24), (18, 21), (10, 8), (30, 3), (23, 14), (17, 32), (19, 16), (1, 6), (9, 9), (1, 12), (8, 11), (7, 8), (23, 33), (24, 23), (1, 14), (17, 10), (19, 6), (15, 0), (23, 22), (10, 3), (12, 9), (28, 16), (15, 20), (6, 11), (29, 11), (25, 26), (23, 30), (3, 1), (13, 25), (22, 20), (22, 26), (15, 26), (11, 5), (12, 14), (5, 9), (16, 30), (25, 32), (26, 8), (1, 23), (21, 16), (18, 18), (9, 5), (2, 20), (3, 17), (16, 14), (30, 28), (0, 2), (3, 24), (18, 25), (28, 1), (14, 26), (8, 5), (9, 24), (8, 15), (15, 10), (19, 10), (29, 17), (18, 20), (0, 29), (6, 12), (30, 6), (7, 14), (5, 0), (2, 7), (2, 12), (18, 10), (26, 2), (23, 32), (4, 11), (19, 17), (30, 10), (2, 33), (23, 27), (19, 21), (21, 20), (9, 12), (7, 12), (23, 26), (3, 28), (23, 20), (30, 19), (10, 18), (22, 30), (22, 21), (17, 17), (13, 2), (25, 12), (8, 6), (28, 22), (20, 21), (1, 28), (16, 31), (16, 27), (12, 28), (28, 7), (18, 24), (3, 8), (14, 0), (17, 29), (17, 6), (28, 26), (25, 18), (28, 15), (1, 11), (2, 22), (8, 28), (21, 25), (5, 16), (2, 15), (22, 2), (28, 29), (19, 3), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "538650", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), 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), (10, 13), (33, 1), (1, 17), (14, 8), (4, 20), (22, 0), (13, 17), (4, 8), (9, 20), (13, 2), (20, 30), (25, 2), (23, 3), (0, 3), (16, 0), (29, 15), (14, 21), (22, 15), (28, 8), (11, 15), (28, 4), (27, 12), (8, 0), (6, 27), (9, 2), (30, 19), (28, 27), (4, 6), (29, 13), (6, 24), (35, 21), (26, 24), (14, 28), (17, 15), (32, 7), (34, 30), (2, 3), (27, 14), (17, 14), (3, 21), (6, 26), (10, 9), (11, 8), (5, 29), (29, 4), (36, 8), (5, 13), (7, 5), (27, 30), (5, 6), (14, 18), (23, 19), (22, 11), (16, 23), (0, 26), (21, 8), (26, 27), (27, 24), (9, 22), (10, 23), (9, 10), (14, 15), (12, 18), (13, 24), (20, 14), (35, 16), (21, 17), (29, 14), (9, 16), (12, 10), (0, 1), (2, 12), (1, 30), (7, 21), (31, 0), (7, 27), (13, 29), (12, 31), (5, 30), (18, 0), (21, 30), (17, 20), (32, 2), (29, 27), (36, 7), (31, 15), (0, 28), (28, 17), (32, 10), (22, 12), (15, 30), (12, 5), (23, 1), (0, 8), (22, 23), (24, 6), (13, 13), (25, 26), (23, 22), (11, 23), (18, 10), (12, 21), (24, 27), (29, 5), (8, 25), (2, 8), (32, 8), (10, 1), (32, 19), (24, 7), (16, 12), (36, 10), (22, 25), (3, 1), (18, 27), (28, 14), (29, 18), (10, 7), (18, 9), (9, 23), (18, 29), (35, 12), (14, 25), (34, 18), (6, 10), (4, 9), (3, 12), (19, 23), (6, 3), (18, 16), (7, 18), (4, 16), (35, 7), (0, 23), (7, 20), (27, 4), (30, 12), (5, 8), (18, 24), (16, 7), (23, 23), (27, 21), (7, 11), (1, 25), (9, 8), (11, 27), (36, 27), (24, 28), (34, 5), (22, 1), (2, 5), (15, 10), (27, 7), (16, 26), (28, 10), (16, 13), (12, 22), (36, 26), (10, 10), (30, 27), (33, 31), (22, 16), (21, 10), (32, 16), (16, 20), (34, 12), (8, 16), (31, 5), (35, 10), (27, 6), (34, 9), (24, 25), (14, 10), (25, 30), (1, 8), (15, 26), (20, 1), (9, 11), (8, 20), (12, 2), (33, 0), (18, 17), (2, 2), (35, 27), (35, 29), (5, 18), (20, 13), (11, 12), (27, 3), (23, 16), (20, 9), (19, 11), (35, 3), (3, 0), (13, 25), (31, 19), (29, 26), (21, 0), (16, 17), (4, 11), (24, 30), (27, 10), (17, 11), (32, 9), (12, 7), (31, 25), (16, 31), (14, 29), (15, 17), (8, 30), (35, 25), (18, 30), (9, 27), (14, 30), (34, 20), (30, 15), (36, 6), (7, 19), (23, 26), (19, 30), (32, 1), (15, 14), (24, 3), (22, 13), (33, 2), (35, 13), (32, 3), (23, 31), (34, 29), (6, 30), (16, 25), (23, 7), (31, 8), (12, 19), (15, 23), (31, 30), (14, 23), (21, 21), (8, 13), (1, 26), (30, 5), (32, 23), (8, 28), (24, 14), (29, 16), (26, 5), (27, 26), (25, 31), (34, 21), (33, 10), (19, 26), (27, 28), (6, 25), (0, 7), (28, 22), (1, 22), (2, 9), (11, 17), (17, 30), (3, 4), (30, 3), (2, 18), (5, 27), (19, 7), (9, 6), (18, 8), (25, 16), (17, 29), (27, 1), (36, 18), (30, 26), (24, 22), (30, 31), (35, 18), (30, 10), (8, 6), (31, 1), (15, 24), (24, 19), (33, 18), (2, 7), (9, 5), (33, 20), (5, 10), (33, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907920", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 28), (7, 23), (20, 13), (13, 26), (26, 29), (29, 2), (10, 3), (0, 12), (5, 3), (17, 6), (18, 28), (13, 31), (8, 23), (14, 10), (14, 18), (4, 9), (29, 11), (4, 13), (4, 28), (9, 4), (24, 24), (0, 16), (4, 38), (19, 15), (2, 36), (1, 35), (15, 33), (13, 8), (8, 2), (5, 20), (19, 4), (24, 15), (15, 34), (13, 13), (3, 1), (10, 0), (22, 30), (24, 31), (6, 17), (18, 26), (9, 2), (13, 28), (2, 1), (28, 11), (23, 32), (10, 15), (3, 36), (23, 27), (1, 33), (20, 25), (29, 3), (16, 1), (15, 30), (17, 31), (7, 19), (16, 30), (17, 5), (13, 17), (6, 35), (13, 12), (23, 20), (25, 23), (4, 26), (22, 37), (29, 6), (28, 0), (25, 35), (4, 19), (23, 37), (3, 9), (21, 16), (19, 32), (14, 5), (27, 26), (0, 3), (19, 18), (2, 21), (9, 28), (12, 13), (3, 12), (20, 17), (5, 27), (29, 32), (26, 14), (5, 32), (12, 28), (26, 2), (16, 8), (23, 3), (19, 37), (5, 14), (25, 21), (20, 10), (25, 18), (29, 1), (28, 2), (2, 34), (7, 36), (19, 12), (22, 12), (24, 32), (20, 8), (26, 5), (4, 35), (17, 24), (14, 14), (20, 18), (28, 27), (1, 29), (17, 33), (20, 29), (8, 12), (19, 21), (24, 11), (7, 9), (22, 18), (5, 5), (0, 23), (13, 3), (6, 9), (11, 35), (18, 0), (25, 3), (3, 5), (1, 27), (17, 25), (10, 6), (0, 8), (29, 34), (16, 34), (6, 10), (2, 12), (17, 13), (1, 7), (24, 22), (18, 9), (11, 32), (27, 21), (9, 15), (20, 6), (15, 6), (18, 7), (12, 16), (10, 35), (17, 9), (6, 11), (5, 34), (1, 34), (28, 22), (29, 23), (11, 18), (23, 38), (15, 35), (21, 3), (28, 26), (12, 0), (5, 7), (27, 33), (5, 16), (8, 8), (21, 34), (1, 21), (4, 31), (15, 5), (9, 24), (16, 10), (21, 37), (28, 7), (23, 26), (29, 15), (27, 23), (9, 30), (27, 7), (15, 3), (16, 21), (2, 31), (28, 28), (22, 21), (18, 36), (1, 4), (23, 15), (4, 33), (3, 35), (10, 20), (24, 36), (6, 20), (9, 10), (26, 16), (6, 0), (14, 4), (16, 19), (6, 27), (2, 22), (10, 22), (15, 29), (2, 14), (27, 8), (15, 32), (29, 29), (14, 26), (7, 37), (14, 28), (22, 20), (13, 37), (23, 0), (11, 11), (26, 26), (12, 34), (6, 36), (24, 0), (7, 20), (24, 12), (21, 23), (3, 0), (22, 32), (10, 21), (15, 22), (1, 14), (21, 11), (15, 36), (26, 31), (0, 1), (12, 1), (28, 36), (11, 36), (2, 18), (3, 34), (9, 18), (0, 36), (5, 25), (12, 37), (24, 10), (18, 13), (20, 38), (9, 8), (6, 16), (25, 38), (6, 31), (17, 15), (14, 25), (16, 7), (14, 6), (17, 27), (5, 30), (18, 38), (27, 15), (20, 27), (27, 5), (23, 2), (21, 22), (10, 30), (11, 3), (4, 14), (7, 8), (17, 23), (20, 15), (14, 7), (7, 32), (3, 14), (15, 26), (14, 35), (24, 4), (23, 9), (22, 31), (16, 29), (21, 4), (2, 35), (11, 25), (1, 20), (1, 31), (21, 26), (2, 0), (10, 29), (2, 5), (18, 22), (17, 12), (17, 3), (28, 35), (24, 18), (9, 21), (29, 12), (0, 14), (9, 0), (7, 26), (10, 33), (10, 25), (20, 26), (27, 31), (2, 28), (15, 12), (11, 5), (18, 31), (11, 10), (14, 11), (12, 22), (6, 30), (18, 4), (11, 34), (2, 25), (22, 38), (8, 33), (5, 10), (16, 15), (10, 1), (6, 13), (12, 30), (1, 24), (11, 29), (6, 12), (13, 20), (5, 8), (21, 8), (9, 1), (23, 21), (3, 18), (17, 8), (20, 34), (6, 24), (21, 19), (9, 22), (14, 3), (25, 14), (12, 36), (24, 23), (27, 24), (24, 26), (26, 10), (25, 0), (13, 33), (28, 17), (12, 32), (27, 11), (13, 35), (20, 24), (7, 18), (12, 6), (18, 29), (14, 9), (25, 37), (5, 21), (11, 37), (2, 30), (29, 10), (29, 30), (21, 5), (25, 24), (9, 16), (8, 24), (26, 22), (2, 20), (27, 18), (17, 17), (25, 28), (27, 20), (15, 21), (23, 22), (13, 34), (5, 4), (1, 18), (6, 26), (26, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "671895", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 4), (3, 26), (33, 23), (8, 14), (0, 25), (7, 17), (15, 29), (1, 3), (1, 8), (3, 24), (26, 0), (10, 26), (8, 29), (3, 4), (34, 32), (17, 23), (32, 23), (6, 10), (15, 19), (16, 12), (31, 0), (16, 4), (15, 9), (30, 1), (5, 20), (14, 33), (30, 33), (14, 7), (16, 26), (3, 25), (13, 32), (18, 24), (3, 30), (13, 16), (10, 11), (5, 28), (1, 22), (34, 0), (1, 23), (11, 3), (15, 2), (2, 34), (26, 1), (2, 7), (1, 11), (17, 21), (21, 5), (30, 34), (22, 14), (13, 10), (32, 26), (20, 26), (11, 21), (13, 22), (0, 5), (31, 5), (25, 13), (20, 33), (12, 31), (29, 10), (24, 25), (25, 25), (15, 32), (19, 6), (6, 16), (0, 24), (25, 15), (24, 28), (10, 27), (8, 24), (20, 16), (12, 24), (15, 10), (13, 14), (11, 26), (33, 17), (13, 4), (13, 9), (9, 27), (27, 10), (20, 6), (23, 32), (28, 34), (4, 26), (1, 21), (19, 16), (33, 5), (9, 33), (20, 4), (10, 15), (6, 14), (22, 9), (6, 34), (31, 25), (0, 12), (23, 4), (1, 19), (32, 21), (28, 27), (4, 32), (25, 29), (23, 25), (11, 20), (11, 32), (26, 9), (6, 22), (3, 9), (19, 0), (21, 7), (8, 34), (20, 28), (7, 25), (6, 2), (1, 24), (27, 4), (8, 1), (2, 15), (11, 1), (3, 23), (7, 3), (28, 25), (28, 33), (20, 5), (17, 7), (12, 8), (23, 0), (27, 19), (4, 0), (21, 14), (10, 10), (31, 13), (15, 0), (13, 8), (8, 3), (22, 15), (8, 8), (2, 8), (32, 25), (16, 22), (34, 33), (27, 31), (0, 28), (33, 6), (32, 29), (26, 32), (28, 13), (29, 31), (28, 26), (15, 18), (5, 3), (10, 34), (27, 32), (8, 32), (20, 29), (32, 22), (16, 23), (6, 17), (13, 0), (1, 17), (16, 19), (26, 24), (31, 31), (9, 12), (10, 20), (5, 5), (11, 13), (21, 18), (2, 26), (23, 24), (23, 20), (30, 32), (29, 9), (9, 14), (18, 10), (15, 17), (0, 17), (2, 20), (19, 25), (20, 25), (26, 19), (8, 27), (16, 1), (0, 31), (28, 28), (17, 10), (17, 22), (9, 6), (11, 31), (30, 26), (0, 2), (15, 16), (22, 16), (3, 20), (30, 27), (18, 16), (12, 16), (4, 23), (1, 18), (1, 5), (6, 8), (28, 11), (2, 6), (23, 7), (20, 13), (24, 17), (13, 27), (22, 1), (19, 34), (22, 6), (17, 8), (3, 0), (21, 0), (19, 28), (14, 29), (32, 1), (15, 12), (26, 15), (30, 3), (24, 22), (21, 30), (23, 30), (19, 18), (5, 18), (10, 3), (25, 0), (5, 12), (12, 1), (15, 4), (29, 1), (27, 3), (4, 31), (24, 16), (32, 19), (12, 20), (3, 15), (26, 16), (18, 32), (25, 10), (7, 32), (17, 33), (14, 21), (4, 19), (8, 23), (25, 9), (24, 2), (16, 2), (29, 14), (16, 9), (14, 31), (32, 6), (7, 5), (28, 31), (19, 20), (0, 6), (26, 6), (13, 23), (21, 23), (28, 15), (15, 5), (5, 25), (24, 19), (24, 31), (5, 10), (18, 34), (0, 13), (16, 31), (24, 11), (0, 23), (8, 5), (33, 3), (27, 15), (4, 27), (17, 16), (4, 21), (8, 10), (28, 9), (8, 15), (7, 12), (33, 9), (19, 3), (2, 14), (34, 14), (25, 12), (29, 16), (2, 27), (5, 34), (11, 27), (22, 10), (1, 34), (22, 11), (34, 4), (1, 10), (26, 18), (19, 17), (33, 13), (20, 2), (25, 19), (8, 9), (4, 6), (26, 31), (10, 1), (5, 27), (17, 29), (32, 28), (0, 27), (15, 8), (8, 20), (3, 17), (0, 18), (16, 32), (13, 26), (20, 7), (4, 24), (7, 22), (3, 29), (21, 21), (14, 6), (5, 26), (11, 7), (9, 15), (22, 19), (31, 33), (17, 0), (23, 2), (1, 9), (4, 15), (23, 21), (21, 27), (26, 2), (7, 9), (34, 1), (2, 1), (7, 18), (16, 10), (1, 13), (33, 19), (9, 26), (17, 13), (29, 24), (2, 21), (27, 9), (6, 3), (11, 14), (17, 18), (19, 33), (25, 7), (2, 17), (31, 3), (34, 20), (33, 14), (30, 10), (23, 10), (27, 28), (13, 19), (7, 31), (10, 16), (7, 26), (5, 4), (33, 33), (24, 13), (1, 27), (32, 16), (3, 19), (11, 16), (30, 25), (9, 19), (5, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "361920", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 31), (26, 17), (33, 10), (24, 9), (21, 21), (34, 29), (12, 25), (3, 5), (5, 23), (6, 22), (20, 29), (25, 26), (35, 17), (3, 23), (22, 0), (35, 3), (21, 2), (18, 2), (8, 24), (21, 13), (17, 28), (22, 29), (27, 24), (17, 19), (29, 10), (36, 6), (13, 20), (11, 28), (27, 5), (3, 1), (6, 20), (31, 3), (21, 0), (1, 2), (4, 14), (35, 18), (32, 20), (29, 7), (3, 28), (6, 6), (27, 17), (26, 16), (29, 24), (19, 20), (8, 21), (28, 5), (13, 8), (2, 28), (2, 8), (33, 2), (3, 31), (26, 18), (10, 11), (15, 5), (29, 18), (4, 23), (3, 27), (15, 12), (12, 24), (2, 19), (1, 11), (37, 6), (34, 26), (9, 28), (12, 8), (2, 13), (36, 19), (38, 4), (22, 7), (33, 21), (38, 22), (35, 14), (18, 16), (21, 10), (37, 10), (20, 9), (4, 2), (14, 2), (11, 13), (18, 8), (17, 16), (21, 15), (26, 6), (5, 4), (8, 19), (23, 23), (30, 29), (27, 6), (37, 15), (21, 1), (12, 30), (5, 6), (38, 27), (21, 20), (13, 1), (30, 10), (8, 11), (7, 2), (37, 22), (21, 3), (18, 30), (11, 7), (22, 17), (18, 25), (8, 4), (25, 10), (24, 25), (7, 24), (21, 4), (36, 13), (8, 20), (37, 7), (22, 6), (17, 23), (28, 19), (22, 4), (25, 9), (16, 2), (10, 31), (19, 15), (13, 6), (37, 13), (37, 30), (36, 0), (12, 19), (34, 6), (20, 4), (35, 0), (31, 25), (36, 15), (2, 20), (20, 26), (10, 30), (12, 22), (2, 17), (33, 17), (16, 5), (38, 14), (2, 15), (24, 13), (10, 15), (3, 21), (1, 19), (27, 8), (25, 23), (27, 21), (13, 27), (26, 3), (28, 16), (19, 2), (35, 26), (25, 21), (7, 4), (6, 12), (12, 14), (35, 12), (23, 9), (17, 13), (26, 10), (33, 29), (32, 0), (30, 4), (14, 21), (1, 27), (32, 14), (13, 12), (2, 6), (33, 11), (15, 4), (0, 15), (17, 4), (20, 20), (27, 0), (15, 16), (28, 27), (9, 29), (4, 1), (33, 31), (9, 10), (7, 25), (3, 24), (8, 13), (10, 5), (32, 5), (17, 31), (11, 2), (16, 21), (33, 24), (12, 18), (7, 29), (25, 3), (13, 0), (21, 26), (33, 22), (2, 21), (10, 10), (16, 27), (28, 17), (27, 4), (6, 9), (30, 3), (8, 26), (35, 4), (36, 24), (25, 1), (23, 27), (24, 26), (13, 15), (34, 21), (13, 3), (7, 3), (27, 9), (18, 1), (32, 10), (31, 1), (2, 22), (23, 16), (23, 26), (22, 22), (18, 26), (29, 29), (26, 9), (20, 18), (20, 14), (32, 1), (6, 3), (33, 28), (3, 11), (18, 6), (24, 3), (3, 0), (12, 15), (5, 26), (11, 29), (6, 16), (33, 13), (31, 22), (7, 8), (25, 8), (4, 22), (22, 14), (17, 24), (27, 27), (7, 28), (3, 10), (14, 26), (38, 18), (16, 28), (35, 29), (16, 12), (4, 15), (1, 6), (0, 2), (6, 5), (6, 15), (18, 28), (11, 22), (29, 16), (13, 16), (26, 1), (7, 5), (37, 28), (10, 3), (13, 18), (16, 25), (21, 23), (24, 28), (0, 8), (15, 18), (34, 7), (12, 21), (38, 8), (25, 0), (19, 23), (2, 5), (0, 10), (22, 13), (15, 26), (9, 6), (32, 25), (18, 21), (18, 7), (21, 5), (14, 4), (23, 28), (6, 11), (4, 12), (2, 0), (25, 30), (0, 5), (23, 2), (14, 18), (30, 31), (31, 28), (23, 21), (16, 31), (33, 19), (11, 3), (22, 31), (32, 30), (24, 4), (22, 26), (33, 23), (28, 11), (14, 17), (33, 26), (7, 10), (28, 1), (34, 19), (14, 13), (29, 19), (31, 12), (18, 10), (11, 0), (16, 26), (25, 14), (11, 18), (8, 29), (35, 16), (25, 7), (17, 3), (4, 31), (37, 11), (5, 17), (10, 19), (3, 20), (3, 25), (14, 16), (11, 31), (11, 11), (19, 28), (19, 21), (12, 12), (31, 15), (36, 26), (22, 9), (7, 21), (1, 24), (19, 8), (8, 2), (38, 3), (0, 27), (32, 13), (36, 5), (25, 28), (26, 20), (21, 18), (6, 25), (20, 7), (10, 22), (23, 6), (19, 24), (21, 9), (10, 17), (21, 27), (1, 25), (22, 30), (2, 26), (11, 8), (10, 1), (12, 16), (16, 6), (35, 8), (16, 16), (0, 24), (15, 9), (4, 9), (15, 11), (3, 19), (33, 9), (16, 18), (35, 19), (26, 28), (18, 0), (37, 27), (7, 17), (14, 19), (0, 28), (19, 31), (5, 13), (1, 17), (33, 15), (24, 1), (7, 20), (30, 19), (21, 8), (0, 1), (9, 23), (9, 9), (4, 20), (1, 3), (24, 27), (14, 15), (35, 9), (19, 30), (5, 19), (34, 15), (17, 18), (8, 14), (35, 6), (35, 27), (17, 20), (38, 0), (13, 31), (36, 20), (31, 17), (30, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890400", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 37), (5, 19), (11, 24), (29, 10), (9, 17), (7, 12), (24, 18), (28, 17), (4, 35), (32, 7), (5, 31), (9, 10), (6, 1), (31, 3), (16, 31), (24, 25), (26, 32), (32, 5), (15, 7), (27, 29), (23, 6), (27, 10), (9, 33), (29, 3), (1, 29), (27, 19), (0, 11), (14, 14), (10, 22), (4, 9), (2, 6), (21, 37), (15, 24), (11, 5), (7, 5), (24, 31), (5, 21), (16, 1), (16, 22), (5, 16), (29, 26), (17, 20), (24, 35), (14, 18), (19, 21), (0, 27), (16, 36), (22, 4), (6, 9), (7, 3), (21, 15), (14, 23), (2, 25), (7, 6), (30, 5), (23, 26), (30, 26), (18, 13), (8, 19), (30, 29), (33, 33), (17, 6), (21, 26), (18, 14), (26, 9), (2, 27), (9, 26), (31, 34), (6, 21), (9, 6), (7, 19), (8, 7), (29, 33), (13, 13), (21, 18), (16, 2), (31, 8), (11, 1), (8, 25), (30, 24), (13, 26), (13, 14), (20, 15), (19, 25), (25, 23), (30, 16), (28, 12), (33, 1), (12, 25), (29, 35), (19, 1), (20, 19), (27, 28), (2, 21), (33, 14), (29, 5), (24, 3), (7, 22), (25, 27), (17, 3), (28, 35), (31, 0), (13, 30), (24, 15), (28, 6), (17, 27), (25, 32), (32, 18), (19, 6), (32, 12), (18, 28), (32, 19), (20, 8), (23, 30), (25, 24), (7, 34), (25, 13), (13, 20), (5, 17), (0, 3), (26, 14), (8, 6), (12, 29), (12, 24), (24, 37), (16, 20), (13, 33), (3, 31), (12, 22), (19, 15), (2, 0), (9, 25), (30, 6), (20, 23), (3, 9), (33, 22), (32, 28), (12, 3), (13, 6), (22, 22), (16, 10), (4, 29), (7, 13), (20, 0), (15, 25), (33, 27), (8, 12), (27, 24), (1, 18), (28, 3), (2, 30), (26, 20), (12, 19), (6, 11), (18, 37), (23, 2), (33, 20), (8, 5), (13, 28), (0, 23), (21, 5), (15, 16), (31, 15), (25, 30), (4, 12), (2, 37), (22, 37), (11, 2), (26, 17), (12, 30), (19, 34), (21, 28), (10, 24), (18, 1), (12, 14), (33, 0), (15, 30), (12, 36), (6, 27), (9, 24), (19, 31), (17, 37), (13, 24), (1, 6), (4, 11), (33, 21), (8, 14), (14, 8), (14, 33), (28, 7), (29, 13), (31, 19), (28, 37), (11, 34), (23, 7), (23, 0), (14, 25), (6, 8), (15, 23), (1, 16), (18, 33), (28, 33), (7, 20), (13, 22), (14, 24), (24, 8), (5, 3), (11, 37), (28, 9), (20, 7), (16, 33), (7, 32), (7, 35), (30, 25), (8, 17), (19, 22), (1, 9), (23, 35), (29, 19), (1, 30), (24, 22), (8, 21), (1, 23), (33, 34), (32, 14), (4, 7), (15, 26), (29, 21), (19, 19), (32, 3), (31, 2), (31, 35), (30, 22), (30, 32), (23, 20), (15, 20), (32, 29), (29, 20), (17, 10), (6, 29), (26, 8), (12, 2), (11, 12), (7, 23), (23, 17), (11, 20), (13, 21), (0, 29), (12, 35), (9, 16), (29, 37), (3, 18), (25, 25), (21, 22), (11, 21), (24, 7), (13, 10), (1, 1), (10, 0), (29, 29), (20, 32), (16, 23), (25, 17), (8, 23), (24, 28), (16, 4), (8, 31), (31, 6), (8, 8), (14, 0), (23, 8), (30, 33), (20, 28), (13, 34), (17, 12), (18, 35), (32, 8), (23, 21), (4, 15), (24, 2), (33, 28), (25, 33), (23, 3), (2, 1), (2, 10), (1, 28), (4, 13), (29, 36), (13, 4), (25, 22), (22, 12), (2, 20), (4, 37), (5, 33), (8, 3), (8, 20), (8, 24), (1, 14), (26, 25), (33, 30), (17, 22), (12, 11), (14, 4), (21, 8), (28, 21), (12, 27), (23, 13), (4, 1), (18, 26), (20, 26), (29, 15), (18, 9), (4, 5), (11, 8), (13, 18), (33, 23), (6, 26), (18, 34), (17, 15), (7, 26), (15, 11), (22, 34), (0, 18), (6, 22), (11, 25), (5, 5), (15, 35), (14, 17), (10, 3), (23, 25), (26, 21), (13, 32), (16, 7), (5, 30), (11, 10), (3, 29), (7, 10), (32, 0), (10, 26), (23, 10), (31, 13), (16, 14), (14, 9), (23, 19), (6, 35), (33, 4), (5, 0), (11, 17), (12, 13), (22, 13), (6, 2), (3, 10), (22, 27), (25, 8), (30, 4), (27, 25), (29, 14), (24, 29), (4, 27), (5, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991440", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (16, 4), (22, 18), (14, 28), (34, 17), (35, 3), (9, 25), (30, 13), (25, 12), (26, 7), (3, 7), (0, 2), (18, 27), (34, 26), (24, 27), (35, 5), (2, 17), (15, 1), (25, 8), (34, 0), (29, 23), (17, 29), (28, 21), (0, 12), (35, 17), (34, 3), (3, 13), (11, 31), (5, 15), (3, 9), (15, 18), (30, 8), (25, 6), (11, 17), (18, 28), (6, 30), (17, 3), (12, 10), (7, 5), (1, 18), (11, 12), (32, 2), (6, 5), (32, 9), (10, 11), (2, 26), (1, 2), (7, 27), (12, 15), (32, 21), (18, 21), (22, 4), (7, 31), (12, 22), (21, 13), (16, 22), (19, 31), (17, 30), (5, 3), (6, 6), (15, 0), (11, 10), (1, 21), (11, 7), (25, 5), (15, 15), (33, 19), (22, 28), (15, 22), (20, 27), (33, 17), (22, 0), (5, 12), (23, 4), (23, 25), (21, 8), (29, 0), (35, 7), (13, 23), (17, 26), (26, 24), (1, 10), (14, 20), (33, 28), (4, 0), (1, 16), (25, 18), (15, 9), (31, 1), (21, 25), (35, 28), (8, 6), (24, 23), (33, 0), (7, 1), (21, 9), (2, 21), (27, 23), (12, 5), (19, 1), (1, 20), (32, 3), (3, 11), (25, 17), (16, 15), (8, 20), (6, 12), (32, 10), (7, 29), (25, 1), (3, 4), (6, 7), (31, 28), (13, 8), (13, 31), (0, 31), (32, 13), (3, 2), (4, 11), (31, 4), (4, 21), (29, 17), (29, 11), (12, 21), (28, 18), (16, 25), (29, 29), (4, 6), (16, 0), (35, 0), (31, 25), (35, 18), (30, 29), (2, 18), (0, 1), (14, 30), (20, 14), (2, 2), (15, 8), (22, 16), (11, 30), (33, 15), (31, 14), (18, 22), (32, 4), (18, 8), (34, 12), (2, 20), (2, 31), (19, 6), (18, 9), (0, 10), (21, 22), (28, 2), (2, 7), (12, 1), (14, 5), (23, 5), (12, 30), (3, 14), (19, 13), (2, 10), (25, 23), (35, 20), (29, 30), (18, 4), (31, 0), (21, 6), (28, 15), (18, 7), (24, 4), (8, 28), (25, 0), (17, 8), (17, 22), (29, 25), (10, 3), (12, 14), (9, 10), (21, 24), (24, 13), (21, 10), (32, 22), (28, 30), (16, 20), (31, 27), (30, 11), (23, 30), (19, 24), (9, 23), (29, 26), (27, 8), (9, 26), (15, 17), (29, 16), (28, 31), (14, 19), (27, 14), (27, 6), (20, 25), (7, 13), (18, 6), (8, 29), (29, 28), (4, 2), (11, 19), (20, 29), (19, 4), (11, 27), (2, 27), (0, 14), (15, 20), (18, 18), (31, 2), (6, 16), (7, 24), (30, 17), (24, 20), (10, 15), (28, 4), (1, 27), (22, 6), (17, 4), (24, 26), (29, 2), (11, 22), (21, 2), (28, 24), (13, 7), (34, 11), (30, 18), (28, 26), (34, 18), (29, 5), (17, 0), (6, 9), (6, 13), (1, 14), (24, 17), (11, 6), (0, 23), (34, 9), (16, 27), (14, 18), (34, 22), (31, 7), (7, 3), (2, 0), (17, 5), (24, 7), (33, 26), (30, 22), (23, 2), (26, 26), (0, 26), (14, 0), (11, 14), (18, 1), (21, 16), (26, 19), (35, 22), (22, 27), (8, 1), (1, 31), (18, 13), (18, 2), (28, 8), (20, 5), (23, 20), (11, 1), (25, 25), (28, 14), (34, 27), (22, 24), (6, 17), (27, 19), (14, 13), (26, 11), (8, 17), (5, 23), (30, 7), (26, 12), (5, 19), (35, 4), (5, 14), (10, 26), (22, 23), (31, 26), (3, 31), (4, 18), (9, 12), (15, 4), (26, 15), (33, 7), (34, 31), (20, 13), (18, 25), (23, 26), (31, 17), (12, 9), (0, 25), (34, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948480", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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), (4, 11), (6, 7), (16, 31), (7, 30), (19, 15), (20, 10), (24, 13), (16, 27), (18, 8), (1, 23), (10, 30), (29, 2), (6, 11), (16, 24), (3, 9), (11, 31), (10, 24), (8, 27), (26, 28), (13, 13), (15, 30), (19, 19), (11, 27), (5, 0), (9, 31), (20, 13), (7, 5), (10, 14), (29, 7), (7, 4), (20, 5), (26, 0), (0, 22), (12, 4), (25, 5), (3, 0), (15, 24), (26, 7), (23, 25), (24, 31), (4, 3), (17, 25), (27, 0), (26, 17), (16, 17), (24, 29), (26, 12), (7, 8), (23, 7), (19, 25), (8, 2), (29, 14), (22, 14), (1, 3), (8, 21), (21, 30), (24, 10), (11, 15), (3, 27), (1, 27), (14, 9), (4, 13), (12, 32), (17, 20), (7, 1), (19, 20), (9, 14), (0, 10), (14, 6), (5, 5), (3, 8), (14, 16), (5, 22), (29, 31), (9, 0), (11, 4), (25, 28), (25, 25), (21, 23), (24, 32), (0, 12), (25, 4), (13, 17), (22, 29), (18, 3), (11, 30), (14, 24), (2, 6), (5, 8), (22, 8), (10, 8), (17, 13), (25, 2), (19, 3), (7, 12), (13, 2), (17, 27), (2, 31), (18, 12), (12, 1), (14, 19), (7, 21), (19, 31), (27, 21), (24, 5), (4, 25), (26, 10), (15, 0), (5, 4), (8, 7), (29, 16), (29, 25), (29, 12), (10, 13), (27, 26), (19, 9), (0, 7), (6, 32), (12, 5), (2, 13), (20, 20), (27, 27), (2, 3), (10, 27), (21, 22), (18, 28), (22, 24), (12, 22), (5, 1), (16, 4), (10, 5), (29, 27), (10, 2), (29, 17), (8, 28), (21, 26), (18, 32), (29, 6), (8, 23), (23, 10), (17, 12), (29, 4), (5, 11), (18, 4), (25, 29), (3, 6), (22, 16), (21, 13), (2, 32), (19, 17), (6, 30), (7, 26), (11, 5), (5, 24), (10, 10), (23, 6), (24, 27), (3, 31), (17, 6), (23, 15), (18, 23), (15, 16), (0, 17), (20, 21), (5, 30), (6, 8), (3, 20), (16, 3), (20, 23), (20, 1), (1, 26), (15, 25), (18, 25), (20, 2), (6, 20), (23, 20), (10, 4), (11, 28), (25, 24), (3, 12), (17, 32), (23, 1), (18, 21), (23, 32), (16, 19), (24, 20), (29, 29), (4, 4), (19, 14), (24, 4), (19, 0), (7, 10), (0, 27), (1, 8), (16, 21), (15, 6), (8, 10), (13, 0), (3, 13), (15, 29), (29, 3), (26, 3), (1, 16), (16, 0), (27, 16), (26, 6), (22, 28), (16, 7), (14, 1), (8, 29), (23, 26), (6, 13), (14, 29), (5, 16), (29, 8), (27, 30), (13, 26), (25, 6), (17, 15), (12, 13), (25, 12), (10, 17), (5, 26), (26, 1), (2, 25), (22, 20), (12, 28), (19, 1), (15, 13), (13, 32), (26, 16), (16, 6), (12, 17), (13, 18), (28, 19), (26, 9), (20, 31), (26, 11), (26, 25), (27, 5), (3, 23), (28, 9), (0, 9), (23, 17), (2, 12), (1, 22), (24, 16), (27, 9), (0, 6), (28, 6), (8, 4), (7, 0), (6, 26), (2, 28), (0, 25), (5, 9), (20, 27), (2, 24), (25, 1), (23, 16), (13, 22), (6, 16), (16, 20), (9, 1), (6, 10), (28, 13), (0, 28), (3, 22), (25, 16), (25, 22), (24, 12), (23, 11), (12, 0), (16, 18), (23, 8), (17, 19), (20, 4), (3, 11), (27, 28), (3, 21), (11, 3), (1, 9), (8, 24), (19, 21), (0, 30), (16, 11), (15, 5), (2, 7), (22, 7), (19, 30), (28, 14), (26, 24), (21, 18), (4, 22), (1, 10), (12, 6), (2, 17), (21, 1), (24, 3), (15, 31), (7, 11), (7, 14), (4, 18), (24, 7), (4, 19), (2, 21), (5, 14), (15, 20), (26, 32), (12, 9), (13, 27), (21, 27), (13, 4), (20, 7), (12, 16), (1, 29), (24, 11), (27, 12), (0, 3), (15, 12), (8, 18), (21, 21), (3, 29), (2, 18), (18, 9), (29, 21), (7, 32), (26, 5), (28, 12), (21, 2), (4, 29), (4, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "891288", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (19, 25), (32, 2), (2, 17), (12, 8), (32, 7), (17, 1), (28, 23), (34, 0), (3, 3), (2, 29), (5, 15), (11, 9), (29, 14), (4, 25), (3, 5), (32, 9), (22, 31), (19, 11), (25, 34), (35, 32), (34, 21), (29, 22), (16, 33), (33, 18), (1, 27), (16, 0), (33, 28), (12, 25), (7, 22), (36, 27), (12, 11), (2, 34), (17, 25), (9, 20), (22, 30), (21, 3), (29, 27), (17, 2), (0, 24), (15, 21), (35, 30), (19, 34), (17, 32), (26, 5), (7, 11), (14, 3), (24, 28), (9, 26), (6, 24), (8, 26), (36, 7), (9, 0), (16, 19), (9, 29), (26, 13), (35, 27), (23, 7), (10, 22), (33, 12), (2, 33), (6, 8), (27, 10), (18, 16), (13, 2), (16, 8), (2, 22), (12, 15), (34, 8), (12, 24), (31, 1), (20, 1), (2, 10), (35, 13), (29, 29), (11, 23), (6, 17), (4, 28), (8, 23), (14, 8), (19, 10), (24, 21), (2, 16), (23, 25), (32, 0), (13, 8), (22, 34), (18, 9), (1, 3), (10, 4), (14, 20), (12, 21), (9, 12), (4, 24), (34, 13), (35, 26), (31, 8), (19, 27), (9, 8), (2, 21), (15, 32), (3, 33), (7, 34), (15, 3), (17, 15), (26, 6), (7, 27), (12, 31), (31, 34), (24, 13), (5, 13), (20, 6), (34, 14), (19, 19), (21, 8), (6, 16), (21, 26), (20, 30), (20, 20), (25, 2), (22, 14), (26, 17), (5, 26), (36, 8), (27, 33), (34, 18), (22, 5), (6, 14), (32, 11), (29, 4), (8, 10), (14, 12), (6, 33), (16, 2), (21, 6), (3, 2), (24, 17), (35, 5), (9, 21), (0, 15), (29, 1), (24, 6), (4, 1), (25, 33), (0, 25), (23, 17), (0, 9), (33, 7), (26, 23), (24, 24), (24, 26), (18, 28), (3, 10), (5, 29), (15, 5), (17, 6), (32, 25), (26, 7), (36, 1), (31, 10), (16, 26), (19, 31), (0, 30), (6, 2), (3, 29), (30, 17), (13, 4), (1, 5), (17, 5), (18, 17), (20, 16), (20, 22), (33, 9), (33, 33), (31, 19), (8, 6), (29, 17), (11, 34), (16, 28), (4, 18), (24, 25), (32, 21), (33, 24), (3, 14), (22, 33), (8, 19), (21, 0), (25, 28), (0, 6), (17, 33), (11, 7), (29, 12), (23, 32), (35, 28), (23, 27), (28, 20), (9, 18), (16, 5), (36, 23), (23, 23), (32, 16), (6, 26), (15, 27), (34, 31), (29, 7), (9, 10), (34, 22), (4, 30), (14, 10), (33, 14), (7, 24), (3, 8), (0, 3), (16, 6), (15, 31), (23, 30), (36, 5), (31, 24), (35, 11), (18, 2), (25, 10), (35, 14), (29, 20), (22, 4), (24, 22), (27, 16), (6, 13), (13, 9), (33, 22), (26, 34), (33, 29), (12, 18), (10, 14), (15, 19), (31, 27), (21, 19), (21, 10), (35, 29), (13, 13), (11, 4), (3, 13), (25, 15), (31, 22), (6, 5), (17, 7), (22, 28), (5, 6), (31, 28), (35, 6), (8, 20), (21, 4), (11, 15), (12, 6), (24, 34), (8, 14), (34, 3), (35, 22), (34, 17), (23, 20), (1, 23), (2, 27), (15, 10), (10, 7), (19, 9), (21, 18), (30, 30), (34, 29), (10, 8), (31, 16), (16, 30), (11, 11), (0, 32), (2, 6), (18, 27), (9, 23), (12, 0), (4, 2), (28, 26), (13, 17), (1, 25), (23, 33), (12, 29), (14, 14), (18, 5), (6, 22), (33, 20), (18, 18), (3, 7), (4, 3), (14, 16), (11, 18), (1, 33), (28, 28), (2, 18), (21, 23), (3, 24), (31, 13), (20, 26), (9, 25), (33, 16), (28, 17), (3, 0), (0, 21), (21, 27), (5, 8), (14, 31), (6, 28), (36, 25), (24, 23), (8, 30), (31, 30), (26, 15), (23, 8), (25, 32), (7, 28), (19, 17), (8, 16), (12, 32), (8, 15), (13, 7), (32, 13), (33, 6), (7, 16), (31, 17), (25, 3), (10, 11), (5, 10), (10, 0), (27, 11), (3, 12), (34, 33), (13, 5), (28, 27), (3, 31), (9, 7), (23, 1), (1, 13), (13, 12), (25, 8), (1, 0), (3, 19), (1, 31), (14, 2), (24, 29), (7, 29), (2, 28), (20, 21), (30, 18), (11, 30), (36, 16), (35, 24), (7, 21), (8, 7), (10, 34), (7, 18), (8, 11), (7, 3), (23, 9), (19, 18), (10, 17), (25, 19), (14, 0), (14, 18), (19, 30), (8, 17), (33, 31), (12, 4), (2, 5), (16, 23), (26, 25), (19, 29), (31, 6), (32, 4), (20, 29), (7, 8), (21, 11), (22, 9), (26, 32), (15, 28), (14, 17), (1, 24), (26, 26), (11, 19), (27, 25), (21, 29), (11, 29), (10, 32), (6, 21), (13, 3), (21, 25), (21, 7), (15, 1), (28, 9), (20, 17), (27, 5), (5, 24), (16, 15), (5, 28), (35, 23), (7, 17), (29, 33), (33, 19), (32, 19), (17, 10), (8, 31), (11, 3), (29, 18), (26, 22), (33, 30), (5, 12), (36, 29), (31, 15), (14, 23), (29, 5), (31, 18), (26, 21), (33, 1), (25, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "371790", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), 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), (10, 35), (13, 3), (33, 21), (17, 2), (27, 10), (12, 30), (18, 1), (29, 35), (4, 7), (4, 3), (30, 18), (17, 9), (1, 15), (13, 10), (14, 27), (9, 33), (2, 16), (30, 6), (8, 12), (26, 6), (25, 17), (14, 5), (32, 6), (23, 29), (7, 21), (24, 22), (0, 35), (12, 1), (30, 25), (31, 29), (6, 0), (33, 18), (27, 18), (3, 18), (29, 33), (5, 0), (9, 21), (3, 11), (26, 2), (22, 34), (24, 11), (8, 26), (6, 33), (32, 21), (24, 0), (30, 0), (23, 33), (21, 14), (7, 15), (21, 23), (9, 34), (24, 32), (23, 2), (26, 23), (19, 10), (10, 13), (29, 20), (1, 33), (8, 14), (29, 21), (11, 5), (19, 11), (21, 19), (29, 28), (25, 19), (8, 3), (5, 16), (7, 9), (31, 15), (12, 22), (33, 26), (25, 7), (2, 28), (30, 2), (7, 1), (31, 0), (4, 1), (1, 20), (2, 25), (33, 27), (1, 16), (26, 20), (27, 26), (26, 8), (8, 17), (14, 6), (1, 35), (24, 9), (11, 9), (9, 15), (11, 22), (23, 1), (1, 8), (5, 28), (33, 6), (20, 2), (23, 12), (17, 25), (31, 25), (27, 5), (30, 21), (13, 9), (5, 15), (29, 0), (30, 35), (7, 19), (30, 33), (5, 27), (9, 35), (17, 15), (14, 8), (0, 22), (4, 25), (5, 2), (10, 4), (23, 17), (4, 8), (22, 7), (19, 8), (31, 22), (0, 8), (32, 25), (3, 24), (21, 35), (12, 19), (16, 7), (8, 10), (3, 19), (15, 32), (26, 31), (22, 8), (21, 11), (22, 25), (22, 0), (7, 27), (8, 8), (2, 21), (4, 14), (18, 35), (18, 27), (10, 33), (3, 3), (27, 22), (15, 23), (28, 12), (3, 1), (26, 21), (32, 35), (14, 18), (1, 4), (33, 10), (14, 29), (27, 27), (22, 3), (11, 16), (31, 21), (22, 32), (16, 13), (24, 33), (30, 4), (30, 5), (21, 17), (1, 17), (27, 14), (4, 18), (6, 7), (8, 24), (10, 25), (16, 11), (2, 10), (31, 12), (20, 4), (3, 16), (8, 33), (11, 29), (12, 31), (13, 35), (27, 25), (13, 27), (21, 5), (18, 7), (7, 20), (24, 29), (12, 34), (11, 6), (32, 18), (1, 34), (18, 16), (15, 2), (26, 13), (11, 27), (16, 3), (20, 31), (22, 14), (17, 12), (30, 14), (9, 0), (27, 31), (22, 21), (31, 17), (33, 31), (32, 13), (30, 10), (19, 14), (31, 23), (16, 32), (5, 10), (8, 19), (13, 17), (17, 6), (15, 26), (18, 18), (8, 18), (27, 23), (26, 16), (29, 31), (15, 5), (11, 17), (6, 11), (27, 17), (16, 24), (9, 13), (12, 10), (28, 5), (10, 5), (2, 8), (7, 23), (11, 21), (2, 5), (30, 12), (19, 13), (14, 28), (30, 7), (2, 17), (18, 6), (24, 23), (12, 28), (9, 27), (20, 11), (31, 24), (10, 2), (12, 29), (28, 24), (9, 26), (0, 26), (16, 26), (14, 23), (18, 20), (17, 0), (20, 15), (24, 15), (21, 9), (1, 24), (10, 8), (6, 4), (18, 2), (32, 9), (5, 9), (12, 12), (32, 1), (28, 3), (32, 11), (5, 18), (33, 11), (4, 34), (0, 27), (29, 9), (28, 33), (7, 14), (26, 15), (1, 2), (12, 27), (0, 20), (32, 28), (10, 27), (4, 30), (16, 16), (27, 30), (2, 1), (26, 5), (8, 9), (28, 9), (12, 26), (18, 31), (17, 33), (1, 18), (8, 16), (3, 32), (4, 4), (14, 17), (16, 31), (13, 4), (8, 23), (20, 1), (28, 15), (31, 6), (7, 33), (28, 1), (21, 21), (1, 9), (6, 5), (30, 31), (19, 4), (29, 22), (8, 29), (8, 30), (27, 1), (5, 7), (23, 14), (18, 25), (27, 24), (28, 25), (4, 26), (4, 19), (13, 30), (23, 3), (11, 8), (21, 33), (11, 15), (8, 2), (24, 7), (21, 32), (19, 19), (29, 19), (13, 34), (24, 28), (6, 19), (5, 25), (6, 13), (16, 30), (16, 19), (13, 13), (9, 5), (0, 5), (23, 20), (6, 3), (20, 25), (14, 14), (30, 30), (18, 12), (33, 12), (21, 12), (26, 7), (15, 28), (24, 12), (14, 0), (30, 16), (1, 6), (19, 2), (1, 12), (26, 34), (16, 5), (12, 14), (2, 15), (29, 3), (4, 28), (16, 6), (18, 3), (5, 34), (5, 23), (30, 22), (27, 13), (11, 0), (22, 23), (2, 19), (4, 22), (18, 22), (17, 3), (1, 28), (13, 0), (22, 28), (27, 4), (28, 21), (20, 16), (16, 14), (26, 17), (19, 20), (25, 29), (0, 10), (3, 33), (5, 12), (21, 15), (18, 11), (33, 32), (20, 28), (4, 10), (18, 21), (2, 11), (18, 8), (7, 4), (24, 2), (12, 18), (9, 11), (30, 27), (3, 26), (29, 10), (17, 22), (14, 20), (33, 30), (32, 34), (32, 8), (26, 9), (15, 27), (10, 28), (10, 6), (12, 16), (7, 28), (9, 28), (15, 8), (25, 18), (6, 15), (6, 17), (14, 10), (27, 3), (17, 10), (9, 30), (18, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "465480", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), 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), (25, 9), (10, 14), (10, 12), (21, 35), (34, 11), (18, 26), (11, 17), (5, 17), (16, 21), (12, 8), (19, 18), (8, 12), (25, 7), (4, 23), (19, 9), (34, 5), (8, 6), (1, 5), (23, 20), (4, 18), (22, 3), (23, 34), (28, 27), (29, 8), (7, 16), (1, 9), (19, 0), (9, 32), (19, 7), (31, 20), (3, 34), (2, 17), (13, 32), (31, 8), (32, 15), (35, 12), (23, 7), (5, 31), (1, 3), (2, 6), (18, 17), (0, 27), (1, 34), (37, 26), (12, 35), (13, 16), (6, 24), (13, 27), (6, 8), (1, 4), (13, 6), (7, 20), (10, 20), (15, 32), (22, 18), (35, 18), (11, 0), (36, 22), (12, 23), (2, 20), (32, 18), (24, 31), (6, 28), (29, 2), (29, 25), (26, 32), (19, 26), (30, 27), (34, 22), (11, 25), (32, 1), (12, 32), (28, 24), (17, 33), (11, 10), (8, 34), (17, 25), (17, 31), (13, 21), (12, 4), (28, 17), (9, 11), (18, 2), (1, 30), (14, 7), (9, 10), (1, 24), (10, 21), (26, 7), (2, 23), (34, 28), (24, 11), (5, 18), (5, 12), (12, 28), (13, 30), (18, 20), (35, 1), (12, 5), (0, 1), (28, 1), (9, 13), (28, 18), (29, 31), (35, 22), (7, 5), (37, 34), (7, 29), (27, 5), (8, 31), (13, 1), (25, 2), (9, 8), (1, 1), (36, 11), (34, 6), (29, 20), (14, 0), (33, 10), (36, 33), (5, 1), (28, 6), (10, 31), (6, 34), (2, 4), (4, 2), (2, 24), (10, 10), (21, 34), (8, 0), (2, 1), (34, 17), (32, 13), (0, 34), (26, 10), (9, 28), (26, 33), (2, 12), (31, 25), (16, 7), (29, 7), (21, 2), (23, 33), (27, 35), (30, 16), (4, 33), (21, 5), (13, 5), (28, 34), (18, 13), (25, 5), (33, 13), (11, 16), (33, 12), (5, 3), (31, 27), (15, 27), (19, 11), (15, 20), (14, 34), (13, 0), (24, 33), (31, 2), (8, 32), (34, 19), (30, 29), (10, 28), (20, 27), (17, 9), (30, 32), (2, 33), (37, 1), (27, 16), (15, 22), (5, 34), (3, 27), (20, 2), (3, 25), (6, 17), (9, 24), (12, 7), (21, 17), (22, 6), (31, 19), (0, 19), (28, 28), (35, 30), (25, 18), (4, 20), (14, 11), (30, 17), (3, 19), (35, 4), (2, 9), (25, 28), (3, 24), (16, 32), (5, 11), (7, 2), (8, 10), (37, 10), (37, 31), (0, 8), (13, 15), (21, 25), (27, 30), (29, 29), (21, 9), (34, 31), (26, 21), (7, 24), (3, 15), (14, 16), (30, 22), (13, 10), (20, 30), (11, 8), (11, 30), (6, 5), (35, 33), (6, 13), (36, 3), (34, 20), (5, 20), (35, 19), (26, 6), (29, 0), (10, 18), (27, 24), (14, 30), (1, 13), (9, 5), (37, 7), (17, 13), (0, 5), (7, 15), (33, 29), (7, 6), (24, 9), (16, 34), (20, 16), (15, 21), (5, 24), (31, 31), (23, 18), (3, 10), (33, 28), (19, 19), (18, 35), (3, 32), (30, 21), (22, 35), (17, 3), (35, 32), (20, 33), (27, 34), (1, 27), (34, 33), (20, 29), (9, 0), (27, 1), (25, 10), (37, 30), (30, 30), (37, 13), (14, 3), (6, 18), (23, 12), (10, 1), (4, 29), (36, 1), (8, 3), (7, 19), (4, 28), (26, 2), (36, 29), (25, 33), (23, 32), (26, 19), (15, 5), (28, 31), (17, 8), (5, 8), (7, 18), (0, 7), (26, 4), (25, 24), (27, 6), (26, 18), (11, 20), (4, 13), (34, 1), (13, 13), (30, 13), (15, 13), (14, 35), (10, 17), (24, 20), (10, 16), (34, 24), (21, 8), (1, 33), (9, 29), (28, 0), (1, 18), (37, 6), (32, 32), (24, 32), (22, 0), (1, 35), (36, 0), (30, 14), (5, 15), (21, 28), (24, 7), (29, 13), (3, 17), (17, 32), (17, 29), (8, 20), (13, 12), (29, 27), (19, 33), (15, 14), (24, 28), (6, 9), (15, 16), (10, 2), (5, 19), (17, 2), (14, 18), (15, 17), (18, 25), (22, 8), (31, 35), (30, 20), (35, 5), (32, 20), (15, 4), (3, 23), (5, 7), (31, 10), (17, 16), (20, 5), (5, 29), (28, 26), (0, 13), (10, 23), (22, 19), (24, 1), (31, 30), (19, 24), (16, 0), (36, 6), (27, 33), (17, 7), (33, 16), (14, 13), (0, 15), (36, 31), (9, 17), (4, 1), (19, 28), (33, 23), (37, 17), (21, 26), (16, 8), (17, 18), (1, 16), (34, 2), (35, 21), (7, 21), (17, 6), (17, 5), (26, 5), (22, 24), (13, 7), (34, 29), (15, 8), (26, 27), (25, 20), (24, 21), (18, 12), (24, 22), (20, 24), (16, 2), (32, 25), (23, 25), (4, 19), (22, 22), (20, 0), (30, 11), (30, 1), (16, 3), (3, 29), (11, 31), (28, 19), (23, 1), (17, 11), (20, 28), (8, 19), (10, 0), (36, 34), (29, 4), (5, 25), (7, 27), (18, 27), (18, 15), (23, 0), (8, 28), (10, 13), (14, 10), (34, 8), (22, 13), (25, 26), (8, 7), (18, 28), (25, 23), (23, 24), (32, 33), (9, 18), (16, 14), (19, 25), (0, 24), (16, 13), (5, 5), (20, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475200", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), 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), (16, 11), (19, 14), (1, 17), (18, 21), (4, 13), (12, 8), (8, 18), (0, 16), (15, 5), (9, 12), (33, 9), (15, 6), (21, 24), (3, 7), (0, 27), (1, 4), (8, 25), (24, 25), (27, 23), (19, 29), (12, 1), (7, 25), (34, 4), (34, 22), (28, 25), (4, 10), (3, 10), (10, 26), (21, 1), (15, 7), (28, 13), (19, 10), (4, 15), (31, 22), (9, 23), (11, 2), (21, 13), (25, 21), (9, 1), (19, 15), (7, 12), (10, 25), (12, 17), (11, 27), (31, 10), (32, 26), (1, 27), (22, 18), (17, 24), (26, 9), (5, 1), (22, 9), (19, 4), (32, 9), (21, 16), (2, 26), (15, 0), (23, 21), (7, 21), (29, 19), (3, 29), (2, 10), (22, 20), (17, 23), (3, 27), (23, 19), (25, 22), (25, 20), (9, 10), (28, 17), (22, 2), (34, 5), (24, 10), (30, 8), (30, 3), (33, 14), (26, 0), (25, 29), (5, 27), (23, 26), (31, 9), (21, 3), (19, 26), (29, 10), (9, 17), (25, 12), (4, 0), (23, 27), (3, 13), (8, 7), (1, 3), (12, 15), (0, 8), (7, 10), (29, 2), (25, 5), (20, 10), (29, 12), (33, 29), (30, 4), (2, 11), (33, 11), (26, 13), (1, 8), (7, 19), (9, 22), (23, 12), (31, 26), (15, 17), (0, 10), (14, 5), (34, 11), (27, 13), (17, 10), (10, 1), (7, 9), (19, 18), (26, 21), (16, 20), (6, 14), (32, 28), (0, 11), (26, 2), (5, 22), (21, 8), (8, 20), (9, 8), (8, 0), (4, 4), (14, 9), (13, 10), (13, 24), (21, 28), (7, 20), (27, 11), (33, 28), (16, 9), (28, 1), (2, 8), (12, 16), (5, 14), (16, 17), (27, 17), (33, 5), (9, 28), (20, 18), (11, 0), (6, 12), (23, 7), (32, 8), (18, 11), (33, 6), (17, 26), (13, 27), (25, 1), (6, 4), (30, 12), (9, 29), (2, 28), (3, 6), (18, 3), (7, 11), (0, 14), (5, 15), (12, 19), (12, 12), (5, 25), (3, 8), (13, 5), (5, 0), (3, 5), (16, 16), (20, 12), (20, 5), (28, 21), (25, 8), (14, 10), (25, 23), (14, 18), (15, 10), (8, 17), (29, 5), (25, 16), (7, 14), (31, 6), (27, 25), (12, 18), (7, 5), (21, 7), (30, 6), (9, 18), (34, 26), (28, 0), (13, 28), (31, 11), (15, 11), (2, 2), (13, 12), (22, 12), (1, 18), (33, 16), (16, 13), (0, 25), (18, 0), (20, 22), (32, 11), (21, 27), (14, 25), (25, 7), (12, 20), (24, 7), (4, 27), (30, 27), (14, 1), (19, 27), (20, 9), (31, 12), (23, 2), (13, 4), (13, 7), (31, 19), (13, 29), (15, 16), (12, 11), (15, 22), (7, 27), (17, 25), (29, 11), (27, 16), (23, 16), (21, 22), (7, 26), (34, 25), (27, 28), (2, 22), (27, 3), (18, 26), (16, 0), (27, 21), (26, 8), (12, 25), (22, 19), (0, 21), (25, 2), (12, 27), (2, 27), (30, 29), (8, 28), (0, 6), (15, 18), (4, 21), (7, 0), (20, 19), (19, 6), (14, 28), (10, 4), (33, 15), (5, 12), (33, 18), (6, 23), (21, 5), (6, 7), (31, 16), (34, 12), (14, 26), (22, 28), (30, 15), (12, 13), (17, 20), (11, 20), (11, 10), (14, 4), (25, 27), (16, 5), (30, 19), (22, 0), (19, 23), (7, 7), (26, 6), (24, 23), (24, 20), (3, 12), (23, 0), (12, 24), (1, 9), (3, 23), (17, 28), (20, 2), (32, 25), (25, 0), (24, 2), (28, 8), (21, 2), (7, 13), (4, 6), (34, 24), (34, 9), (21, 0), (10, 20), (2, 21), (0, 12), (13, 6), (18, 20), (22, 4), (29, 3), (4, 12), (32, 4), (8, 1), (23, 24), (2, 13), (14, 16), (24, 21), (21, 14), (30, 21), (18, 22), (8, 2), (32, 23), (5, 19), (8, 3), (22, 11), (30, 23), (29, 13), (19, 2), (33, 1), (1, 24), (2, 29), (27, 14), (0, 28), (24, 12), (28, 11), (29, 21), (4, 24), (9, 2), (5, 24), (19, 19), (8, 14), (13, 17), (26, 14), (14, 0), (25, 9), (23, 6), (16, 14), (19, 12), (29, 22), (19, 0), (18, 8), (20, 8), (29, 18), (0, 29), (5, 3), (22, 23), (20, 4), (10, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "786240", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 34), (7, 9), (10, 7), (2, 1), (4, 10), (18, 5), (4, 8), (11, 9), (19, 37), (0, 7), (28, 30), (13, 32), (0, 15), (19, 7), (26, 24), (2, 21), (20, 14), (22, 21), (12, 34), (28, 31), (18, 10), (22, 19), (25, 8), (28, 8), (7, 32), (7, 8), (0, 10), (11, 4), (22, 0), (5, 26), (32, 37), (1, 16), (32, 8), (25, 9), (8, 10), (15, 36), (4, 23), (25, 26), (1, 14), (11, 30), (6, 7), (13, 0), (31, 27), (30, 24), (13, 20), (24, 25), (6, 14), (26, 37), (12, 4), (20, 26), (5, 3), (6, 34), (1, 6), (17, 2), (25, 28), (21, 29), (18, 37), (24, 29), (5, 0), (8, 32), (18, 25), (12, 29), (4, 7), (12, 7), (10, 9), (10, 1), (2, 30), (30, 18), (8, 19), (17, 17), (27, 36), (4, 30), (11, 10), (9, 16), (29, 36), (16, 35), (30, 33), (1, 4), (8, 14), (5, 9), (13, 1), (9, 1), (5, 8), (17, 19), (11, 36), (16, 7), (22, 38), (31, 35), (7, 17), (13, 33), (3, 5), (29, 32), (14, 29), (2, 17), (6, 37), (0, 13), (8, 3), (26, 38), (11, 21), (5, 38), (1, 21), (25, 38), (32, 10), (7, 5), (24, 34), (3, 34), (22, 31), (28, 24), (2, 25), (13, 29), (28, 38), (31, 10), (17, 1), (12, 36), (22, 35), (12, 8), (13, 18), (15, 32), (24, 17), (9, 25), (13, 6), (4, 11), (12, 22), (25, 7), (1, 20), (30, 12), (28, 17), (1, 25), (18, 17), (6, 25), (19, 35), (17, 20), (0, 18), (6, 33), (4, 36), (20, 17), (26, 12), (9, 12), (8, 29), (20, 27), (23, 13), (23, 14), (22, 4), (9, 36), (2, 19), (19, 6), (13, 35), (2, 18), (6, 22), (21, 14), (27, 0), (11, 32), (1, 12), (13, 8), (30, 30), (18, 15), (14, 31), (16, 27), (21, 4), (11, 18), (7, 36), (22, 23), (12, 38), (0, 23), (7, 15), (30, 32), (21, 3), (18, 0), (29, 33), (10, 27), (0, 34), (10, 25), (17, 33), (17, 16), (3, 27), (7, 3), (32, 28), (27, 35), (20, 3), (6, 8), (23, 25), (28, 26), (29, 1), (6, 0), (0, 6), (15, 29), (30, 15), (24, 26), (16, 11), (3, 7), (2, 12), (32, 4), (23, 20), (32, 2), (25, 23), (6, 30), (6, 24), (8, 20), (12, 33), (9, 7), (0, 14), (6, 6), (24, 38), (28, 6), (27, 18), (12, 30), (5, 12), (17, 13), (25, 32), (1, 22), (16, 0), (15, 38), (4, 6), (13, 25), (22, 7), (31, 5), (31, 3), (10, 21), (19, 30), (17, 32), (31, 33), (23, 5), (0, 5), (11, 37), (20, 18), (27, 29), (17, 3), (22, 11), (25, 3), (30, 20), (5, 22), (5, 29), (14, 5), (2, 11), (1, 13), (20, 10), (23, 23), (29, 18), (22, 14), (3, 37), (24, 21), (27, 34), (14, 23), (19, 0), (1, 23), (32, 14), (1, 9), (14, 21), (16, 16), (16, 22), (10, 15), (13, 30), (30, 26), (24, 7), (18, 34), (9, 35), (21, 33), (29, 3), (15, 9), (22, 16), (17, 27), (14, 24), (12, 13), (28, 12), (18, 4), (32, 16), (16, 17), (32, 23), (31, 7), (29, 13), (29, 2), (26, 30), (17, 35), (11, 24), (14, 9), (26, 14), (21, 32), (18, 3), (9, 10), (30, 8), (21, 25), (13, 14), (21, 37), (22, 26), (22, 15), (21, 34), (21, 13), (29, 14), (16, 24), (12, 10), (30, 4), (11, 31), (15, 6), (13, 4), (22, 12), (15, 2), (25, 14), (1, 35), (7, 7), (1, 0), (5, 33), (13, 13), (9, 20), (12, 12), (25, 2), (29, 8), (26, 3), (27, 25), (4, 15), (25, 37), (24, 31), (27, 38), (14, 25), (29, 28), (24, 14), (28, 25), (3, 32), (28, 7), (2, 15), (30, 25), (24, 28), (11, 27), (2, 23), (4, 14), (13, 19), (2, 20), (23, 28), (22, 1), (25, 35), (26, 11), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "733824", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 24), (27, 6), (20, 22), (14, 28), (10, 6), (6, 5), (24, 22), (23, 35), (23, 33), (24, 21), (11, 3), (5, 15), (16, 6), (0, 12), (1, 9), (23, 18), (13, 33), (1, 16), (7, 9), (19, 21), (21, 23), (13, 7), (11, 10), (21, 24), (22, 3), (5, 22), (15, 14), (25, 9), (29, 23), (15, 36), (22, 31), (23, 14), (2, 12), (18, 29), (19, 18), (15, 34), (23, 31), (8, 9), (25, 0), (0, 9), (10, 3), (7, 5), (30, 29), (5, 36), (25, 21), (24, 4), (8, 31), (22, 21), (20, 8), (25, 18), (7, 8), (29, 11), (30, 4), (0, 25), (9, 15), (12, 34), (2, 14), (9, 32), (28, 13), (4, 33), (5, 10), (21, 35), (30, 31), (28, 24), (19, 16), (23, 24), (1, 0), (12, 9), (10, 12), (4, 14), (26, 9), (10, 20), (18, 0), (28, 10), (19, 12), (14, 34), (28, 28), (13, 24), (20, 5), (23, 30), (13, 10), (23, 25), (29, 15), (26, 30), (6, 27), (6, 18), (20, 18), (26, 6), (1, 19), (16, 36), (12, 18), (3, 12), (25, 25), (0, 17), (12, 29), (28, 36), (22, 24), (6, 16), (10, 33), (8, 4), (29, 31), (3, 26), (28, 22), (6, 9), (8, 10), (26, 36), (10, 17), (23, 7), (14, 12), (26, 18), (25, 31), (18, 14), (26, 13), (21, 19), (3, 4), (30, 5), (1, 22), (15, 7), (12, 27), (20, 29), (0, 20), (5, 9), (1, 14), (5, 25), (23, 29), (20, 33), (27, 2), (20, 0), (2, 26), (16, 29), (2, 27), (8, 23), (25, 10), (28, 6), (3, 10), (4, 2), (18, 33), (29, 34), (15, 23), (0, 15), (7, 17), (20, 6), (30, 13), (2, 9), (25, 6), (14, 6), (2, 19), (8, 27), (8, 26), (2, 4), (11, 26), (24, 13), (14, 23), (10, 27), (6, 34), (20, 35), (28, 17), (23, 3), (13, 16), (18, 18), (28, 19), (12, 21), (0, 34), (25, 24), (6, 23), (12, 0), (30, 17), (13, 28), (21, 20), (26, 4), (3, 8), (11, 11), (15, 3), (8, 30), (9, 28), (7, 31), (7, 12), (2, 21), (6, 17), (28, 16), (1, 17), (12, 23), (25, 34), (14, 27), (1, 36), (10, 18), (2, 18), (30, 9), (16, 16), (12, 26), (4, 34), (14, 5), (6, 1), (27, 25), (30, 15), (21, 33), (15, 13), (12, 33), (12, 6), (1, 11), (14, 11), (11, 14), (3, 5), (21, 31), (15, 31), (12, 14), (16, 14), (21, 25), (19, 33), (29, 21), (30, 6), (26, 21), (0, 26), (21, 36), (9, 2), (4, 8), (22, 30), (24, 33), (19, 25), (8, 12), (5, 32), (5, 13), (1, 5), (16, 30), (12, 22), (29, 13), (17, 15), (6, 10), (15, 28), (7, 0), (2, 3), (19, 28), (14, 31), (8, 16), (3, 6), (1, 31), (0, 2), (30, 12), (23, 27), (8, 28), (4, 0), (5, 26), (24, 3), (0, 6), (4, 4), (15, 15), (1, 12), (3, 15), (19, 9), (29, 10), (28, 30), (10, 8), (21, 10), (21, 27), (26, 10), (27, 35), (7, 32), (4, 35), (11, 9), (22, 19), (19, 8), (4, 3), (20, 19), (15, 6), (25, 5), (18, 32), (0, 14), (18, 36), (24, 16), (1, 4), (10, 24), (29, 33), (16, 13), (3, 22), (15, 5), (18, 12), (0, 13), (3, 2), (17, 7), (3, 3), (2, 11), (29, 25), (7, 29), (9, 34), (11, 28), (0, 18), (27, 31), (23, 1), (4, 24), (1, 24), (9, 18), (10, 13), (26, 33), (11, 6), (6, 30), (13, 8), (13, 17), (10, 22), (13, 0), (7, 26), (27, 4), (19, 4), (22, 18), (12, 24), (30, 10), (0, 22), (27, 22), (0, 5), (27, 15), (29, 20), (12, 30), (25, 35), (28, 11), (8, 32), (15, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "905268", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 29), (13, 15), (0, 19), (36, 21), (8, 15), (21, 1), (17, 20), (30, 24), (7, 15), (7, 10), (21, 12), (21, 36), (13, 11), (13, 26), (21, 21), (34, 4), (6, 30), (0, 16), (7, 17), (31, 18), (22, 25), (37, 26), (20, 36), (30, 31), (34, 22), (34, 28), (7, 29), (2, 10), (6, 6), (7, 22), (24, 27), (22, 19), (16, 18), (24, 16), (32, 19), (36, 0), (29, 20), (12, 25), (9, 3), (10, 4), (15, 20), (16, 14), (28, 27), (14, 25), (10, 34), (34, 17), (13, 23), (15, 6), (15, 15), (3, 30), (14, 24), (5, 4), (15, 25), (24, 8), (22, 21), (11, 23), (13, 17), (8, 7), (36, 27), (4, 14), (21, 2), (15, 4), (20, 12), (15, 19), (33, 29), (30, 26), (0, 11), (4, 11), (2, 0), (12, 6), (0, 25), (12, 27), (16, 24), (9, 37), (20, 23), (30, 33), (33, 27), (15, 14), (28, 2), (17, 4), (11, 16), (36, 23), (15, 0), (32, 10), (1, 29), (33, 28), (32, 4), (23, 1), (26, 21), (2, 7), (20, 14), (20, 25), (31, 10), (7, 14), (24, 2), (12, 35), (4, 12), (36, 9), (8, 27), (6, 1), (22, 24), (4, 37), (25, 28), (25, 15), (29, 9), (6, 18), (20, 17), (7, 23), (27, 7), (29, 35), (17, 34), (25, 33), (37, 28), (3, 24), (0, 15), (36, 31), (3, 33), (8, 21), (34, 18), (15, 11), (34, 15), (16, 36), (19, 16), (35, 4), (20, 1), (20, 0), (37, 23), (24, 32), (2, 12), (22, 22), (6, 7), (28, 16), (9, 31), (6, 29), (7, 33), (26, 12), (26, 22), (2, 8), (5, 16), (24, 28), (11, 2), (31, 33), (13, 34), (10, 2), (3, 35), (33, 34), (19, 21), (30, 11), (35, 10), (35, 0), (5, 11), (11, 19), (26, 17), (6, 33), (1, 3), (16, 17), (35, 37), (8, 33), (19, 9), (9, 24), (22, 20), (24, 0), (33, 25), (4, 24), (34, 30), (11, 31), (24, 26), (1, 17), (18, 37), (21, 18), (6, 13), (30, 0), (7, 31), (14, 5), (13, 20), (11, 4), (13, 14), (17, 15), (14, 4), (30, 4), (35, 9), (20, 13), (21, 13), (18, 35), (20, 18), (15, 23), (23, 2), (2, 13), (12, 0), (25, 34), (27, 31), (26, 31), (37, 17), (31, 3), (1, 0), (6, 15), (11, 1), (11, 35), (34, 32), (8, 24), (23, 24), (24, 15), (16, 10), (35, 15), (21, 6), (24, 23), (28, 33), (0, 9), (37, 2), (32, 9), (2, 33), (21, 29), (29, 22), (0, 23), (10, 36), (5, 25), (21, 0), (32, 36), (23, 31), (10, 3), (27, 24), (15, 24), (12, 14), (3, 29), (35, 8), (27, 15), (29, 6), (5, 29), (7, 35), (18, 21), (3, 2), (37, 8), (30, 30), (8, 30), (26, 0), (26, 2), (23, 6), (19, 22), (8, 4), (36, 30), (35, 22), (10, 6), (19, 0), (30, 9), (25, 32), (36, 29), (22, 11), (27, 14), (35, 1), (27, 6), (9, 17), (21, 26), (32, 0), (23, 21), (18, 9), (35, 24), (4, 26), (28, 15), (4, 0), (34, 3), (15, 31), (23, 23), (10, 33), (15, 8), (33, 33), (0, 37), (3, 5), (17, 30), (28, 28), (31, 1), (25, 17), (11, 6), (18, 33), (15, 27), (11, 13), (11, 15), (3, 20), (29, 27), (30, 29), (9, 12), (16, 21), (1, 4), (8, 12), (29, 28), (14, 13), (17, 9), (25, 21), (27, 18), (22, 18), (25, 12), (12, 23), (8, 28), (3, 23), (23, 36), (5, 13), (29, 32), (12, 17), (23, 11), (23, 28), (12, 29), (19, 18), (32, 7), (30, 7), (32, 31), (6, 16), (31, 12), (3, 8), (37, 16), (15, 10), (27, 16), (17, 24), (33, 18), (18, 29), (33, 24), (23, 25), (8, 34), (3, 7), (28, 26), (4, 22), (27, 26), (6, 3), (32, 6), (7, 3), (36, 19), (14, 16), (20, 35), (20, 8), (9, 20), (27, 2), (0, 18), (23, 9), (25, 23), (3, 11), (0, 33), (6, 4), (32, 12), (36, 20), (4, 20), (17, 8), (4, 25), (20, 2), (35, 33), (0, 2), (3, 28), (14, 12), (34, 29), (34, 8), (5, 31), (31, 31), (0, 30), (2, 37), (14, 9), (37, 0), (21, 31), (22, 2), (27, 28), (18, 22), (19, 36), (16, 32), (20, 16), (36, 33), (30, 32), (33, 3), (27, 12), (26, 23), (28, 37), (35, 17), (21, 30), (16, 20), (20, 22), (8, 26), (2, 2), (24, 3), (7, 34), (31, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706350", "dataset": "MATH"}
{"messages": [{"content": "In a 37x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 30), (34, 14), (0, 11), (1, 15), (2, 26), (34, 38), (8, 10), (25, 24), (23, 34), (14, 8), (33, 38), (29, 12), (32, 4), (5, 29), (35, 16), (29, 15), (6, 27), (16, 13), (11, 7), (13, 4), (12, 25), (7, 34), (25, 10), (25, 19), (25, 22), (10, 38), (19, 30), (19, 12), (30, 38), (8, 24), (2, 5), (14, 27), (27, 37), (8, 12), (32, 38), (30, 24), (24, 24), (8, 1), (21, 20), (28, 4), (11, 9), (19, 20), (33, 10), (30, 12), (25, 7), (17, 13), (36, 3), (31, 19), (32, 8), (1, 29), (17, 21), (7, 32), (1, 31), (12, 35), (36, 12), (27, 35), (18, 32), (19, 36), (19, 28), (33, 24), (4, 36), (14, 19), (10, 6), (10, 37), (23, 8), (12, 12), (21, 12), (20, 16), (16, 9), (19, 6), (20, 0), (0, 33), (8, 11), (4, 5), (20, 10), (4, 25), (36, 34), (13, 25), (27, 30), (4, 11), (5, 32), (33, 32), (28, 35), (2, 11), (23, 26), (32, 28), (28, 34), (23, 5), (12, 23), (35, 4), (9, 4), (28, 37), (8, 27), (30, 22), (15, 19), (9, 27), (14, 36), (27, 25), (35, 20), (31, 16), (34, 5), (3, 38), (14, 18), (9, 31), (30, 23), (17, 31), (10, 19), (15, 3), (0, 4), (5, 16), (6, 35), (34, 19), (17, 6), (16, 30), (3, 11), (2, 4), (17, 16), (31, 5), (20, 1), (25, 30), (3, 27), (21, 0), (34, 12), (21, 14), (30, 1), (18, 15), (12, 20), (0, 2), (25, 32), (17, 9), (4, 2), (36, 30), (18, 23), (25, 34), (22, 28), (21, 31), (12, 31), (35, 10), (29, 31), (13, 36), (23, 4), (28, 16), (32, 22), (2, 27), (6, 18), (20, 20), (21, 25), (9, 22), (34, 23), (23, 19), (14, 15), (13, 32), (3, 24), (22, 33), (23, 0), (32, 21), (29, 6), (15, 28), (12, 26), (3, 12), (31, 0), (25, 11), (24, 35), (7, 25), (13, 15), (24, 32), (27, 5), (26, 33), (8, 32), (22, 12), (18, 37), (29, 5), (3, 32), (33, 16), (2, 1), (11, 10), (3, 14), (11, 22), (7, 18), (28, 6), (10, 11), (29, 11), (3, 4), (34, 1), (12, 8), (21, 6), (18, 5), (34, 26), (8, 29), (24, 20), (26, 22), (15, 17), (28, 5), (27, 9), (18, 0), (1, 12), (4, 38), (3, 25), (3, 36), (30, 18), (34, 7), (2, 32), (9, 33), (29, 14), (21, 38), (13, 14), (30, 11), (6, 11), (10, 28), (16, 26), (28, 29), (20, 13), (36, 8), (0, 34), (15, 35), (35, 34), (35, 1), (11, 8), (34, 11), (5, 27), (4, 16), (3, 6), (0, 27), (4, 32), (6, 10), (16, 28), (11, 34), (21, 36), (31, 21), (21, 16), (7, 23), (19, 31), (2, 14), (3, 23), (17, 20), (31, 24), (22, 4), (30, 15), (35, 11), (24, 26), (35, 35), (8, 28), (29, 17), (35, 33), (21, 24), (22, 2), (6, 28), (31, 31), (20, 8), (32, 7), (2, 31), (29, 7), (33, 9), (28, 9), (25, 0), (35, 9), (25, 21), (11, 2), (7, 26), (19, 23), (0, 32), (15, 36), (19, 13), (9, 26), (10, 22), (10, 24), (8, 34), (5, 20), (4, 34), (2, 34), (14, 2), (31, 25), (7, 0), (23, 18), (22, 22), (21, 19), (15, 37), (35, 26), (26, 38), (27, 33), (17, 19), (23, 9), (26, 28), (1, 32), (7, 15), (20, 26), (14, 11), (24, 23), (17, 29), (5, 37), (8, 23), (4, 37), (1, 26), (32, 2), (14, 5), (9, 12), (17, 32), (15, 30), (32, 16), (5, 26), (13, 13), (16, 23), (34, 13), (8, 3), (7, 22), (19, 37), (4, 30), (32, 23), (3, 5), (20, 2), (15, 24), (33, 29), (12, 5), (35, 2), (29, 25), (27, 32), (4, 31), (5, 36), (35, 37), (2, 37), (26, 8), (35, 14), (16, 6), (17, 4), (0, 10), (30, 26), (22, 24), (1, 6), (22, 25), (3, 17), (1, 1), (9, 11), (19, 5), (32, 11), (33, 21), (30, 7), (32, 30), (35, 24), (30, 16), (13, 19), (13, 38), (8, 18), (6, 20), (9, 7), (26, 20), (11, 18), (12, 33), (10, 31), (13, 3), (23, 20), (34, 17), (8, 35), (33, 23), (17, 11), (32, 35), (19, 7), (20, 17), (34, 4), (8, 13), (23, 29), (18, 31), (20, 15), (6, 6), (11, 5), (18, 10), (9, 38), (19, 25), (36, 31), (5, 14), (13, 12), (24, 34), (19, 10), (36, 25), (33, 35), (3, 1), (35, 15), (31, 3), (2, 29), (11, 3), (25, 6), (4, 10), (34, 10), (8, 36), (5, 22), (26, 10), (27, 34), (21, 10), (33, 20), (36, 10), (35, 32), (17, 26), (21, 2), (11, 37), (34, 8), (27, 20), (6, 33), (28, 18), (21, 1), (14, 9), (0, 37), (36, 0), (26, 12), (23, 17), (31, 4), (29, 9), (26, 5), (18, 11), (6, 8), (33, 2), (1, 10), (31, 1), (29, 33), (16, 14), (33, 14), (26, 14), (33, 0), (12, 29), (15, 15), (3, 15), (18, 1), (27, 31), (23, 32), (15, 27), (23, 25), (20, 25), (9, 9), (4, 14), (25, 37), (17, 34), (17, 37), (22, 18), (19, 33), (19, 14), (28, 38), (32, 36), (23, 3), (28, 2), (28, 21), (3, 26), (12, 17), (24, 31), (19, 1), (2, 22), (13, 26), (16, 18), (24, 33), (8, 31), (29, 29), (18, 28), (29, 30), (5, 34), (14, 16), (36, 1), (1, 24), (16, 38), (11, 26), (28, 11), (17, 1), (1, 34), (9, 30), (17, 30), (6, 34), (14, 38), (26, 13), (36, 35), (17, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 2), (29, 37), (31, 26), (3, 36), (20, 30), (27, 10), (19, 11), (30, 16), (16, 9), (11, 20), (8, 6), (14, 26), (8, 17), (22, 24), (21, 2), (21, 33), (3, 11), (27, 31), (13, 2), (20, 6), (18, 4), (24, 26), (30, 17), (5, 32), (24, 16), (29, 17), (14, 31), (22, 29), (31, 14), (21, 28), (4, 9), (27, 29), (3, 16), (20, 29), (20, 19), (10, 15), (19, 37), (8, 12), (1, 12), (16, 17), (2, 0), (16, 1), (24, 29), (33, 5), (2, 37), (28, 3), (7, 22), (6, 19), (21, 13), (17, 18), (5, 6), (6, 28), (7, 5), (26, 15), (16, 36), (14, 4), (16, 12), (3, 13), (6, 26), (24, 18), (5, 26), (28, 33), (5, 19), (32, 20), (33, 19), (5, 5), (19, 36), (27, 23), (25, 21), (32, 1), (31, 21), (16, 0), (15, 25), (7, 38), (13, 11), (30, 30), (13, 33), (5, 2), (12, 6), (5, 9), (33, 27), (7, 8), (11, 35), (32, 32), (7, 10), (8, 26), (17, 20), (2, 32), (33, 4), (29, 35), (6, 4), (6, 2), (25, 9), (5, 28), (6, 38), (14, 13), (7, 9), (30, 32), (19, 26), (10, 3), (20, 16), (10, 14), (4, 10), (11, 23), (23, 28), (22, 19), (13, 38), (31, 4), (29, 22), (32, 3), (29, 32), (28, 13), (0, 11), (27, 38), (18, 32), (1, 35), (26, 10), (17, 17), (25, 3), (2, 31), (25, 22), (25, 14), (13, 37), (24, 13), (7, 32), (17, 33), (32, 15), (13, 29), (18, 2), (6, 30), (20, 34), (9, 14), (17, 7), (6, 14), (28, 8), (4, 24), (4, 15), (23, 20), (5, 37), (9, 10), (3, 30), (26, 34), (21, 17), (21, 31), (4, 22), (8, 3), (22, 30), (17, 14), (20, 4), (2, 1), (20, 26), (9, 19), (7, 37), (6, 32), (8, 1), (1, 13), (33, 11), (18, 14), (23, 31), (29, 28), (28, 36), (20, 21), (32, 14), (10, 9), (14, 36), (30, 29), (15, 14), (7, 13), (25, 31), (17, 2), (15, 6), (15, 10), (30, 38), (5, 10), (23, 13), (16, 23), (10, 4), (30, 26), (4, 28), (6, 7), (3, 31), (19, 4), (23, 34), (26, 28), (11, 19), (9, 11), (33, 29), (11, 24), (10, 34), (0, 21), (0, 31), (18, 20), (21, 1), (22, 17), (8, 31), (13, 34), (26, 4), (15, 19), (0, 9), (19, 34), (12, 27), (1, 31), (1, 32), (32, 16), (32, 12), (10, 33), (22, 16), (27, 30), (25, 20), (8, 36), (28, 6), (29, 29), (2, 9), (11, 10), (0, 29), (21, 37), (20, 38), (0, 38), (10, 16), (10, 36), (21, 0), (0, 36), (19, 20), (28, 2), (3, 21), (23, 15), (2, 15), (19, 32), (5, 14), (14, 18), (27, 33), (2, 5), (7, 36), (19, 3), (6, 22), (22, 14), (21, 6), (13, 18), (32, 4), (10, 35), (0, 20), (22, 1), (13, 8), (9, 20), (19, 23), (9, 22), (5, 13), (29, 21), (20, 35), (32, 34), (3, 38), (24, 37), (11, 28), (17, 13), (8, 19), (30, 21), (0, 3), (4, 34), (23, 14), (6, 6), (31, 5), (26, 6), (13, 5), (4, 31), (17, 9), (1, 4), (25, 25), (0, 8), (11, 3), (18, 22), (4, 8), (2, 36), (32, 31), (16, 30), (18, 17), (7, 6), (31, 32), (2, 12), (8, 13), (28, 28), (7, 19), (8, 38), (4, 25), (30, 23), (23, 25), (13, 0), (3, 19), (32, 36), (24, 20), (26, 21), (21, 22), (10, 19), (27, 6), (21, 29), (12, 35), (15, 4), (3, 37), (6, 13), (18, 18), (16, 19), (15, 15), (30, 19), (28, 34), (15, 7), (31, 30), (0, 1), (26, 13), (12, 31), (23, 9), (33, 14), (13, 14), (20, 5), (14, 0), (17, 34), (8, 34), (19, 29), (7, 0), (8, 9), (8, 23), (21, 25), (15, 5), (20, 12), (24, 6), (11, 32), (6, 10), (0, 30), (4, 1), (11, 30), (32, 24), (25, 38), (31, 35), (19, 2), (18, 12), (18, 34), (33, 10), (21, 35), (16, 37), (17, 37), (15, 13), (25, 7), (13, 30), (7, 26), (2, 8), (14, 24), (8, 24), (9, 24), (12, 28), (24, 3), (10, 6), (15, 21), (18, 37), (27, 21), (2, 24), (14, 9), (23, 6), (5, 18), (15, 37), (15, 11), (6, 35), (27, 32), (29, 11), (18, 11), (9, 4), (9, 27), (9, 35), (9, 33), (2, 23), (28, 19), (31, 38), (0, 14), (6, 5), (0, 27), (30, 18), (22, 32), (29, 4), (5, 8), (9, 38), (9, 1), (23, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793104", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (38, 18), (33, 17), (24, 15), (37, 6), (4, 27), (6, 6), (8, 10), (2, 21), (13, 9), (21, 4), (7, 2), (29, 16), (8, 22), (22, 20), (30, 12), (4, 20), (34, 4), (7, 24), (35, 31), (0, 11), (6, 18), (32, 24), (15, 22), (22, 30), (19, 8), (6, 26), (14, 15), (29, 7), (20, 13), (17, 20), (24, 18), (12, 14), (31, 20), (2, 1), (26, 18), (15, 17), (16, 31), (10, 30), (36, 27), (19, 0), (27, 4), (36, 0), (36, 10), (5, 6), (34, 22), (7, 28), (34, 18), (24, 4), (26, 26), (33, 11), (30, 9), (36, 23), (35, 23), (32, 18), (0, 8), (23, 25), (24, 21), (27, 3), (35, 8), (16, 7), (3, 19), (33, 12), (16, 8), (8, 3), (11, 14), (17, 8), (32, 20), (21, 27), (13, 23), (38, 1), (30, 17), (7, 4), (34, 17), (31, 23), (2, 30), (35, 30), (3, 30), (37, 2), (31, 25), (24, 27), (4, 29), (32, 1), (25, 24), (27, 28), (37, 28), (10, 4), (20, 19), (35, 19), (34, 1), (37, 18), (22, 13), (34, 31), (7, 7), (31, 0), (20, 28), (22, 14), (30, 31), (26, 15), (26, 10), (13, 17), (31, 24), (1, 6), (14, 17), (3, 18), (13, 29), (20, 18), (33, 18), (7, 21), (30, 10), (31, 10), (8, 2), (10, 13), (35, 4), (36, 26), (9, 16), (4, 12), (28, 3), (2, 17), (8, 0), (14, 9), (21, 28), (25, 19), (25, 11), (23, 30), (4, 26), (10, 11), (19, 29), (32, 14), (32, 5), (21, 31), (33, 19), (21, 30), (24, 23), (24, 31), (31, 4), (12, 26), (37, 21), (18, 31), (14, 19), (23, 2), (23, 14), (38, 17), (24, 10), (36, 25), (17, 31), (14, 31), (17, 21), (33, 25), (0, 23), (21, 3), (37, 25), (17, 1), (6, 20), (2, 13), (31, 2), (19, 4), (22, 16), (38, 24), (9, 18), (26, 31), (27, 27), (25, 3), (32, 3), (2, 28), (36, 2), (12, 0), (0, 17), (8, 6), (29, 14), (19, 14), (29, 28), (15, 24), (20, 10), (26, 22), (31, 31), (12, 5), (6, 25), (19, 5), (17, 30), (2, 3), (1, 14), (10, 14), (0, 20), (17, 18), (27, 11), (32, 15), (5, 10), (9, 29), (14, 23), (19, 9), (27, 31), (27, 0), (18, 20), (25, 25), (9, 15), (30, 6), (13, 14), (25, 10), (1, 2), (11, 22), (5, 23), (24, 13), (31, 15), (34, 0), (12, 22), (13, 12), (4, 1), (11, 29), (30, 20), (8, 31), (28, 2), (26, 19), (2, 5), (22, 29), (9, 0), (14, 25), (3, 11), (36, 4), (16, 22), (10, 29), (38, 28), (1, 4), (8, 24), (7, 27), (16, 20), (18, 10), (4, 10), (21, 0), (12, 18), (2, 7), (14, 21), (28, 12), (10, 8), (32, 27), (12, 17), (7, 10), (25, 15), (11, 0), (10, 19), (38, 11), (15, 2), (33, 3), (19, 21), (31, 22), (7, 25), (36, 3), (37, 10), (1, 0), (34, 16), (34, 19), (33, 2), (25, 23), (8, 13), (23, 19), (31, 17), (28, 27), (29, 27), (22, 10), (3, 24), (22, 21), (15, 23), (33, 22), (29, 10), (18, 21), (27, 22), (17, 29), (26, 3), (9, 2), (6, 23), (33, 29), (35, 16), (3, 1), (20, 0), (35, 10), (11, 30), (12, 20), (7, 30), (18, 18), (16, 12), (16, 10), (25, 1), (19, 27), (26, 8), (23, 21), (26, 23), (5, 1), (25, 27), (3, 23), (17, 22), (26, 7), (0, 13), (30, 11), (26, 28), (14, 4), (35, 24), (31, 19), (19, 11), (10, 22), (24, 25), (28, 4), (33, 9), (14, 26), (36, 28), (17, 16), (6, 22), (21, 16), (30, 16), (11, 9), (27, 1), (35, 15), (10, 12), (23, 8), (8, 18), (29, 30), (36, 16), (6, 8), (16, 14), (26, 0), (18, 0), (20, 15), (28, 7), (12, 8), (36, 24), (26, 12), (4, 24), (12, 2), (8, 28), (38, 15), (30, 5), (32, 31), (15, 16), (27, 25), (21, 6), (4, 9), (9, 14), (11, 16), (18, 4), (16, 28), (16, 27), (32, 19), (30, 19), (20, 26), (10, 2), (32, 26), (11, 6), (29, 23), (31, 3), (26, 30), (11, 21), (29, 26), (28, 10), (18, 12), (4, 17), (13, 3), (30, 7), (31, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864000", "dataset": "MATH"}
{"messages": [{"content": "In a 37x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 34), (6, 32), (2, 6), (7, 10), (5, 7), (4, 14), (21, 33), (36, 6), (13, 31), (5, 9), (25, 15), (29, 34), (36, 29), (19, 31), (1, 22), (4, 4), (26, 5), (11, 33), (7, 23), (32, 14), (31, 18), (9, 7), (8, 24), (33, 10), (1, 35), (17, 12), (22, 6), (23, 11), (32, 3), (29, 24), (20, 9), (32, 13), (8, 9), (29, 2), (4, 28), (20, 13), (2, 11), (4, 30), (9, 11), (2, 27), (12, 7), (25, 30), (32, 18), (4, 9), (10, 8), (32, 15), (12, 15), (35, 34), (22, 20), (31, 24), (34, 17), (7, 33), (10, 11), (0, 10), (27, 36), (14, 34), (16, 2), (36, 8), (35, 29), (35, 10), (14, 28), (15, 13), (11, 9), (8, 4), (5, 23), (12, 8), (26, 26), (21, 25), (35, 15), (5, 36), (3, 35), (22, 26), (35, 19), (14, 0), (27, 33), (29, 30), (33, 36), (16, 12), (30, 12), (12, 12), (12, 20), (21, 7), (23, 21), (34, 35), (32, 23), (29, 3), (20, 34), (32, 0), (10, 21), (30, 30), (8, 31), (28, 25), (15, 7), (26, 25), (24, 4), (9, 14), (18, 26), (28, 0), (30, 4), (23, 12), (32, 33), (21, 27), (30, 25), (26, 3), (21, 36), (20, 31), (4, 8), (24, 9), (21, 11), (18, 20), (9, 36), (11, 15), (9, 23), (20, 2), (0, 21), (34, 23), (18, 15), (33, 8), (29, 33), (7, 21), (29, 11), (14, 24), (29, 32), (8, 8), (25, 25), (2, 31), (15, 11), (14, 1), (16, 5), (28, 9), (24, 20), (6, 31), (4, 36), (6, 29), (24, 6), (3, 16), (9, 0), (26, 22), (11, 4), (29, 23), (31, 2), (5, 19), (18, 28), (32, 25), (31, 9), (15, 18), (27, 30), (7, 29), (8, 22), (34, 6), (2, 0), (34, 7), (21, 26), (29, 20), (14, 29), (30, 18), (2, 7), (18, 8), (21, 10), (6, 12), (22, 15), (32, 22), (33, 13), (7, 13), (28, 24), (21, 24), (20, 33), (21, 20), (20, 17), (28, 28), (16, 7), (18, 3), (35, 17), (6, 17), (19, 24), (12, 24), (10, 33), (23, 23), (28, 18), (21, 3), (10, 9), (5, 32), (27, 29), (26, 18), (26, 28), (28, 30), (5, 8), (33, 26), (25, 12), (15, 12), (17, 19), (12, 6), (33, 5), (35, 16), (19, 23), (22, 21), (0, 2), (26, 0), (10, 29), (8, 5), (25, 9), (26, 14), (2, 5), (22, 3), (17, 24), (35, 33), (18, 21), (6, 9), (34, 12), (2, 26), (19, 20), (11, 17), (32, 31), (28, 36), (12, 22), (22, 29), (22, 14), (20, 0), (22, 7), (0, 28), (7, 1), (21, 22), (17, 4), (4, 34), (5, 31), (16, 25), (26, 10), (31, 12), (7, 11), (25, 34), (8, 14), (1, 8), (10, 12), (8, 20), (1, 16), (20, 12), (11, 11), (28, 19), (3, 17), (3, 4), (8, 23), (0, 20), (15, 5), (36, 25), (10, 0), (1, 2), (19, 32), (35, 32), (7, 24), (10, 7), (27, 25), (20, 3), (0, 36), (14, 2), (9, 9), (27, 7), (16, 6), (36, 3), (5, 5), (13, 35), (2, 30), (27, 3), (19, 34), (22, 1), (19, 15), (10, 14), (31, 3), (0, 6), (35, 6), (14, 35), (14, 19), (14, 20), (13, 21), (12, 26), (1, 19), (33, 18), (11, 34), (34, 20), (15, 0), (27, 6), (33, 0), (33, 19), (5, 17), (9, 17), (29, 14), (12, 2), (12, 5), (30, 24), (15, 32), (5, 27), (15, 31), (18, 31), (13, 27), (25, 4), (17, 3), (7, 17), (30, 15), (27, 15), (25, 3), (17, 9), (24, 2), (26, 20), (16, 18), (12, 21), (24, 3), (16, 22), (28, 3), (23, 36), (23, 22), (15, 34), (24, 25), (17, 36), (23, 8), (11, 25), (20, 35), (14, 30), (27, 14), (7, 26), (22, 13), (32, 24), (8, 2), (6, 24), (26, 4), (24, 31), (26, 19), (25, 16), (16, 30), (4, 17), (16, 35), (35, 27), (33, 29), (28, 32), (21, 30), (29, 17), (5, 24), (4, 16), (34, 5), (35, 21), (19, 8), (17, 21), (17, 11), (33, 23), (9, 28), (2, 29), (9, 26), (24, 22), (35, 36), (34, 18), (30, 6), (29, 29), (28, 15), (10, 16), (30, 1), (3, 22), (17, 10), (36, 26), (4, 25), (36, 0), (24, 29), (17, 16), (15, 19), (2, 8), (6, 13), (14, 4), (3, 31), (18, 12), (0, 35), (11, 18), (23, 13), (22, 25), (7, 12), (30, 8), (35, 9), (31, 31), (1, 12), (16, 8), (21, 5), (15, 15), (5, 1), (31, 5), (12, 33), (19, 22), (8, 15), (28, 26), (31, 23), (1, 14), (30, 5), (1, 4), (25, 29), (31, 35), (14, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "745920", "dataset": "MATH"}
{"messages": [{"content": "In a 33x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 5), (6, 5), (24, 10), (0, 6), (25, 0), (20, 6), (30, 27), (32, 7), (28, 16), (20, 13), (18, 4), (25, 24), (26, 23), (0, 25), (2, 16), (27, 0), (4, 20), (30, 23), (20, 15), (28, 21), (13, 1), (18, 8), (26, 18), (19, 29), (7, 19), (29, 21), (21, 25), (10, 12), (3, 11), (3, 1), (4, 10), (11, 9), (2, 10), (27, 10), (29, 18), (26, 6), (25, 29), (7, 10), (11, 13), (10, 16), (7, 24), (29, 5), (13, 27), (2, 18), (4, 18), (3, 22), (22, 15), (8, 2), (27, 23), (31, 14), (8, 17), (0, 9), (24, 29), (20, 0), (14, 12), (10, 8), (29, 16), (14, 11), (26, 14), (1, 11), (17, 22), (1, 16), (6, 15), (24, 17), (7, 6), (7, 0), (13, 9), (13, 25), (1, 6), (8, 14), (25, 5), (32, 15), (18, 27), (6, 0), (17, 16), (14, 7), (0, 15), (10, 10), (20, 1), (17, 17), (22, 5), (27, 29), (28, 27), (23, 1), (15, 20), (11, 2), (5, 16), (31, 7), (3, 6), (6, 19), (18, 5), (32, 3), (26, 29), (4, 19), (7, 14), (5, 19), (16, 19), (3, 28), (8, 10), (5, 2), (31, 20), (13, 0), (27, 13), (10, 29), (16, 13), (21, 9), (0, 22), (15, 27), (31, 2), (7, 21), (30, 15), (25, 27), (23, 11), (17, 25), (8, 18), (12, 14), (3, 5), (25, 20), (4, 23), (16, 25), (12, 10), (23, 3), (26, 1), (24, 9), (13, 17), (25, 25), (12, 3), (7, 13), (17, 24), (4, 29), (0, 28), (6, 25), (1, 7), (6, 7), (27, 15), (14, 9), (9, 21), (12, 28), (22, 26), (19, 16), (11, 23), (19, 2), (14, 5), (17, 9), (12, 0), (21, 5), (16, 3), (28, 26), (0, 5), (12, 13), (3, 24), (5, 15), (10, 27), (19, 10), (8, 27), (28, 3), (3, 2), (6, 10), (30, 24), (14, 25), (1, 15), (4, 3), (19, 24), (10, 21), (19, 11), (22, 2), (17, 0), (15, 11), (2, 26), (7, 12), (10, 25), (11, 21), (30, 5), (32, 4), (21, 28), (0, 12), (22, 20), (28, 1), (2, 25), (8, 9), (4, 12), (16, 16), (0, 27), (1, 28), (11, 11), (22, 3), (13, 26), (18, 24), (9, 24), (30, 21), (25, 22), (2, 3), (6, 28), (22, 8), (26, 25), (23, 0), (10, 3), (29, 23), (9, 5), (30, 20), (1, 21), (13, 19), (4, 1), (15, 25), (21, 12), (16, 21), (2, 24), (1, 25), (26, 7), (10, 23), (9, 14), (21, 3), (24, 22), (1, 23), (13, 16), (24, 28), (3, 12), (23, 10), (14, 27), (22, 27), (15, 29), (7, 17), (25, 3), (8, 21), (27, 3), (4, 13), (18, 2), (25, 14), (17, 29), (22, 7), (8, 22), (6, 4), (23, 26), (22, 1), (13, 22), (29, 27), (29, 22), (28, 9), (12, 8), (19, 26), (12, 21), (0, 4), (27, 21), (27, 12), (22, 0), (24, 27), (6, 29), (31, 17), (29, 1), (23, 19), (32, 2), (24, 5), (20, 29), (9, 8), (16, 26), (31, 25), (29, 25), (0, 26), (15, 4), (13, 20), (0, 29), (17, 5), (15, 18), (13, 4), (31, 4), (7, 3), (28, 10), (11, 14), (17, 15), (13, 12), (4, 26), (30, 12), (31, 27), (27, 16), (8, 5), (14, 15), (11, 24), (16, 20), (11, 7), (24, 15), (19, 14), (6, 3), (18, 28), (14, 4), (3, 13), (3, 17), (11, 29), (20, 19), (25, 13), (29, 15), (1, 29), (18, 21), (19, 0), (23, 28), (31, 9), (0, 1), (31, 28), (2, 11), (25, 12), (9, 15), (24, 3), (14, 2), (22, 19), (14, 1), (2, 13), (5, 8), (13, 3), (2, 8), (13, 6), (22, 6), (7, 9), (21, 14), (3, 15), (21, 27), (27, 7), (16, 15), (32, 19), (21, 0), (32, 18), (18, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25920", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 33), (27, 3), (15, 18), (11, 10), (3, 4), (33, 26), (3, 31), (17, 34), (6, 10), (20, 21), (24, 11), (25, 29), (26, 8), (38, 17), (8, 0), (37, 27), (5, 15), (17, 7), (19, 16), (5, 1), (11, 35), (4, 14), (35, 7), (20, 36), (6, 11), (11, 30), (38, 19), (20, 25), (20, 3), (7, 12), (5, 25), (10, 30), (20, 10), (17, 6), (8, 20), (38, 5), (14, 20), (12, 32), (20, 29), (29, 25), (31, 21), (6, 5), (11, 36), (22, 10), (38, 23), (0, 23), (33, 19), (24, 30), (30, 12), (22, 20), (19, 14), (6, 6), (38, 13), (12, 1), (31, 35), (37, 1), (10, 34), (36, 36), (21, 37), (11, 5), (1, 17), (34, 24), (14, 24), (15, 25), (31, 28), (26, 26), (36, 10), (18, 36), (33, 31), (33, 15), (8, 16), (15, 12), (13, 35), (21, 16), (6, 17), (24, 24), (18, 4), (24, 34), (4, 5), (8, 19), (25, 28), (16, 0), (12, 6), (20, 4), (19, 35), (14, 36), (3, 8), (23, 17), (7, 19), (4, 37), (11, 22), (31, 25), (1, 36), (24, 13), (37, 9), (28, 34), (32, 7), (19, 30), (10, 21), (8, 27), (9, 29), (4, 28), (10, 26), (24, 17), (9, 2), (10, 0), (22, 19), (4, 34), (1, 28), (6, 23), (24, 21), (29, 9), (35, 9), (17, 16), (5, 14), (14, 14), (10, 8), (18, 19), (21, 8), (16, 33), (33, 11), (1, 0), (21, 15), (18, 6), (25, 2), (6, 31), (31, 12), (26, 34), (16, 30), (22, 14), (10, 27), (12, 33), (3, 35), (33, 29), (14, 21), (18, 0), (31, 26), (23, 2), (35, 10), (31, 17), (4, 1), (23, 3), (4, 10), (29, 14), (5, 9), (18, 25), (31, 7), (11, 7), (10, 25), (5, 18), (29, 32), (4, 7), (34, 15), (12, 5), (9, 13), (19, 34), (3, 37), (29, 31), (26, 1), (15, 28), (20, 6), (4, 0), (14, 29), (8, 17), (21, 27), (25, 33), (13, 23), (19, 22), (13, 21), (36, 28), (29, 26), (17, 18), (29, 1), (25, 23), (24, 5), (6, 27), (12, 34), (19, 25), (16, 20), (34, 20), (12, 9), (3, 25), (22, 17), (23, 19), (26, 36), (12, 17), (22, 36), (9, 17), (22, 28), (0, 30), (2, 34), (32, 22), (26, 15), (16, 4), (36, 37), (9, 30), (28, 19), (15, 35), (2, 32), (14, 32), (1, 27), (11, 31), (32, 25), (20, 19), (17, 17), (19, 10), (30, 16), (33, 22), (0, 37), (4, 30), (31, 11), (3, 1), (0, 11), (18, 9), (35, 19), (6, 34), (35, 34), (24, 18), (38, 28), (23, 13), (34, 0), (37, 34), (3, 30), (36, 9), (34, 32), (8, 35), (6, 32), (9, 15), (23, 8), (8, 33), (20, 18), (30, 1), (36, 21), (8, 23), (36, 35), (5, 37), (26, 35), (37, 14), (36, 23), (10, 15), (5, 11), (13, 25), (33, 8), (21, 20), (3, 27), (22, 22), (28, 20), (29, 6), (8, 24), (5, 21), (36, 0), (9, 12), (32, 33), (38, 11), (7, 20), (18, 13), (34, 8), (27, 7), (2, 37), (17, 15), (21, 18), (0, 36), (12, 8), (35, 25), (18, 37), (25, 0), (36, 1), (33, 35), (10, 12), (0, 7), (10, 37), (26, 25), (10, 17), (14, 4), (35, 32), (17, 33), (9, 1), (12, 36), (9, 28), (3, 32), (1, 13), (36, 7), (17, 20), (18, 17), (11, 29), (7, 31), (32, 27), (0, 2), (2, 4), (10, 23), (24, 9), (25, 27), (32, 11), (20, 37), (37, 31), (27, 11), (22, 6), (4, 8), (16, 8), (8, 4), (28, 33), (34, 17), (1, 11), (9, 7), (31, 33), (17, 22), (30, 30), (9, 6), (36, 27), (33, 6), (9, 34), (36, 24), (21, 23), (36, 22), (18, 12), (16, 37), (21, 17), (1, 19), (1, 30), (33, 21), (13, 16), (7, 16), (30, 29), (21, 36), (34, 4), (23, 37), (15, 10), (33, 12), (16, 10), (18, 27), (28, 25), (20, 24), (29, 16), (0, 3), (38, 1), (5, 16), (14, 16), (9, 33), (29, 8), (35, 37), (31, 34), (3, 23), (38, 18), (31, 19), (5, 36), (28, 6), (35, 30), (31, 1), (8, 5), (19, 21), (25, 21), (0, 18), (35, 13), (23, 27), (30, 17), (12, 22), (14, 34), (29, 37), (29, 19), (8, 1), (18, 26), (24, 31), (34, 37), (29, 4), (35, 0), (22, 31), (12, 28), (28, 13), (10, 20), (5, 33), (29, 10), (2, 18), (34, 7), (9, 24), (5, 13), (12, 13), (12, 2), (38, 32), (23, 9), (31, 22), (22, 7), (12, 16), (17, 30), (3, 3), (0, 32), (25, 35), (30, 31), (35, 27), (25, 17), (1, 4), (16, 31), (8, 32), (4, 29), (7, 14), (6, 22), (5, 0), (22, 21), (30, 9), (14, 5), (33, 0), (28, 27), (16, 15), (6, 29), (3, 34), (15, 36), (26, 17), (5, 32), (38, 29), (6, 12), (23, 25), (26, 33), (6, 24), (31, 10), (18, 31), (20, 0), (33, 16), (25, 24), (28, 35), (7, 24), (28, 9), (1, 34), (17, 27), (6, 14), (1, 21), (31, 4), (5, 24), (9, 32), (33, 14), (20, 14), (21, 13), (19, 3), (24, 29), (37, 25), (9, 37), (23, 5), (22, 8), (29, 35), (37, 20), (17, 12), (18, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632880", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), 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), (28, 8), (25, 17), (29, 33), (7, 32), (21, 29), (34, 9), (32, 13), (4, 1), (33, 17), (33, 1), (7, 9), (13, 12), (12, 4), (27, 25), (11, 38), (15, 26), (12, 25), (25, 31), (31, 3), (22, 16), (34, 21), (18, 27), (14, 13), (12, 13), (16, 26), (1, 10), (34, 14), (22, 33), (28, 31), (14, 23), (8, 25), (31, 19), (36, 19), (4, 27), (0, 19), (18, 24), (33, 27), (14, 35), (38, 25), (21, 9), (9, 9), (24, 12), (8, 8), (19, 36), (3, 22), (30, 13), (32, 11), (30, 21), (7, 5), (38, 17), (12, 27), (17, 32), (19, 35), (12, 21), (34, 36), (15, 22), (3, 2), (33, 29), (5, 36), (24, 8), (30, 10), (24, 5), (28, 23), (24, 16), (30, 6), (11, 10), (15, 14), (15, 36), (22, 27), (14, 15), (15, 28), (7, 35), (22, 17), (5, 22), (9, 23), (24, 20), (32, 32), (17, 23), (34, 33), (22, 31), (35, 28), (19, 5), (38, 15), (27, 36), (24, 3), (18, 17), (28, 12), (31, 35), (12, 36), (4, 26), (9, 21), (10, 0), (12, 35), (19, 20), (0, 12), (7, 38), (8, 9), (11, 28), (16, 36), (17, 18), (34, 17), (22, 30), (26, 24), (19, 4), (17, 11), (26, 7), (11, 24), (23, 29), (15, 18), (13, 2), (28, 15), (10, 3), (4, 14), (16, 19), (1, 20), (27, 37), (9, 32), (0, 20), (14, 33), (16, 14), (16, 13), (12, 5), (19, 8), (11, 16), (18, 14), (21, 30), (35, 5), (14, 11), (7, 14), (30, 26), (33, 33), (35, 27), (2, 4), (20, 16), (18, 33), (35, 12), (13, 16), (23, 32), (3, 4), (14, 24), (11, 26), (30, 3), (29, 13), (11, 0), (8, 20), (11, 35), (34, 0), (20, 37), (30, 31), (26, 18), (26, 29), (3, 1), (2, 12), (37, 17), (36, 5), (27, 26), (13, 38), (1, 31), (25, 29), (3, 12), (37, 8), (35, 17), (21, 28), (15, 20), (9, 4), (16, 23), (36, 23), (10, 15), (4, 24), (25, 36), (16, 8), (23, 22), (7, 11), (9, 25), (27, 16), (25, 16), (21, 26), (22, 24), (38, 20), (0, 18), (17, 16), (21, 14), (18, 26), (37, 18), (9, 20), (30, 11), (10, 1), (31, 2), (27, 27), (3, 36), (36, 26), (15, 12), (37, 22), (22, 8), (21, 20), (16, 22), (17, 9), (9, 1), (0, 14), (27, 15), (20, 35), (0, 8), (38, 19), (16, 0), (21, 5), (34, 28), (6, 12), (17, 31), (31, 13), (23, 19), (3, 29), (14, 20), (28, 36), (37, 13), (15, 17), (3, 26), (19, 6), (25, 38), (16, 6), (1, 34), (23, 3), (35, 16), (26, 32), (5, 8), (34, 1), (23, 38), (36, 27), (15, 11), (21, 22), (17, 5), (19, 31), (20, 22), (1, 12), (35, 31), (27, 4), (32, 28), (32, 17), (23, 15), (8, 3), (7, 8), (24, 22), (11, 5), (24, 30), (26, 3), (12, 12), (16, 35), (18, 16), (28, 21), (30, 34), (23, 33), (19, 37), (10, 20), (13, 4), (0, 26), (22, 25), (25, 26), (33, 9), (24, 18), (38, 16), (14, 16), (11, 34), (24, 25), (28, 13), (7, 16), (5, 23), (17, 3), (20, 12), (18, 36), (31, 23), (17, 25), (18, 29), (17, 6), (37, 21), (20, 38), (31, 5), (5, 31), (3, 30), (32, 27), (24, 14), (27, 23), (38, 10), (8, 36), (4, 33), (14, 28), (7, 13), (5, 6), (3, 31), (0, 36), (7, 12), (12, 32), (22, 23), (6, 3), (30, 23), (37, 25), (33, 21), (6, 22), (19, 3), (1, 30), (20, 26), (24, 13), (36, 33), (11, 4), (1, 24), (24, 9), (37, 4), (25, 2), (33, 19), (18, 6), (12, 17), (2, 35), (19, 22), (10, 30), (2, 17), (27, 3), (19, 13), (23, 26), (24, 31), (33, 13), (10, 7), (33, 4), (32, 20), (28, 3), (32, 16), (32, 21), (27, 11), (36, 34), (8, 23), (22, 12), (13, 7), (6, 2), (6, 28), (21, 8), (33, 34), (11, 32), (35, 13), (6, 9), (10, 11), (26, 8), (5, 3), (30, 20), (23, 24), (0, 29), (30, 28), (22, 14), (22, 38), (2, 1), (31, 7), (33, 30), (4, 17), (29, 12), (10, 9), (0, 2), (10, 22), (29, 11), (13, 21), (36, 2), (4, 30), (32, 22), (10, 35), (0, 17), (24, 2), (36, 17), (24, 7), (36, 6), (20, 17), (9, 34), (2, 11), (14, 7), (3, 16), (12, 20), (0, 21), (23, 17), (36, 35), (34, 11), (2, 9), (32, 0), (17, 27), (38, 22), (22, 36), (25, 14), (19, 21), (31, 22), (34, 2), (28, 28), (21, 31), (8, 6), (3, 0), (9, 11), (16, 5), (38, 13), (20, 30), (19, 9), (35, 35), (1, 11), (32, 26), (23, 27), (25, 9), (12, 33), (34, 8), (4, 19), (36, 13), (5, 5), (31, 18), (34, 4), (9, 35), (32, 2), (10, 37), (31, 9), (13, 24), (28, 30), (32, 36), (33, 3), (3, 7), (1, 25), (11, 33), (23, 16), (30, 0), (30, 36), (38, 29), (29, 1), (9, 22), (13, 32), (5, 0), (22, 15), (10, 12), (32, 31), (36, 18), (21, 13), (8, 13), (1, 19), (22, 7), (15, 7), (29, 24), (37, 16), (10, 14), (10, 2), (13, 35), (19, 11), (23, 31), (22, 29), (29, 9), (36, 16), (1, 3), (19, 0), (34, 7), (15, 37), (29, 35), (22, 3), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355152", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (6, 3), (24, 7), (27, 13), (2, 4), (10, 29), (27, 32), (3, 4), (10, 25), (19, 17), (9, 5), (15, 16), (16, 19), (30, 7), (13, 15), (32, 0), (25, 29), (9, 11), (10, 33), (29, 28), (31, 16), (14, 24), (4, 33), (13, 12), (2, 5), (22, 25), (17, 3), (4, 31), (17, 20), (18, 22), (27, 16), (21, 12), (13, 10), (16, 33), (10, 31), (22, 18), (11, 7), (21, 29), (8, 7), (24, 24), (30, 33), (25, 11), (31, 21), (11, 27), (5, 9), (26, 21), (23, 21), (26, 27), (31, 32), (4, 22), (23, 8), (28, 9), (21, 34), (13, 26), (9, 7), (8, 11), (16, 8), (31, 35), (23, 0), (11, 3), (6, 32), (18, 9), (17, 34), (20, 4), (20, 16), (6, 35), (24, 6), (6, 33), (2, 11), (5, 24), (23, 4), (9, 26), (5, 10), (23, 22), (9, 6), (25, 15), (11, 25), (8, 21), (11, 12), (22, 24), (0, 2), (31, 2), (28, 34), (5, 28), (11, 6), (6, 9), (5, 15), (23, 34), (7, 17), (6, 11), (30, 27), (23, 11), (21, 30), (0, 30), (28, 0), (20, 33), (4, 30), (13, 34), (17, 13), (27, 14), (17, 17), (3, 19), (13, 28), (8, 30), (30, 2), (16, 29), (2, 17), (25, 25), (16, 0), (17, 30), (19, 26), (16, 34), (1, 32), (26, 18), (5, 18), (5, 34), (29, 7), (21, 25), (20, 35), (22, 27), (29, 22), (27, 3), (30, 18), (10, 3), (15, 0), (29, 24), (11, 16), (30, 15), (32, 18), (29, 20), (26, 26), (28, 35), (22, 19), (26, 16), (25, 23), (22, 0), (13, 25), (17, 23), (10, 5), (0, 6), (7, 32), (25, 7), (17, 35), (5, 11), (11, 2), (29, 14), (11, 31), (16, 11), (11, 35), (23, 28), (4, 4), (0, 18), (22, 20), (26, 0), (7, 35), (29, 9), (15, 35), (22, 3), (8, 2), (5, 23), (3, 31), (19, 15), (12, 21), (15, 23), (1, 21), (21, 26), (24, 23), (19, 11), (20, 29), (0, 28), (22, 32), (8, 8), (26, 33), (23, 16), (4, 17), (28, 1), (20, 34), (13, 19), (13, 35), (30, 8), (27, 27), (21, 24), (15, 30), (12, 7), (14, 23), (0, 17), (15, 19), (28, 26), (22, 22), (11, 21), (2, 13), (31, 6), (25, 12), (20, 32), (18, 5), (26, 2), (32, 24), (15, 31), (21, 10), (5, 14), (16, 15), (13, 23), (6, 18), (15, 22), (5, 8), (30, 14), (21, 3), (29, 6), (24, 25), (5, 12), (24, 33), (29, 32), (27, 11), (29, 1), (26, 9), (24, 1), (9, 27), (12, 10), (5, 17), (21, 0), (13, 27), (25, 24), (28, 25), (19, 1), (0, 32), (27, 17), (19, 27), (19, 5), (3, 20), (31, 24), (16, 14), (19, 16), (2, 28), (9, 15), (1, 14), (26, 35), (1, 11), (18, 19), (14, 32), (6, 21), (4, 13), (7, 28), (7, 20), (31, 34), (3, 15), (24, 17), (22, 4), (31, 19), (32, 13), (7, 7), (1, 12), (25, 3), (1, 27), (32, 26), (32, 19), (4, 2), (23, 3), (2, 25), (14, 16), (28, 30), (27, 1), (30, 26), (32, 22), (14, 7), (28, 14), (28, 4), (3, 22), (31, 22), (6, 19), (29, 30), (20, 13), (11, 17), (23, 7), (3, 13), (3, 25), (23, 2), (24, 14), (9, 29), (19, 21), (23, 24), (26, 13), (28, 24), (4, 27), (3, 34), (17, 29), (1, 15), (29, 8), (28, 23), (19, 18), (32, 17), (30, 28), (24, 16), (6, 13), (26, 14), (28, 10), (25, 19), (18, 10), (8, 16), (2, 20), (20, 9), (9, 12), (20, 28), (15, 14), (0, 8), (22, 28), (25, 0), (2, 24), (32, 5), (11, 0), (0, 24), (14, 3), (13, 33), (25, 17), (8, 9), (18, 12), (22, 21), (22, 16), (4, 1), (32, 28), (18, 2), (28, 21), (19, 30), (21, 33), (11, 11), (26, 5), (8, 31), (3, 28), (7, 34), (23, 32), (11, 33), (12, 11), (18, 35), (1, 9), (17, 6), (12, 26), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 18), (20, 0), (14, 5), (2, 20), (6, 8), (19, 3), (22, 31), (5, 18), (11, 4), (12, 25), (13, 1), (15, 23), (10, 11), (13, 18), (13, 24), (9, 7), (29, 9), (10, 2), (27, 5), (29, 5), (22, 35), (22, 12), (14, 19), (27, 35), (20, 4), (11, 0), (11, 9), (15, 27), (7, 36), (0, 9), (4, 16), (4, 23), (8, 18), (19, 23), (11, 13), (14, 35), (15, 9), (14, 20), (22, 26), (17, 29), (9, 24), (9, 9), (25, 16), (6, 1), (1, 3), (27, 15), (25, 6), (21, 19), (10, 17), (23, 16), (11, 14), (17, 8), (10, 12), (26, 6), (2, 25), (14, 1), (24, 30), (4, 29), (0, 11), (27, 18), (15, 15), (26, 0), (29, 26), (15, 2), (5, 26), (7, 23), (14, 27), (27, 23), (11, 25), (26, 26), (18, 19), (21, 3), (29, 30), (4, 35), (17, 12), (18, 31), (4, 22), (19, 9), (28, 34), (3, 2), (1, 15), (22, 28), (0, 13), (14, 17), (5, 8), (22, 14), (2, 8), (10, 21), (16, 9), (23, 22), (6, 27), (4, 31), (28, 4), (2, 7), (25, 19), (2, 13), (4, 21), (21, 20), (12, 12), (14, 34), (3, 35), (20, 24), (17, 23), (14, 29), (21, 14), (13, 3), (3, 33), (9, 1), (6, 6), (8, 26), (3, 32), (8, 6), (21, 9), (6, 24), (19, 6), (13, 19), (14, 2), (24, 17), (24, 12), (12, 10), (6, 0), (18, 9), (5, 14), (13, 15), (13, 20), (4, 32), (2, 9), (3, 10), (2, 27), (16, 25), (4, 28), (7, 9), (0, 7), (20, 31), (19, 0), (27, 26), (9, 29), (1, 22), (28, 11), (13, 35), (19, 28), (17, 24), (12, 8), (26, 11), (26, 35), (5, 21), (24, 28), (23, 26), (0, 24), (22, 24), (23, 10), (9, 12), (29, 27), (2, 3), (1, 12), (28, 15), (26, 24), (16, 36), (10, 32), (23, 35), (10, 10), (12, 24), (3, 16), (20, 26), (10, 34), (3, 13), (17, 33), (4, 1), (14, 32), (26, 10), (28, 27), (5, 33), (4, 30), (13, 0), (14, 0), (20, 14), (24, 6), (1, 16), (23, 0), (13, 4), (1, 10), (6, 29), (9, 18), (24, 23), (16, 18), (10, 29), (6, 33), (25, 11), (16, 12), (19, 12), (8, 5), (6, 16), (11, 34), (12, 21), (5, 34), (16, 26), (14, 28), (6, 12), (15, 7), (19, 29), (26, 28), (2, 29), (3, 12), (7, 32), (23, 17), (2, 35), (19, 2), (23, 34), (23, 11), (0, 19), (17, 14), (25, 2), (19, 22), (15, 33), (5, 22), (21, 33), (4, 25), (28, 29), (13, 11), (10, 22), (9, 22), (21, 18), (12, 35), (15, 3), (14, 3), (27, 0), (14, 18), (25, 1), (21, 12), (20, 11), (0, 10), (22, 34), (19, 15), (1, 35), (1, 23), (26, 33), (19, 17), (28, 32), (28, 13), (22, 17), (15, 13), (19, 36), (17, 28), (27, 6), (1, 18), (14, 15), (10, 30), (7, 10), (16, 21), (16, 2), (14, 8), (8, 17), (19, 31), (0, 1), (22, 27), (11, 36), (27, 12), (23, 2), (11, 23), (0, 36), (13, 13), (0, 27), (3, 20), (24, 34), (6, 23), (21, 35), (19, 24), (26, 27), (18, 33), (14, 26), (15, 21), (21, 36), (12, 7), (1, 6), (21, 29), (20, 21), (8, 32), (8, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380160", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), 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), (13, 28), (6, 11), (8, 30), (30, 0), (10, 10), (16, 24), (30, 29), (26, 9), (16, 34), (12, 25), (31, 15), (26, 6), (21, 11), (26, 27), (13, 10), (26, 2), (8, 3), (10, 15), (28, 20), (0, 20), (0, 24), (8, 10), (7, 27), (12, 4), (21, 19), (15, 30), (20, 22), (23, 12), (18, 25), (7, 29), (24, 9), (24, 28), (2, 9), (3, 8), (1, 19), (16, 21), (29, 14), (22, 19), (16, 12), (3, 5), (21, 21), (26, 17), (9, 19), (11, 29), (27, 3), (11, 1), (12, 30), (12, 18), (15, 20), (6, 27), (18, 16), (15, 16), (10, 0), (10, 22), (19, 6), (29, 16), (23, 20), (21, 26), (20, 2), (20, 9), (23, 30), (5, 23), (11, 30), (22, 24), (30, 14), (25, 7), (27, 7), (13, 8), (25, 18), (5, 1), (1, 31), (24, 14), (2, 13), (21, 32), (5, 4), (19, 29), (4, 20), (23, 2), (6, 9), (9, 28), (17, 19), (1, 32), (4, 10), (9, 13), (5, 5), (24, 20), (24, 16), (9, 3), (0, 6), (25, 11), (9, 17), (17, 1), (27, 21), (5, 16), (29, 0), (27, 16), (17, 4), (22, 28), (31, 10), (29, 24), (9, 12), (28, 13), (7, 19), (27, 34), (16, 19), (1, 21), (28, 19), (21, 1), (10, 31), (6, 5), (20, 8), (9, 31), (2, 11), (19, 16), (16, 16), (2, 15), (24, 26), (11, 27), (12, 1), (30, 32), (13, 31), (19, 21), (0, 4), (30, 28), (20, 1), (24, 19), (13, 29), (24, 31), (6, 31), (31, 30), (28, 27), (4, 19), (3, 6), (3, 26), (13, 11), (22, 27), (13, 24), (9, 5), (9, 18), (22, 0), (30, 10), (10, 3), (25, 6), (7, 12), (14, 9), (18, 21), (0, 33), (22, 34), (25, 13), (0, 13), (17, 31), (1, 27), (19, 7), (29, 20), (8, 22), (13, 13), (30, 24), (29, 34), (18, 24), (17, 16), (18, 8), (26, 34), (6, 29), (28, 29), (24, 32), (7, 34), (28, 12), (25, 3), (31, 27), (9, 24), (4, 6), (24, 4), (29, 29), (13, 12), (3, 28), (2, 29), (2, 22), (25, 5), (0, 15), (25, 14), (29, 15), (8, 7), (27, 15), (23, 22), (28, 18), (24, 23), (29, 12), (31, 26), (5, 18), (15, 31), (24, 13), (22, 33), (26, 33), (3, 30), (3, 12), (26, 14), (20, 0), (3, 27), (6, 12), (4, 5), (7, 21), (3, 20), (28, 25), (18, 18), (17, 33), (28, 5), (31, 25), (1, 25), (1, 1), (17, 8), (30, 7), (7, 15), (17, 0), (12, 21), (1, 0), (4, 1), (27, 19), (3, 4), (16, 7), (23, 23), (28, 3), (30, 6), (6, 25), (4, 9), (2, 6), (10, 20), (18, 7), (15, 8), (18, 2), (0, 32), (30, 19), (19, 9), (20, 20), (30, 12), (31, 28), (4, 32), (5, 20), (12, 24), (12, 23), (31, 1), (10, 23), (13, 0), (9, 4), (11, 34), (1, 8), (7, 31), (17, 23), (14, 28), (14, 22), (25, 31), (26, 18), (13, 16), (9, 33), (15, 19), (25, 9), (20, 10), (10, 32), (12, 26), (1, 18), (0, 34), (28, 30), (0, 29), (30, 13), (25, 26), (28, 33), (21, 34), (16, 26), (19, 30), (30, 4), (6, 3), (16, 28), (12, 11), (18, 14), (10, 9), (6, 34), (8, 21), (23, 14), (0, 3), (21, 9), (15, 15), (21, 25), (24, 10), (16, 22), (21, 20), (5, 0), (23, 32), (31, 0), (26, 31), (18, 26), (22, 11), (7, 28), (25, 17), (7, 4), (30, 22), (6, 15), (9, 25), (8, 24), (23, 0), (27, 28), (25, 15), (27, 17), (5, 31), (2, 25), (10, 33), (5, 17), (10, 12), (6, 22), (20, 29), (29, 4), (4, 8), (12, 8), (29, 21), (7, 18), (19, 1), (11, 32), (7, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "791560", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 13), (4, 13), (0, 12), (26, 8), (0, 29), (14, 16), (29, 3), (2, 18), (26, 27), (23, 2), (24, 30), (26, 9), (25, 22), (25, 27), (1, 27), (18, 17), (23, 0), (18, 14), (1, 5), (27, 12), (5, 20), (9, 9), (3, 7), (26, 21), (21, 14), (9, 20), (29, 11), (28, 29), (8, 10), (3, 27), (12, 10), (27, 14), (3, 28), (24, 4), (7, 20), (27, 26), (21, 22), (12, 6), (13, 26), (12, 25), (20, 20), (28, 17), (9, 14), (19, 23), (10, 23), (23, 8), (12, 5), (26, 19), (10, 29), (25, 6), (30, 15), (18, 12), (11, 26), (14, 12), (26, 4), (25, 14), (13, 6), (7, 16), (14, 3), (31, 5), (9, 5), (4, 22), (5, 3), (6, 26), (13, 20), (6, 17), (21, 12), (15, 30), (16, 23), (30, 21), (30, 29), (14, 8), (1, 16), (12, 2), (27, 4), (22, 15), (12, 14), (1, 10), (15, 29), (30, 1), (2, 2), (2, 1), (4, 4), (19, 5), (19, 24), (19, 27), (9, 18), (10, 25), (19, 6), (21, 25), (4, 5), (23, 10), (23, 7), (24, 12), (16, 18), (28, 25), (3, 5), (30, 11), (30, 12), (12, 26), (27, 28), (8, 23), (13, 10), (24, 17), (14, 2), (12, 15), (1, 3), (31, 12), (31, 11), (1, 4), (31, 4), (8, 29), (30, 28), (18, 23), (23, 15), (0, 5), (2, 3), (27, 20), (18, 18), (24, 2), (1, 8), (13, 25), (28, 10), (9, 28), (6, 12), (17, 0), (25, 26), (3, 19), (22, 18), (0, 13), (17, 30), (11, 7), (11, 14), (27, 13), (15, 17), (24, 27), (16, 22), (31, 26), (6, 29), (22, 16), (14, 13), (14, 25), (7, 18), (30, 8), (14, 17), (21, 17), (4, 16), (31, 10), (15, 25), (27, 17), (8, 11), (19, 22), (6, 2), (27, 1), (15, 15), (20, 0), (16, 17), (14, 21), (17, 5), (14, 14), (11, 6), (9, 15), (4, 29), (8, 30), (3, 26), (3, 8), (0, 23), (8, 21), (2, 28), (4, 8), (30, 13), (10, 24), (18, 20), (6, 19), (2, 13), (14, 15), (21, 10), (23, 22), (25, 15), (18, 25), (9, 10), (11, 2), (12, 13), (8, 27), (19, 16), (18, 8), (9, 1), (25, 1), (12, 20), (20, 8), (26, 0), (9, 29), (23, 29), (27, 22), (20, 6), (13, 12), (26, 13), (4, 20), (30, 18), (8, 8), (13, 9), (16, 26), (1, 28), (12, 21), (9, 22), (2, 25), (19, 20), (19, 18), (21, 26), (15, 9), (2, 12), (9, 19), (28, 9), (6, 9), (31, 17), (23, 30), (27, 29), (18, 10), (8, 28), (11, 21), (31, 13), (2, 9), (2, 4), (28, 5), (16, 27), (26, 20), (4, 27), (0, 9), (24, 25), (28, 15), (5, 10), (10, 30), (14, 30), (9, 13), (14, 9), (29, 20), (26, 24), (5, 29), (0, 4), (15, 1), (11, 17), (22, 20), (4, 19), (31, 8), (7, 29), (23, 12), (10, 17), (22, 28), (17, 10), (18, 2), (4, 26), (28, 20), (17, 18), (7, 19), (1, 26), (3, 9), (12, 1), (24, 10), (5, 16), (23, 17), (3, 4), (9, 8), (26, 23), (9, 2), (25, 16), (4, 0), (29, 6), (23, 9), (11, 22), (19, 13), (6, 27), (15, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "856550", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (11, 8), (30, 11), (29, 29), (18, 19), (15, 4), (3, 19), (35, 17), (11, 29), (17, 18), (10, 8), (30, 9), (34, 21), (17, 23), (4, 0), (35, 2), (26, 24), (23, 14), (3, 31), (14, 29), (13, 30), (33, 18), (4, 10), (3, 8), (11, 4), (1, 21), (0, 16), (22, 11), (27, 10), (5, 16), (25, 33), (6, 2), (12, 18), (26, 32), (13, 33), (12, 20), (14, 17), (14, 23), (31, 31), (4, 18), (26, 16), (11, 11), (20, 10), (10, 34), (30, 22), (8, 31), (11, 34), (11, 19), (2, 6), (28, 22), (9, 34), (9, 13), (0, 18), (32, 4), (12, 9), (2, 34), (34, 14), (1, 8), (5, 6), (16, 32), (0, 29), (32, 17), (7, 9), (22, 28), (5, 29), (1, 5), (23, 10), (16, 19), (33, 33), (31, 14), (19, 9), (32, 23), (5, 24), (20, 5), (35, 30), (16, 22), (4, 4), (8, 25), (8, 24), (22, 17), (16, 4), (8, 7), (20, 29), (21, 10), (19, 12), (18, 25), (15, 34), (30, 4), (13, 31), (12, 24), (11, 20), (23, 24), (1, 19), (25, 6), (8, 10), (2, 23), (15, 15), (35, 7), (26, 5), (31, 21), (1, 32), (31, 25), (14, 12), (29, 14), (6, 32), (5, 10), (23, 1), (33, 2), (13, 19), (32, 13), (8, 29), (23, 2), (23, 8), (17, 1), (4, 13), (26, 27), (22, 9), (12, 22), (30, 34), (0, 4), (22, 30), (10, 12), (30, 29), (20, 11), (0, 26), (23, 7), (16, 15), (2, 29), (21, 27), (20, 7), (24, 31), (33, 28), (6, 22), (22, 22), (10, 10), (20, 26), (29, 3), (14, 18), (23, 3), (28, 0), (30, 6), (28, 27), (2, 28), (1, 0), (10, 32), (13, 13), (24, 0), (9, 32), (28, 25), (29, 34), (13, 22), (29, 5), (34, 4), (26, 1), (13, 12), (4, 11), (20, 0), (35, 19), (20, 17), (15, 20), (21, 0), (10, 16), (19, 22), (13, 8), (11, 5), (16, 20), (4, 16), (1, 3), (23, 25), (5, 26), (29, 4), (29, 20), (26, 8), (14, 3), (24, 22), (28, 2), (20, 13), (16, 7), (27, 14), (24, 3), (19, 25), (8, 28), (19, 21), (14, 2), (0, 30), (11, 1), (21, 25), (35, 29), (25, 24), (34, 32), (23, 33), (30, 20), (22, 6), (27, 6), (35, 6), (32, 15), (13, 16), (33, 8), (8, 34), (33, 16), (23, 23), (2, 22), (24, 2), (4, 7), (23, 22), (1, 28), (23, 17), (3, 5), (11, 24), (29, 27), (9, 11), (0, 6), (11, 10), (32, 9), (25, 28), (2, 33), (7, 11), (7, 4), (18, 2), (29, 24), (24, 10), (1, 25), (9, 26), (10, 17), (5, 23), (32, 29), (13, 26), (8, 1), (9, 14), (2, 31), (26, 7), (13, 27), (9, 22), (30, 8), (3, 22), (16, 8), (26, 33), (3, 24), (24, 14), (4, 26), (18, 28), (20, 25), (12, 1), (33, 27), (17, 0), (7, 32), (32, 25), (18, 4), (13, 23), (15, 26), (23, 34), (15, 9), (27, 34), (2, 13), (4, 15), (0, 32), (15, 3), (30, 12), (0, 2), (7, 14), (24, 5), (0, 15), (12, 34), (3, 1), (1, 2), (13, 15), (29, 11), (0, 8), (1, 13), (9, 3), (19, 0), (15, 28), (25, 3), (10, 11), (16, 9), (30, 27), (6, 31), (18, 29), (3, 28), (16, 27), (26, 19), (29, 26), (14, 34), (4, 24), (1, 9), (20, 3), (9, 28), (18, 14), (35, 24), (21, 8), (12, 19), (4, 3), (24, 32), (21, 5), (0, 22), (2, 24), (33, 14), (29, 31), (7, 19), (7, 28), (28, 26), (15, 25), (26, 4), (12, 6), (10, 31), (1, 6), (29, 28), (33, 29), (5, 11), (12, 26), (21, 20), (26, 18), (19, 30), (26, 20), (31, 0), (29, 32), (20, 19), (25, 21), (28, 31), (13, 7), (35, 14), (3, 13), (0, 11), (16, 24), (15, 13), (9, 20), (28, 5), (25, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "613800", "dataset": "MATH"}
{"messages": [{"content": "In a 39x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 36), (14, 30), (11, 25), (26, 18), (31, 24), (25, 4), (28, 2), (16, 37), (2, 4), (24, 0), (25, 19), (15, 4), (17, 9), (23, 33), (8, 7), (28, 38), (35, 6), (17, 37), (19, 8), (30, 1), (37, 25), (30, 37), (37, 30), (1, 2), (28, 25), (24, 22), (0, 13), (6, 10), (9, 16), (5, 1), (35, 3), (30, 34), (22, 33), (8, 1), (13, 21), (2, 34), (14, 31), (29, 26), (38, 30), (33, 29), (29, 15), (6, 11), (23, 22), (11, 10), (7, 12), (1, 30), (13, 25), (23, 5), (34, 34), (7, 8), (13, 5), (8, 28), (9, 22), (27, 29), (19, 29), (3, 31), (7, 27), (12, 18), (30, 14), (12, 12), (16, 8), (32, 21), (1, 29), (15, 27), (5, 6), (0, 32), (14, 4), (26, 30), (38, 6), (6, 16), (10, 33), (24, 5), (33, 6), (35, 27), (37, 24), (28, 19), (26, 27), (2, 11), (30, 8), (15, 16), (9, 17), (16, 2), (25, 17), (34, 4), (10, 15), (7, 6), (13, 24), (28, 7), (1, 14), (12, 19), (9, 4), (37, 35), (19, 24), (29, 21), (33, 30), (35, 0), (15, 9), (36, 35), (7, 29), (24, 8), (28, 4), (12, 30), (12, 24), (15, 10), (4, 23), (0, 21), (28, 5), (37, 8), (34, 28), (5, 36), (21, 38), (8, 30), (28, 17), (25, 37), (18, 17), (8, 23), (25, 26), (30, 3), (19, 5), (37, 13), (9, 6), (7, 17), (0, 26), (15, 0), (8, 27), (23, 8), (24, 2), (0, 24), (23, 1), (32, 30), (23, 19), (6, 37), (1, 11), (18, 27), (13, 11), (26, 26), (24, 38), (21, 25), (16, 1), (33, 33), (11, 26), (27, 30), (35, 10), (21, 9), (8, 5), (0, 16), (35, 38), (19, 6), (26, 16), (4, 18), (0, 25), (28, 6), (4, 19), (10, 27), (33, 24), (23, 12), (14, 24), (9, 27), (27, 28), (32, 38), (13, 16), (2, 7), (19, 21), (34, 18), (22, 12), (3, 20), (3, 4), (4, 16), (2, 31), (37, 6), (17, 20), (18, 29), (5, 15), (16, 14), (27, 4), (36, 32), (17, 15), (3, 17), (20, 12), (7, 28), (16, 21), (17, 23), (6, 30), (4, 28), (3, 9), (20, 21), (0, 29), (31, 3), (37, 3), (13, 32), (18, 38), (9, 21), (7, 36), (25, 24), (9, 38), (3, 11), (24, 3), (32, 13), (27, 31), (17, 11), (6, 0), (15, 36), (4, 14), (30, 32), (0, 19), (30, 35), (16, 26), (22, 16), (33, 17), (15, 38), (32, 32), (29, 2), (2, 6), (13, 7), (3, 2), (11, 17), (8, 21), (35, 5), (12, 13), (22, 18), (18, 5), (6, 9), (17, 6), (18, 13), (12, 25), (2, 9), (38, 2), (18, 28), (0, 4), (36, 2), (21, 35), (17, 32), (37, 23), (17, 25), (3, 36), (30, 19), (23, 3), (12, 38), (27, 18), (20, 11), (34, 14), (6, 15), (37, 32), (15, 33), (35, 14), (24, 21), (31, 20), (15, 3), (5, 12), (0, 9), (33, 4), (3, 10), (21, 11), (18, 22), (18, 9), (31, 9), (31, 6), (4, 5), (7, 33), (21, 2), (7, 4), (31, 7), (14, 1), (16, 31), (7, 31), (11, 0), (10, 4), (27, 8), (26, 24), (8, 32), (21, 24), (25, 1), (20, 4), (6, 32), (10, 2), (17, 14), (20, 32), (30, 10), (7, 3), (16, 12), (2, 14), (11, 29), (20, 19), (25, 33), (10, 14), (25, 14), (26, 36), (12, 3), (38, 13), (38, 4), (0, 30), (20, 14), (8, 2), (9, 10), (29, 24), (12, 5), (30, 36), (11, 8), (34, 15), (29, 14), (24, 15), (0, 33), (12, 32), (27, 9), (27, 25), (21, 32), (3, 7), (20, 29), (19, 3), (26, 10), (6, 20), (11, 33), (15, 23), (18, 34), (26, 28), (19, 4), (30, 21), (13, 29), (19, 16), (21, 8), (5, 21), (14, 9), (12, 20), (25, 23), (32, 3), (27, 35), (26, 37), (7, 0), (9, 0), (34, 19), (12, 21), (26, 14), (2, 17), (3, 1), (33, 32), (3, 6), (24, 7), (33, 7), (6, 38), (38, 22), (35, 9), (32, 14), (17, 1), (11, 7), (14, 25), (17, 24), (8, 9), (17, 5), (4, 34), (36, 0), (31, 34), (18, 15), (5, 34), (28, 10), (24, 9), (1, 36), (10, 30), (20, 13), (31, 19), (2, 10), (24, 17), (32, 29), (27, 36), (4, 32), (22, 15), (16, 25), (36, 25), (37, 29), (8, 24), (7, 32), (29, 28), (5, 38), (6, 8), (33, 3), (34, 27), (29, 25), (11, 31), (12, 4), (20, 9), (14, 19), (22, 27), (38, 11), (29, 1), (34, 5), (15, 25), (29, 37), (28, 22), (13, 31), (21, 36), (18, 19), (26, 33), (5, 0), (24, 10), (32, 5), (22, 1), (32, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "365148", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 4), (13, 9), (12, 3), (5, 15), (12, 9), (19, 28), (34, 23), (31, 12), (10, 5), (4, 22), (13, 8), (25, 25), (26, 14), (35, 12), (10, 7), (14, 8), (28, 0), (20, 14), (29, 28), (21, 29), (2, 21), (6, 2), (13, 33), (15, 0), (36, 16), (8, 12), (22, 28), (15, 19), (1, 8), (19, 29), (33, 4), (29, 0), (2, 32), (36, 1), (16, 5), (5, 10), (30, 3), (20, 12), (14, 26), (4, 1), (7, 12), (18, 21), (27, 8), (36, 31), (3, 27), (24, 9), (29, 7), (3, 17), (8, 9), (18, 5), (32, 24), (13, 2), (33, 13), (8, 22), (17, 33), (37, 9), (35, 19), (35, 26), (2, 8), (32, 32), (11, 1), (9, 17), (33, 27), (25, 8), (25, 20), (29, 14), (20, 9), (0, 33), (26, 10), (3, 24), (28, 29), (20, 20), (34, 18), (21, 23), (8, 25), (10, 29), (22, 0), (30, 0), (21, 14), (19, 16), (0, 10), (34, 3), (9, 0), (9, 15), (4, 21), (4, 3), (25, 31), (13, 6), (29, 11), (5, 11), (29, 13), (33, 16), (4, 32), (8, 30), (13, 25), (19, 12), (31, 27), (34, 14), (23, 10), (32, 21), (1, 33), (5, 31), (28, 9), (31, 7), (23, 32), (26, 3), (31, 2), (10, 6), (33, 30), (23, 5), (28, 7), (16, 22), (14, 11), (4, 25), (36, 2), (6, 21), (28, 2), (28, 5), (5, 6), (23, 29), (22, 23), (17, 26), (26, 1), (9, 32), (33, 10), (17, 21), (22, 25), (17, 27), (29, 3), (13, 16), (9, 9), (33, 28), (22, 24), (8, 33), (23, 23), (8, 17), (32, 10), (2, 18), (4, 33), (2, 9), (5, 28), (31, 19), (26, 19), (27, 31), (33, 15), (5, 8), (21, 19), (21, 0), (25, 1), (17, 19), (7, 1), (2, 20), (28, 31), (21, 13), (0, 20), (17, 20), (6, 15), (24, 17), (36, 9), (36, 10), (14, 22), (31, 26), (32, 26), (19, 19), (28, 4), (12, 19), (7, 18), (21, 1), (21, 21), (9, 6), (0, 9), (36, 0), (8, 6), (11, 3), (20, 19), (31, 11), (25, 29), (12, 11), (19, 20), (35, 11), (7, 11), (2, 14), (24, 20), (37, 28), (18, 25), (4, 27), (28, 28), (27, 16), (33, 21), (37, 29), (4, 28), (29, 9), (2, 5), (27, 22), (25, 11), (18, 22), (20, 29), (23, 16), (6, 17), (26, 23), (14, 5), (37, 20), (4, 5), (17, 13), (26, 6), (24, 5), (0, 24), (8, 21), (24, 33), (16, 26), (24, 30), (10, 31), (2, 12), (28, 10), (23, 4), (4, 16), (13, 10), (28, 6), (24, 10), (34, 4), (28, 22), (15, 15), (12, 4), (14, 18), (16, 6), (2, 10), (34, 30), (14, 24), (3, 21), (0, 15), (26, 18), (24, 3), (16, 31), (33, 17), (18, 31), (18, 24), (14, 0), (9, 13), (14, 12), (7, 33), (6, 0), (3, 20), (16, 29), (11, 19), (0, 8), (18, 10), (36, 4), (16, 20), (31, 22), (29, 23), (36, 13), (7, 7), (6, 32), (13, 18), (23, 30), (15, 30), (1, 22), (12, 7), (6, 30), (11, 9), (37, 4), (27, 28), (22, 2), (9, 8), (11, 27), (32, 4), (3, 23), (11, 23), (31, 31), (28, 26), (30, 32), (25, 30), (12, 16), (35, 13), (18, 30), (12, 14), (15, 5), (12, 24), (6, 10), (25, 18), (28, 19), (3, 9), (17, 2), (17, 6), (32, 6), (20, 13), (18, 18), (2, 3), (9, 16), (33, 18), (30, 25), (31, 28), (10, 25), (20, 16), (11, 32), (3, 22), (16, 14), (33, 19), (9, 1), (10, 24), (8, 0), (15, 25), (5, 7), (6, 5), (7, 13), (29, 12), (31, 23), (9, 4), (18, 0), (32, 8), (29, 26), (5, 13), (6, 16), (24, 8), (7, 0), (34, 12), (24, 6), (33, 32), (29, 18), (35, 10), (25, 32), (21, 27), (5, 4), (3, 2), (15, 28), (12, 8), (13, 3), (31, 30), (5, 21), (10, 19), (25, 28), (30, 14), (3, 6), (0, 7), (5, 22), (17, 24), (6, 25), (23, 28), (8, 27), (37, 21), (35, 14), (24, 2), (9, 7), (24, 21), (6, 11), (5, 9), (36, 3), (27, 9), (2, 28), (19, 30), (35, 31), (14, 32), (13, 4), (24, 28), (35, 29), (23, 14), (19, 1), (27, 17), (7, 23), (16, 7), (20, 5), (18, 29), (32, 3), (18, 8), (36, 20), (15, 13), (18, 32), (7, 17), (19, 4), (0, 16), (19, 14), (1, 10), (7, 27), (34, 1), (35, 16), (23, 15), (4, 20), (2, 1), (18, 13), (32, 5), (0, 21), (27, 4), (33, 2), (5, 30), (23, 3), (7, 3), (15, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "853776", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 31), (26, 4), (19, 15), (13, 17), (25, 34), (12, 0), (16, 1), (29, 14), (34, 24), (2, 33), (8, 12), (16, 6), (7, 11), (6, 33), (11, 22), (22, 10), (0, 32), (32, 6), (17, 26), (31, 20), (20, 29), (3, 33), (32, 29), (30, 30), (28, 0), (27, 15), (8, 34), (3, 29), (25, 19), (24, 0), (31, 17), (24, 2), (13, 31), (4, 6), (11, 26), (13, 26), (19, 4), (24, 21), (30, 32), (0, 22), (29, 15), (30, 1), (10, 30), (26, 32), (5, 17), (5, 16), (15, 13), (18, 6), (12, 12), (34, 5), (35, 20), (24, 3), (29, 19), (9, 12), (15, 23), (18, 31), (26, 28), (18, 14), (26, 17), (2, 4), (20, 28), (9, 27), (16, 28), (25, 33), (2, 5), (34, 15), (26, 19), (8, 29), (5, 20), (22, 34), (27, 32), (20, 13), (9, 7), (5, 28), (21, 3), (4, 28), (11, 34), (24, 34), (2, 9), (10, 7), (16, 32), (12, 9), (15, 22), (25, 13), (25, 5), (33, 20), (22, 27), (22, 25), (35, 4), (17, 1), (7, 18), (20, 26), (28, 26), (15, 18), (4, 20), (21, 26), (28, 5), (35, 24), (0, 21), (28, 9), (0, 1), (24, 1), (27, 21), (6, 9), (2, 11), (4, 22), (19, 16), (34, 30), (33, 24), (26, 2), (31, 24), (31, 19), (2, 0), (23, 31), (7, 32), (20, 7), (34, 0), (4, 7), (3, 16), (28, 14), (33, 6), (10, 31), (6, 15), (29, 12), (31, 3), (24, 20), (26, 0), (18, 15), (4, 32), (21, 19), (1, 7), (20, 30), (18, 33), (6, 3), (34, 8), (2, 34), (8, 31), (28, 32), (32, 34), (5, 29), (26, 26), (26, 30), (35, 31), (1, 32), (26, 15), (28, 23), (29, 24), (25, 27), (18, 28), (31, 12), (14, 9), (14, 2), (22, 29), (7, 16), (19, 28), (35, 1), (33, 18), (19, 17), (32, 12), (2, 2), (7, 0), (8, 24), (29, 21), (5, 34), (13, 5), (19, 21), (25, 3), (4, 0), (16, 31), (20, 18), (2, 18), (33, 34), (9, 13), (14, 24), (32, 4), (0, 23), (11, 23), (18, 3), (10, 2), (10, 34), (12, 10), (3, 27), (11, 21), (31, 0), (7, 7), (18, 34), (14, 19), (14, 34), (24, 32), (1, 31), (13, 22), (27, 25), (30, 27), (34, 32), (3, 11), (31, 22), (31, 8), (7, 2), (20, 17), (27, 6), (34, 25), (8, 5), (1, 30), (12, 19), (6, 20), (10, 9), (24, 8), (0, 28), (20, 15), (13, 16), (23, 12), (2, 20), (32, 13), (18, 1), (27, 0), (15, 28), (21, 20), (16, 27), (19, 18), (21, 22), (12, 15), (2, 10), (31, 31), (16, 11), (12, 6), (2, 14), (0, 6), (3, 20), (34, 6), (2, 19), (10, 24), (2, 17), (15, 9), (22, 17), (2, 21), (32, 3), (30, 4), (24, 11), (33, 12), (9, 22), (35, 17), (33, 26), (20, 33), (26, 18), (3, 18), (14, 11), (3, 12), (12, 21), (12, 25), (19, 12), (23, 32), (13, 4), (24, 14), (34, 31), (17, 14), (33, 15), (12, 7), (33, 28), (19, 8), (22, 0), (24, 22), (8, 4), (17, 0), (15, 29), (2, 7), (13, 21), (19, 6), (30, 8), (33, 31), (16, 22), (16, 14), (1, 33), (32, 20), (21, 23), (11, 3), (27, 22), (19, 9), (5, 9), (6, 27), (23, 30), (9, 3), (15, 2), (17, 9), (25, 23), (2, 8), (27, 24), (2, 12), (0, 18), (15, 5), (33, 3), (32, 2), (9, 26), (4, 12), (29, 22), (7, 25), (31, 11), (18, 26), (24, 4), (20, 6), (16, 33), (6, 30), (30, 3), (24, 28), (18, 10), (5, 22), (5, 11), (30, 21), (31, 2), (32, 28), (19, 1), (11, 25), (21, 16), (1, 10), (12, 29), (17, 6), (16, 20), (34, 20), (14, 23), (24, 25), (34, 11), (25, 2), (20, 27), (19, 31), (23, 7), (18, 0), (18, 24), (14, 29), (4, 11), (35, 12), (1, 11), (21, 29), (29, 16), (30, 20), (4, 21), (27, 26), (32, 1), (22, 2), (19, 0), (30, 10), (6, 18), (17, 20), (11, 7), (27, 5), (17, 12), (12, 17), (5, 33), (34, 14), (24, 33), (14, 1), (18, 11), (34, 18), (17, 10), (20, 34), (10, 26), (32, 7), (27, 16), (14, 27), (10, 6), (30, 22), (29, 28), (29, 11), (31, 15), (16, 8), (5, 32), (19, 22), (19, 30), (4, 24), (11, 32), (7, 24), (8, 3), (30, 16), (35, 23), (33, 9), (30, 6), (23, 4), (3, 17), (25, 12), (15, 33), (13, 7), (9, 4), (22, 9), (14, 14), (26, 11), (13, 32), (0, 7), (11, 10), (25, 6), (22, 7), (8, 11), (28, 29), (17, 16), (21, 17), (29, 18), (8, 9), (2, 1), (26, 1), (14, 26), (30, 2), (9, 5), (32, 10), (8, 8), (31, 7), (25, 31), (11, 19), (15, 12), (23, 34), (19, 3), (20, 1), (34, 17), (1, 27), (3, 34), (29, 13), (15, 1), (15, 10), (9, 16), (9, 0), (10, 27), (35, 10), (24, 31), (20, 25), (4, 19), (17, 24), (35, 7), (20, 2), (14, 20), (32, 22), (19, 20), (24, 18), (30, 13), (9, 20), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45360", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), 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), (1, 13), (33, 26), (20, 24), (17, 16), (32, 12), (18, 10), (11, 20), (26, 22), (10, 33), (29, 29), (5, 35), (16, 13), (26, 35), (22, 6), (23, 2), (25, 21), (26, 2), (3, 16), (1, 9), (15, 20), (28, 18), (13, 7), (9, 12), (20, 7), (15, 7), (24, 23), (12, 11), (23, 1), (1, 10), (22, 18), (25, 5), (3, 15), (21, 25), (6, 9), (24, 29), (1, 26), (18, 6), (19, 7), (9, 35), (9, 25), (5, 20), (17, 24), (34, 10), (16, 17), (1, 5), (14, 11), (28, 28), (21, 29), (10, 22), (31, 11), (34, 4), (12, 34), (29, 26), (18, 34), (12, 33), (5, 23), (29, 18), (15, 10), (8, 26), (15, 19), (11, 29), (11, 9), (5, 11), (26, 17), (33, 7), (14, 3), (13, 19), (3, 28), (34, 27), (21, 34), (17, 32), (15, 22), (3, 12), (3, 11), (31, 25), (28, 6), (14, 16), (15, 17), (5, 6), (16, 2), (12, 18), (27, 0), (25, 7), (18, 32), (15, 25), (32, 31), (18, 0), (2, 2), (28, 9), (1, 8), (33, 34), (27, 26), (13, 28), (22, 16), (7, 11), (3, 5), (10, 27), (18, 26), (8, 24), (16, 11), (6, 14), (23, 35), (32, 0), (15, 11), (29, 24), (33, 10), (6, 4), (9, 33), (0, 14), (10, 30), (2, 17), (9, 7), (3, 34), (33, 28), (6, 10), (24, 18), (16, 21), (12, 21), (9, 20), (5, 27), (6, 1), (20, 27), (7, 16), (1, 12), (22, 10), (8, 28), (29, 30), (7, 22), (19, 29), (27, 5), (21, 22), (28, 19), (23, 24), (5, 3), (32, 2), (26, 8), (0, 33), (22, 24), (23, 13), (32, 34), (33, 30), (33, 11), (30, 12), (31, 19), (29, 17), (0, 27), (12, 2), (10, 14), (11, 2), (6, 22), (23, 14), (32, 24), (8, 27), (29, 19), (32, 7), (20, 14), (2, 11), (10, 35), (19, 16), (19, 30), (21, 4), (7, 14), (20, 33), (23, 30), (17, 19), (10, 20), (15, 13), (28, 16), (11, 4), (8, 22), (23, 26), (11, 7), (14, 22), (30, 7), (1, 18), (13, 24), (31, 27), (32, 4), (10, 24), (25, 27), (11, 12), (24, 20), (15, 1), (3, 27), (11, 15), (31, 28), (33, 15), (24, 5), (8, 7), (10, 10), (27, 7), (16, 7), (15, 16), (8, 34), (4, 24), (17, 14), (4, 0), (29, 22), (11, 16), (25, 13), (11, 8), (33, 22), (0, 13), (9, 27), (5, 14), (33, 35), (30, 17), (29, 11), (26, 18), (8, 21), (28, 2), (14, 4), (20, 6), (28, 34), (12, 12), (3, 19), (14, 34), (30, 35), (31, 5), (1, 24), (27, 32), (32, 6), (26, 14), (4, 9), (26, 0), (10, 17), (17, 35), (13, 31), (20, 10), (14, 2), (27, 24), (34, 1), (5, 1), (34, 22), (31, 34), (5, 0), (23, 23), (12, 27), (20, 32), (4, 19), (6, 11), (19, 8), (26, 7), (26, 21), (1, 27), (10, 5), (22, 14), (30, 24), (28, 15), (18, 31), (16, 23), (21, 27), (7, 30), (27, 14), (5, 8), (28, 33), (30, 6), (32, 19), (1, 33), (14, 27), (20, 12), (26, 26), (6, 27), (0, 35), (23, 21), (18, 18), (2, 27), (8, 8), (29, 23), (18, 2), (20, 35), (6, 20), (27, 16), (16, 10), (7, 8), (24, 17), (15, 32), (30, 28), (6, 24), (17, 31), (12, 26), (2, 31), (30, 19), (34, 21), (26, 23), (19, 23), (5, 16), (4, 27), (28, 30), (16, 28), (12, 29), (15, 9), (25, 19), (31, 1), (2, 19), (19, 19), (7, 32), (1, 3), (12, 6), (19, 26), (30, 16), (29, 27), (20, 22), (24, 15), (26, 29), (4, 2), (2, 1), (13, 13), (4, 35), (31, 14), (3, 35), (14, 7), (17, 15), (0, 5), (28, 25), (13, 3), (7, 29), (29, 32), (18, 15), (14, 25), (26, 13), (27, 21), (9, 2), (18, 20), (5, 7), (7, 26), (11, 14), (28, 27), (31, 2), (12, 24), (18, 21), (34, 20), (18, 1), (30, 27), (7, 35), (12, 35), (23, 19), (16, 32), (32, 35), (4, 21), (18, 7), (25, 11), (15, 21), (12, 30), (10, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "629100", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 26), (19, 5), (13, 18), (17, 19), (5, 27), (24, 22), (12, 22), (6, 12), (16, 3), (23, 11), (24, 19), (11, 2), (18, 18), (21, 26), (14, 5), (3, 8), (5, 23), (3, 9), (7, 6), (27, 2), (1, 5), (21, 3), (3, 29), (17, 1), (10, 14), (23, 20), (17, 9), (22, 26), (14, 2), (26, 10), (19, 10), (25, 11), (21, 20), (25, 14), (22, 22), (26, 1), (24, 16), (20, 11), (27, 20), (4, 26), (2, 21), (23, 28), (22, 9), (0, 16), (2, 7), (7, 30), (15, 7), (3, 12), (0, 27), (27, 8), (11, 8), (15, 19), (24, 2), (24, 23), (6, 9), (14, 0), (23, 12), (9, 20), (18, 13), (8, 24), (22, 1), (6, 26), (28, 25), (11, 10), (26, 3), (29, 11), (24, 27), (18, 23), (24, 9), (19, 0), (23, 30), (1, 3), (15, 23), (0, 4), (19, 30), (29, 13), (28, 13), (18, 16), (22, 20), (28, 24), (13, 28), (7, 18), (29, 19), (21, 19), (25, 0), (1, 19), (10, 27), (26, 5), (27, 9), (17, 0), (26, 4), (9, 16), (21, 28), (9, 29), (3, 2), (3, 27), (26, 9), (9, 28), (18, 19), (12, 12), (18, 26), (0, 3), (12, 10), (20, 4), (28, 2), (10, 9), (8, 12), (12, 16), (24, 1), (16, 18), (10, 26), (3, 7), (18, 5), (6, 14), (20, 6), (4, 19), (23, 26), (5, 12), (2, 25), (4, 5), (17, 16), (19, 21), (10, 6), (22, 15), (6, 3), (29, 28), (18, 20), (25, 10), (3, 22), (1, 24), (12, 25), (19, 28), (7, 26), (9, 0), (10, 1), (5, 28), (17, 25), (15, 14), (22, 14), (26, 6), (12, 4), (25, 24), (27, 29), (29, 21), (4, 8), (0, 7), (3, 28), (7, 22), (6, 16), (7, 19), (1, 26), (8, 14), (2, 12), (17, 14), (27, 14), (21, 18), (29, 16), (26, 13), (26, 20), (29, 5), (28, 16), (17, 5), (21, 2), (19, 14), (29, 27), (12, 7), (27, 25), (22, 0), (16, 10), (5, 6), (11, 29), (18, 9), (20, 28), (7, 23), (11, 15), (5, 8), (10, 7), (18, 28), (27, 24), (17, 24), (23, 23), (24, 8), (29, 24), (13, 11), (19, 22), (4, 0), (4, 21), (1, 0), (21, 12), (23, 10), (26, 18), (23, 5), (16, 1), (18, 22), (22, 29), (23, 22), (23, 1), (12, 11), (17, 4), (24, 6), (28, 7), (28, 19), (10, 30), (9, 3), (21, 14), (4, 4), (27, 15), (13, 0), (23, 8), (19, 2), (4, 15), (13, 30), (12, 19), (18, 1), (10, 19), (17, 2), (17, 21), (3, 23), (4, 10), (5, 1), (23, 21), (14, 24), (22, 16), (20, 27), (19, 24), (19, 3), (27, 5), (14, 10), (21, 17), (7, 17), (27, 13), (5, 26), (27, 7), (9, 10), (13, 13), (24, 17), (16, 28), (3, 20), (15, 13), (0, 15), (29, 12), (2, 11), (3, 26), (6, 25), (22, 21), (13, 26), (6, 22), (25, 6), (9, 9), (23, 2), (1, 29), (16, 5), (13, 3), (8, 28), (16, 9), (25, 13), (16, 2), (17, 29), (7, 8), (21, 5), (23, 13), (22, 24), (15, 9), (27, 17), (22, 17), (27, 0), (26, 28), (18, 6), (8, 23), (29, 22), (25, 5), (20, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "805000", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 10), (10, 20), (8, 14), (8, 5), (17, 0), (33, 28), (8, 7), (15, 7), (11, 0), (34, 11), (28, 5), (11, 33), (15, 16), (23, 21), (1, 23), (23, 8), (14, 1), (32, 24), (8, 36), (0, 31), (10, 30), (29, 10), (29, 30), (20, 26), (32, 8), (0, 19), (32, 13), (32, 21), (25, 17), (25, 18), (13, 10), (12, 11), (1, 37), (7, 36), (18, 0), (6, 20), (30, 20), (1, 4), (30, 25), (4, 38), (34, 37), (6, 6), (10, 16), (31, 20), (31, 38), (9, 3), (21, 15), (16, 25), (4, 32), (8, 35), (32, 33), (22, 9), (27, 28), (2, 21), (33, 35), (15, 6), (6, 1), (17, 3), (24, 27), (33, 32), (0, 35), (19, 24), (14, 22), (23, 0), (22, 34), (5, 12), (2, 33), (21, 7), (12, 18), (15, 19), (1, 1), (15, 33), (29, 13), (14, 6), (11, 20), (32, 5), (21, 1), (3, 21), (24, 23), (27, 38), (30, 18), (22, 38), (32, 31), (20, 21), (8, 16), (23, 9), (9, 6), (9, 32), (4, 30), (29, 7), (0, 2), (18, 19), (16, 7), (22, 23), (7, 5), (34, 27), (26, 9), (29, 22), (4, 5), (16, 27), (16, 28), (6, 36), (35, 22), (25, 25), (0, 26), (5, 3), (1, 28), (33, 8), (24, 33), (20, 15), (16, 5), (29, 0), (7, 22), (17, 4), (26, 0), (11, 34), (9, 25), (10, 17), (33, 23), (24, 17), (15, 20), (28, 23), (13, 22), (23, 7), (10, 2), (23, 11), (17, 6), (28, 20), (4, 15), (8, 2), (32, 7), (33, 21), (23, 27), (0, 34), (13, 15), (12, 6), (12, 26), (17, 31), (26, 32), (9, 33), (15, 12), (14, 37), (5, 34), (29, 11), (29, 32), (27, 26), (15, 28), (9, 29), (4, 28), (0, 32), (0, 3), (34, 22), (20, 12), (8, 0), (19, 7), (32, 16), (16, 34), (29, 14), (35, 13), (26, 30), (14, 10), (16, 8), (9, 9), (30, 2), (20, 22), (9, 14), (35, 35), (33, 20), (24, 6), (27, 30), (31, 4), (14, 18), (12, 29), (3, 5), (24, 2), (7, 14), (5, 27), (7, 33), (16, 2), (2, 18), (12, 33), (6, 4), (25, 12), (3, 8), (13, 4), (6, 22), (28, 8), (20, 28), (18, 11), (12, 23), (7, 2), (6, 31), (31, 28), (5, 18), (9, 13), (23, 15), (4, 0), (28, 10), (9, 22), (15, 23), (9, 11), (13, 20), (24, 29), (2, 29), (5, 0), (24, 32), (32, 12), (26, 22), (2, 25), (10, 29), (11, 21), (8, 4), (11, 9), (3, 16), (4, 22), (28, 30), (27, 14), (1, 17), (7, 4), (25, 23), (24, 8), (30, 17), (2, 20), (0, 13), (28, 22), (9, 16), (25, 27), (7, 20), (33, 11), (3, 1), (7, 13), (35, 36), (22, 36), (24, 37), (9, 1), (8, 11), (6, 2), (21, 4), (29, 21), (11, 24), (29, 19), (0, 22), (35, 25), (34, 24), (18, 29), (17, 28), (4, 19), (3, 33), (30, 19), (4, 25), (28, 3), (13, 18), (11, 28), (28, 38), (8, 21), (31, 35), (16, 31), (31, 2), (0, 25), (6, 5), (10, 3), (18, 16), (33, 34), (15, 32), (6, 24), (30, 21), (25, 2), (34, 34), (26, 5), (18, 26), (16, 12), (5, 26), (18, 5), (35, 3), (16, 16), (19, 19), (19, 1), (21, 37), (32, 10), (0, 17), (23, 19), (5, 28), (34, 36), (24, 19), (33, 7), (32, 37), (30, 22), (14, 29), (10, 34), (19, 35), (15, 8), (19, 23), (4, 11), (7, 0), (6, 30), (33, 12), (21, 31), (19, 3), (9, 24), (16, 19), (32, 15), (5, 17), (26, 37), (12, 24), (34, 4), (4, 14), (29, 17), (28, 24), (6, 21), (25, 5), (16, 11), (22, 17), (23, 3), (21, 21), (30, 12), (34, 14), (33, 31), (18, 23), (1, 32), (31, 24), (4, 8), (28, 17), (30, 13), (4, 7), (11, 29), (24, 13), (6, 7), (5, 5), (11, 2), (1, 36), (33, 15), (23, 38), (34, 16), (31, 22), (19, 2), (34, 25), (35, 23), (7, 12), (4, 16), (16, 37), (24, 10), (12, 17), (14, 17), (26, 36), (19, 21), (10, 18), (13, 14), (34, 32), (2, 11), (26, 38), (21, 13), (7, 7), (18, 27), (29, 25), (25, 6), (35, 8), (15, 18), (20, 27), (17, 15), (24, 34), (22, 26), (10, 11), (4, 37), (2, 35), (18, 17), (22, 8), (28, 35), (16, 24), (20, 24), (3, 36), (33, 33), (1, 33), (17, 34), (0, 5), (25, 34), (24, 20), (26, 33), (12, 30), (24, 35), (34, 7), (10, 5), (27, 16), (31, 3), (30, 23), (1, 26), (17, 25), (1, 14), (35, 4), (2, 27), (19, 22), (10, 28), (9, 7), (18, 4), (11, 22), (34, 33), (10, 26), (22, 18), (24, 15), (12, 20), (0, 15), (4, 34), (10, 35), (10, 7), (26, 18), (31, 7), (30, 30), (11, 23), (29, 24), (30, 4), (14, 33), (19, 38), (28, 28), (27, 18), (8, 19), (21, 27), (7, 35), (2, 13), (11, 4), (17, 37), (7, 6), (19, 18), (29, 16), (4, 18), (15, 9), (22, 15), (25, 21), (1, 7), (13, 36), (28, 4), (9, 10), (7, 34), (14, 5), (21, 33), (34, 29), (26, 20), (0, 10), (21, 24), (19, 6), (24, 24), (16, 35), (1, 13), (27, 22), (18, 35), (25, 0), (34, 12), (14, 14), (6, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "863700", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (27, 20), (33, 32), (0, 19), (2, 23), (34, 27), (21, 20), (3, 31), (33, 18), (32, 9), (7, 13), (21, 29), (4, 8), (16, 26), (4, 23), (19, 19), (3, 14), (21, 16), (27, 12), (20, 5), (11, 4), (20, 15), (3, 4), (2, 15), (21, 23), (5, 1), (22, 13), (31, 28), (20, 30), (27, 25), (12, 29), (27, 10), (27, 32), (34, 30), (25, 10), (34, 29), (8, 17), (5, 28), (21, 13), (1, 8), (29, 0), (29, 21), (28, 7), (15, 18), (9, 0), (1, 27), (30, 19), (4, 6), (1, 21), (19, 14), (4, 1), (20, 20), (11, 16), (8, 25), (31, 25), (17, 16), (30, 14), (11, 29), (9, 30), (6, 18), (34, 26), (2, 3), (25, 7), (8, 3), (3, 18), (24, 30), (33, 6), (8, 12), (9, 27), (2, 7), (33, 7), (25, 17), (15, 3), (17, 11), (22, 19), (19, 21), (11, 20), (13, 2), (21, 3), (33, 25), (21, 32), (20, 2), (2, 27), (11, 7), (28, 5), (16, 0), (32, 24), (26, 11), (13, 31), (27, 31), (15, 27), (32, 20), (12, 7), (30, 9), (30, 18), (20, 24), (1, 23), (25, 9), (9, 26), (2, 29), (19, 12), (22, 30), (7, 9), (20, 32), (15, 22), (0, 6), (11, 8), (28, 6), (21, 31), (30, 5), (34, 24), (1, 6), (0, 20), (13, 12), (9, 16), (6, 25), (22, 31), (17, 5), (13, 1), (9, 18), (10, 20), (11, 31), (15, 29), (29, 26), (27, 27), (5, 22), (26, 4), (19, 27), (31, 14), (14, 23), (34, 0), (26, 0), (7, 29), (21, 5), (1, 28), (18, 27), (20, 3), (14, 32), (17, 13), (23, 14), (10, 11), (6, 3), (32, 26), (5, 27), (23, 29), (0, 7), (33, 22), (23, 1), (2, 30), (16, 15), (23, 3), (14, 9), (18, 24), (7, 20), (32, 1), (28, 13), (29, 17), (24, 3), (28, 1), (11, 32), (22, 27), (7, 27), (2, 8), (3, 1), (10, 32), (11, 6), (27, 23), (9, 17), (13, 13), (18, 11), (23, 17), (4, 14), (19, 26), (15, 4), (23, 19), (7, 5), (2, 25), (15, 15), (14, 20), (34, 2), (6, 31), (31, 17), (16, 3), (29, 5), (7, 15), (3, 8), (2, 9), (28, 0), (12, 19), (7, 6), (32, 0), (15, 19), (23, 2), (18, 14), (30, 24), (29, 2), (16, 8), (33, 14), (25, 29), (26, 17), (17, 26), (12, 3), (32, 11), (5, 12), (1, 2), (0, 23), (25, 13), (12, 12), (3, 5), (34, 11), (12, 11), (17, 7), (0, 25), (34, 13), (12, 18), (31, 24), (19, 25), (13, 29), (19, 29), (10, 0), (3, 20), (15, 24), (24, 20), (28, 18), (29, 31), (32, 25), (27, 30), (19, 1), (2, 24), (34, 28), (18, 3), (11, 30), (25, 25), (19, 13), (0, 5), (6, 8), (29, 24), (16, 28), (9, 12), (18, 16), (15, 16), (10, 26), (17, 32), (7, 10), (29, 20), (4, 30), (13, 27), (23, 26), (25, 26), (16, 24), (28, 27), (13, 4), (4, 26), (13, 26), (7, 11), (27, 24), (24, 4), (12, 27), (7, 3), (23, 10), (9, 2), (10, 3), (4, 0), (30, 21), (22, 29), (16, 5), (32, 19), (7, 30), (16, 10), (11, 13), (32, 5), (32, 2), (23, 24), (19, 31), (17, 15), (27, 9), (15, 11), (0, 30), (20, 7), (18, 20), (33, 13), (18, 5), (15, 23), (5, 15), (9, 9), (14, 25), (18, 8), (26, 16), (24, 23), (13, 23), (14, 22), (25, 18), (20, 4), (0, 27), (13, 19), (28, 4), (10, 30), (5, 31), (26, 31), (9, 20), (0, 11), (20, 22), (3, 21), (22, 8), (7, 28), (6, 12), (20, 11), (6, 16), (13, 16), (33, 26), (32, 21), (20, 1), (28, 31), (33, 15), (32, 28), (21, 25), (9, 8), (12, 13), (12, 9), (10, 15), (3, 32), (22, 20), (14, 8), (9, 28), (20, 6), (31, 8), (24, 8), (13, 22), (15, 1), (34, 18), (25, 3), (4, 21), (25, 8), (3, 6), (15, 13), (23, 5), (13, 32), (9, 10), (21, 30), (22, 10), (8, 10), (17, 24), (23, 4), (1, 15), (22, 17), (3, 10), (10, 2), (16, 18), (12, 31), (8, 24), (3, 12), (33, 16), (14, 19), (31, 1), (12, 14), (23, 27), (28, 22), (11, 9), (5, 7), (32, 7), (7, 24), (27, 15), (6, 24), (20, 12), (18, 18), (30, 25), (26, 32), (28, 26), (13, 30), (0, 29), (10, 27), (26, 5), (6, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117936", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), 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), (14, 18), (7, 35), (18, 1), (1, 1), (2, 1), (10, 12), (14, 26), (32, 34), (1, 11), (37, 21), (12, 35), (28, 6), (9, 19), (11, 27), (37, 30), (32, 33), (34, 16), (21, 31), (11, 31), (14, 6), (10, 19), (12, 10), (21, 25), (6, 20), (8, 19), (3, 21), (34, 21), (9, 18), (19, 8), (8, 17), (27, 31), (20, 34), (15, 34), (20, 14), (4, 10), (5, 7), (30, 30), (4, 25), (5, 0), (25, 9), (25, 21), (10, 10), (26, 25), (9, 15), (35, 16), (28, 3), (17, 10), (20, 3), (33, 22), (6, 16), (34, 8), (13, 16), (0, 15), (5, 31), (24, 23), (18, 32), (19, 7), (7, 24), (26, 35), (4, 22), (12, 1), (21, 2), (10, 6), (19, 31), (29, 30), (1, 33), (5, 32), (12, 11), (33, 31), (19, 35), (37, 19), (29, 16), (32, 10), (35, 29), (3, 28), (31, 10), (35, 8), (32, 0), (10, 17), (9, 7), (11, 35), (37, 32), (31, 0), (20, 8), (6, 6), (16, 28), (18, 31), (33, 35), (23, 6), (4, 9), (5, 23), (8, 33), (21, 9), (5, 30), (15, 9), (22, 18), (2, 3), (4, 19), (10, 33), (37, 5), (22, 30), (5, 2), (10, 29), (15, 15), (7, 26), (1, 9), (16, 0), (34, 6), (10, 3), (32, 4), (3, 24), (22, 12), (26, 13), (16, 5), (21, 34), (10, 8), (29, 4), (26, 4), (37, 10), (31, 24), (19, 21), (13, 27), (24, 35), (34, 7), (21, 14), (17, 2), (17, 26), (6, 14), (37, 0), (20, 12), (36, 30), (25, 4), (35, 28), (12, 2), (26, 33), (15, 16), (22, 7), (29, 14), (1, 12), (34, 22), (1, 25), (35, 33), (6, 8), (27, 25), (8, 3), (6, 5), (14, 27), (29, 9), (10, 18), (0, 8), (26, 22), (7, 22), (2, 19), (13, 7), (37, 27), (4, 29), (8, 28), (14, 0), (17, 15), (28, 24), (29, 8), (21, 7), (13, 28), (5, 27), (36, 34), (16, 11), (35, 34), (20, 23), (1, 22), (3, 34), (37, 17), (18, 6), (13, 18), (19, 9), (3, 27), (5, 28), (19, 3), (32, 8), (11, 29), (1, 29), (13, 34), (15, 28), (32, 3), (33, 23), (35, 0), (8, 35), (24, 2), (22, 0), (23, 1), (4, 5), (15, 12), (6, 24), (3, 7), (8, 12), (22, 22), (19, 0), (33, 6), (15, 18), (28, 4), (23, 35), (31, 5), (26, 12), (28, 30), (3, 6), (15, 20), (28, 33), (30, 23), (15, 14), (22, 2), (37, 34), (21, 30), (26, 2), (6, 19), (35, 13), (9, 9), (25, 25), (4, 14), (19, 4), (2, 18), (20, 15), (11, 3), (15, 11), (31, 11), (26, 14), (32, 27), (18, 2), (3, 15), (17, 22), (29, 28), (5, 11), (17, 21), (34, 19), (27, 1), (0, 29), (7, 7), (35, 17), (10, 9), (12, 7), (3, 13), (28, 34), (18, 5), (31, 6), (23, 26), (18, 16), (9, 12), (0, 31), (2, 15), (33, 19), (25, 10), (37, 6), (23, 31), (30, 24), (34, 23), (32, 11), (16, 13), (5, 26), (16, 30), (13, 33), (24, 26), (27, 13), (7, 30), (2, 29), (26, 21), (22, 21), (34, 4), (0, 18), (16, 2), (15, 7), (28, 35), (6, 3), (4, 23), (28, 5), (18, 10), (30, 32), (27, 9), (7, 4), (34, 0), (33, 33), (34, 3), (11, 24), (9, 13), (3, 25), (13, 15), (36, 20), (20, 29), (27, 0), (17, 5), (24, 3), (16, 19), (9, 22), (2, 30), (18, 24), (6, 22), (10, 2), (20, 11), (16, 34), (11, 25), (7, 21), (36, 7), (35, 1), (7, 27), (25, 33), (11, 7), (33, 2), (16, 7), (17, 18), (16, 21), (20, 5), (10, 20), (0, 21), (19, 23), (35, 20), (26, 1), (15, 6), (9, 16), (28, 17), (15, 10), (13, 30), (18, 15), (33, 32), (19, 32), (31, 22), (12, 29), (27, 11), (30, 16), (6, 1), (1, 6), (30, 11), (25, 11), (24, 4), (32, 7), (12, 34), (9, 26), (14, 10), (15, 29), (26, 7), (18, 7), (34, 14), (19, 29), (14, 28), (13, 0), (21, 6), (33, 25), (23, 16), (7, 18), (7, 14), (3, 33), (32, 1), (8, 14), (2, 7), (10, 30), (7, 10), (19, 20), (20, 7), (17, 7), (34, 28), (24, 15), (3, 19), (5, 24), (37, 12), (2, 10), (3, 1), (33, 12), (18, 0), (26, 15), (1, 17), (15, 24), (3, 16), (0, 34), (2, 14), (17, 12), (23, 4), (36, 4), (25, 7), (5, 14), (30, 31), (4, 4), (35, 19), (29, 5), (6, 25), (24, 21), (5, 10), (36, 6), (28, 23), (24, 17), (27, 23), (30, 0), (27, 18), (16, 15), (5, 1), (1, 3), (13, 29), (16, 16), (1, 10), (13, 5), (31, 23), (31, 20), (12, 9), (32, 20), (28, 31), (9, 14), (24, 9), (27, 15), (2, 28), (4, 34), (30, 6), (36, 1), (23, 13), (8, 26), (9, 10), (27, 34), (15, 5), (23, 18), (20, 4), (25, 8), (8, 6), (7, 34), (7, 8), (5, 5), (32, 24), (10, 28), (1, 26), (11, 30), (1, 14), (14, 14), (20, 30), (11, 26), (22, 3), (3, 5), (26, 30), (20, 9), (3, 10), (2, 2), (14, 16), (2, 34), (10, 23), (1, 16), (35, 15), (8, 27), (31, 32), (6, 18), (4, 12), (30, 12), (9, 32), (26, 5), (22, 8), (16, 26), (8, 23), (6, 12), (21, 19), (28, 13), (12, 0), (4, 20), (8, 34), (4, 18), (25, 15), (23, 8), (32, 12), (33, 3), (14, 3), (14, 23), (15, 8), (12, 17), (27, 21), (7, 13), (34, 12), (3, 30), (15, 33), (9, 29), (4, 1), (24, 33), (29, 33), (11, 4), (7, 29), (9, 6), (36, 17), (32, 15), (32, 22), (16, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "902776", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 23), (6, 28), (9, 8), (6, 15), (13, 26), (21, 13), (30, 11), (25, 9), (16, 3), (16, 7), (31, 28), (6, 3), (23, 26), (28, 8), (13, 10), (1, 6), (5, 0), (24, 28), (33, 3), (29, 12), (31, 14), (24, 12), (27, 29), (7, 17), (18, 7), (18, 22), (28, 17), (10, 15), (23, 29), (27, 22), (34, 11), (32, 22), (10, 29), (4, 29), (28, 18), (5, 16), (19, 15), (31, 7), (17, 27), (31, 11), (32, 13), (34, 9), (19, 14), (20, 23), (18, 23), (31, 21), (23, 20), (20, 11), (5, 21), (6, 1), (18, 28), (31, 27), (23, 25), (6, 2), (22, 9), (4, 1), (5, 22), (32, 16), (24, 7), (13, 21), (16, 0), (11, 8), (27, 13), (3, 24), (1, 26), (14, 8), (1, 25), (26, 12), (12, 10), (12, 22), (18, 16), (19, 29), (20, 8), (21, 11), (14, 4), (24, 27), (13, 1), (20, 1), (11, 10), (17, 13), (1, 29), (24, 9), (27, 9), (17, 2), (10, 1), (27, 1), (26, 29), (32, 7), (26, 3), (33, 15), (27, 5), (6, 22), (12, 20), (16, 14), (2, 12), (5, 3), (16, 11), (15, 16), (34, 21), (29, 28), (3, 1), (34, 15), (27, 24), (7, 3), (22, 15), (20, 6), (8, 17), (14, 15), (5, 17), (33, 19), (18, 13), (6, 0), (23, 0), (16, 9), (12, 0), (19, 5), (2, 9), (18, 20), (28, 13), (8, 23), (34, 4), (20, 0), (32, 15), (33, 0), (10, 19), (30, 8), (10, 3), (16, 6), (16, 8), (28, 24), (34, 0), (30, 26), (6, 16), (16, 25), (21, 6), (9, 12), (28, 9), (34, 14), (2, 20), (3, 14), (29, 29), (34, 1), (8, 25), (14, 14), (17, 1), (16, 5), (31, 29), (30, 23), (12, 21), (23, 11), (23, 24), (19, 19), (3, 6), (24, 6), (30, 21), (18, 29), (3, 2), (2, 26), (4, 28), (21, 22), (17, 28), (19, 11), (7, 24), (32, 1), (27, 28), (18, 12), (19, 7), (34, 28), (8, 20), (28, 27), (9, 0), (2, 0), (15, 8), (30, 9), (29, 23), (18, 18), (30, 6), (30, 22), (11, 21), (25, 24), (19, 22), (12, 9), (16, 21), (2, 6), (17, 8), (17, 7), (15, 26), (8, 12), (26, 5), (11, 26), (28, 26), (9, 18), (4, 16), (7, 18), (1, 20), (2, 25), (26, 11), (34, 24), (2, 3), (7, 7), (20, 9), (32, 0), (6, 21), (28, 6), (30, 7), (8, 3), (2, 7), (23, 3), (7, 26), (1, 8), (13, 29), (8, 2), (8, 22), (17, 29), (33, 28), (1, 7), (31, 4), (20, 19), (34, 19), (3, 19), (5, 1), (2, 17), (12, 29), (20, 13), (23, 2), (5, 10), (23, 7), (30, 14), (13, 7), (17, 17), (7, 16), (26, 18), (2, 16), (14, 6), (25, 4), (13, 14), (13, 17), (3, 18), (25, 8), (0, 25), (29, 7), (17, 12), (6, 14), (34, 18), (18, 2), (4, 18), (27, 26), (25, 2), (20, 16), (31, 16), (6, 26), (21, 27), (1, 10), (3, 28), (15, 1), (33, 16), (3, 17), (8, 10), (20, 27), (12, 11), (4, 27), (19, 17), (23, 10), (11, 29), (27, 20), (15, 3), (22, 2), (17, 21), (14, 24), (9, 6), (18, 4), (12, 28), (4, 24), (0, 23), (19, 6), (15, 11), (7, 27), (19, 25), (10, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "665500", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 27), (28, 34), (32, 0), (30, 20), (34, 8), (35, 7), (15, 10), (33, 21), (3, 34), (17, 3), (34, 6), (35, 20), (4, 14), (31, 27), (29, 6), (10, 14), (14, 11), (25, 32), (33, 20), (27, 34), (3, 7), (3, 33), (25, 11), (24, 5), (29, 34), (12, 29), (30, 33), (33, 6), (17, 21), (14, 34), (33, 19), (2, 34), (13, 15), (32, 34), (17, 19), (21, 33), (16, 18), (29, 28), (35, 4), (9, 9), (4, 32), (11, 26), (14, 4), (29, 33), (32, 26), (26, 17), (2, 4), (15, 17), (10, 21), (1, 6), (18, 2), (21, 27), (20, 17), (19, 34), (7, 23), (8, 1), (21, 10), (4, 23), (4, 27), (33, 24), (29, 8), (17, 31), (28, 29), (19, 19), (23, 33), (27, 10), (14, 29), (23, 17), (19, 12), (5, 24), (13, 9), (24, 20), (30, 4), (2, 15), (1, 7), (8, 16), (22, 16), (5, 1), (13, 7), (25, 6), (20, 27), (9, 4), (9, 20), (3, 26), (18, 21), (23, 6), (32, 31), (33, 10), (8, 27), (7, 3), (24, 19), (1, 3), (35, 8), (0, 11), (28, 8), (31, 5), (27, 28), (9, 21), (31, 3), (26, 20), (0, 29), (27, 26), (11, 2), (21, 9), (11, 11), (33, 31), (11, 18), (3, 11), (17, 11), (30, 0), (19, 14), (16, 21), (7, 18), (30, 31), (14, 22), (23, 23), (7, 12), (32, 30), (18, 27), (34, 13), (19, 26), (17, 24), (28, 0), (7, 0), (10, 16), (4, 34), (20, 26), (28, 14), (34, 17), (19, 15), (27, 20), (14, 2), (20, 16), (33, 25), (25, 26), (2, 28), (0, 7), (24, 2), (25, 19), (9, 2), (18, 1), (35, 22), (21, 1), (3, 4), (6, 34), (20, 24), (0, 5), (1, 21), (15, 3), (28, 3), (33, 30), (32, 19), (12, 16), (26, 13), (24, 31), (8, 14), (31, 28), (15, 16), (2, 30), (24, 29), (0, 21), (5, 11), (18, 20), (3, 3), (28, 4), (3, 6), (7, 29), (6, 22), (6, 18), (21, 18), (33, 12), (0, 9), (28, 12), (27, 7), (9, 16), (27, 21), (14, 21), (30, 8), (32, 33), (34, 18), (14, 30), (33, 9), (1, 34), (20, 33), (2, 25), (27, 33), (32, 6), (29, 10), (22, 34), (1, 26), (7, 33), (26, 29), (32, 20), (24, 14), (14, 16), (5, 5), (35, 27), (7, 17), (30, 16), (17, 17), (6, 15), (20, 0), (32, 27), (10, 3), (17, 6), (8, 22), (32, 10), (20, 11), (3, 5), (24, 26), (13, 16), (20, 15), (9, 6), (24, 7), (26, 4), (29, 19), (4, 13), (10, 31), (31, 15), (21, 32), (6, 32), (33, 8), (12, 3), (0, 15), (26, 34), (31, 10), (6, 25), (2, 2), (16, 31), (9, 14), (32, 16), (3, 2), (13, 3), (8, 11), (28, 18), (22, 6), (34, 24), (17, 29), (31, 33), (33, 11), (1, 17), (0, 28), (6, 9), (1, 11), (1, 27), (16, 9), (2, 6), (16, 2), (15, 12), (15, 24), (27, 1), (1, 18), (21, 25), (29, 11), (23, 26), (25, 2), (11, 19), (24, 22), (7, 26), (25, 23), (20, 5), (12, 21), (21, 3), (27, 0), (26, 23), (23, 19), (9, 26), (19, 23), (11, 5), (15, 26), (31, 24), (34, 2), (24, 27), (6, 6), (11, 10), (29, 15), (9, 13), (12, 9), (34, 30), (12, 0), (22, 28), (2, 24), (10, 28), (31, 26), (16, 4), (3, 23), (15, 21), (33, 7), (1, 16), (23, 11), (10, 5), (24, 11), (2, 26), (31, 8), (7, 14), (18, 32), (30, 3), (18, 8), (18, 18), (3, 28), (18, 4), (3, 8), (22, 33), (1, 31), (16, 27), (32, 9), (26, 32), (22, 10), (14, 32), (13, 29), (26, 18), (25, 3), (26, 9), (12, 10), (3, 9), (32, 7), (13, 21), (6, 16), (21, 13), (8, 34), (12, 15), (9, 3), (12, 25), (30, 2), (7, 7), (9, 29), (26, 7), (24, 18), (29, 32), (1, 2), (13, 33), (31, 14), (16, 8), (1, 12), (10, 32), (6, 14), (11, 21), (7, 5), (32, 12), (16, 30), (27, 18), (20, 30), (27, 31), (32, 28), (14, 18), (0, 10), (26, 12), (19, 18), (4, 30), (17, 23), (22, 22), (1, 9), (16, 1), (15, 7), (25, 9), (28, 17), (23, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11880", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (36, 31), (16, 27), (11, 13), (27, 32), (22, 33), (27, 18), (11, 7), (10, 16), (19, 9), (21, 3), (10, 3), (4, 2), (4, 3), (21, 34), (33, 25), (14, 11), (34, 12), (36, 2), (19, 14), (7, 21), (0, 22), (4, 25), (26, 26), (33, 4), (16, 29), (16, 23), (5, 6), (6, 29), (27, 30), (9, 8), (13, 31), (10, 0), (7, 33), (11, 19), (3, 30), (7, 31), (16, 33), (31, 12), (24, 25), (12, 24), (3, 8), (25, 22), (28, 26), (5, 22), (9, 30), (21, 13), (15, 22), (26, 32), (35, 28), (5, 3), (35, 25), (9, 0), (16, 18), (9, 9), (23, 8), (30, 30), (27, 13), (2, 34), (16, 25), (5, 1), (16, 1), (31, 26), (8, 9), (27, 20), (34, 20), (8, 29), (14, 22), (7, 32), (4, 27), (9, 32), (10, 18), (31, 9), (11, 6), (14, 25), (17, 34), (1, 18), (26, 33), (15, 32), (15, 11), (28, 1), (0, 6), (17, 26), (0, 10), (27, 4), (1, 34), (34, 17), (15, 0), (5, 19), (34, 7), (10, 6), (23, 22), (16, 32), (2, 12), (23, 21), (8, 30), (33, 6), (8, 26), (11, 31), (27, 7), (18, 25), (0, 15), (15, 6), (13, 33), (24, 13), (15, 13), (9, 4), (16, 0), (17, 23), (19, 17), (27, 9), (7, 4), (14, 24), (2, 15), (30, 0), (19, 2), (15, 34), (30, 18), (32, 7), (5, 9), (13, 13), (16, 20), (26, 19), (24, 28), (9, 6), (30, 22), (24, 30), (7, 27), (35, 32), (24, 17), (11, 28), (17, 3), (0, 26), (29, 14), (18, 23), (32, 24), (0, 1), (35, 6), (34, 33), (34, 15), (3, 14), (12, 23), (20, 4), (7, 14), (17, 30), (17, 33), (32, 25), (12, 26), (30, 20), (15, 1), (34, 31), (25, 34), (6, 17), (3, 22), (1, 30), (21, 23), (18, 21), (23, 17), (30, 33), (19, 32), (18, 8), (28, 19), (22, 14), (21, 32), (4, 14), (8, 24), (24, 11), (25, 28), (18, 26), (7, 24), (6, 32), (34, 19), (19, 20), (6, 19), (27, 21), (22, 4), (29, 25), (29, 7), (31, 10), (10, 21), (33, 8), (21, 12), (14, 21), (31, 5), (31, 33), (25, 32), (25, 19), (10, 30), (20, 17), (15, 20), (25, 17), (29, 8), (12, 27), (19, 29), (11, 34), (4, 9), (15, 2), (26, 13), (16, 8), (36, 0), (9, 18), (7, 22), (26, 30), (20, 6), (18, 10), (27, 0), (4, 26), (16, 31), (14, 6), (5, 16), (36, 13), (0, 12), (9, 15), (15, 26), (23, 2), (26, 28), (32, 17), (36, 33), (2, 10), (20, 5), (23, 30), (6, 3), (4, 4), (13, 10), (27, 1), (33, 14), (15, 7), (19, 27), (20, 32), (9, 19), (9, 22), (0, 13), (21, 8), (4, 8), (16, 15), (26, 3), (22, 21), (32, 33), (6, 12), (7, 25), (23, 26), (34, 25), (18, 29), (34, 2), (32, 22), (22, 28), (32, 30), (28, 5), (21, 2), (16, 5), (23, 34), (32, 19), (13, 1), (31, 20), (19, 18), (30, 3), (29, 24), (13, 15), (20, 24), (28, 31), (5, 12), (2, 20), (6, 5), (28, 24), (2, 17), (22, 20), (7, 12), (7, 15), (11, 9), (34, 5), (1, 26), (20, 9), (20, 14), (33, 23), (3, 7), (10, 32), (17, 24), (0, 21), (12, 20), (36, 10), (14, 0), (36, 3), (15, 15), (32, 0), (25, 7), (35, 26), (24, 26), (0, 27), (2, 14), (1, 11), (19, 0), (13, 2), (19, 33), (6, 8), (2, 31), (10, 10), (27, 2), (32, 9), (33, 2), (14, 10), (23, 13), (12, 6), (10, 11), (16, 4), (31, 29), (9, 20), (27, 23), (22, 12), (10, 1), (13, 20), (28, 16), (12, 16), (36, 28), (33, 7), (36, 15), (2, 32), (8, 12), (24, 32), (0, 2), (17, 1), (26, 7), (21, 17), (31, 2), (13, 3), (13, 23), (24, 5), (12, 8), (6, 18), (18, 1), (35, 8), (36, 29), (7, 23), (0, 14), (20, 8), (3, 33), (24, 22), (8, 28), (14, 8), (6, 11), (3, 10), (36, 17), (23, 23), (34, 16), (4, 31), (12, 12), (26, 24), (2, 4), (7, 34), (28, 25), (1, 31), (0, 24), (29, 13), (9, 1), (30, 2), (5, 21), (19, 21), (15, 3), (1, 23), (14, 34), (34, 29), (2, 22), (6, 31), (35, 2), (0, 7), (21, 1), (3, 29), (17, 27), (31, 23), (3, 0), (16, 34), (5, 24), (20, 11), (33, 3), (11, 20), (25, 6), (24, 8), (9, 29), (25, 14), (14, 30), (6, 15), (31, 17), (2, 6), (31, 4), (22, 27), (24, 9), (25, 9), (32, 14), (26, 29), (10, 9), (18, 6), (7, 19), (9, 2), (12, 2), (18, 4), (3, 21), (3, 13), (25, 25), (29, 33), (9, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949200", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (2, 17), (11, 26), (16, 25), (7, 28), (5, 22), (1, 28), (26, 14), (32, 26), (7, 5), (31, 4), (21, 14), (0, 23), (2, 2), (11, 22), (12, 29), (2, 14), (9, 25), (20, 36), (17, 33), (23, 6), (6, 2), (19, 22), (16, 26), (10, 7), (12, 20), (13, 0), (0, 36), (2, 10), (6, 14), (28, 8), (22, 18), (25, 10), (2, 15), (31, 20), (29, 20), (27, 25), (17, 15), (26, 28), (9, 0), (28, 25), (7, 31), (15, 23), (17, 7), (17, 5), (32, 36), (7, 24), (21, 2), (11, 5), (18, 35), (18, 3), (12, 1), (1, 22), (1, 24), (1, 8), (26, 32), (33, 18), (6, 29), (16, 0), (14, 10), (27, 19), (20, 3), (5, 27), (28, 0), (18, 27), (9, 15), (32, 24), (32, 16), (7, 16), (7, 7), (18, 31), (33, 9), (23, 1), (8, 15), (12, 36), (31, 33), (7, 33), (27, 5), (29, 1), (18, 25), (27, 33), (6, 0), (21, 0), (16, 10), (10, 26), (18, 7), (30, 33), (31, 23), (20, 1), (2, 4), (6, 23), (30, 36), (7, 15), (2, 11), (26, 13), (28, 14), (12, 25), (8, 8), (13, 11), (17, 22), (19, 2), (30, 24), (29, 11), (0, 14), (31, 11), (1, 25), (11, 17), (25, 23), (13, 14), (16, 1), (8, 12), (20, 14), (19, 34), (21, 13), (32, 17), (0, 34), (32, 34), (6, 35), (1, 16), (19, 28), (33, 10), (18, 1), (32, 0), (0, 2), (4, 5), (3, 17), (3, 31), (29, 10), (8, 22), (0, 15), (13, 30), (27, 0), (0, 32), (13, 2), (29, 14), (10, 1), (14, 8), (30, 4), (14, 15), (33, 30), (26, 27), (31, 0), (6, 25), (9, 26), (21, 24), (14, 26), (17, 11), (33, 0), (17, 13), (15, 11), (19, 33), (10, 29), (5, 28), (2, 16), (15, 18), (20, 10), (31, 2), (32, 19), (12, 9), (29, 8), (8, 34), (15, 17), (18, 13), (2, 21), (25, 31), (22, 11), (4, 27), (32, 23), (8, 4), (10, 10), (31, 31), (32, 10), (29, 0), (33, 31), (31, 32), (21, 8), (33, 1), (6, 3), (4, 0), (15, 14), (30, 31), (5, 32), (13, 21), (5, 21), (28, 3), (2, 33), (9, 29), (23, 24), (0, 18), (9, 10), (13, 35), (2, 30), (22, 23), (11, 30), (17, 9), (23, 31), (7, 17), (27, 13), (16, 19), (13, 15), (9, 32), (33, 16), (10, 25), (9, 6), (26, 36), (0, 7), (26, 26), (20, 12), (1, 9), (16, 9), (33, 21), (3, 19), (4, 1), (4, 30), (27, 36), (5, 17), (23, 34), (31, 25), (20, 4), (26, 30), (28, 12), (20, 23), (16, 7), (18, 32), (22, 25), (19, 10), (29, 34), (11, 13), (27, 1), (23, 8), (0, 26), (12, 2), (4, 32), (25, 7), (9, 14), (25, 15), (2, 28), (23, 11), (17, 6), (25, 2), (20, 30), (16, 13), (3, 16), (12, 6), (14, 11), (9, 35), (23, 29), (23, 17), (29, 27), (25, 6), (28, 21), (7, 27), (30, 20), (17, 21), (14, 28), (7, 3), (24, 36), (10, 21), (22, 9), (23, 5), (32, 6), (5, 23), (15, 36), (2, 20), (33, 11), (5, 2), (22, 26), (24, 27), (9, 20), (29, 25), (3, 30), (20, 22), (3, 7), (29, 15), (27, 9), (10, 22), (18, 15), (33, 14), (2, 8), (26, 8), (27, 24), (5, 0), (9, 16), (6, 16), (22, 35), (0, 4), (16, 27), (9, 36), (32, 28), (1, 11), (13, 22), (19, 32), (27, 31), (24, 31), (16, 23), (3, 21), (26, 23), (2, 31), (14, 18), (22, 27), (14, 4), (15, 29), (18, 0), (8, 20), (24, 28), (1, 14), (14, 22), (13, 25), (19, 20), (29, 26), (7, 12), (29, 19), (29, 18), (15, 27), (16, 18), (18, 20), (6, 33), (15, 2), (23, 22), (1, 21), (17, 25), (15, 1), (24, 19), (20, 9), (32, 15), (6, 26), (6, 22), (3, 23), (20, 24), (29, 31), (31, 9), (6, 34), (16, 22), (19, 11), (30, 15), (28, 20), (7, 35), (3, 11), (12, 11), (16, 35), (7, 22), (16, 20), (3, 10), (16, 17), (6, 4), (9, 4), (10, 18), (23, 33), (23, 28), (1, 10), (33, 17), (11, 23), (24, 7), (3, 0), (14, 5), (19, 23), (27, 2), (2, 12), (20, 35), (29, 36), (3, 3), (25, 22), (30, 9), (6, 32), (0, 29), (11, 6), (33, 33), (0, 33), (3, 24), (0, 28), (5, 1), (4, 13), (21, 21), (14, 23), (10, 27), (12, 13), (1, 31), (30, 8), (13, 28), (10, 30), (22, 28), (8, 36), (26, 20), (6, 13), (19, 31), (1, 12), (16, 36), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165240", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), 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), (12, 19), (31, 22), (27, 22), (15, 12), (31, 26), (19, 32), (29, 9), (10, 2), (27, 31), (22, 32), (3, 24), (15, 34), (22, 0), (8, 34), (21, 29), (23, 12), (30, 34), (6, 27), (30, 7), (24, 1), (4, 18), (15, 27), (9, 30), (13, 28), (31, 11), (23, 15), (10, 14), (8, 15), (10, 34), (29, 24), (6, 34), (19, 9), (26, 21), (7, 0), (16, 31), (20, 13), (14, 28), (9, 18), (2, 7), (13, 24), (24, 6), (29, 18), (28, 30), (11, 20), (16, 30), (25, 8), (12, 20), (4, 19), (16, 14), (17, 25), (9, 19), (7, 33), (5, 16), (11, 9), (19, 13), (19, 11), (4, 30), (25, 3), (1, 32), (5, 7), (12, 26), (12, 3), (20, 27), (21, 24), (25, 33), (2, 12), (10, 16), (14, 4), (9, 24), (0, 2), (3, 23), (9, 29), (24, 32), (11, 21), (18, 21), (23, 6), (14, 18), (13, 27), (13, 5), (13, 23), (27, 14), (9, 8), (11, 18), (15, 18), (27, 25), (30, 1), (23, 16), (23, 23), (14, 29), (29, 6), (16, 10), (26, 1), (2, 14), (28, 1), (18, 17), (2, 20), (30, 5), (22, 7), (6, 25), (11, 23), (3, 28), (15, 20), (18, 26), (23, 32), (25, 27), (22, 3), (14, 34), (17, 12), (20, 22), (22, 14), (19, 15), (25, 1), (26, 15), (28, 4), (18, 29), (18, 19), (18, 9), (24, 23), (18, 27), (9, 13), (14, 3), (23, 8), (12, 15), (20, 10), (28, 15), (8, 33), (30, 15), (7, 15), (10, 24), (15, 2), (16, 6), (16, 5), (11, 28), (1, 14), (10, 31), (3, 2), (24, 30), (22, 2), (26, 23), (15, 32), (12, 1), (23, 10), (28, 33), (30, 4), (8, 21), (7, 32), (6, 18), (0, 4), (26, 14), (15, 6), (3, 13), (1, 3), (10, 29), (3, 20), (21, 5), (22, 25), (24, 5), (13, 0), (1, 29), (18, 31), (1, 5), (31, 20), (25, 20), (16, 12), (1, 23), (2, 5), (12, 32), (12, 28), (29, 11), (29, 19), (15, 30), (3, 30), (21, 23), (24, 17), (28, 31), (27, 26), (24, 12), (4, 5), (31, 19), (5, 25), (19, 25), (18, 5), (7, 24), (25, 9), (20, 8), (14, 30), (4, 12), (29, 8), (0, 1), (24, 13), (4, 27), (15, 4), (23, 25), (9, 15), (3, 4), (23, 17), (31, 17), (19, 31), (27, 9), (7, 26), (1, 2), (14, 24), (9, 2), (3, 14), (2, 15), (16, 9), (19, 4), (27, 23), (4, 32), (25, 14), (31, 2), (9, 5), (22, 17), (21, 6), (31, 7), (22, 12), (29, 22), (8, 4), (6, 23), (11, 27), (26, 28), (5, 10), (17, 28), (27, 16), (27, 13), (8, 7), (24, 0), (18, 33), (30, 27), (9, 22), (27, 5), (14, 8), (28, 24), (17, 24), (17, 10), (18, 14), (1, 13), (29, 15), (1, 30), (26, 8), (14, 19), (14, 10), (2, 32), (26, 34), (18, 3), (8, 31), (7, 21), (30, 23), (14, 0), (25, 28), (7, 16), (19, 1), (19, 6), (13, 10), (16, 34), (2, 17), (13, 20), (31, 28), (20, 23), (4, 7), (18, 28), (27, 19), (0, 24), (12, 31), (10, 20), (28, 10), (17, 16), (21, 22), (9, 1), (10, 27), (23, 18), (8, 5), (5, 0), (6, 2), (24, 14), (31, 16), (15, 29), (27, 11), (9, 6), (11, 12), (20, 3), (6, 17), (22, 23), (6, 21), (19, 24), (27, 1), (21, 32), (31, 13), (18, 4), (27, 3), (15, 14), (25, 26), (11, 6), (0, 5), (14, 33), (7, 13), (2, 19), (13, 18), (1, 8), (6, 10), (0, 9), (0, 23), (11, 33), (5, 17), (9, 10), (13, 17), (18, 15), (30, 10), (5, 3), (2, 2), (1, 25), (24, 20), (20, 9), (11, 15), (8, 9), (7, 11), (28, 3), (22, 21), (3, 18), (7, 14), (8, 25), (3, 15), (5, 2), (27, 4), (2, 31), (31, 30), (5, 22), (3, 21), (26, 33), (25, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964800", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), 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), (9, 12), (28, 34), (4, 15), (6, 15), (2, 12), (6, 3), (27, 0), (13, 38), (10, 30), (0, 26), (21, 17), (13, 8), (5, 8), (9, 22), (8, 15), (5, 13), (14, 23), (6, 7), (25, 16), (25, 36), (28, 31), (16, 37), (27, 18), (18, 2), (21, 27), (12, 12), (26, 17), (5, 21), (26, 9), (23, 31), (2, 24), (3, 20), (10, 24), (1, 1), (2, 33), (20, 20), (22, 28), (15, 20), (3, 2), (25, 34), (11, 10), (8, 32), (8, 17), (13, 21), (17, 12), (25, 2), (21, 28), (14, 5), (25, 24), (10, 1), (14, 18), (3, 13), (2, 8), (14, 30), (13, 19), (27, 19), (0, 19), (13, 23), (21, 3), (0, 27), (3, 11), (1, 3), (20, 34), (7, 38), (9, 14), (14, 37), (11, 22), (5, 2), (26, 1), (10, 6), (28, 36), (2, 6), (4, 36), (20, 6), (15, 35), (21, 35), (0, 2), (2, 5), (16, 29), (28, 29), (20, 1), (29, 1), (29, 8), (20, 3), (9, 20), (17, 5), (14, 7), (25, 29), (21, 14), (12, 0), (25, 4), (16, 19), (5, 3), (23, 16), (9, 26), (5, 6), (19, 28), (24, 7), (12, 19), (24, 5), (16, 8), (26, 2), (7, 30), (24, 19), (20, 16), (24, 3), (17, 8), (18, 18), (11, 28), (18, 5), (0, 15), (27, 37), (5, 31), (29, 37), (16, 7), (23, 18), (14, 3), (22, 37), (21, 34), (13, 36), (1, 11), (6, 13), (4, 32), (10, 21), (18, 13), (16, 12), (5, 11), (14, 26), (9, 6), (13, 26), (24, 26), (11, 37), (9, 13), (18, 15), (4, 12), (22, 25), (7, 37), (11, 9), (15, 31), (22, 16), (16, 6), (29, 20), (24, 14), (6, 19), (20, 10), (13, 0), (16, 25), (16, 34), (23, 8), (16, 15), (1, 25), (27, 23), (13, 4), (19, 15), (27, 4), (22, 35), (18, 14), (11, 6), (8, 7), (18, 1), (29, 29), (29, 14), (24, 37), (7, 17), (26, 16), (17, 38), (12, 17), (27, 8), (14, 29), (6, 37), (17, 31), (5, 5), (18, 29), (21, 12), (11, 34), (23, 35), (25, 15), (19, 34), (14, 33), (22, 31), (1, 18), (19, 29), (0, 33), (20, 30), (1, 5), (23, 33), (12, 24), (15, 24), (29, 32), (7, 11), (11, 12), (1, 27), (0, 3), (19, 37), (28, 25), (5, 28), (11, 16), (6, 10), (4, 19), (1, 6), (4, 21), (15, 7), (2, 21), (23, 10), (26, 37), (3, 35), (4, 26), (16, 32), (4, 6), (13, 5), (26, 36), (6, 25), (29, 21), (20, 14), (23, 30), (23, 36), (4, 29), (10, 13), (7, 5), (24, 0), (10, 34), (14, 14), (12, 33), (21, 20), (18, 7), (20, 19), (14, 35), (28, 17), (22, 23), (1, 33), (22, 20), (9, 21), (2, 22), (2, 15), (10, 12), (17, 9), (29, 4), (7, 3), (12, 26), (9, 23), (2, 27), (15, 5), (7, 19), (10, 38), (25, 11), (12, 28), (3, 1), (20, 11), (12, 18), (19, 32), (28, 35), (22, 3), (28, 5), (28, 20), (29, 18), (15, 23), (18, 37), (10, 31), (11, 36), (25, 12), (9, 28), (12, 36), (15, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "777933", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 5), (26, 25), (15, 26), (28, 2), (14, 6), (25, 23), (21, 9), (33, 16), (23, 1), (32, 20), (14, 30), (1, 10), (21, 4), (22, 6), (0, 19), (10, 31), (29, 29), (31, 0), (33, 28), (11, 2), (20, 18), (13, 9), (13, 3), (27, 2), (7, 13), (30, 14), (23, 7), (16, 28), (25, 20), (28, 5), (11, 16), (27, 12), (27, 4), (21, 8), (4, 13), (24, 13), (11, 27), (11, 18), (21, 27), (27, 14), (29, 26), (34, 19), (20, 22), (11, 4), (19, 28), (8, 1), (30, 12), (12, 8), (21, 17), (10, 0), (25, 1), (15, 29), (12, 10), (20, 29), (22, 17), (20, 6), (17, 5), (16, 5), (24, 3), (10, 9), (2, 30), (26, 31), (0, 8), (17, 15), (21, 6), (1, 29), (21, 0), (9, 9), (6, 4), (9, 28), (7, 30), (34, 24), (35, 26), (34, 1), (34, 11), (15, 0), (6, 1), (31, 21), (31, 2), (1, 14), (27, 1), (10, 28), (4, 24), (10, 7), (8, 6), (34, 22), (32, 23), (34, 6), (17, 3), (5, 20), (5, 14), (10, 20), (17, 26), (22, 28), (16, 23), (0, 26), (35, 4), (13, 28), (24, 31), (28, 1), (7, 8), (1, 5), (31, 9), (24, 27), (3, 19), (11, 15), (16, 29), (17, 24), (20, 17), (33, 15), (30, 24), (29, 19), (23, 2), (4, 15), (12, 7), (15, 2), (9, 1), (4, 20), (15, 4), (14, 18), (11, 31), (5, 2), (14, 28), (13, 24), (19, 17), (14, 15), (7, 14), (34, 12), (28, 23), (24, 4), (28, 27), (3, 31), (10, 14), (11, 10), (0, 2), (14, 27), (22, 30), (17, 23), (24, 14), (30, 20), (0, 15), (19, 23), (34, 18), (29, 15), (9, 23), (9, 21), (5, 0), (3, 22), (26, 18), (0, 16), (5, 3), (25, 17), (35, 2), (15, 5), (33, 24), (28, 10), (24, 12), (16, 2), (24, 15), (0, 29), (28, 21), (25, 18), (15, 1), (17, 13), (1, 13), (14, 29), (22, 24), (20, 15), (31, 4), (16, 4), (12, 16), (19, 8), (1, 28), (3, 6), (29, 3), (2, 3), (35, 8), (14, 0), (23, 25), (33, 31), (28, 30), (10, 4), (7, 23), (24, 7), (30, 21), (3, 8), (11, 25), (5, 30), (29, 31), (34, 8), (19, 18), (19, 5), (1, 26), (25, 10), (22, 13), (12, 1), (18, 12), (3, 13), (15, 20), (12, 6), (24, 25), (21, 1), (21, 22), (8, 17), (25, 14), (6, 6), (23, 22), (2, 28), (2, 26), (31, 7), (34, 23), (1, 16), (24, 21), (14, 5), (13, 18), (20, 11), (6, 28), (8, 27), (8, 11), (25, 21), (9, 0), (21, 30), (10, 26), (20, 5), (10, 30), (13, 19), (1, 8), (1, 22), (8, 16), (22, 25), (26, 28), (32, 31), (27, 22), (6, 0), (4, 25), (8, 10), (25, 30), (16, 0), (32, 13), (22, 29), (3, 10), (22, 23), (11, 24), (16, 6), (17, 28), (19, 12), (26, 12), (26, 9), (15, 14), (29, 20), (0, 24), (17, 11), (24, 28), (33, 7), (2, 2), (13, 25), (11, 20), (34, 27), (18, 16), (22, 9), (11, 28), (14, 25), (2, 27), (3, 30), (35, 3), (34, 17), (7, 22), (6, 14), (2, 25), (0, 14), (12, 0), (14, 16), (12, 30), (7, 18), (15, 18), (31, 22), (12, 5), (25, 4), (0, 13), (10, 15), (22, 18), (23, 12), (17, 31), (7, 0), (22, 12), (2, 29), (0, 23), (34, 2), (1, 23), (13, 0), (20, 30), (32, 25), (9, 31), (30, 30), (17, 25), (6, 24), (18, 30), (2, 11), (14, 9), (13, 21), (27, 18), (29, 4), (24, 29), (5, 18), (34, 30), (1, 0), (9, 26), (26, 7), (32, 24), (21, 29), (17, 27), (6, 29), (30, 18), (9, 24), (27, 8), (12, 28), (5, 26), (18, 9), (35, 6), (11, 5), (8, 28), (26, 13), (20, 23), (2, 7), (3, 2), (13, 2), (31, 30), (17, 0), (10, 22), (9, 13), (33, 9), (21, 12), (26, 4), (13, 7), (22, 14), (29, 8), (6, 13), (16, 3), (19, 15), (30, 19), (6, 11), (3, 20), (23, 6), (11, 0), (27, 5), (24, 26), (20, 26), (21, 13), (32, 27), (10, 5), (23, 30), (21, 31), (28, 13), (29, 7), (4, 21), (30, 5), (17, 6), (35, 0), (19, 4), (9, 17), (19, 6), (31, 1), (11, 13), (21, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "816480", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 6), (8, 22), (18, 22), (16, 23), (1, 21), (18, 12), (18, 23), (21, 4), (23, 26), (15, 4), (16, 22), (8, 32), (32, 37), (7, 20), (18, 32), (28, 7), (21, 31), (32, 34), (28, 30), (4, 20), (21, 32), (15, 6), (4, 2), (22, 5), (31, 35), (12, 5), (33, 22), (29, 30), (6, 27), (28, 33), (18, 19), (24, 8), (7, 33), (29, 27), (14, 30), (16, 27), (28, 11), (32, 27), (30, 0), (13, 33), (9, 36), (0, 3), (15, 30), (20, 30), (19, 30), (4, 4), (0, 20), (24, 23), (18, 21), (2, 34), (15, 3), (21, 8), (30, 37), (4, 33), (19, 9), (11, 1), (25, 3), (29, 37), (3, 21), (9, 32), (14, 36), (22, 4), (22, 10), (26, 33), (28, 4), (12, 7), (5, 9), (32, 14), (0, 31), (21, 28), (1, 18), (5, 21), (3, 24), (16, 35), (6, 1), (19, 28), (5, 11), (15, 22), (12, 12), (29, 14), (25, 7), (4, 8), (17, 7), (19, 17), (15, 9), (5, 16), (7, 30), (26, 21), (16, 0), (6, 33), (23, 5), (4, 22), (17, 28), (27, 24), (23, 36), (23, 7), (30, 22), (8, 18), (1, 19), (0, 10), (31, 14), (18, 14), (3, 8), (33, 13), (29, 11), (15, 8), (20, 38), (12, 22), (2, 24), (6, 34), (17, 13), (7, 15), (27, 19), (31, 26), (15, 25), (0, 37), (29, 19), (8, 28), (23, 12), (26, 10), (1, 17), (16, 7), (24, 37), (19, 11), (5, 35), (22, 22), (21, 16), (3, 14), (11, 12), (33, 8), (23, 20), (3, 31), (0, 26), (26, 13), (33, 27), (27, 32), (8, 31), (15, 0), (16, 37), (23, 23), (23, 17), (3, 29), (23, 22), (31, 6), (21, 7), (5, 28), (9, 11), (10, 35), (22, 24), (17, 35), (32, 2), (7, 14), (29, 15), (8, 4), (30, 4), (5, 17), (29, 13), (20, 0), (25, 13), (15, 14), (23, 21), (29, 3), (22, 1), (18, 5), (29, 1), (32, 22), (15, 32), (27, 22), (24, 36), (26, 12), (2, 18), (4, 6), (12, 1), (14, 34), (7, 10), (4, 9), (11, 25), (8, 23), (15, 35), (3, 38), (9, 15), (14, 29), (28, 8), (3, 9), (0, 15), (27, 20), (26, 8), (29, 28), (5, 34), (14, 12), (3, 25), (15, 33), (4, 18), (14, 1), (9, 29), (13, 5), (30, 3), (20, 24), (1, 3), (31, 17), (13, 9), (2, 15), (0, 30), (2, 6), (22, 23), (19, 20), (16, 31), (24, 25), (6, 28), (8, 0), (1, 34), (27, 35), (22, 29), (12, 30), (26, 38), (32, 25), (15, 26), (25, 38), (4, 19), (28, 35), (12, 32), (12, 37), (17, 4), (32, 26), (4, 7), (27, 23), (7, 24), (23, 34), (5, 27), (22, 28), (28, 0), (31, 9), (22, 18), (11, 13), (33, 5), (1, 4), (6, 12), (33, 12), (31, 38), (10, 13), (1, 7), (26, 18), (9, 0), (3, 27), (25, 30), (32, 23), (5, 4), (1, 25), (14, 24), (27, 26), (24, 30), (13, 16), (32, 6), (20, 16), (14, 10), (30, 27), (22, 35), (18, 35), (14, 37), (3, 32), (6, 11), (29, 18), (3, 28), (2, 5), (4, 5), (33, 0), (0, 5), (8, 37), (12, 25), (6, 35), (0, 13), (28, 18), (7, 25), (10, 38), (14, 35), (5, 25), (33, 30), (27, 28), (23, 11), (23, 28), (10, 8), (0, 1), (24, 3), (18, 7), (10, 29), (14, 13), (28, 26), (21, 10), (15, 37), (30, 7), (22, 37), (16, 26), (17, 16), (3, 36), (3, 16), (20, 37), (11, 31), (29, 9), (10, 28), (31, 29), (20, 22), (22, 11), (31, 22), (33, 25), (30, 6), (31, 27), (13, 2), (6, 26), (24, 27), (9, 34), (23, 35), (15, 19), (20, 25), (3, 22), (11, 21), (30, 21), (32, 30), (15, 7), (1, 8), (14, 9), (2, 35), (2, 38), (20, 13), (26, 1), (20, 27), (28, 10), (24, 14), (3, 11), (23, 10), (2, 10), (30, 36), (4, 13), (32, 0), (32, 29), (17, 22), (11, 20), (8, 8), (1, 31), (9, 2), (21, 37), (11, 23), (21, 38), (10, 26), (7, 12), (16, 28), (12, 13), (17, 15), (20, 5), (14, 15), (7, 37), (18, 11), (24, 17), (27, 29), (0, 36), (23, 14), (22, 31), (16, 8), (23, 19), (0, 4), (27, 4), (10, 23), (19, 12), (1, 2), (20, 11), (8, 29), (21, 3), (19, 10), (31, 37), (17, 19), (21, 35), (32, 31), (10, 12), (10, 7), (7, 11), (26, 35), (2, 3), (3, 30), (32, 5), (29, 6), (17, 34), (25, 9), (3, 35), (4, 35), (2, 17), (20, 33), (27, 11), (13, 3), (28, 14), (20, 9), (12, 35), (4, 38), (25, 37), (28, 20), (28, 22), (25, 2), (10, 22), (1, 30), (20, 8), (9, 21), (13, 19), (33, 10), (19, 2), (7, 5), (14, 32), (27, 33), (26, 16), (27, 18), (15, 20), (27, 27), (19, 18), (25, 8), (9, 19), (31, 24), (13, 28), (5, 6), (9, 24), (14, 16), (10, 31), (18, 36), (11, 30), (17, 26), (31, 15), (17, 5), (11, 33), (5, 36), (22, 17), (17, 6), (30, 16), (32, 19), (31, 5), (9, 10), (16, 2), (27, 5), (13, 14), (4, 1), (4, 30), (30, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474600", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 24), (8, 19), (20, 36), (10, 16), (1, 10), (14, 26), (4, 13), (26, 37), (15, 24), (18, 19), (31, 13), (23, 8), (16, 10), (7, 11), (10, 28), (4, 31), (11, 8), (2, 31), (3, 20), (12, 30), (28, 32), (16, 37), (16, 5), (19, 24), (21, 8), (11, 1), (30, 10), (31, 29), (1, 9), (16, 1), (8, 23), (26, 14), (26, 30), (20, 24), (20, 19), (26, 5), (9, 7), (22, 4), (29, 9), (28, 37), (15, 28), (19, 12), (0, 37), (8, 1), (6, 25), (9, 32), (2, 11), (20, 16), (30, 9), (2, 4), (28, 12), (29, 13), (7, 33), (28, 9), (22, 7), (12, 38), (23, 12), (11, 23), (4, 8), (2, 1), (21, 24), (3, 24), (24, 15), (10, 0), (16, 22), (1, 11), (9, 18), (1, 15), (18, 0), (11, 2), (7, 23), (13, 31), (8, 20), (13, 36), (1, 19), (11, 35), (2, 34), (4, 15), (30, 37), (12, 11), (28, 3), (1, 16), (13, 38), (29, 35), (30, 4), (1, 27), (24, 12), (18, 20), (13, 33), (31, 0), (9, 8), (15, 3), (18, 12), (29, 16), (7, 3), (4, 7), (9, 6), (29, 7), (2, 3), (14, 16), (14, 15), (13, 25), (10, 26), (21, 30), (20, 5), (0, 17), (24, 35), (16, 0), (11, 6), (23, 19), (15, 34), (17, 7), (17, 16), (18, 14), (23, 1), (4, 38), (24, 24), (5, 18), (12, 35), (27, 32), (12, 3), (9, 15), (14, 0), (15, 26), (23, 24), (24, 20), (17, 20), (31, 1), (29, 8), (27, 23), (14, 2), (13, 37), (9, 28), (30, 11), (20, 0), (25, 8), (20, 17), (8, 18), (28, 33), (19, 11), (31, 14), (6, 6), (8, 14), (9, 10), (30, 8), (25, 27), (25, 15), (7, 8), (3, 4), (12, 8), (31, 20), (4, 27), (12, 27), (7, 5), (18, 28), (9, 36), (16, 32), (24, 37), (13, 21), (10, 4), (9, 33), (7, 35), (11, 4), (15, 0), (28, 17), (19, 28), (1, 21), (8, 31), (8, 16), (20, 3), (5, 5), (4, 2), (31, 23), (5, 25), (12, 24), (19, 30), (1, 14), (0, 15), (27, 38), (2, 19), (10, 6), (16, 13), (14, 30), (10, 25), (10, 10), (23, 26), (15, 29), (11, 20), (0, 10), (5, 29), (20, 4), (24, 4), (25, 36), (8, 30), (11, 19), (16, 25), (20, 9), (15, 30), (1, 30), (21, 10), (31, 16), (21, 31), (2, 5), (22, 6), (23, 31), (11, 14), (18, 22), (28, 26), (3, 16), (30, 18), (18, 18), (4, 12), (24, 28), (23, 10), (15, 25), (31, 21), (18, 36), (17, 6), (22, 22), (15, 11), (23, 2), (26, 35), (30, 23), (9, 4), (13, 28), (1, 13), (20, 7), (27, 33), (12, 29), (12, 20), (2, 21), (15, 8), (7, 29), (27, 3), (13, 13), (1, 6), (28, 5), (22, 35), (31, 5), (15, 13), (26, 22), (26, 34), (5, 16), (7, 32), (25, 38), (19, 8), (24, 30), (0, 19), (18, 27), (3, 14), (28, 20), (0, 26), (25, 23), (21, 9), (15, 18), (17, 9), (9, 31), (21, 20), (27, 16), (25, 1), (15, 20), (5, 32), (7, 28), (29, 14), (16, 35), (17, 14), (9, 2), (22, 11), (21, 26), (8, 29), (6, 18), (1, 26), (25, 31), (5, 11), (27, 10), (30, 27), (13, 5), (16, 21), (29, 38), (20, 8), (25, 37), (23, 3), (18, 13), (24, 1), (3, 32), (16, 27), (26, 36), (1, 4), (25, 28), (0, 36), (30, 5), (6, 33), (10, 17), (8, 17), (29, 5), (19, 9), (9, 17), (29, 23), (20, 11), (0, 9), (27, 15), (21, 15), (17, 26), (2, 10), (28, 1), (19, 3), (1, 0), (30, 26), (17, 18), (3, 31), (8, 26), (5, 1), (15, 10), (29, 22), (16, 7), (0, 5), (9, 23), (16, 2), (19, 7), (2, 36), (20, 23), (0, 25), (26, 29), (14, 12), (14, 25), (23, 21), (18, 38), (29, 29), (23, 9), (14, 18), (3, 15), (6, 9), (23, 38), (17, 12), (9, 34), (6, 3), (6, 27), (31, 27), (10, 21), (17, 8), (19, 33), (18, 16), (12, 32), (27, 18), (19, 1), (7, 26), (29, 4), (20, 34), (7, 31), (3, 10), (17, 3), (17, 23), (20, 12), (4, 4), (7, 9), (22, 8), (31, 10), (4, 24), (31, 3), (21, 37), (15, 32), (23, 5), (4, 14), (5, 38), (19, 29), (2, 14), (7, 21), (8, 34), (10, 7), (14, 8), (6, 2), (28, 24), (10, 35), (31, 34), (11, 21), (17, 27), (23, 32), (6, 12), (12, 7), (5, 8), (14, 22), (29, 0), (7, 2), (2, 8), (13, 11), (0, 4), (24, 27), (28, 25), (8, 38), (27, 7), (30, 14), (23, 6), (7, 20), (27, 6), (0, 32), (28, 31), (22, 30), (19, 5), (11, 10), (19, 0), (26, 16), (15, 4), (4, 18), (22, 27), (16, 8), (17, 35), (10, 11), (17, 30), (26, 15), (20, 37), (23, 13), (17, 36), (14, 10), (31, 2), (22, 37), (19, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "785840", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (29, 27), (10, 6), (23, 1), (5, 4), (6, 27), (3, 26), (27, 30), (11, 2), (7, 28), (5, 3), (11, 22), (17, 10), (6, 36), (2, 19), (2, 20), (1, 25), (12, 3), (19, 30), (22, 3), (25, 18), (7, 20), (16, 9), (4, 27), (0, 26), (13, 15), (31, 24), (0, 2), (30, 35), (18, 35), (17, 24), (1, 17), (10, 31), (6, 33), (13, 23), (14, 20), (15, 8), (13, 13), (26, 8), (4, 16), (21, 35), (13, 10), (28, 13), (12, 25), (13, 8), (23, 7), (29, 14), (8, 1), (12, 13), (10, 25), (6, 13), (5, 18), (14, 32), (4, 4), (16, 19), (22, 20), (17, 11), (15, 15), (21, 5), (20, 36), (25, 9), (21, 31), (12, 31), (11, 11), (20, 4), (2, 13), (5, 23), (21, 18), (23, 32), (16, 0), (13, 4), (31, 10), (1, 35), (18, 19), (20, 7), (0, 23), (16, 29), (4, 6), (5, 33), (0, 10), (25, 17), (25, 10), (24, 28), (26, 27), (1, 13), (30, 7), (25, 14), (30, 17), (2, 4), (30, 1), (13, 6), (8, 14), (10, 0), (28, 26), (31, 33), (2, 23), (11, 10), (10, 22), (13, 3), (2, 31), (30, 3), (23, 18), (9, 33), (21, 13), (1, 29), (21, 30), (12, 19), (29, 35), (12, 17), (24, 30), (7, 25), (6, 8), (6, 9), (20, 14), (31, 6), (9, 24), (27, 28), (17, 6), (31, 7), (29, 18), (2, 15), (26, 36), (20, 17), (23, 25), (30, 32), (31, 9), (26, 7), (15, 18), (13, 5), (8, 23), (2, 18), (30, 25), (16, 17), (2, 26), (30, 8), (17, 13), (23, 22), (6, 16), (8, 32), (27, 35), (23, 20), (20, 22), (11, 27), (2, 1), (18, 24), (28, 24), (22, 8), (28, 9), (27, 10), (9, 30), (28, 14), (30, 5), (22, 10), (25, 6), (7, 19), (23, 16), (28, 23), (26, 10), (19, 24), (8, 21), (16, 30), (23, 10), (18, 27), (0, 30), (18, 4), (28, 2), (13, 9), (5, 31), (10, 20), (6, 3), (22, 33), (22, 9), (20, 30), (11, 5), (16, 7), (9, 12), (4, 20), (24, 24), (9, 19), (17, 30), (18, 1), (15, 2), (6, 18), (26, 19), (8, 24), (3, 35), (27, 31), (14, 16), (8, 7), (16, 1), (29, 28), (20, 3), (11, 25), (10, 35), (12, 5), (6, 35), (6, 2), (19, 28), (18, 26), (3, 15), (17, 9), (10, 21), (0, 1), (8, 27), (8, 16), (18, 3), (21, 15), (22, 5), (25, 31), (15, 22), (23, 24), (24, 18), (26, 6), (19, 32), (15, 17), (24, 25), (22, 32), (23, 14), (24, 29), (29, 7), (11, 1), (31, 18), (26, 33), (23, 36), (11, 9), (27, 21), (14, 4), (11, 4), (4, 28), (31, 32), (11, 6), (29, 22), (10, 1), (5, 5), (3, 3), (24, 1), (13, 2), (17, 23), (14, 34), (2, 17), (5, 14), (7, 36), (16, 3), (5, 12), (22, 34), (14, 36), (23, 30), (7, 15), (9, 4), (25, 11), (7, 6), (4, 5), (13, 30), (15, 31), (4, 11), (28, 7), (1, 16), (15, 36), (11, 26), (10, 8), (23, 0), (17, 2), (16, 27), (25, 0), (2, 28), (6, 10), (2, 3), (17, 22), (7, 16), (29, 31), (25, 5), (13, 26), (9, 32), (18, 16), (24, 16), (27, 34), (12, 10), (15, 24), (18, 15), (1, 27), (6, 15), (23, 29), (7, 35), (24, 35), (20, 15), (25, 22), (15, 30), (30, 22), (29, 16), (14, 31), (31, 25), (14, 2), (11, 8), (26, 2), (11, 33), (26, 34), (28, 22), (4, 22), (7, 32), (25, 2), (7, 33), (19, 15), (24, 8), (7, 4), (19, 5), (7, 29), (25, 15), (3, 31), (2, 21), (2, 7), (2, 27), (23, 11), (25, 26), (8, 11), (7, 34), (24, 11), (1, 31), (20, 19), (21, 7), (13, 34), (18, 21), (8, 13), (20, 12), (14, 8), (14, 23), (16, 16), (10, 28), (27, 26), (26, 31), (12, 28), (7, 27), (5, 6), (13, 35), (18, 9), (6, 0), (30, 29), (29, 10), (21, 28), (30, 18), (9, 36), (7, 13), (15, 13), (0, 31), (14, 21), (27, 8), (26, 16), (15, 27), (4, 8), (4, 1), (24, 20), (22, 23), (22, 36), (22, 22), (30, 9), (26, 29), (9, 17), (29, 23), (19, 1), (9, 22), (17, 25), (20, 11), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799380", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), 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), (25, 26), (11, 28), (8, 29), (18, 23), (10, 2), (3, 28), (4, 21), (4, 17), (24, 13), (31, 14), (29, 13), (26, 13), (26, 14), (27, 25), (18, 7), (25, 10), (6, 18), (6, 13), (12, 17), (22, 11), (0, 8), (4, 26), (9, 6), (25, 29), (19, 29), (11, 15), (12, 24), (14, 2), (18, 26), (11, 18), (11, 27), (3, 1), (18, 14), (21, 25), (22, 18), (11, 22), (20, 10), (19, 3), (3, 27), (18, 22), (20, 30), (4, 0), (23, 26), (30, 9), (15, 16), (27, 1), (27, 4), (25, 23), (4, 30), (16, 11), (8, 6), (22, 7), (22, 10), (7, 24), (31, 12), (31, 0), (5, 7), (17, 20), (32, 16), (9, 25), (29, 26), (8, 22), (26, 22), (7, 5), (17, 31), (32, 7), (13, 10), (18, 20), (29, 16), (9, 20), (13, 28), (0, 30), (17, 8), (13, 20), (28, 11), (25, 4), (19, 27), (15, 22), (15, 18), (33, 7), (19, 5), (21, 14), (4, 25), (14, 17), (15, 10), (17, 14), (27, 14), (9, 10), (11, 29), (18, 8), (15, 17), (27, 27), (15, 28), (3, 14), (23, 27), (11, 2), (22, 2), (0, 29), (8, 1), (21, 27), (29, 15), (26, 27), (16, 12), (13, 1), (7, 14), (14, 31), (25, 18), (14, 11), (7, 2), (31, 26), (12, 9), (17, 1), (12, 21), (23, 4), (26, 5), (13, 24), (9, 7), (25, 0), (33, 3), (25, 19), (24, 17), (17, 17), (12, 4), (15, 15), (26, 19), (27, 6), (3, 26), (6, 0), (30, 1), (19, 19), (0, 9), (8, 5), (17, 29), (20, 31), (10, 13), (14, 4), (8, 24), (33, 10), (1, 14), (21, 19), (27, 30), (2, 13), (9, 17), (17, 16), (12, 8), (17, 22), (25, 9), (28, 18), (17, 27), (20, 7), (29, 1), (1, 11), (1, 3), (6, 16), (16, 9), (24, 16), (19, 10), (13, 6), (21, 21), (3, 18), (29, 20), (25, 2), (12, 27), (1, 12), (5, 31), (0, 27), (33, 25), (30, 2), (4, 3), (8, 18), (20, 0), (29, 0), (19, 0), (11, 0), (20, 27), (3, 21), (19, 24), (3, 19), (4, 8), (18, 2), (0, 1), (21, 20), (30, 30), (22, 3), (19, 26), (10, 29), (30, 3), (33, 15), (19, 17), (16, 0), (32, 4), (20, 14), (27, 19), (9, 29), (6, 7), (17, 30), (19, 11), (33, 28), (26, 29), (25, 15), (8, 27), (18, 31), (16, 10), (23, 2), (8, 30), (16, 29), (11, 30), (1, 25), (5, 13), (21, 5), (30, 21), (33, 30), (18, 15), (16, 6), (13, 11), (25, 21), (24, 7), (0, 22), (6, 17), (12, 29), (0, 31), (12, 13), (18, 30), (15, 11), (8, 21), (14, 12), (30, 26), (24, 19), (20, 11), (31, 19), (17, 9), (10, 20), (21, 0), (8, 10), (2, 17), (3, 2), (33, 14), (0, 12), (22, 24), (23, 19), (22, 31), (21, 6), (18, 9), (26, 26), (27, 16), (5, 4), (13, 18), (8, 2), (26, 16), (12, 7), (15, 25), (2, 19), (20, 3), (32, 23), (26, 4), (20, 20), (22, 13), (13, 9), (21, 9), (19, 4), (17, 23), (27, 28), (7, 12), (11, 4), (14, 27), (17, 26), (16, 20), (27, 3), (28, 27), (30, 23), (21, 18), (3, 29), (8, 14), (12, 6), (10, 28), (29, 8), (4, 20), (26, 10), (32, 29), (3, 9), (22, 1), (1, 10), (13, 7), (26, 8), (2, 27), (20, 1), (13, 13), (2, 25), (14, 14), (2, 11), (3, 4), (9, 5), (10, 7), (12, 30), (32, 12), (7, 28), (5, 2), (20, 25), (29, 5), (22, 22), (32, 26), (20, 5), (10, 11), (24, 28), (12, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "787968", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (24, 26), (29, 12), (20, 23), (30, 6), (4, 28), (7, 24), (8, 11), (30, 24), (23, 25), (1, 17), (3, 8), (28, 24), (17, 2), (23, 27), (12, 30), (9, 3), (16, 31), (11, 28), (23, 10), (28, 20), (14, 9), (5, 2), (16, 2), (7, 27), (1, 10), (17, 14), (2, 31), (22, 11), (25, 7), (21, 23), (29, 21), (18, 3), (15, 1), (24, 4), (27, 17), (26, 0), (12, 3), (9, 8), (22, 28), (27, 12), (24, 19), (0, 23), (15, 11), (16, 30), (10, 14), (4, 3), (7, 12), (1, 15), (22, 23), (22, 27), (19, 26), (29, 24), (17, 12), (13, 15), (10, 31), (11, 20), (13, 7), (8, 28), (14, 12), (9, 31), (0, 22), (7, 31), (7, 14), (26, 4), (26, 26), (30, 11), (8, 14), (12, 21), (21, 18), (14, 4), (18, 26), (4, 7), (0, 26), (14, 26), (8, 8), (21, 13), (20, 22), (14, 8), (23, 28), (29, 0), (19, 21), (18, 5), (22, 15), (16, 16), (14, 3), (9, 30), (3, 29), (6, 13), (5, 18), (23, 7), (15, 4), (5, 13), (14, 25), (28, 10), (12, 12), (11, 8), (6, 6), (28, 27), (16, 15), (21, 25), (9, 13), (25, 8), (20, 10), (28, 17), (4, 15), (23, 22), (7, 30), (18, 18), (15, 6), (14, 10), (23, 16), (23, 19), (30, 12), (22, 13), (7, 16), (13, 8), (27, 28), (25, 21), (2, 1), (28, 22), (22, 25), (29, 14), (30, 3), (11, 13), (18, 13), (5, 23), (16, 12), (8, 20), (27, 21), (14, 1), (20, 0), (2, 30), (0, 16), (1, 16), (2, 20), (7, 6), (15, 2), (7, 17), (27, 18), (14, 23), (24, 27), (19, 22), (21, 6), (3, 30), (29, 23), (4, 6), (14, 20), (10, 9), (10, 28), (11, 17), (2, 22), (2, 28), (14, 28), (23, 24), (26, 29), (21, 17), (15, 23), (3, 0), (3, 24), (26, 5), (1, 26), (12, 20), (24, 23), (5, 19), (24, 9), (5, 0), (6, 25), (0, 13), (12, 28), (8, 3), (3, 25), (20, 2), (8, 21), (15, 20), (22, 19), (14, 0), (17, 22), (26, 8), (4, 22), (11, 19), (19, 12), (0, 5), (28, 9), (25, 24), (23, 4), (29, 9), (2, 8), (2, 26), (3, 1), (9, 14), (21, 21), (29, 18), (3, 15), (25, 0), (25, 18), (19, 24), (25, 9), (5, 16), (8, 30), (29, 11), (20, 12), (22, 3), (4, 21), (25, 12), (11, 12), (26, 21), (6, 20), (7, 4), (0, 4), (6, 2), (7, 1), (20, 24), (4, 9), (28, 14), (11, 22), (10, 7), (3, 22), (5, 3), (24, 8), (28, 5), (30, 0), (15, 26), (1, 9), (1, 11), (2, 23), (8, 26), (19, 17), (0, 12), (18, 1), (14, 16), (19, 14), (24, 13), (20, 5), (26, 13), (3, 11), (30, 13), (10, 10), (30, 4), (9, 16), (21, 0), (11, 27), (1, 24), (29, 17), (18, 17), (1, 29), (17, 17), (27, 6), (25, 27), (13, 10), (17, 13), (19, 20), (9, 22), (6, 4), (21, 7), (9, 17), (4, 27), (0, 15), (27, 10), (28, 7), (25, 28), (23, 3), (19, 11), (15, 27), (18, 22), (29, 6), (8, 2), (22, 24), (16, 22), (17, 18), (27, 15), (0, 10), (25, 6), (30, 27), (15, 0), (5, 9), (7, 10), (9, 23), (6, 29), (13, 29), (26, 15), (30, 5), (23, 9), (18, 31), (8, 15), (18, 2), (29, 1), (24, 6), (2, 3), (4, 5), (14, 7), (28, 18), (19, 8), (2, 18), (23, 14), (16, 26), (22, 0), (15, 9), (4, 25), (23, 1), (17, 10), (15, 30), (6, 10), (13, 1), (26, 30), (18, 25), (19, 7), (24, 5), (28, 3), (17, 29), (22, 12), (24, 15), (25, 4), (3, 12), (30, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "754110", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 28), (18, 33), (10, 21), (23, 2), (29, 2), (10, 24), (25, 13), (6, 11), (23, 9), (15, 16), (1, 14), (2, 3), (27, 6), (3, 3), (17, 27), (12, 3), (18, 17), (6, 10), (22, 5), (29, 7), (24, 33), (0, 30), (7, 4), (16, 3), (15, 18), (9, 11), (18, 28), (21, 26), (13, 18), (16, 26), (18, 22), (3, 2), (15, 17), (27, 16), (4, 35), (24, 35), (9, 14), (15, 12), (5, 13), (22, 25), (29, 11), (8, 4), (1, 0), (3, 7), (25, 16), (20, 0), (13, 25), (23, 30), (15, 3), (27, 22), (20, 14), (6, 25), (9, 6), (20, 2), (8, 6), (18, 2), (6, 27), (5, 33), (15, 15), (1, 27), (7, 0), (22, 23), (14, 22), (29, 23), (9, 35), (11, 32), (8, 14), (4, 7), (15, 25), (19, 35), (19, 7), (18, 34), (23, 22), (30, 2), (30, 20), (1, 17), (22, 20), (14, 18), (27, 10), (15, 31), (5, 16), (23, 6), (12, 22), (11, 20), (19, 11), (6, 16), (29, 35), (1, 23), (28, 30), (30, 16), (8, 30), (24, 0), (4, 22), (1, 20), (27, 2), (28, 28), (24, 6), (29, 9), (15, 32), (17, 23), (6, 15), (29, 5), (29, 27), (9, 33), (2, 8), (22, 12), (12, 12), (1, 21), (26, 27), (9, 17), (17, 35), (29, 20), (11, 9), (22, 34), (23, 20), (14, 9), (27, 25), (9, 19), (12, 8), (20, 32), (24, 31), (5, 21), (11, 11), (16, 18), (30, 13), (1, 29), (17, 2), (24, 13), (8, 15), (29, 26), (16, 5), (12, 1), (18, 27), (3, 24), (27, 7), (25, 17), (16, 16), (7, 6), (18, 10), (25, 14), (20, 30), (23, 5), (17, 31), (14, 11), (23, 26), (25, 1), (4, 32), (7, 7), (9, 5), (0, 3), (19, 3), (3, 11), (15, 34), (2, 10), (0, 23), (26, 22), (11, 26), (25, 29), (29, 13), (23, 17), (23, 11), (1, 34), (1, 22), (26, 11), (10, 8), (7, 33), (30, 29), (9, 24), (6, 4), (24, 17), (21, 14), (5, 11), (22, 15), (3, 17), (24, 7), (21, 10), (24, 3), (21, 19), (30, 18), (7, 32), (17, 30), (11, 6), (3, 25), (16, 10), (21, 4), (26, 30), (3, 27), (15, 27), (28, 14), (2, 25), (8, 3), (17, 20), (12, 0), (24, 27), (25, 32), (27, 28), (20, 29), (20, 26), (13, 1), (6, 19), (7, 8), (3, 33), (21, 24), (22, 19), (1, 28), (28, 26), (29, 34), (6, 12), (5, 24), (18, 31), (13, 17), (4, 19), (17, 28), (25, 4), (29, 14), (29, 8), (17, 15), (8, 24), (17, 13), (27, 14), (9, 29), (7, 25), (3, 34), (27, 33), (4, 17), (21, 20), (10, 26), (25, 7), (27, 9), (23, 1), (29, 0), (25, 0), (10, 6), (29, 1), (6, 2), (15, 10), (6, 32), (10, 2), (12, 20), (28, 18), (5, 26), (0, 13), (25, 22), (16, 34), (9, 4), (21, 30), (20, 31), (1, 33), (27, 24), (12, 28), (3, 10), (19, 32), (15, 30), (23, 33), (3, 30), (30, 5), (24, 15), (0, 8), (1, 18), (3, 28), (5, 34), (3, 21), (19, 9), (20, 16), (16, 35), (2, 0), (12, 6), (17, 11), (2, 7), (29, 32), (28, 12), (22, 6), (11, 2), (25, 9), (27, 30), (22, 4), (19, 19), (9, 30), (4, 18), (16, 11), (28, 17), (24, 16), (25, 26), (26, 13), (16, 12), (6, 5), (5, 3), (17, 0), (29, 28), (20, 33), (19, 2), (11, 8), (18, 7), (22, 1), (14, 5), (24, 23), (11, 14), (2, 5), (17, 26), (21, 12), (24, 19), (11, 15), (19, 14), (13, 3), (4, 15), (12, 21), (13, 19), (20, 10), (23, 28), (21, 28), (16, 14), (8, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "499968", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 28), (7, 36), (18, 21), (23, 23), (10, 30), (0, 19), (14, 12), (6, 36), (0, 7), (27, 0), (1, 35), (8, 1), (26, 24), (37, 19), (20, 1), (30, 34), (1, 26), (18, 12), (37, 20), (0, 35), (35, 31), (18, 1), (21, 33), (11, 9), (26, 9), (10, 16), (19, 36), (2, 20), (26, 13), (10, 12), (8, 37), (11, 0), (13, 6), (29, 33), (20, 29), (19, 27), (14, 18), (24, 16), (9, 13), (13, 38), (8, 18), (22, 21), (19, 23), (23, 34), (16, 19), (28, 0), (0, 22), (16, 1), (3, 37), (6, 8), (35, 12), (2, 12), (20, 32), (15, 35), (5, 18), (9, 6), (30, 15), (7, 19), (20, 33), (36, 33), (19, 17), (17, 7), (24, 13), (9, 2), (29, 38), (31, 16), (37, 10), (8, 2), (7, 20), (28, 20), (36, 37), (18, 33), (16, 5), (1, 31), (6, 7), (27, 13), (25, 5), (7, 18), (2, 27), (23, 4), (16, 34), (32, 4), (2, 8), (12, 0), (33, 37), (32, 19), (32, 32), (7, 10), (21, 28), (36, 11), (15, 21), (8, 11), (12, 23), (20, 19), (0, 17), (35, 19), (24, 18), (30, 25), (37, 27), (30, 28), (12, 1), (25, 21), (15, 14), (26, 3), (15, 0), (26, 38), (17, 25), (9, 17), (5, 28), (4, 37), (2, 11), (19, 35), (13, 24), (35, 10), (23, 7), (35, 14), (22, 12), (10, 5), (11, 8), (31, 38), (32, 3), (2, 24), (22, 6), (4, 13), (28, 29), (37, 18), (24, 9), (28, 32), (4, 17), (36, 8), (8, 33), (24, 33), (33, 11), (20, 27), (16, 32), (12, 11), (25, 11), (10, 23), (26, 23), (26, 21), (28, 28), (7, 3), (34, 7), (34, 37), (22, 3), (37, 14), (30, 38), (36, 17), (35, 15), (31, 28), (24, 29), (34, 28), (15, 29), (14, 20), (14, 14), (32, 11), (24, 0), (17, 35), (2, 31), (27, 25), (37, 2), (15, 16), (17, 4), (12, 22), (6, 6), (28, 36), (31, 13), (21, 32), (22, 37), (29, 34), (16, 27), (35, 26), (23, 32), (35, 3), (6, 0), (3, 35), (14, 25), (21, 6), (5, 6), (1, 0), (36, 20), (30, 1), (11, 22), (28, 11), (26, 20), (25, 22), (12, 15), (17, 32), (2, 1), (27, 16), (13, 19), (19, 19), (12, 17), (14, 32), (32, 38), (13, 17), (31, 20), (21, 12), (4, 22), (2, 13), (3, 28), (7, 4), (12, 29), (3, 2), (36, 25), (1, 12), (31, 17), (36, 14), (15, 7), (19, 24), (28, 25), (19, 30), (32, 14), (2, 23), (34, 5), (24, 4), (31, 9), (32, 1), (21, 24), (27, 26), (32, 34), (25, 18), (35, 33), (10, 32), (27, 9), (20, 35), (27, 14), (2, 38), (8, 15), (4, 38), (11, 24), (3, 34), (23, 8), (29, 29), (36, 15), (8, 5), (16, 15), (23, 19), (11, 12), (0, 6), (31, 35), (11, 19), (21, 30), (25, 37), (6, 27), (33, 18), (36, 38), (13, 11), (5, 27), (26, 26), (0, 38), (27, 5), (35, 37), (17, 21), (12, 37), (7, 31), (3, 22), (18, 35), (2, 5), (32, 18), (22, 23), (18, 15), (19, 20), (16, 22), (12, 4), (19, 38), (33, 20), (30, 14), (7, 34), (25, 7), (19, 16), (34, 21), (2, 17), (27, 20), (6, 24), (0, 32), (11, 6), (35, 23), (13, 23), (11, 32), (2, 30), (2, 6), (9, 36), (34, 34), (25, 25), (32, 12), (4, 14), (25, 17), (8, 23), (9, 10), (13, 21), (31, 2), (13, 1), (10, 34), (24, 23), (0, 36), (17, 8), (28, 19), (26, 8), (15, 30), (23, 9), (6, 32), (27, 18), (15, 23), (6, 18), (34, 26), (30, 13), (8, 28), (27, 29), (20, 31), (13, 29), (1, 4), (19, 9), (21, 18), (9, 15), (19, 21), (22, 19), (17, 37), (27, 8), (10, 35), (9, 5), (0, 13), (35, 24), (26, 37), (19, 29), (28, 5), (33, 13), (14, 6), (30, 22), (15, 12), (36, 16), (29, 20), (10, 31), (19, 8), (5, 21), (10, 14), (11, 35), (9, 9), (4, 15), (5, 33), (14, 36), (14, 29), (7, 22), (2, 35), (23, 12), (30, 7), (6, 11), (24, 31), (18, 23), (29, 14), (15, 15), (12, 13), (9, 23), (5, 5), (34, 1), (3, 9), (9, 18), (8, 4), (16, 7), (32, 22), (16, 8), (31, 18), (21, 1), (33, 4), (6, 19), (22, 15), (29, 6), (3, 21), (23, 0), (8, 22), (30, 37), (30, 19), (11, 1), (34, 0), (22, 26), (8, 26), (36, 18), (29, 26), (20, 37), (14, 8), (20, 18), (7, 7), (11, 5), (5, 36), (21, 11), (36, 23), (33, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "922180", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 0), (26, 19), (9, 35), (14, 30), (21, 30), (17, 13), (32, 20), (28, 30), (26, 10), (26, 16), (14, 24), (6, 28), (0, 20), (18, 29), (19, 17), (9, 25), (5, 7), (10, 30), (15, 28), (12, 23), (9, 0), (6, 34), (26, 1), (8, 36), (16, 8), (33, 31), (29, 13), (9, 14), (35, 36), (27, 13), (29, 34), (17, 8), (15, 37), (33, 17), (25, 33), (15, 23), (33, 21), (10, 16), (18, 23), (1, 25), (18, 0), (21, 36), (11, 30), (34, 28), (32, 15), (19, 13), (6, 15), (30, 23), (19, 33), (21, 31), (14, 26), (33, 11), (22, 10), (5, 12), (13, 23), (2, 22), (1, 4), (23, 35), (29, 10), (1, 15), (4, 19), (35, 11), (28, 0), (20, 17), (3, 34), (4, 9), (12, 28), (7, 12), (16, 6), (10, 0), (0, 11), (12, 20), (10, 15), (34, 26), (33, 24), (2, 11), (19, 7), (12, 1), (7, 22), (26, 12), (7, 28), (1, 26), (32, 14), (34, 22), (8, 17), (24, 13), (19, 18), (28, 1), (23, 1), (7, 4), (5, 4), (23, 17), (19, 36), (8, 37), (35, 12), (1, 29), (1, 33), (2, 10), (23, 12), (20, 30), (7, 31), (34, 32), (6, 21), (20, 2), (10, 1), (6, 11), (31, 19), (28, 9), (28, 25), (28, 22), (28, 18), (7, 38), (11, 18), (4, 2), (17, 14), (17, 19), (17, 29), (7, 35), (11, 22), (18, 37), (29, 30), (21, 3), (30, 20), (0, 28), (22, 37), (18, 19), (13, 29), (12, 7), (13, 21), (1, 37), (35, 18), (6, 19), (35, 14), (24, 14), (30, 31), (20, 4), (2, 36), (27, 3), (2, 21), (14, 32), (22, 3), (29, 24), (18, 21), (32, 18), (30, 8), (31, 22), (30, 32), (6, 6), (15, 26), (2, 12), (22, 27), (31, 12), (17, 11), (24, 0), (30, 9), (12, 26), (9, 13), (20, 5), (23, 18), (13, 26), (3, 14), (13, 8), (18, 8), (24, 2), (24, 20), (16, 9), (8, 24), (13, 13), (30, 18), (1, 24), (8, 31), (0, 7), (8, 18), (29, 2), (35, 17), (1, 3), (27, 20), (14, 21), (26, 26), (29, 3), (21, 18), (2, 23), (24, 19), (21, 24), (27, 5), (21, 2), (1, 35), (9, 32), (23, 15), (13, 14), (21, 21), (6, 37), (2, 37), (20, 6), (17, 23), (23, 22), (18, 32), (4, 22), (5, 6), (5, 15), (4, 21), (22, 29), (26, 15), (23, 5), (9, 28), (34, 12), (13, 30), (8, 29), (13, 10), (13, 5), (17, 32), (20, 1), (19, 6), (26, 3), (14, 7), (6, 4), (13, 34), (31, 4), (17, 20), (31, 28), (23, 16), (8, 30), (31, 38), (21, 4), (13, 20), (34, 21), (29, 5), (6, 26), (17, 4), (35, 9), (10, 11), (30, 11), (4, 34), (10, 14), (32, 2), (20, 12), (5, 38), (33, 34), (8, 0), (8, 15), (17, 12), (14, 23), (33, 33), (3, 18), (32, 29), (15, 17), (28, 34), (35, 7), (14, 33), (16, 21), (3, 23), (21, 37), (27, 4), (19, 38), (7, 20), (15, 6), (29, 18), (21, 12), (26, 4), (21, 11), (14, 2), (17, 25), (29, 26), (10, 34), (16, 2), (8, 6), (34, 9), (24, 29), (1, 5), (15, 21), (2, 2), (26, 7), (5, 10), (23, 0), (3, 4), (2, 38), (26, 34), (27, 0), (12, 14), (25, 27), (32, 32), (28, 5), (26, 27), (12, 16), (15, 30), (27, 27), (10, 23), (21, 8), (23, 9), (27, 33), (35, 2), (29, 35), (11, 3), (5, 3), (5, 32), (34, 25), (9, 7), (10, 24), (8, 28), (17, 24), (3, 3), (25, 13), (26, 20), (35, 24), (30, 22), (22, 14), (27, 30), (9, 20), (30, 16), (26, 14), (25, 12), (4, 25), (22, 17), (24, 11), (11, 12), (24, 34), (15, 29), (18, 27), (22, 20), (14, 4), (2, 3), (4, 20), (1, 1), (28, 2), (18, 25), (29, 8), (33, 22), (24, 12), (18, 18), (16, 32), (14, 31), (24, 26), (6, 36), (13, 16), (25, 20), (29, 4), (29, 38), (24, 5), (18, 30), (16, 5), (7, 19), (28, 15), (4, 16), (16, 0), (24, 28), (31, 25), (16, 12), (24, 31), (25, 11), (8, 32), (13, 33), (28, 17), (23, 36), (23, 2), (12, 34), (7, 10), (14, 36), (34, 33), (10, 18), (19, 2), (23, 6), (5, 33), (14, 34), (6, 24), (6, 0), (9, 33), (11, 37), (3, 30), (21, 9), (7, 30), (29, 23), (7, 16), (9, 31), (13, 2), (12, 36), (10, 20), (7, 17), (31, 26), (10, 29), (25, 18), (0, 35), (15, 35), (21, 27), (33, 27), (22, 8), (4, 35), (25, 8), (24, 27), (27, 21), (1, 36), (22, 16), (18, 9), (7, 13), (16, 17), (28, 6), (26, 5), (33, 16), (17, 35), (7, 3), (15, 16), (7, 9), (35, 26), (14, 22), (21, 19), (35, 5), (10, 28), (6, 25), (29, 22), (34, 16), (22, 38), (35, 6), (0, 8), (12, 4), (18, 3), (26, 25), (18, 14), (20, 14), (26, 18), (2, 28), (35, 27), (32, 10), (31, 35)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770640", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 11), (4, 38), (12, 22), (29, 0), (24, 11), (23, 38), (20, 8), (8, 37), (5, 8), (25, 34), (18, 15), (25, 24), (21, 35), (28, 37), (27, 35), (8, 17), (0, 33), (12, 18), (14, 7), (14, 17), (13, 31), (1, 20), (14, 11), (19, 9), (13, 10), (12, 2), (16, 33), (5, 3), (29, 14), (25, 38), (10, 26), (18, 8), (15, 30), (17, 38), (1, 36), (24, 35), (10, 0), (15, 26), (18, 2), (19, 12), (14, 29), (20, 23), (0, 29), (4, 3), (6, 16), (6, 30), (10, 27), (17, 19), (1, 38), (14, 28), (26, 24), (0, 17), (7, 19), (15, 35), (24, 5), (11, 8), (9, 12), (14, 33), (19, 36), (15, 6), (1, 2), (0, 8), (22, 18), (20, 0), (12, 1), (19, 34), (3, 0), (27, 9), (19, 28), (27, 1), (16, 36), (16, 1), (24, 29), (17, 14), (16, 10), (3, 15), (6, 24), (18, 16), (7, 2), (16, 3), (11, 20), (10, 34), (14, 27), (10, 10), (11, 13), (21, 0), (4, 4), (19, 32), (21, 20), (9, 3), (12, 29), (28, 9), (7, 31), (1, 30), (15, 28), (17, 25), (29, 31), (23, 26), (6, 35), (21, 26), (3, 35), (26, 18), (4, 30), (22, 1), (7, 17), (7, 5), (8, 20), (6, 5), (28, 17), (29, 22), (27, 33), (18, 11), (12, 8), (22, 13), (1, 9), (12, 17), (3, 22), (16, 12), (24, 10), (22, 22), (2, 26), (21, 24), (18, 34), (6, 34), (14, 6), (7, 0), (18, 24), (16, 14), (7, 7), (6, 1), (23, 32), (16, 4), (24, 19), (18, 36), (11, 19), (28, 10), (22, 3), (5, 36), (7, 34), (1, 18), (28, 11), (21, 38), (19, 19), (22, 23), (1, 16), (29, 11), (17, 10), (0, 36), (2, 17), (9, 10), (1, 14), (24, 27), (18, 6), (4, 2), (9, 1), (24, 18), (5, 0), (6, 26), (29, 4), (3, 28), (20, 28), (14, 12), (19, 5), (22, 8), (23, 33), (3, 23), (29, 13), (27, 13), (15, 19), (28, 28), (17, 31), (22, 30), (4, 26), (0, 20), (11, 1), (12, 20), (0, 3), (2, 22), (2, 6), (27, 16), (11, 18), (26, 38), (4, 27), (29, 16), (5, 27), (20, 25), (9, 35), (26, 0), (7, 6), (25, 33), (4, 28), (25, 11), (29, 2), (19, 31), (4, 8), (2, 11), (21, 9), (19, 16), (9, 22), (13, 19), (21, 29), (21, 5), (11, 11), (21, 6), (10, 30), (19, 2), (9, 6), (13, 29), (9, 33), (8, 10), (7, 25), (23, 10), (4, 23), (2, 38), (28, 0), (20, 4), (12, 31), (11, 34), (4, 31), (25, 32), (13, 24), (7, 9), (13, 28), (12, 5), (3, 5), (24, 22), (7, 4), (1, 13), (29, 12), (17, 15), (17, 29), (24, 31), (17, 5), (29, 32), (10, 4), (0, 9), (29, 29), (8, 11), (22, 25), (15, 24), (18, 18), (1, 33), (13, 25), (17, 21), (20, 1), (28, 14), (18, 30), (23, 15), (14, 18), (29, 15), (5, 10), (13, 23), (26, 34), (7, 33), (7, 13), (9, 20), (22, 21), (3, 6), (25, 35), (8, 28), (21, 30), (5, 20), (2, 24), (2, 37), (13, 6), (1, 21), (4, 35), (24, 32), (23, 2), (14, 37), (23, 1), (11, 28), (22, 33), (3, 30), (12, 16), (4, 14), (6, 38), (22, 19), (13, 1), (22, 37), (8, 15), (11, 21), (8, 21), (29, 30), (29, 9), (13, 37), (3, 4), (25, 12), (17, 7), (22, 14), (11, 2), (5, 14), (20, 2), (23, 12), (28, 38), (18, 23), (12, 4), (14, 10), (8, 27), (12, 26), (16, 2), (11, 30), (4, 34), (21, 32), (6, 13), (27, 4), (9, 5), (28, 27), (10, 38), (20, 13), (26, 15), (20, 31), (24, 2), (2, 3), (6, 18), (0, 15), (13, 13), (27, 20), (19, 4), (9, 31), (29, 21), (26, 2), (13, 7), (22, 9), (28, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17820", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (28, 6), (12, 25), (30, 14), (15, 27), (31, 2), (19, 24), (5, 22), (32, 26), (30, 24), (28, 11), (36, 1), (9, 23), (21, 5), (32, 11), (28, 14), (13, 25), (16, 29), (15, 8), (14, 18), (25, 6), (35, 3), (30, 11), (16, 24), (1, 0), (7, 14), (18, 7), (23, 24), (26, 29), (13, 28), (7, 16), (14, 13), (12, 12), (3, 15), (17, 18), (37, 10), (6, 4), (14, 6), (35, 17), (19, 32), (14, 29), (19, 30), (23, 17), (19, 15), (25, 32), (8, 12), (17, 27), (2, 23), (14, 10), (16, 26), (20, 3), (30, 20), (11, 4), (36, 27), (4, 30), (21, 22), (35, 2), (33, 19), (32, 25), (31, 20), (10, 4), (4, 6), (33, 9), (34, 14), (5, 17), (11, 11), (3, 31), (25, 18), (28, 12), (13, 29), (18, 24), (33, 11), (13, 32), (14, 4), (22, 23), (29, 17), (3, 9), (13, 19), (17, 7), (29, 10), (36, 8), (24, 24), (12, 18), (9, 12), (4, 3), (10, 22), (32, 31), (2, 0), (9, 18), (28, 18), (2, 2), (32, 12), (27, 6), (16, 5), (0, 8), (24, 19), (6, 1), (30, 16), (15, 3), (4, 10), (17, 16), (1, 11), (6, 3), (26, 19), (16, 4), (22, 15), (25, 26), (34, 5), (25, 12), (36, 22), (34, 17), (29, 29), (33, 25), (31, 3), (31, 4), (32, 24), (18, 29), (34, 23), (6, 19), (19, 7), (26, 21), (9, 32), (14, 8), (10, 13), (12, 16), (16, 0), (7, 7), (0, 30), (18, 11), (20, 15), (37, 9), (25, 1), (23, 8), (19, 1), (36, 10), (26, 23), (10, 16), (1, 13), (15, 14), (15, 2), (7, 24), (22, 3), (6, 23), (32, 29), (23, 1), (34, 31), (13, 2), (4, 1), (31, 9), (35, 9), (5, 3), (22, 4), (21, 12), (13, 16), (24, 4), (31, 22), (2, 1), (33, 22), (3, 3), (31, 25), (15, 23), (27, 32), (10, 10), (8, 17), (22, 21), (28, 27), (2, 25), (2, 5), (9, 30), (18, 4), (6, 9), (23, 9), (33, 20), (24, 18), (17, 28), (11, 29), (13, 7), (19, 28), (8, 25), (14, 21), (20, 29), (20, 10), (3, 8), (34, 4), (9, 31), (20, 27), (8, 30), (13, 22), (16, 27), (15, 18), (12, 26), (28, 0), (31, 15), (22, 30), (2, 8), (23, 6), (36, 25), (17, 23), (0, 26), (5, 23), (11, 6), (9, 27), (27, 17), (4, 31), (10, 6), (27, 15), (7, 19), (11, 30), (26, 25), (8, 1), (26, 7), (0, 11), (8, 19), (17, 4), (18, 18), (34, 25), (29, 22), (0, 19), (28, 5), (3, 27), (27, 24), (12, 28), (9, 2), (8, 22), (17, 22), (1, 15), (15, 24), (29, 26), (31, 17), (4, 5), (16, 30), (32, 30), (27, 20), (11, 32), (7, 17), (28, 26), (21, 25), (0, 13), (1, 12), (16, 25), (4, 16), (23, 22), (36, 3), (4, 11), (25, 3), (16, 21), (6, 30), (20, 8), (32, 21), (7, 12), (32, 27), (22, 24), (7, 15), (8, 10), (0, 12), (16, 3), (27, 25), (21, 9), (22, 25), (35, 21), (12, 9), (28, 9), (33, 5), (14, 12), (5, 11), (21, 16), (33, 21), (36, 30), (1, 20), (36, 16), (33, 3), (7, 30), (14, 11), (4, 22), (16, 8), (5, 2), (9, 7), (4, 17), (1, 31), (35, 25), (7, 32), (26, 26), (35, 15), (19, 13), (9, 13), (31, 5), (12, 7), (19, 19), (24, 1), (0, 21), (3, 7), (24, 31), (23, 13), (1, 22), (29, 7), (23, 20), (22, 20), (18, 12), (26, 3), (3, 22), (23, 32), (15, 20), (29, 31), (3, 32), (29, 0), (28, 20), (19, 22), (28, 19), (29, 15), (9, 20), (14, 15), (16, 6), (27, 23), (32, 15), (14, 16), (13, 12), (8, 21), (25, 17), (22, 1), (10, 14), (37, 31), (9, 19), (30, 1), (20, 6), (18, 19), (31, 24), (4, 20), (1, 16), (34, 12), (10, 20), (26, 15), (36, 24), (13, 15), (25, 29), (26, 4), (17, 14), (25, 7), (3, 29), (11, 10), (2, 20), (28, 13), (22, 32), (26, 24), (13, 8), (30, 8), (7, 3), (24, 2), (10, 2), (27, 19), (26, 18), (29, 30), (21, 31), (20, 30), (27, 13), (24, 23), (30, 18), (21, 6), (23, 23), (36, 11), (15, 30), (23, 2), (2, 6), (7, 6), (26, 1), (16, 16), (32, 16), (34, 32), (30, 32), (21, 23), (12, 2), (34, 26), (24, 16), (9, 4), (16, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "550704", "dataset": "MATH"}
{"messages": [{"content": "In a 39x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 36), 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), (35, 18), (4, 9), (0, 34), (4, 11), (32, 2), (21, 32), (31, 26), (20, 17), (16, 14), (7, 35), (21, 11), (2, 1), (20, 3), (27, 21), (34, 26), (0, 5), (3, 1), (30, 11), (16, 18), (14, 1), (17, 20), (26, 21), (36, 33), (24, 4), (2, 31), (10, 2), (35, 4), (0, 36), (27, 35), (8, 7), (23, 10), (23, 0), (5, 14), (4, 12), (1, 10), (14, 17), (17, 36), (36, 3), (9, 11), (22, 29), (3, 23), (3, 36), (5, 36), (30, 18), (16, 2), (5, 29), (11, 20), (7, 15), (14, 27), (15, 20), (22, 2), (4, 22), (21, 18), (10, 29), (6, 36), (1, 36), (2, 7), (6, 15), (2, 28), (31, 18), (19, 5), (22, 21), (6, 33), (11, 9), (8, 11), (26, 32), (3, 20), (26, 16), (21, 30), (12, 26), (34, 31), (14, 26), (8, 35), (24, 16), (22, 5), (11, 35), (38, 26), (20, 8), (19, 13), (24, 14), (21, 24), (18, 13), (5, 0), (1, 31), (11, 19), (37, 22), (28, 6), (26, 15), (10, 33), (22, 10), (36, 1), (19, 6), (16, 1), (24, 28), (23, 9), (27, 18), (10, 21), (6, 17), (16, 4), (28, 7), (16, 6), (3, 21), (23, 12), (10, 16), (11, 11), (18, 27), (21, 5), (20, 9), (3, 13), (25, 13), (3, 8), (38, 35), (13, 13), (31, 15), (21, 8), (1, 23), (33, 15), (27, 12), (36, 0), (34, 3), (20, 5), (1, 12), (10, 25), (13, 7), (8, 34), (15, 15), (19, 31), (30, 20), (16, 31), (27, 30), (15, 1), (8, 19), (32, 24), (10, 19), (13, 11), (10, 6), (10, 0), (17, 28), (27, 9), (6, 28), (28, 5), (13, 18), (1, 35), (38, 14), (20, 0), (22, 1), (2, 36), (25, 5), (23, 13), (38, 31), (3, 14), (37, 4), (18, 17), (37, 9), (28, 35), (15, 11), (12, 23), (31, 9), (2, 35), (1, 25), (23, 28), (15, 35), (0, 17), (4, 16), (27, 3), (7, 23), (38, 4), (5, 32), (20, 27), (26, 29), (0, 23), (13, 14), (28, 27), (12, 30), (37, 34), (4, 1), (38, 13), (34, 12), (14, 22), (7, 27), (3, 34), (21, 28), (2, 32), (0, 11), (1, 30), (12, 32), (11, 24), (20, 36), (9, 31), (7, 14), (38, 19), (11, 2), (32, 21), (7, 33), (9, 18), (35, 19), (26, 33), (23, 5), (2, 10), (10, 24), (34, 29), (1, 7), (23, 18), (21, 7), (15, 19), (25, 15), (18, 15), (20, 26), (8, 10), (1, 8), (30, 21), (9, 5), (23, 19), (13, 19), (7, 2), (35, 5), (29, 6), (22, 24), (4, 18), (18, 5), (19, 29), (21, 25), (22, 14), (24, 24), (16, 17), (13, 0), (22, 31), (12, 25), (24, 21), (33, 27), (32, 27), (25, 11), (2, 16), (6, 35), (23, 16), (17, 27), (37, 24), (18, 25), (33, 33), (26, 36), (32, 22), (6, 30), (6, 14), (2, 34), (28, 30), (24, 34), (19, 14), (1, 29), (0, 15), (5, 31), (2, 8), (30, 12), (14, 36), (7, 22), (13, 24), (35, 16), (1, 1), (36, 7), (38, 21), (17, 24), (19, 11), (19, 16), (18, 32), (32, 31), (13, 32), (12, 28), (10, 22), (24, 22), (14, 25), (3, 22), (24, 35), (12, 20), (14, 33), (4, 7), (14, 8), (36, 15), (18, 16), (25, 2), (36, 35), (12, 1), (32, 28), (5, 9), (35, 3), (6, 23), (13, 29), (38, 24), (33, 3), (8, 16), (28, 4), (28, 11), (7, 19), (35, 9), (36, 11), (28, 23), (12, 13), (10, 30), (7, 34), (22, 7), (15, 28), (6, 22), (27, 36), (18, 31), (1, 2), (3, 30), (5, 2), (25, 3), (10, 9), (32, 26), (28, 33), (20, 29), (1, 19), (37, 23), (33, 8), (26, 10), (0, 8), (27, 25), (19, 7), (4, 23), (13, 23), (37, 1), (16, 15), (10, 34), (24, 12), (33, 34), (37, 29), (10, 15), (11, 16), (23, 11), (33, 21), (10, 26), (38, 22), (6, 5), (13, 12), (1, 22), (0, 18), (20, 12), (13, 36), (22, 22), (14, 0), (26, 31), (7, 13), (1, 21), (1, 17), (14, 31), (24, 27), (35, 14), (7, 25), (5, 4), (20, 13), (28, 22), (12, 2), (20, 23), (38, 2), (8, 36), (16, 28), (22, 34), (17, 15), (38, 0), (24, 18), (23, 35), (2, 26), (18, 23), (34, 17), (7, 17), (29, 2), (1, 13), (24, 8), (21, 17), (25, 34), (9, 16), (23, 25), (36, 29), (9, 28), (5, 7), (16, 8), (25, 31), (9, 13), (28, 21), (5, 1), (37, 19), (35, 2), (36, 21), (18, 28), (13, 35), (25, 18), (0, 7), (37, 31), (10, 11), (28, 15), (30, 10), (33, 16), (30, 23), (16, 22), (19, 0), (34, 10), (26, 26), (20, 1), (21, 34), (12, 17), (3, 5), (19, 17), (7, 28), (21, 12), (4, 3), (36, 4), (8, 18), (20, 4), (14, 34), (38, 34), (20, 7), (33, 11), (33, 18), (14, 23), (29, 17), (18, 7), (23, 30), (26, 25), (11, 1), (2, 11), (2, 4), (35, 13), (27, 34), (37, 20), (27, 23), (16, 11), (12, 14), (6, 21), (29, 4), (26, 1), (8, 29), (19, 35), (12, 12), (32, 35), (15, 9), (9, 27), (25, 8), (29, 11), (4, 35), (12, 4), (38, 9), (23, 22), (4, 33), (21, 29), (21, 20), (18, 9), (10, 17), (18, 18), (14, 30), (18, 1), (26, 2), (1, 9), (30, 16), (17, 9), (15, 25), (11, 34), (15, 4), (29, 24), (29, 29), (26, 7), (2, 0), (15, 5), (5, 21), (0, 35), (17, 32), (16, 26), (2, 9), (1, 5), (38, 16), (15, 21), (11, 23), (24, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "570440", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (38, 22), (7, 29), (25, 16), (9, 24), (4, 9), (12, 15), (27, 20), (22, 15), (5, 0), (37, 1), (7, 30), (32, 16), (4, 8), (4, 31), (19, 21), (6, 2), (11, 2), (35, 18), (26, 10), (28, 22), (23, 28), (8, 8), (32, 2), (16, 24), (38, 0), (28, 24), (32, 17), (16, 15), (4, 28), (4, 2), (17, 9), (21, 20), (2, 14), (21, 12), (1, 6), (10, 17), (11, 16), (38, 2), (36, 1), (29, 26), (20, 21), (26, 4), (10, 0), (29, 19), (34, 21), (26, 12), (29, 13), (22, 28), (31, 27), (27, 0), (20, 7), (5, 18), (29, 3), (8, 31), (5, 12), (10, 6), (34, 9), (23, 18), (38, 15), (17, 11), (35, 14), (5, 29), (3, 14), (20, 19), (22, 9), (37, 5), (4, 20), (5, 22), (25, 13), (22, 18), (16, 28), (14, 29), (29, 22), (37, 11), (12, 14), (0, 22), (32, 28), (32, 21), (7, 10), (35, 30), (31, 8), (20, 1), (3, 21), (27, 17), (13, 21), (28, 30), (0, 13), (24, 16), (12, 12), (13, 31), (10, 31), (28, 17), (0, 28), (12, 7), (8, 23), (33, 1), (17, 18), (15, 7), (4, 23), (0, 3), (18, 29), (35, 20), (30, 30), (6, 24), (38, 7), (14, 25), (4, 3), (6, 22), (18, 16), (14, 12), (29, 23), (27, 16), (17, 31), (6, 15), (4, 5), (16, 12), (13, 18), (19, 1), (21, 23), (37, 25), (12, 19), (4, 7), (2, 22), (15, 25), (14, 14), (1, 17), (4, 6), (8, 6), (13, 2), (3, 6), (9, 14), (14, 6), (13, 22), (37, 22), (10, 26), (37, 3), (15, 11), (22, 11), (1, 23), (7, 27), (17, 25), (31, 3), (13, 14), (14, 11), (38, 8), (8, 26), (33, 31), (15, 1), (33, 25), (21, 26), (32, 11), (24, 25), (17, 10), (0, 20), (35, 16), (17, 7), (30, 29), (14, 9), (18, 22), (24, 23), (11, 22), (36, 31), (38, 28), (3, 10), (32, 8), (30, 14), (3, 17), (5, 20), (8, 22), (20, 10), (13, 6), (25, 5), (0, 9), (38, 13), (15, 0), (28, 14), (13, 12), (21, 28), (1, 13), (8, 29), (23, 1), (16, 3), (29, 8), (16, 23), (17, 16), (29, 9), (5, 28), (16, 11), (32, 26), (25, 1), (17, 27), (6, 18), (1, 20), (4, 30), (3, 15), (4, 19), (16, 26), (10, 15), (7, 13), (18, 12), (25, 18), (11, 15), (25, 17), (8, 3), (7, 20), (3, 23), (18, 8), (8, 11), (16, 30), (24, 26), (6, 26), (33, 27), (23, 4), (11, 29), (23, 31), (18, 31), (1, 1), (33, 12), (10, 1), (16, 10), (36, 15), (24, 0), (15, 13), (8, 4), (16, 16), (15, 26), (12, 27), (4, 10), (26, 18), (18, 15), (15, 16), (36, 25), (15, 24), (20, 29), (25, 11), (22, 20), (4, 29), (3, 5), (25, 20), (24, 5), (33, 19), (11, 26), (36, 4), (26, 26), (24, 27), (24, 6), (30, 18), (32, 27), (12, 26), (37, 19), (27, 15), (8, 30), (5, 14), (30, 25), (24, 4), (7, 21), (24, 30), (11, 3), (33, 2), (9, 6), (17, 4), (15, 18), (11, 25), (9, 4), (8, 18), (1, 8), (10, 25), (24, 18), (11, 6), (25, 28), (9, 25), (22, 3), (26, 23), (16, 8), (35, 21), (1, 9), (1, 10), (0, 26), (14, 18), (34, 0), (9, 29), (17, 28), (1, 21), (0, 30), (31, 16), (13, 26), (28, 31), (12, 5), (28, 15), (0, 14), (28, 20), (34, 2), (34, 28), (21, 31), (26, 30), (21, 27), (2, 21), (25, 14), (35, 19), (12, 4), (29, 1), (36, 14), (15, 14), (37, 20), (18, 14), (6, 5), (20, 18), (9, 10), (22, 13), (28, 29), (35, 25), (34, 19), (6, 12), (38, 16), (5, 2), (3, 28), (7, 17), (29, 29), (6, 7), (33, 26), (35, 23), (10, 23), (31, 0), (32, 10), (27, 30), (7, 16), (33, 24), (28, 21), (16, 6), (25, 9), (23, 23), (24, 20), (17, 26), (8, 27), (25, 10), (29, 2), (5, 10), (24, 2), (1, 4), (35, 31), (14, 2), (15, 6), (30, 17), (29, 20), (26, 24), (35, 7), (6, 25), (2, 18), (28, 25), (22, 25), (28, 8), (2, 30), (34, 12), (38, 26), (24, 8), (23, 27), (21, 29), (0, 7), (11, 8), (0, 23), (20, 5), (5, 6), (12, 13), (0, 4), (34, 24), (19, 16), (19, 2), (10, 10), (12, 29), (14, 31), (20, 27), (13, 17), (26, 5), (8, 28), (24, 9), (32, 22), (33, 4), (21, 30), (14, 24), (13, 3), (20, 22), (33, 7), (34, 1), (35, 5), (4, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "907200", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 27), (1, 28), (27, 24), (27, 6), (23, 22), (9, 23), (23, 0), (1, 16), (18, 9), (24, 20), (14, 31), (11, 25), (27, 28), (21, 11), (16, 18), (0, 26), (3, 33), (26, 14), (4, 20), (18, 17), (18, 29), (7, 28), (21, 18), (9, 18), (25, 28), (7, 17), (0, 23), (1, 20), (6, 3), (6, 18), (12, 13), (1, 5), (6, 13), (5, 15), (11, 23), (20, 27), (21, 27), (13, 11), (29, 32), (11, 1), (16, 29), (20, 25), (21, 26), (29, 2), (0, 31), (22, 19), (29, 19), (3, 7), (9, 10), (9, 11), (23, 30), (26, 4), (8, 28), (1, 24), (17, 22), (12, 17), (3, 31), (6, 8), (14, 21), (0, 19), (27, 22), (8, 26), (2, 21), (2, 3), (26, 16), (27, 30), (22, 8), (13, 20), (6, 16), (15, 24), (20, 15), (25, 10), (17, 30), (16, 1), (4, 19), (5, 21), (6, 14), (30, 23), (26, 22), (16, 17), (0, 20), (5, 32), (16, 8), (15, 0), (29, 5), (26, 21), (5, 2), (29, 3), (8, 3), (4, 23), (21, 25), (28, 18), (13, 2), (26, 18), (4, 29), (10, 31), (21, 14), (7, 0), (25, 21), (6, 1), (1, 26), (13, 0), (7, 18), (7, 30), (7, 25), (17, 9), (23, 3), (26, 6), (7, 27), (20, 29), (19, 32), (19, 8), (16, 12), (4, 33), (5, 33), (7, 13), (19, 5), (6, 4), (27, 20), (12, 5), (8, 23), (15, 17), (27, 14), (4, 0), (15, 33), (2, 13), (14, 12), (26, 28), (19, 28), (2, 2), (2, 9), (1, 19), (29, 15), (18, 20), (10, 19), (23, 12), (16, 2), (15, 7), (12, 1), (4, 9), (1, 27), (29, 14), (18, 19), (1, 7), (11, 19), (9, 2), (21, 16), (13, 29), (0, 13), (8, 29), (10, 14), (8, 17), (18, 10), (16, 23), (17, 13), (24, 9), (2, 10), (19, 22), (20, 21), (14, 8), (10, 15), (24, 33), (18, 8), (19, 31), (15, 1), (9, 22), (30, 22), (19, 17), (23, 20), (13, 22), (1, 22), (4, 15), (9, 19), (28, 5), (15, 30), (1, 0), (27, 13), (21, 15), (1, 32), (24, 10), (21, 19), (0, 22), (18, 30), (23, 25), (7, 7), (17, 10), (9, 29), (3, 12), (7, 14), (24, 12), (30, 15), (8, 11), (23, 4), (11, 15), (16, 20), (10, 32), (30, 2), (26, 8), (13, 6), (2, 7), (20, 9), (28, 3), (11, 31), (26, 2), (7, 5), (8, 4), (30, 8), (29, 24), (16, 10), (15, 14), (7, 11), (4, 8), (4, 30), (30, 28), (0, 15), (2, 23), (14, 7), (8, 6), (23, 18), (25, 5), (12, 6), (13, 31), (2, 6), (27, 32), (22, 20), (17, 0), (7, 20), (6, 5), (26, 0), (19, 18), (25, 11), (19, 25), (17, 25), (3, 16), (3, 25), (10, 25), (24, 13), (13, 28), (3, 30), (9, 17), (15, 19), (1, 14), (20, 4), (7, 23), (18, 23), (29, 20), (0, 29), (29, 31), (11, 8), (1, 11), (26, 32), (22, 4), (24, 16), (18, 33), (11, 24), (3, 14), (25, 18), (16, 5), (26, 31), (18, 31), (9, 15), (16, 3), (27, 11), (13, 30), (30, 26), (20, 0), (25, 2), (6, 20), (16, 28), (23, 13), (2, 33), (10, 13), (21, 21), (3, 24), (19, 11), (19, 3), (29, 1), (19, 6), (22, 13), (10, 0), (8, 31), (0, 11), (4, 24), (2, 0), (18, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "913368", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 31), (25, 9), (30, 27), (6, 22), (21, 2), (22, 26), (9, 30), (11, 1), (7, 9), (19, 6), (2, 33), (17, 5), (18, 24), (2, 16), (8, 27), (17, 15), (27, 24), (26, 11), (26, 20), (19, 5), (12, 14), (20, 29), (13, 21), (26, 9), (1, 27), (20, 9), (17, 6), (22, 18), (25, 7), (15, 31), (9, 9), (28, 18), (19, 8), (12, 12), (27, 7), (21, 9), (26, 33), (22, 8), (10, 13), (21, 13), (30, 3), (7, 20), (5, 17), (10, 15), (4, 31), (10, 8), (14, 1), (11, 18), (15, 7), (18, 1), (0, 20), (14, 14), (14, 10), (17, 21), (30, 31), (15, 32), (9, 22), (17, 7), (26, 28), (18, 17), (27, 20), (15, 11), (26, 22), (5, 10), (4, 27), (30, 10), (17, 13), (26, 18), (9, 25), (4, 29), (24, 6), (19, 23), (12, 23), (5, 7), (25, 0), (20, 7), (28, 3), (4, 21), (21, 10), (6, 33), (1, 32), (11, 4), (1, 5), (3, 14), (7, 32), (11, 9), (24, 22), (18, 23), (14, 33), (6, 12), (6, 28), (17, 14), (7, 22), (27, 15), (23, 21), (3, 16), (4, 24), (1, 33), (21, 7), (0, 32), (23, 12), (23, 8), (14, 16), (19, 27), (14, 3), (4, 8), (22, 29), (6, 8), (23, 25), (17, 17), (9, 24), (17, 27), (5, 8), (17, 22), (18, 19), (30, 2), (27, 11), (11, 27), (18, 31), (6, 5), (13, 27), (5, 6), (14, 15), (20, 26), (9, 12), (23, 32), (5, 22), (12, 24), (20, 18), (29, 2), (10, 16), (5, 13), (21, 33), (27, 29), (23, 13), (20, 19), (18, 26), (8, 3), (19, 24), (1, 1), (0, 2), (6, 10), (17, 10), (12, 29), (11, 21), (2, 7), (15, 29), (17, 18), (3, 22), (15, 23), (12, 25), (0, 13), (8, 25), (11, 26), (2, 14), (0, 5), (7, 8), (20, 22), (4, 18), (10, 24), (28, 27), (30, 8), (20, 14), (26, 1), (28, 15), (8, 9), (6, 19), (28, 33), (30, 11), (9, 21), (18, 15), (0, 27), (26, 26), (15, 14), (13, 25), (18, 16), (13, 18), (23, 10), (23, 9), (30, 14), (26, 21), (27, 16), (26, 6), (21, 32), (8, 11), (14, 8), (21, 28), (29, 15), (12, 27), (30, 15), (1, 16), (24, 18), (11, 33), (0, 15), (29, 14), (19, 25), (10, 10), (29, 8), (19, 30), (25, 10), (7, 24), (6, 2), (7, 12), (24, 8), (4, 25), (9, 14), (7, 27), (24, 29), (16, 27), (4, 11), (16, 12), (14, 25), (8, 17), (24, 2), (5, 1), (10, 29), (29, 0), (9, 16), (3, 18), (7, 19), (12, 26), (28, 12), (27, 14), (27, 27), (26, 4), (4, 30), (1, 9), (16, 15), (20, 21), (2, 30), (18, 25), (2, 5), (2, 23), (24, 23), (2, 2), (17, 2), (13, 10), (25, 22), (6, 31), (13, 31), (26, 27), (5, 30), (23, 6), (25, 31), (11, 15), (24, 33), (13, 14), (26, 0), (14, 23), (4, 22), (0, 6), (19, 17), (1, 7), (23, 20), (11, 30), (16, 25), (21, 4), (20, 2), (19, 12), (11, 20), (9, 7), (28, 2), (15, 5), (25, 24), (14, 7), (0, 23), (0, 1), (10, 14), (3, 23), (16, 26), (20, 31), (25, 26), (14, 5), (8, 29), (1, 17), (12, 31), (3, 29), (16, 21), (22, 13), (16, 1), (9, 2), (8, 33), (26, 19), (6, 13), (27, 6), (27, 1), (15, 0), (23, 19), (12, 7), (7, 16), (26, 17), (27, 22), (15, 27), (3, 4), (4, 32), (19, 32), (4, 19), (24, 1), (23, 16), (29, 1), (2, 17), (26, 14), (28, 28), (18, 4), (25, 28), (10, 5), (8, 13), (7, 4), (1, 31), (23, 22), (28, 21), (22, 16), (2, 9), (13, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "547200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), 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), (18, 3), (29, 30), (11, 0), (14, 16), (13, 6), (26, 9), (1, 15), (17, 28), (11, 24), (11, 28), (22, 16), (3, 34), (26, 2), (21, 8), (9, 5), (22, 34), (8, 3), (25, 26), (29, 31), (23, 14), (3, 20), (3, 11), (25, 1), (15, 6), (16, 2), (22, 7), (0, 7), (29, 9), (8, 29), (24, 27), (25, 15), (29, 3), (9, 2), (5, 33), (0, 19), (3, 24), (9, 3), (16, 26), (19, 31), (4, 12), (22, 11), (24, 17), (2, 31), (0, 11), (26, 21), (27, 8), (4, 19), (24, 22), (3, 2), (20, 16), (7, 0), (0, 12), (27, 26), (25, 21), (26, 22), (23, 21), (21, 21), (28, 15), (12, 15), (7, 28), (8, 30), (28, 1), (16, 19), (4, 13), (28, 34), (26, 29), (18, 10), (17, 27), (21, 29), (16, 7), (19, 23), (29, 21), (24, 5), (9, 29), (6, 11), (28, 27), (5, 5), (7, 6), (22, 24), (12, 32), (0, 9), (16, 23), (14, 18), (22, 21), (23, 15), (5, 3), (3, 32), (27, 24), (26, 12), (13, 18), (14, 25), (3, 22), (18, 0), (4, 20), (23, 29), (28, 9), (14, 17), (21, 31), (17, 35), (7, 35), (9, 0), (17, 31), (28, 2), (28, 11), (19, 21), (29, 25), (16, 1), (2, 7), (15, 35), (13, 14), (2, 22), (16, 35), (16, 16), (0, 28), (6, 34), (26, 28), (28, 14), (11, 21), (5, 15), (22, 29), (17, 9), (8, 13), (9, 10), (1, 10), (4, 8), (18, 27), (8, 10), (20, 32), (15, 20), (19, 1), (23, 23), (13, 10), (18, 21), (7, 8), (19, 28), (29, 23), (12, 29), (24, 14), (14, 31), (17, 36), (16, 20), (1, 6), (12, 16), (20, 27), (5, 34), (26, 17), (10, 12), (22, 32), (10, 16), (28, 23), (17, 17), (21, 6), (0, 4), (18, 4), (23, 25), (17, 24), (23, 10), (28, 4), (6, 36), (8, 16), (3, 8), (17, 5), (28, 29), (20, 20), (29, 18), (13, 21), (3, 28), (7, 11), (26, 11), (25, 9), (5, 28), (23, 8), (7, 32), (22, 17), (23, 32), (24, 9), (6, 21), (10, 33), (24, 13), (27, 1), (27, 20), (20, 24), (3, 25), (16, 36), (15, 1), (3, 14), (0, 32), (9, 20), (3, 26), (22, 10), (18, 29), (2, 21), (7, 23), (18, 28), (29, 33), (14, 32), (21, 33), (22, 2), (4, 10), (0, 22), (1, 16), (6, 35), (18, 7), (0, 31), (8, 22), (20, 4), (3, 19), (23, 17), (3, 33), (20, 7), (9, 19), (16, 10), (24, 18), (15, 3), (24, 11), (14, 28), (7, 16), (4, 0), (18, 11), (26, 37), (4, 37), (7, 27), (17, 16), (2, 19), (6, 17), (0, 35), (28, 3), (27, 5), (6, 29), (14, 11), (2, 34), (8, 35), (26, 23), (27, 33), (5, 23), (8, 8), (15, 29), (14, 27), (2, 24), (21, 30), (21, 17), (23, 33), (18, 9), (21, 25), (22, 15), (12, 18), (19, 12), (13, 27), (28, 18), (27, 14), (28, 10), (22, 31), (29, 7), (12, 6), (15, 0), (1, 27), (17, 12), (2, 13), (15, 25), (28, 7), (18, 37), (16, 6), (1, 28), (5, 13), (23, 3), (11, 22), (5, 1), (22, 9), (20, 35), (10, 28), (28, 30), (25, 18), (6, 18), (1, 36), (17, 2), (23, 34), (6, 31), (8, 18), (27, 22), (13, 30), (3, 1), (25, 5), (28, 33), (22, 23), (1, 12), (26, 36), (2, 5), (20, 25), (16, 5), (4, 27), (26, 32), (1, 33), (23, 24), (25, 11), (7, 12), (1, 30), (6, 23), (28, 13), (24, 29), (19, 4), (8, 28), (21, 26), (17, 1), (15, 21), (24, 26), (29, 2), (1, 5), (8, 27), (6, 13), (24, 21), (8, 34), (23, 20), (27, 6), (20, 37), (21, 16), (11, 32), (24, 12), (2, 25), (4, 5), (21, 18), (9, 16), (15, 23), (29, 15), (29, 14), (21, 32), (22, 33), (19, 19), (1, 35), (9, 34), (25, 36), (29, 4), (1, 0), (21, 5), (18, 30), (20, 2), (9, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355824", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (0, 18), (12, 20), (32, 8), (26, 19), (23, 36), (34, 19), (9, 25), (32, 3), (22, 17), (31, 11), (6, 9), (7, 35), (29, 24), (33, 26), (5, 34), (16, 24), (34, 13), (4, 29), (4, 22), (33, 20), (14, 14), (27, 16), (34, 8), (2, 7), (1, 25), (21, 26), (17, 34), (23, 21), (18, 14), (18, 25), (9, 31), (7, 27), (0, 21), (30, 27), (19, 17), (24, 3), (29, 6), (33, 14), (30, 3), (4, 36), (6, 21), (15, 16), (31, 8), (15, 10), (12, 0), (3, 18), (13, 8), (6, 28), (7, 36), (6, 6), (3, 33), (34, 27), (26, 18), (6, 18), (13, 27), (11, 19), (9, 21), (24, 34), (24, 22), (17, 35), (18, 30), (11, 36), (27, 2), (11, 13), (24, 24), (9, 4), (27, 6), (0, 24), (2, 33), (28, 31), (8, 36), (1, 16), (7, 1), (25, 33), (11, 29), (22, 23), (6, 1), (8, 23), (3, 16), (25, 13), (5, 12), (1, 17), (19, 9), (18, 21), (26, 26), (27, 35), (0, 29), (26, 28), (7, 24), (27, 12), (2, 21), (26, 31), (31, 21), (16, 19), (13, 2), (15, 15), (34, 17), (28, 13), (30, 2), (18, 6), (13, 31), (6, 23), (24, 6), (11, 3), (0, 8), (20, 35), (2, 1), (25, 22), (19, 5), (14, 15), (13, 10), (5, 7), (23, 24), (1, 24), (20, 28), (31, 25), (28, 23), (14, 1), (4, 12), (24, 5), (33, 11), (25, 10), (4, 26), (12, 31), (0, 15), (21, 25), (19, 28), (8, 14), (1, 3), (8, 7), (14, 0), (7, 3), (30, 17), (33, 2), (3, 1), (34, 32), (4, 9), (7, 10), (18, 5), (22, 28), (1, 4), (22, 36), (8, 13), (22, 34), (18, 0), (9, 17), (25, 8), (20, 26), (26, 10), (8, 32), (29, 28), (10, 27), (16, 22), (27, 29), (16, 8), (4, 25), (4, 30), (7, 6), (17, 19), (17, 9), (9, 27), (33, 18), (16, 26), (3, 13), (9, 12), (32, 29), (25, 12), (28, 1), (31, 13), (29, 3), (1, 6), (24, 20), (2, 5), (11, 33), (9, 33), (9, 19), (24, 30), (10, 36), (10, 28), (29, 30), (8, 33), (28, 17), (3, 2), (21, 34), (1, 9), (3, 4), (23, 17), (31, 6), (30, 21), (23, 22), (9, 3), (15, 1), (11, 12), (16, 10), (6, 5), (10, 22), (31, 35), (27, 0), (28, 12), (22, 26), (18, 26), (10, 4), (16, 21), (21, 0), (33, 29), (15, 26), (14, 3), (33, 10), (10, 23), (13, 35), (28, 27), (18, 2), (32, 11), (27, 18), (6, 32), (11, 8), (5, 8), (24, 9), (32, 13), (16, 23), (15, 33), (18, 11), (6, 31), (4, 32), (28, 2), (32, 5), (24, 0), (0, 19), (17, 25), (27, 8), (18, 4), (28, 26), (31, 24), (12, 2), (12, 22), (3, 9), (3, 6), (3, 29), (17, 8), (17, 32), (14, 5), (0, 14), (17, 22), (9, 30), (5, 1), (20, 30), (8, 5), (14, 36), (31, 16), (10, 14), (27, 1), (6, 0), (21, 24), (3, 0), (26, 14), (30, 30), (20, 36), (7, 16), (33, 5), (32, 4), (18, 23), (12, 36), (22, 13), (22, 27), (12, 6), (20, 12), (14, 34), (11, 35), (21, 35), (14, 6), (16, 34), (13, 1), (15, 20), (18, 17), (6, 20), (6, 17), (21, 18), (25, 27), (21, 15), (13, 18), (24, 31), (0, 25), (29, 10), (29, 14), (32, 24), (29, 19), (25, 25), (4, 23), (17, 17), (16, 29), (7, 34), (22, 9), (9, 29), (22, 4), (13, 6), (24, 2), (24, 7), (21, 11), (3, 15), (6, 16), (32, 22), (13, 20), (32, 27), (27, 23), (22, 8), (27, 34), (16, 9), (17, 28), (0, 22), (5, 24), (15, 19), (9, 36), (15, 28), (7, 11), (2, 36), (29, 29), (29, 23), (33, 1), (31, 34), (20, 11), (21, 8), (31, 0), (10, 17), (6, 36), (29, 27), (31, 33), (1, 18), (12, 3), (30, 15), (31, 29), (14, 13), (30, 14), (34, 21), (0, 23), (25, 9), (18, 24), (17, 18), (12, 16), (15, 5), (11, 17), (3, 35), (25, 30), (16, 7), (0, 32), (18, 33), (32, 2), (25, 36), (8, 10), (10, 2), (8, 21), (34, 29), (1, 13), (14, 7), (20, 14), (12, 23), (26, 12), (7, 19), (20, 4), (21, 28), (33, 25), (20, 16), (25, 23), (26, 3), (24, 11), (8, 35), (10, 32), (2, 3), (22, 35), (31, 2), (1, 21), (11, 25), (33, 15), (19, 36), (25, 18), (8, 28), (13, 19), (15, 36), (23, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101856", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 18), (15, 32), (8, 8), (2, 32), (25, 6), (9, 3), (4, 6), (25, 26), (25, 17), (13, 0), (29, 34), (13, 21), (12, 30), (7, 22), (7, 15), (31, 26), (13, 32), (17, 23), (22, 18), (29, 10), (24, 4), (20, 32), (9, 30), (31, 24), (20, 13), (3, 0), (27, 14), (0, 5), (16, 0), (20, 7), (13, 27), (6, 0), (26, 13), (8, 0), (27, 9), (13, 9), (9, 12), (16, 13), (11, 10), (30, 34), (22, 1), (27, 8), (13, 25), (4, 32), (18, 22), (19, 7), (11, 4), (0, 16), (31, 17), (26, 6), (27, 19), (3, 29), (30, 14), (24, 17), (23, 22), (30, 29), (27, 28), (1, 23), (28, 34), (3, 18), (10, 3), (1, 35), (7, 35), (23, 28), (24, 33), (0, 11), (29, 17), (2, 8), (10, 25), (7, 17), (17, 14), (14, 8), (23, 8), (22, 20), (3, 30), (11, 22), (6, 3), (21, 24), (6, 10), (29, 24), (8, 10), (5, 17), (3, 14), (17, 5), (23, 29), (19, 29), (9, 28), (19, 6), (4, 27), (29, 26), (23, 13), (17, 19), (22, 10), (22, 24), (28, 9), (17, 3), (25, 33), (8, 3), (14, 20), (22, 21), (28, 6), (20, 17), (29, 35), (24, 34), (29, 15), (26, 30), (32, 7), (20, 31), (25, 15), (2, 4), (5, 14), (3, 1), (15, 14), (15, 17), (3, 12), (24, 35), (22, 17), (14, 19), (15, 6), (11, 15), (1, 4), (8, 33), (8, 19), (4, 19), (23, 1), (15, 20), (14, 14), (14, 4), (27, 15), (10, 15), (15, 25), (3, 31), (3, 13), (15, 23), (23, 7), (0, 6), (19, 26), (13, 29), (32, 15), (5, 9), (28, 30), (12, 15), (12, 17), (18, 24), (22, 26), (9, 5), (10, 24), (32, 11), (25, 25), (21, 33), (14, 29), (8, 22), (11, 1), (23, 11), (8, 9), (2, 14), (26, 28), (20, 34), (7, 16), (13, 31), (24, 8), (32, 24), (7, 28), (1, 11), (32, 17), (24, 12), (18, 15), (7, 30), (23, 16), (8, 24), (21, 26), (7, 25), (14, 28), (21, 22), (2, 23), (16, 15), (30, 0), (26, 32), (14, 27), (32, 14), (3, 20), (29, 19), (19, 15), (7, 5), (23, 10), (18, 21), (26, 11), (22, 9), (4, 31), (11, 18), (7, 32), (9, 10), (18, 30), (3, 24), (0, 35), (3, 23), (10, 22), (9, 0), (4, 12), (19, 4), (15, 13), (8, 29), (18, 6), (6, 9), (29, 1), (24, 22), (29, 13), (13, 6), (14, 11), (26, 10), (9, 34), (10, 11), (14, 9), (2, 35), (31, 9), (6, 6), (2, 9), (11, 35), (15, 30), (7, 8), (28, 1), (31, 10), (9, 15), (30, 26), (18, 34), (16, 8), (8, 26), (26, 27), (18, 23), (9, 23), (20, 12), (8, 20), (2, 15), (27, 26), (20, 29), (10, 13), (31, 14), (16, 7), (18, 25), (9, 27), (17, 17), (29, 20), (29, 5), (13, 17), (15, 16), (9, 11), (24, 16), (25, 13), (2, 18), (19, 3), (18, 35), (1, 28), (7, 19), (30, 2), (5, 28), (28, 33), (11, 27), (16, 4), (14, 18), (8, 34), (25, 31), (31, 2), (17, 0), (6, 25), (20, 6), (28, 7), (2, 34), (4, 17), (21, 19), (16, 2), (29, 30), (18, 7), (30, 4), (22, 35), (10, 35), (2, 28), (0, 22), (25, 0), (29, 9), (6, 14), (7, 34), (4, 11), (27, 7), (24, 23), (9, 22), (29, 11), (13, 20), (26, 31), (9, 8), (17, 18), (11, 7), (6, 2), (10, 14), (14, 21), (29, 31), (19, 22), (27, 1), (12, 29), (2, 26), (15, 34), (7, 2), (9, 13), (31, 5), (28, 12), (4, 35), (18, 16), (22, 22), (17, 24), (11, 29), (6, 31), (14, 7), (5, 30), (8, 21), (1, 0), (31, 22), (29, 7), (13, 35), (25, 16), (18, 31), (22, 29), (21, 20), (15, 4), (3, 32), (3, 27), (26, 5), (3, 6), (0, 12), (4, 26), (30, 32), (20, 20), (12, 6), (18, 5), (26, 12), (8, 2), (17, 11), (10, 20), (31, 3), (28, 29), (30, 21), (25, 4), (8, 6), (12, 35), (24, 19), (6, 19), (10, 12), (27, 35), (29, 0), (1, 14), (16, 11), (13, 12), (5, 11), (7, 10), (21, 15), (24, 10), (13, 34), (24, 29), (11, 5), (16, 33), (14, 31), (22, 2), (14, 23), (15, 31), (6, 13), (17, 1), (14, 0), (27, 29), (23, 19), (5, 32), (1, 10), (29, 14), (0, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "897390", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 34), (17, 21), (6, 22), (21, 4), (23, 19), (4, 0), (2, 33), (29, 35), (36, 20), (25, 12), (34, 36), (29, 11), (31, 31), (21, 16), (9, 20), (38, 14), (34, 28), (13, 27), (37, 29), (3, 32), (9, 17), (1, 33), (6, 2), (18, 36), (34, 20), (13, 7), (23, 7), (8, 11), (32, 10), (14, 10), (37, 26), (7, 32), (8, 5), (9, 26), (32, 25), (18, 27), (13, 10), (29, 8), (10, 34), (26, 24), (24, 8), (27, 36), (7, 36), (31, 1), (18, 2), (16, 8), (4, 22), (1, 1), (8, 9), (32, 18), (22, 11), (33, 8), (6, 11), (9, 13), (1, 35), (38, 29), (20, 7), (35, 12), (25, 29), (14, 15), (35, 29), (32, 31), (2, 3), (33, 32), (9, 0), (5, 12), (8, 37), (16, 29), (25, 15), (33, 21), (11, 2), (22, 15), (10, 24), (37, 1), (28, 1), (2, 36), (38, 5), (21, 18), (16, 20), (21, 17), (20, 16), (24, 4), (10, 35), (34, 34), (19, 0), (25, 25), (35, 4), (36, 3), (29, 18), (1, 28), (13, 2), (18, 26), (28, 2), (0, 1), (17, 20), (11, 34), (3, 2), (21, 13), (37, 31), (18, 8), (8, 27), (11, 17), (11, 10), (7, 21), (21, 0), (22, 35), (2, 7), (17, 35), (22, 0), (35, 30), (7, 17), (19, 6), (29, 0), (24, 31), (11, 16), (10, 28), (34, 24), (31, 3), (23, 29), (28, 10), (11, 3), (23, 6), (26, 11), (6, 9), (20, 18), (9, 30), (24, 16), (5, 37), (8, 6), (34, 4), (1, 19), (16, 24), (34, 5), (30, 17), (8, 15), (12, 5), (29, 5), (22, 21), (10, 27), (33, 23), (26, 26), (7, 16), (28, 24), (16, 18), (12, 3), (22, 37), (19, 1), (33, 30), (31, 11), (14, 11), (8, 7), (32, 32), (24, 28), (35, 26), (25, 17), (33, 14), (14, 14), (28, 11), (6, 13), (36, 7), (34, 23), (0, 26), (36, 5), (25, 4), (19, 13), (26, 1), (26, 4), (37, 35), (37, 8), (5, 26), (21, 22), (2, 22), (7, 24), (33, 18), (6, 37), (31, 9), (14, 21), (9, 28), (10, 11), (21, 26), (20, 5), (22, 12), (34, 1), (0, 24), (14, 8), (14, 19), (1, 18), (0, 6), (9, 11), (30, 26), (8, 3), (27, 18), (12, 9), (28, 35), (13, 17), (38, 2), (3, 30), (27, 7), (4, 8), (2, 35), (2, 25), (19, 30), (13, 24), (7, 25), (35, 3), (32, 36), (15, 24), (34, 33), (3, 27), (6, 30), (12, 20), (29, 7), (2, 34), (16, 21), (4, 36), (28, 4), (16, 3), (25, 1), (26, 5), (17, 6), (32, 13), (7, 14), (9, 22), (5, 21), (21, 36), (2, 20), (13, 23), (16, 14), (11, 32), (28, 33), (27, 27), (28, 9), (11, 21), (28, 25), (35, 18), (23, 24), (38, 33), (11, 0), (38, 20), (3, 7), (10, 26), (25, 28), (38, 13), (18, 21), (17, 4), (30, 37), (12, 24), (32, 4), (0, 13), (23, 0), (15, 35), (13, 9), (35, 21), (7, 8), (4, 14), (21, 29), (32, 3), (34, 27), (36, 11), (15, 16), (34, 25), (31, 36), (37, 32), (3, 13), (8, 8), (24, 14), (36, 9), (33, 33), (1, 27), (26, 25), (8, 0), (19, 20), (27, 34), (28, 15), (37, 21), (12, 19), (6, 6), (23, 11), (15, 22), (2, 5), (8, 16), (29, 2), (38, 26), (22, 24), (7, 20), (31, 19), (21, 9), (20, 30), (27, 23), (1, 3), (21, 32), (30, 5), (36, 25), (29, 16), (29, 28), (2, 11), (16, 5), (24, 29), (26, 0), (16, 28), (36, 37), (10, 18), (7, 6), (22, 13), (5, 4), (23, 28), (26, 14), (38, 7), (7, 31), (5, 5), (4, 4), (25, 32), (33, 24), (30, 13), (12, 21), (21, 33), (32, 37), (13, 22), (27, 1), (31, 26), (35, 20), (12, 15), (38, 3), (0, 37), (26, 22), (0, 14), (27, 29), (23, 32), (27, 37), (38, 4), (7, 35), (20, 3), (25, 23), (35, 2), (1, 15), (1, 20), (11, 22), (4, 30), (8, 19), (27, 31), (27, 2), (18, 33), (19, 37), (7, 33), (17, 33), (20, 17), (3, 17), (33, 9), (32, 27), (33, 15), (22, 25), (18, 17), (23, 10), (21, 20), (33, 28), (7, 34), (21, 14), (29, 31), (15, 27), (19, 10), (3, 26), (30, 2), (16, 22), (2, 23), (29, 3), (5, 19), (17, 24), (38, 32), (23, 30), (16, 10), (1, 11), (25, 37), (9, 21), (0, 15), (4, 2), (27, 10), (33, 25), (29, 24), (32, 15), (0, 30), (10, 25), (7, 28), (3, 23), (35, 34), (17, 22), (16, 19), (37, 11), (24, 15), (0, 2), (26, 6), (6, 36), (7, 13), (0, 36), (15, 9), (14, 4), (11, 18), (37, 33), (24, 19), (11, 27), (37, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "741840", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 32), (32, 12), (15, 0), (29, 23), (22, 4), (18, 25), (24, 10), (14, 27), (26, 0), (1, 23), (8, 4), (14, 35), (17, 10), (22, 11), (27, 19), (22, 7), (11, 6), (20, 12), (9, 35), (28, 3), (21, 17), (12, 12), (1, 32), (4, 4), (15, 12), (12, 4), (26, 34), (9, 1), (33, 25), (11, 31), (2, 9), (18, 16), (9, 16), (1, 7), (33, 32), (9, 21), (14, 33), (25, 17), (26, 24), (23, 27), (12, 3), (15, 18), (27, 18), (27, 12), (9, 19), (8, 7), (12, 9), (17, 7), (9, 7), (21, 27), (17, 25), (6, 22), (2, 1), (10, 21), (10, 5), (16, 12), (12, 26), (23, 4), (2, 4), (1, 34), (26, 20), (29, 12), (26, 30), (10, 4), (25, 27), (14, 31), (32, 28), (14, 1), (8, 27), (12, 11), (16, 35), (10, 24), (8, 10), (30, 21), (32, 6), (28, 6), (25, 2), (33, 34), (13, 23), (2, 7), (6, 6), (11, 17), (19, 29), (18, 24), (11, 15), (5, 33), (30, 2), (15, 9), (15, 16), (8, 2), (29, 34), (30, 30), (0, 18), (6, 27), (18, 34), (33, 21), (19, 31), (25, 15), (29, 22), (6, 21), (23, 17), (27, 24), (32, 10), (10, 20), (17, 15), (23, 34), (14, 24), (18, 6), (30, 31), (18, 12), (13, 14), (13, 30), (27, 13), (8, 1), (1, 3), (4, 12), (1, 30), (13, 5), (21, 22), (0, 26), (2, 8), (8, 9), (8, 13), (24, 7), (14, 7), (0, 11), (23, 29), (9, 3), (19, 0), (19, 6), (7, 26), (10, 8), (25, 30), (25, 18), (32, 2), (1, 12), (9, 27), (33, 16), (1, 9), (19, 22), (0, 17), (11, 7), (29, 35), (33, 22), (23, 20), (2, 25), (33, 10), (17, 22), (28, 19), (9, 10), (7, 10), (16, 33), (29, 28), (28, 29), (32, 16), (16, 8), (3, 21), (5, 8), (15, 29), (0, 20), (5, 1), (16, 16), (9, 13), (0, 3), (21, 9), (19, 3), (8, 26), (7, 24), (29, 29), (28, 17), (23, 23), (2, 11), (14, 5), (21, 20), (20, 19), (13, 8), (12, 5), (8, 20), (17, 33), (30, 27), (7, 20), (19, 27), (6, 16), (20, 24), (24, 22), (8, 12), (0, 22), (4, 13), (9, 17), (25, 1), (9, 11), (16, 10), (13, 13), (21, 5), (10, 18), (30, 8), (26, 6), (9, 6), (8, 23), (8, 35), (32, 17), (17, 17), (32, 34), (25, 13), (0, 13), (7, 8), (33, 17), (8, 6), (11, 5), (11, 12), (29, 1), (2, 27), (23, 13), (30, 33), (4, 28), (24, 13), (20, 28), (28, 20), (13, 16), (16, 27), (32, 31), (19, 23), (3, 14), (32, 5), (12, 17), (12, 2), (9, 30), (11, 30), (31, 31), (23, 32), (12, 20), (0, 2), (20, 23), (21, 24), (3, 11), (1, 21), (2, 3), (15, 25), (25, 35), (24, 34), (30, 11), (5, 10), (6, 34), (17, 32), (31, 14), (20, 4), (12, 31), (7, 19), (25, 28), (23, 7), (11, 13), (6, 12), (12, 27), (21, 10), (27, 33), (11, 33), (3, 8), (33, 11), (15, 13), (13, 6), (16, 28), (17, 5), (1, 25), (0, 19), (32, 7), (3, 28), (27, 11), (2, 10), (3, 17), (23, 31), (13, 33), (12, 19), (30, 23), (30, 17), (5, 34), (19, 34), (4, 23), (12, 8), (10, 23), (29, 27), (27, 21), (7, 12), (7, 13), (8, 14), (10, 22), (23, 6), (26, 9), (1, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3420", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), 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), (15, 3), (9, 15), (28, 24), (27, 13), (19, 11), (15, 10), (19, 8), (8, 7), (11, 24), (3, 2), (23, 13), (12, 10), (2, 9), (23, 16), (11, 12), (6, 11), (3, 16), (22, 26), (28, 35), (11, 5), (5, 21), (1, 9), (4, 18), (36, 29), (0, 25), (3, 7), (23, 4), (19, 1), (8, 24), (37, 21), (22, 24), (0, 4), (37, 1), (3, 18), (17, 22), (32, 22), (37, 10), (18, 0), (14, 23), (34, 32), (37, 24), (11, 4), (4, 5), (2, 7), (22, 15), (0, 5), (2, 22), (16, 34), (34, 3), (26, 17), (31, 27), (33, 3), (37, 13), (7, 11), (12, 24), (0, 21), (37, 17), (13, 34), (2, 4), (5, 13), (8, 27), (27, 20), (8, 18), (21, 20), (27, 4), (7, 17), (7, 27), (34, 23), (6, 32), (30, 25), (8, 8), (24, 23), (3, 32), (1, 27), (17, 2), (24, 15), (26, 29), (0, 23), (23, 27), (11, 16), (7, 19), (31, 28), (26, 7), (20, 26), (24, 10), (12, 3), (22, 16), (26, 35), (34, 11), (5, 35), (17, 31), (0, 28), (35, 20), (4, 17), (3, 0), (2, 13), (36, 34), (1, 31), (19, 14), (24, 8), (11, 6), (19, 25), (19, 21), (11, 0), (36, 27), (22, 14), (26, 22), (21, 22), (33, 35), (32, 19), (19, 31), (22, 12), (36, 6), (35, 4), (16, 7), (22, 32), (1, 8), (36, 17), (19, 0), (1, 24), (29, 30), (12, 12), (21, 18), (18, 34), (35, 6), (23, 17), (36, 28), (7, 6), (29, 14), (17, 11), (12, 2), (34, 24), (34, 15), (4, 21), (17, 24), (12, 6), (36, 11), (15, 15), (6, 24), (33, 14), (19, 13), (31, 23), (10, 33), (22, 0), (20, 9), (22, 29), (15, 24), (31, 6), (8, 23), (36, 2), (23, 32), (1, 2), (27, 25), (10, 8), (6, 0), (9, 26), (27, 8), (26, 15), (14, 14), (30, 30), (4, 1), (36, 4), (24, 30), (7, 34), (21, 4), (15, 9), (19, 3), (24, 16), (37, 19), (12, 19), (26, 3), (18, 16), (10, 6), (33, 33), (19, 29), (4, 3), (12, 16), (14, 4), (13, 24), (15, 11), (29, 32), (14, 25), (32, 24), (25, 3), (8, 25), (8, 31), (32, 31), (22, 6), (6, 2), (26, 14), (26, 23), (33, 31), (20, 15), (6, 34), (31, 16), (5, 0), (4, 13), (0, 2), (19, 18), (20, 20), (37, 27), (12, 31), (33, 28), (4, 16), (31, 20), (29, 8), (12, 34), (10, 26), (34, 0), (33, 19), (10, 34), (26, 6), (28, 1), (36, 9), (23, 0), (16, 35), (32, 12), (20, 35), (26, 18), (6, 26), (5, 34), (13, 3), (29, 29), (30, 3), (34, 28), (8, 21), (18, 10), (16, 19), (14, 7), (5, 33), (5, 9), (2, 15), (16, 15), (36, 31), (3, 12), (15, 13), (28, 15), (11, 1), (5, 3), (27, 19), (31, 22), (10, 11), (12, 25), (34, 30), (11, 9), (24, 33), (14, 1), (31, 5), (11, 8), (14, 28), (37, 32), (35, 0), (16, 4), (9, 1), (26, 28), (13, 15), (7, 4), (26, 25), (10, 14), (30, 13), (35, 18), (15, 34), (19, 2), (0, 1), (15, 18), (34, 14), (26, 9), (14, 8), (9, 29), (19, 33), (8, 35), (34, 35), (29, 17), (6, 35), (8, 14), (29, 35), (20, 34), (11, 28), (6, 3), (37, 2), (33, 29), (30, 18), (18, 32), (22, 18), (33, 18), (31, 2), (31, 11), (6, 5), (35, 34), (24, 5), (18, 26), (22, 2), (7, 9), (1, 4), (3, 15), (1, 29), (18, 9), (22, 8), (2, 29), (9, 4), (5, 23), (3, 5), (17, 30), (21, 6), (25, 17), (34, 29), (2, 28), (35, 35), (19, 9), (12, 18), (18, 11), (0, 16), (7, 13), (20, 6), (3, 26), (2, 25), (37, 11), (1, 22), (24, 34), (1, 35), (0, 17), (6, 19), (14, 27), (7, 25), (26, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78240", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 36), (13, 3), (32, 2), (21, 26), (34, 38), (1, 24), (2, 5), (27, 14), (12, 24), (14, 38), (2, 31), (30, 37), (35, 1), (3, 16), (33, 8), (4, 10), (35, 27), (21, 6), (25, 32), (28, 16), (8, 17), (27, 2), (32, 26), (29, 9), (5, 9), (35, 15), (35, 26), (17, 6), (29, 17), (3, 24), (34, 14), (32, 9), (14, 26), (13, 2), (20, 34), (18, 1), (35, 6), (4, 28), (6, 26), (15, 23), (35, 21), (25, 1), (25, 38), (33, 16), (8, 28), (11, 12), (18, 38), (9, 26), (3, 8), (32, 19), (34, 35), (18, 10), (23, 38), (24, 29), (33, 25), (10, 27), (28, 35), (6, 16), (21, 2), (30, 32), (33, 3), (26, 29), (19, 3), (14, 32), (7, 2), (33, 2), (34, 33), (1, 21), (15, 25), (30, 4), (2, 33), (34, 4), (32, 24), (5, 32), (29, 12), (12, 6), (29, 7), (0, 6), (6, 1), (29, 29), (17, 7), (9, 8), (2, 29), (21, 11), (11, 0), (27, 21), (16, 28), (21, 23), (23, 18), (27, 22), (15, 2), (12, 20), (28, 0), (35, 12), (16, 22), (5, 22), (31, 7), (5, 19), (0, 27), (14, 25), (27, 12), (31, 19), (27, 17), (2, 38), (28, 10), (9, 17), (1, 22), (0, 22), (9, 30), (18, 5), (32, 13), (22, 3), (32, 18), (1, 31), (25, 14), (32, 31), (19, 9), (25, 5), (34, 1), (0, 19), (25, 6), (7, 15), (0, 24), (33, 10), (10, 19), (27, 36), (8, 25), (11, 1), (4, 23), (29, 37), (18, 20), (4, 7), (10, 32), (13, 27), (18, 31), (28, 3), (23, 19), (5, 26), (19, 12), (1, 2), (19, 4), (9, 25), (15, 35), (9, 9), (26, 22), (27, 30), (6, 32), (25, 15), (12, 30), (6, 10), (10, 2), (19, 36), (33, 15), (1, 26), (13, 8), (23, 7), (1, 16), (22, 9), (25, 18), (3, 38), (15, 32), (15, 31), (28, 14), (13, 9), (28, 4), (21, 34), (21, 10), (32, 27), (32, 20), (20, 25), (27, 24), (26, 8), (20, 0), (28, 32), (22, 5), (2, 36), (30, 21), (18, 37), (31, 8), (21, 17), (31, 18), (4, 4), (13, 29), (11, 22), (11, 35), (22, 21), (25, 2), (32, 28), (19, 30), (18, 35), (22, 8), (30, 23), (25, 3), (29, 34), (16, 29), (22, 1), (32, 37), (12, 36), (26, 23), (11, 3), (27, 27), (22, 14), (3, 15), (31, 30), (30, 18), (5, 31), (35, 4), (14, 11), (4, 6), (12, 14), (6, 37), (5, 33), (11, 11), (3, 35), (0, 10), (14, 20), (4, 12), (19, 25), (11, 33), (8, 24), (30, 38), (23, 28), (2, 21), (16, 27), (14, 37), (12, 22), (17, 9), (5, 2), (29, 20), (23, 30), (27, 9), (20, 35), (16, 15), (22, 29), (30, 10), (21, 19), (21, 9), (9, 2), (14, 12), (7, 21), (30, 0), (34, 37), (19, 6), (17, 35), (26, 9), (8, 18), (9, 38), (15, 37), (20, 24), (20, 37), (32, 12), (32, 33), (22, 7), (14, 24), (21, 36), (6, 38), (32, 32), (29, 0), (19, 27), (20, 2), (3, 7), (8, 27), (7, 22), (35, 10), (28, 24), (11, 32), (35, 28), (24, 5), (20, 20), (30, 7), (27, 34), (33, 24), (18, 0), (3, 12), (6, 19), (35, 14), (34, 8), (29, 32), (30, 33), (16, 14), (22, 27), (29, 35), (28, 33), (14, 1), (30, 27), (29, 10), (5, 27), (14, 23), (12, 38), (21, 12), (0, 9), (19, 38), (21, 21), (5, 8), (0, 12), (21, 18), (17, 30), (2, 25), (20, 36), (7, 20), (17, 19), (22, 37), (29, 6), (17, 12), (22, 12), (17, 1), (19, 34), (18, 7), (16, 12), (26, 24), (14, 15), (8, 4), (26, 11), (15, 9), (14, 34), (34, 0), (9, 10), (32, 23), (11, 30), (33, 21), (2, 23), (1, 3), (32, 38), (14, 33), (24, 31), (6, 4), (18, 27), (29, 14), (11, 26), (11, 38), (35, 17), (5, 3), (7, 19), (4, 2), (26, 2), (26, 15), (26, 27), (29, 26), (26, 16), (31, 14), (1, 29), (2, 14), (35, 34), (14, 27), (14, 3), (18, 32), (21, 8), (22, 17), (1, 34), (3, 32), (33, 23), (7, 6), (33, 27), (31, 31), (35, 0), (5, 25), (13, 0), (8, 31), (4, 31), (7, 27), (26, 18), (33, 29), (15, 20), (24, 14), (20, 27), (13, 36), (19, 33), (28, 1), (12, 23), (28, 19), (17, 3), (33, 6), (12, 0), (19, 1), (20, 11), (16, 8), (7, 7), (29, 13), (2, 26), (5, 0), (34, 9), (18, 11), (26, 6), (10, 4), (7, 37), (21, 16), (30, 1), (16, 18), (31, 36), (11, 34), (26, 30), (10, 30), (6, 9), (32, 1), (7, 4), (7, 10), (27, 25), (28, 8), (10, 35), (7, 0), (32, 7), (16, 19), (3, 10), (20, 21), (20, 9), (30, 16), (16, 24), (24, 7), (6, 28), (35, 7), (20, 22), (4, 34), (0, 33), (21, 29), (10, 29), (7, 33), (21, 15), (34, 16), (14, 6), (5, 24), (7, 28), (14, 7), (20, 26), (30, 26), (5, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99696", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 31), (15, 24), (15, 25), (21, 18), (13, 3), (21, 29), (12, 6), (3, 17), (19, 13), (22, 22), (15, 26), (16, 14), (15, 3), (5, 1), (21, 15), (29, 23), (17, 0), (11, 25), (19, 25), (13, 20), (2, 29), (10, 8), (11, 8), (25, 15), (22, 3), (19, 5), (5, 26), (18, 18), (3, 30), (2, 0), (1, 28), (5, 3), (13, 16), (8, 7), (22, 0), (11, 1), (17, 21), (20, 15), (9, 23), (1, 2), (23, 6), (28, 2), (28, 3), (7, 1), (6, 27), (24, 19), (30, 3), (1, 27), (8, 9), (27, 22), (14, 5), (0, 12), (9, 31), (27, 9), (6, 13), (23, 0), (23, 31), (8, 10), (19, 24), (14, 30), (17, 7), (27, 28), (7, 22), (23, 3), (18, 6), (22, 15), (29, 30), (11, 21), (12, 18), (17, 23), (22, 1), (5, 20), (28, 18), (10, 14), (14, 24), (20, 10), (13, 0), (0, 26), (6, 24), (25, 10), (5, 10), (30, 9), (21, 12), (25, 2), (7, 24), (0, 9), (21, 25), (4, 21), (2, 2), (20, 9), (16, 18), (22, 5), (15, 19), (4, 17), (26, 3), (10, 20), (26, 1), (10, 31), (16, 17), (1, 24), (2, 18), (22, 20), (19, 21), (0, 23), (0, 4), (28, 6), (7, 13), (22, 28), (0, 5), (29, 9), (0, 31), (25, 9), (10, 19), (23, 13), (4, 11), (26, 15), (24, 12), (29, 28), (4, 4), (18, 11), (1, 4), (22, 8), (23, 26), (19, 4), (10, 29), (0, 14), (23, 9), (14, 6), (14, 31), (28, 24), (15, 23), (1, 6), (16, 28), (16, 19), (14, 27), (26, 9), (28, 9), (29, 19), (6, 14), (17, 6), (8, 0), (5, 24), (16, 21), (0, 25), (1, 10), (16, 24), (8, 24), (1, 7), (24, 22), (26, 11), (5, 4), (25, 3), (13, 7), (26, 31), (1, 31), (24, 2), (22, 19), (0, 17), (3, 0), (17, 12), (16, 2), (23, 15), (27, 20), (1, 22), (10, 16), (24, 27), (8, 5), (4, 31), (8, 18), (30, 22), (15, 18), (0, 3), (0, 22), (17, 22), (21, 19), (20, 28), (20, 1), (12, 20), (27, 11), (3, 11), (25, 5), (12, 26), (10, 17), (30, 4), (2, 8), (29, 8), (18, 8), (20, 17), (29, 5), (12, 3), (30, 0), (24, 6), (20, 3), (5, 22), (18, 24), (27, 16), (21, 14), (20, 20), (26, 13), (2, 6), (19, 20), (28, 25), (5, 0), (27, 2), (17, 31), (30, 23), (2, 11), (11, 28), (29, 17), (8, 14), (18, 0), (7, 21), (11, 20), (29, 14), (26, 0), (17, 3), (21, 16), (19, 0), (7, 8), (0, 27), (4, 24), (11, 6), (27, 6), (25, 16), (14, 22), (7, 31), (25, 17), (2, 22), (20, 27), (18, 25), (14, 18), (1, 0), (27, 13), (24, 13), (1, 11), (18, 28), (25, 11), (4, 5), (22, 16), (13, 2), (23, 1), (11, 5), (30, 7), (7, 28), (20, 0), (6, 18), (8, 19), (20, 22), (13, 14), (10, 21), (8, 8), (15, 10), (25, 13), (9, 27), (8, 13), (0, 6), (21, 8), (29, 21), (7, 16), (30, 18), (16, 22), (12, 12), (25, 27), (20, 11), (20, 29), (22, 6), (3, 6), (7, 18), (1, 16), (25, 6), (1, 20), (8, 31), (13, 25), (5, 21), (17, 10), (10, 11), (2, 16), (19, 26), (23, 7), (30, 19), (11, 27), (22, 25), (21, 4), (28, 23), (18, 7), (8, 30), (14, 4), (3, 14), (3, 8), (24, 14), (16, 23), (24, 29), (30, 30), (6, 15), (9, 15), (11, 17), (14, 25), (13, 18), (25, 20), (4, 23), (30, 6), (25, 29), (24, 18), (5, 27), (6, 11), (9, 18), (2, 7), (15, 14), (13, 5), (23, 8), (17, 26), (23, 19), (6, 1), (4, 10), (9, 3), (17, 9), (9, 21), (8, 17), (2, 28), (22, 2), (13, 6), (2, 19), (30, 11), (20, 12), (26, 7), (6, 4), (22, 24), (21, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "763168", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 20), (5, 23), (16, 32), (28, 4), (14, 9), (14, 3), (7, 6), (4, 1), (17, 15), (27, 27), (14, 6), (4, 16), (29, 10), (4, 13), (20, 20), (21, 20), (24, 0), (14, 12), (19, 12), (22, 7), (15, 20), (0, 14), (7, 16), (25, 20), (4, 6), (26, 13), (5, 11), (7, 17), (19, 2), (12, 13), (3, 8), (3, 1), (25, 23), (12, 32), (21, 14), (23, 31), (29, 9), (3, 25), (13, 7), (15, 14), (23, 12), (9, 12), (17, 0), (10, 11), (15, 32), (4, 32), (26, 24), (23, 20), (2, 24), (23, 14), (5, 2), (17, 28), (11, 32), (7, 22), (24, 16), (29, 27), (12, 8), (7, 31), (14, 24), (7, 14), (2, 28), (22, 16), (25, 27), (9, 23), (10, 2), (4, 31), (20, 2), (15, 12), (16, 15), (6, 22), (6, 5), (7, 8), (28, 28), (9, 22), (18, 28), (26, 1), (22, 26), (22, 14), (24, 10), (23, 2), (2, 23), (12, 29), (5, 25), (24, 12), (1, 19), (21, 1), (7, 23), (22, 32), (12, 2), (2, 16), (14, 32), (18, 22), (25, 7), (13, 20), (3, 31), (8, 32), (15, 24), (16, 21), (4, 9), (17, 25), (28, 27), (28, 7), (10, 21), (11, 11), (14, 31), (23, 21), (19, 23), (21, 18), (18, 24), (16, 22), (10, 10), (4, 22), (25, 29), (21, 21), (18, 0), (13, 2), (17, 9), (10, 29), (6, 26), (11, 19), (1, 14), (1, 8), (2, 13), (7, 26), (11, 4), (10, 14), (1, 30), (29, 8), (8, 4), (19, 4), (14, 17), (0, 13), (6, 28), (18, 17), (6, 19), (8, 31), (20, 27), (12, 30), (7, 24), (28, 3), (12, 26), (3, 7), (29, 14), (5, 7), (5, 16), (25, 16), (20, 28), (18, 16), (22, 6), (24, 4), (10, 18), (22, 21), (23, 0), (12, 17), (19, 17), (2, 30), (2, 8), (11, 9), (23, 16), (20, 26), (24, 7), (0, 21), (29, 15), (11, 30), (21, 5), (29, 13), (0, 5), (2, 3), (21, 10), (27, 11), (25, 0), (29, 21), (15, 21), (11, 0), (26, 22), (26, 18), (3, 17), (14, 22), (17, 29), (3, 6), (14, 30), (0, 19), (1, 5), (18, 3), (28, 30), (25, 15), (10, 13), (22, 9), (1, 16), (10, 30), (26, 4), (24, 24), (12, 1), (14, 19), (10, 17), (21, 16), (18, 26), (1, 28), (2, 11), (2, 7), (20, 4), (28, 26), (1, 10), (24, 3), (25, 17), (9, 3), (6, 13), (15, 8), (19, 13), (4, 26), (11, 14), (2, 9), (27, 4), (6, 25), (7, 18), (16, 1), (1, 2), (19, 30), (5, 5), (19, 28), (8, 27), (2, 14), (14, 8), (9, 31), (17, 24), (5, 26), (26, 21), (3, 14), (19, 15), (20, 23), (2, 18), (11, 18), (29, 16), (20, 16), (29, 11), (18, 4), (16, 18), (23, 28), (3, 32), (13, 5), (26, 23), (1, 29), (17, 17), (20, 32), (25, 3), (23, 15), (14, 11), (27, 32), (16, 10), (12, 19), (7, 10), (15, 9), (11, 24), (23, 24), (22, 10), (18, 32), (7, 1), (4, 4), (3, 12), (24, 21), (24, 14), (16, 30), (20, 8), (2, 1), (6, 9), (12, 4), (24, 32), (28, 0), (26, 17), (18, 12), (1, 27), (19, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "972648", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (13, 27), (0, 20), (28, 16), (19, 22), (33, 13), (14, 11), (15, 10), (10, 3), (15, 13), (13, 10), (33, 15), (19, 28), (3, 26), (22, 8), (11, 10), (3, 19), (19, 6), (16, 10), (14, 10), (7, 0), (7, 23), (4, 27), (6, 8), (23, 2), (26, 12), (30, 14), (16, 11), (9, 9), (26, 10), (10, 14), (0, 29), (20, 6), (12, 28), (14, 0), (31, 23), (20, 22), (9, 18), (0, 19), (6, 14), (20, 12), (23, 0), (18, 13), (6, 27), (31, 13), (8, 31), (1, 10), (1, 5), (28, 30), (0, 12), (23, 8), (1, 21), (5, 9), (3, 2), (3, 28), (4, 5), (25, 5), (20, 13), (31, 5), (0, 15), (2, 30), (24, 27), (20, 26), (4, 24), (29, 14), (8, 18), (26, 17), (11, 19), (19, 7), (27, 12), (17, 4), (10, 18), (10, 7), (30, 13), (10, 1), (13, 22), (16, 14), (33, 29), (1, 2), (34, 9), (22, 28), (14, 29), (7, 18), (16, 18), (15, 11), (17, 24), (7, 22), (6, 23), (18, 1), (27, 26), (19, 27), (11, 15), (10, 21), (4, 2), (33, 14), (7, 19), (21, 4), (14, 1), (11, 21), (28, 23), (31, 6), (23, 4), (6, 10), (2, 24), (10, 9), (29, 7), (29, 23), (22, 5), (18, 22), (30, 12), (28, 1), (14, 15), (32, 27), (18, 10), (3, 8), (28, 7), (11, 12), (21, 1), (10, 29), (25, 2), (20, 8), (31, 22), (15, 16), (26, 32), (12, 30), (22, 4), (34, 1), (31, 25), (2, 26), (26, 21), (10, 25), (0, 18), (5, 23), (19, 8), (34, 5), (13, 15), (15, 12), (17, 27), (34, 6), (9, 14), (24, 11), (30, 19), (18, 27), (8, 30), (21, 17), (30, 25), (19, 31), (0, 26), (24, 13), (31, 29), (16, 2), (15, 25), (1, 19), (11, 3), (23, 25), (2, 16), (16, 29), (11, 18), (10, 6), (22, 11), (23, 7), (20, 21), (22, 19), (20, 28), (22, 24), (11, 9), (7, 5), (31, 17), (11, 6), (9, 3), (27, 32), (15, 14), (1, 31), (12, 7), (19, 5), (11, 2), (30, 0), (30, 11), (20, 32), (3, 16), (11, 8), (26, 8), (32, 11), (21, 3), (21, 7), (17, 25), (20, 0), (16, 20), (22, 7), (30, 26), (20, 7), (15, 4), (4, 30), (2, 15), (20, 25), (23, 30), (10, 11), (19, 2), (32, 14), (23, 6), (23, 9), (23, 26), (16, 0), (17, 18), (6, 31), (2, 31), (13, 18), (20, 2), (13, 19), (22, 30), (2, 2), (7, 14), (9, 13), (1, 29), (22, 6), (32, 32), (24, 20), (19, 1), (34, 2), (18, 9), (25, 11), (5, 13), (0, 22), (5, 24), (26, 18), (29, 17), (18, 24), (22, 16), (9, 26), (16, 27), (27, 20), (4, 15), (9, 25), (12, 31), (17, 9), (33, 20), (14, 28), (25, 13), (6, 9), (18, 31), (12, 11), (7, 20), (31, 19), (4, 21), (30, 31), (26, 3), (32, 9), (16, 6), (2, 32), (16, 15), (22, 20), (29, 1), (25, 14), (28, 25), (16, 9), (23, 31), (27, 19), (14, 3), (7, 4), (29, 32), (31, 14), (30, 29), (28, 18), (2, 12), (32, 10), (10, 22), (34, 0), (26, 27), (12, 21), (9, 24), (3, 31), (22, 17), (3, 10), (24, 23), (16, 13), (27, 23), (4, 23), (2, 13), (15, 26), (17, 20), (7, 29), (22, 25), (33, 31), (29, 18), (0, 21), (11, 26), (18, 15), (30, 23), (23, 20), (31, 11), (20, 3), (12, 0), (27, 6), (5, 27), (7, 11), (30, 6), (2, 10), (10, 13), (6, 20), (28, 26), (18, 7), (9, 31), (0, 7), (5, 8), (15, 30), (3, 3), (28, 2), (30, 1), (34, 15), (19, 14), (11, 27), (29, 8), (13, 20), (19, 32), (27, 14), (10, 32), (32, 15), (1, 32), (26, 16), (1, 24), (12, 14), (24, 14), (2, 28), (6, 22), (18, 23), (31, 24), (30, 24), (12, 6), (8, 2), (24, 29), (9, 21), (9, 7), (26, 30), (32, 13), (9, 17), (18, 0), (23, 10), (15, 17), (15, 31), (5, 11), (25, 6), (0, 16), (22, 13), (27, 25), (14, 5), (17, 23), (31, 0), (19, 9), (20, 29), (3, 6), (1, 6), (1, 15), (33, 10), (29, 11), (5, 29), (9, 28), (33, 11), (27, 5), (20, 17), (1, 0), (19, 10), (12, 10), (5, 32), (14, 14), (13, 16), (9, 5), (8, 8), (17, 13), (21, 19), (24, 10), (8, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417312", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 20), (35, 16), (20, 7), (31, 21), (36, 21), (16, 7), (11, 27), (23, 1), (12, 8), (34, 9), (38, 10), (26, 27), (22, 9), (3, 18), (20, 11), (37, 28), (31, 12), (21, 9), (15, 31), (26, 14), (1, 1), (9, 30), (24, 10), (32, 22), (35, 29), (36, 33), (25, 26), (11, 23), (34, 1), (24, 31), (28, 7), (13, 7), (26, 3), (17, 25), (6, 4), (25, 33), (15, 4), (13, 13), (30, 16), (34, 20), (12, 12), (11, 24), (5, 0), (2, 15), (32, 9), (2, 33), (24, 23), (5, 33), (37, 22), (27, 26), (16, 11), (18, 24), (24, 33), (35, 5), (35, 20), (11, 18), (29, 18), (8, 4), (19, 25), (33, 7), (36, 15), (3, 5), (20, 25), (11, 34), (11, 3), (17, 12), (21, 16), (8, 15), (11, 30), (13, 20), (14, 5), (4, 28), (25, 25), (23, 31), (4, 2), (22, 2), (0, 20), (0, 8), (26, 25), (24, 2), (32, 8), (34, 4), (7, 13), (13, 15), (26, 8), (14, 33), (7, 27), (36, 6), (28, 6), (37, 13), (26, 5), (26, 32), (19, 8), (37, 34), (12, 5), (36, 18), (12, 3), (16, 3), (18, 28), (24, 19), (9, 9), (8, 30), (20, 19), (7, 30), (0, 30), (28, 1), (4, 14), (7, 23), (1, 30), (29, 3), (6, 9), (21, 25), (28, 18), (35, 17), (5, 7), (27, 24), (33, 31), (38, 17), (7, 4), (15, 13), (12, 29), (6, 32), (24, 17), (12, 25), (35, 34), (29, 0), (17, 21), (38, 8), (22, 14), (27, 21), (14, 25), (21, 0), (0, 16), (38, 24), (32, 29), (18, 18), (7, 8), (7, 12), (29, 32), (27, 34), (4, 30), (22, 20), (30, 27), (3, 7), (24, 8), (0, 10), (0, 13), (33, 15), (25, 16), (36, 5), (14, 15), (1, 32), (36, 0), (9, 7), (16, 4), (38, 0), (6, 22), (20, 13), (34, 16), (30, 11), (13, 4), (19, 33), (7, 6), (0, 24), (26, 33), (24, 0), (21, 33), (32, 28), (28, 27), (32, 12), (28, 12), (33, 6), (26, 15), (14, 10), (23, 20), (31, 15), (26, 7), (27, 0), (33, 11), (12, 21), (18, 8), (2, 20), (7, 9), (22, 0), (24, 29), (34, 14), (33, 13), (33, 32), (29, 22), (30, 19), (8, 14), (1, 11), (1, 22), (0, 31), (10, 28), (7, 20), (19, 6), (25, 28), (3, 29), (11, 15), (14, 29), (12, 14), (16, 34), (22, 18), (0, 3), (38, 23), (12, 31), (0, 19), (38, 18), (37, 10), (26, 16), (35, 0), (23, 6), (34, 7), (11, 0), (10, 9), (27, 14), (7, 18), (6, 15), (4, 21), (26, 20), (34, 23), (10, 6), (38, 15), (6, 17), (0, 18), (25, 27), (17, 6), (37, 1), (4, 31), (2, 13), (29, 9), (11, 29), (2, 21), (33, 1), (36, 8), (1, 16), (25, 22), (7, 31), (31, 31), (34, 0), (3, 0), (30, 0), (32, 25), (15, 21), (27, 31), (36, 14), (8, 18), (20, 9), (24, 13), (34, 27), (16, 29), (24, 11), (24, 16), (2, 19), (33, 27), (32, 23), (32, 16), (8, 28), (14, 19), (1, 17), (15, 27), (2, 1), (24, 1), (17, 15), (32, 7), (13, 5), (37, 26), (5, 18), (28, 10), (3, 9), (12, 34), (29, 11), (20, 23), (11, 33), (23, 14), (34, 26), (1, 34), (12, 27), (10, 17), (27, 32), (13, 18), (9, 10), (5, 15), (15, 2), (36, 12), (28, 4), (6, 3), (27, 3), (29, 21), (19, 12), (3, 26), (24, 26), (13, 25), (14, 7), (14, 9), (30, 12), (4, 23), (23, 11), (24, 20), (18, 25), (30, 6), (6, 2), (35, 19), (22, 31), (25, 24), (17, 22), (9, 27), (1, 12), (0, 26), (36, 17), (0, 21), (9, 20), (13, 17), (20, 31), (2, 24), (16, 22), (23, 27), (30, 13), (37, 5), (37, 31), (36, 13), (20, 22), (21, 3), (4, 25), (29, 8), (35, 30), (5, 28), (35, 12), (37, 16), (14, 8), (28, 2), (10, 2), (16, 27), (7, 25), (22, 12), (9, 6), (9, 24), (5, 19), (22, 10), (12, 0), (26, 1), (15, 26), (13, 26), (1, 18), (30, 7), (5, 21), (20, 32), (8, 27), (28, 5), (21, 34), (26, 17), (36, 31), (33, 29), (37, 18), (38, 30), (6, 7), (36, 7), (7, 21), (27, 22), (12, 28), (32, 10), (37, 33), (1, 19), (5, 4), (36, 2), (11, 5), (24, 4), (35, 14), (26, 0), (21, 23), (0, 29), (14, 20), (31, 16), (22, 4), (16, 33), (3, 3), (19, 13), (26, 22), (26, 9), (26, 21), (27, 11), (28, 32), (30, 17), (35, 8), (7, 16), (8, 0), (18, 19), (14, 13), (17, 31), (7, 2), (32, 0), (26, 28), (17, 13), (16, 21), (30, 34), (3, 32), (35, 1), (8, 32), (28, 9), (28, 28), (21, 27), (27, 8), (17, 0), (8, 22), (24, 5), (11, 12), (18, 12), (30, 8), (32, 33), (35, 7), (15, 29), (25, 18), (19, 3), (1, 4), (35, 21), (3, 17), (20, 16), (30, 5), (4, 34), (30, 10), (5, 25), (20, 29), (27, 9), (13, 16), (15, 9), (19, 5), (35, 10), (16, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367056", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (26, 21), (32, 17), (2, 27), (2, 12), (16, 24), (11, 30), (10, 28), (22, 1), (12, 24), (10, 1), (5, 32), (28, 19), (20, 28), (5, 31), (0, 13), (19, 1), (35, 31), (4, 15), (15, 22), (33, 16), (15, 30), (5, 3), (15, 11), (22, 9), (16, 10), (29, 16), (3, 14), (2, 9), (20, 22), (35, 3), (29, 18), (28, 15), (14, 31), (28, 6), (26, 27), (9, 7), (10, 6), (0, 15), (23, 18), (20, 10), (25, 5), (24, 22), (34, 17), (26, 16), (36, 1), (37, 30), (11, 19), (30, 13), (31, 6), (11, 32), (25, 27), (21, 3), (3, 9), (5, 8), (30, 30), (11, 24), (18, 24), (10, 26), (11, 1), (33, 2), (29, 27), (29, 31), (27, 15), (13, 0), (11, 28), (1, 5), (10, 5), (15, 5), (27, 21), (11, 25), (8, 6), (0, 16), (6, 31), (0, 9), (26, 31), (6, 1), (28, 25), (18, 29), (2, 31), (26, 8), (4, 0), (29, 14), (24, 19), (27, 11), (37, 13), (13, 5), (33, 12), (22, 24), (30, 24), (26, 6), (16, 20), (13, 28), (20, 8), (23, 31), (37, 11), (19, 17), (35, 22), (9, 9), (24, 11), (6, 17), (15, 29), (27, 32), (4, 28), (25, 8), (35, 17), (27, 31), (6, 21), (6, 24), (23, 29), (14, 9), (29, 21), (2, 15), (11, 12), (13, 29), (32, 16), (26, 9), (14, 29), (31, 22), (21, 27), (6, 11), (15, 9), (34, 18), (32, 10), (27, 2), (37, 18), (21, 15), (7, 11), (27, 24), (2, 17), (14, 15), (14, 23), (35, 12), (8, 21), (25, 13), (25, 17), (24, 4), (33, 22), (34, 15), (6, 5), (34, 21), (26, 24), (32, 4), (32, 5), (36, 5), (37, 20), (22, 13), (9, 3), (0, 30), (12, 7), (2, 18), (28, 14), (29, 23), (1, 9), (37, 26), (11, 21), (5, 1), (31, 4), (9, 4), (25, 6), (15, 7), (33, 7), (23, 27), (33, 31), (19, 25), (15, 23), (36, 24), (35, 18), (36, 27), (3, 12), (18, 22), (6, 0), (3, 16), (12, 25), (5, 19), (21, 31), (0, 1), (10, 23), (35, 32), (7, 17), (12, 29), (8, 31), (34, 5), (32, 15), (19, 19), (30, 7), (22, 0), (26, 2), (34, 0), (23, 14), (22, 14), (19, 11), (12, 16), (18, 10), (21, 25), (15, 13), (7, 27), (36, 8), (8, 28), (33, 4), (32, 25), (16, 13), (28, 22), (27, 0), (2, 23), (3, 26), (9, 0), (30, 21), (6, 4), (3, 13), (9, 29), (33, 19), (15, 21), (9, 19), (14, 1), (29, 19), (5, 13), (7, 13), (24, 6), (30, 31), (9, 15), (32, 20), (12, 28), (16, 1), (34, 24), (22, 10), (18, 28), (6, 8), (7, 6), (19, 16), (26, 26), (31, 20), (12, 32), (13, 12), (36, 11), (0, 18), (13, 18), (31, 0), (7, 26), (33, 8), (28, 3), (17, 5), (10, 24), (5, 25), (26, 19), (26, 20), (12, 27), (6, 7), (9, 28), (16, 9), (19, 6), (37, 28), (37, 4), (28, 0), (29, 32), (12, 12), (15, 20), (32, 19), (9, 26), (36, 21), (16, 26), (2, 30), (1, 7), (4, 30), (23, 6), (11, 15), (24, 1), (32, 22), (9, 17), (8, 1), (16, 29), (24, 30), (34, 6), (17, 32), (21, 20), (3, 22), (24, 31), (27, 23), (20, 12), (6, 14), (20, 26), (26, 13), (8, 10), (34, 27), (13, 32), (25, 16), (31, 3), (1, 2), (15, 2), (32, 2), (33, 30), (6, 28), (1, 12), (9, 1), (31, 23), (10, 30), (25, 23), (35, 26), (33, 13), (37, 27), (10, 27), (35, 30), (20, 27), (36, 13), (13, 2), (34, 22), (18, 31), (28, 27), (23, 20), (8, 17), (31, 8), (2, 3), (17, 17), (17, 24), (17, 3), (0, 12), (12, 9), (30, 5), (4, 24), (33, 3), (17, 14), (4, 14), (1, 6), (5, 0), (35, 13), (22, 15), (24, 16), (30, 27), (36, 15), (24, 20), (21, 4), (31, 2), (29, 6), (25, 24), (34, 19), (5, 7), (18, 30), (5, 10), (36, 2), (24, 7), (19, 24), (34, 7), (0, 11), (37, 29), (10, 17), (11, 11), (4, 1), (21, 9), (19, 10), (2, 24), (7, 12), (11, 29), (27, 19), (14, 25), (25, 9), (5, 6), (28, 9), (17, 10), (32, 29), (26, 15), (4, 20), (30, 2), (19, 8), (24, 0), (1, 4), (0, 23), (8, 4), (24, 13), (4, 32), (5, 28), (26, 1), (5, 23), (23, 11), (0, 29), (15, 16), (17, 0), (14, 2), (24, 28), (22, 2), (19, 13), (12, 17), (15, 10), (9, 14), (35, 6), (8, 20), (16, 0), (18, 23), (24, 9), (32, 18), (14, 3), (25, 1), (16, 7), (26, 5), (34, 20), (18, 8), (1, 18), (25, 10), (27, 17), (9, 20), (34, 32), (22, 27), (7, 31), (3, 4), (13, 17), (12, 23), (27, 3), (10, 13), (6, 27), (15, 12), (16, 25), (7, 25), (9, 6), (8, 24), (18, 9), (33, 25), (35, 24), (36, 20), (19, 29), (17, 31), (11, 26), (3, 20), (21, 7), (26, 18), (9, 31), (3, 1), (35, 4), (6, 32), (7, 5), (5, 14), (23, 28), (37, 1), (19, 2), (15, 28), (2, 4), (22, 6), (14, 8), (20, 21), (1, 19), (15, 25), (28, 23), (33, 17), (3, 3), (10, 15), (28, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "314496", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 31), (31, 15), (7, 1), (31, 9), (8, 33), (6, 27), (19, 28), (27, 30), (31, 29), (4, 19), (0, 5), (10, 21), (12, 33), (3, 27), (30, 8), (25, 15), (4, 1), (7, 14), (18, 20), (2, 20), (10, 15), (26, 32), (29, 34), (10, 26), (28, 24), (30, 11), (19, 31), (15, 19), (2, 25), (13, 0), (4, 2), (20, 30), (1, 5), (18, 29), (5, 14), (1, 15), (12, 13), (0, 18), (7, 27), (9, 29), (25, 8), (1, 18), (7, 6), (27, 17), (5, 30), (14, 23), (30, 28), (22, 1), (0, 33), (32, 26), (30, 22), (9, 5), (10, 18), (21, 0), (4, 26), (13, 13), (9, 1), (2, 26), (29, 5), (13, 6), (7, 10), (27, 9), (19, 3), (16, 17), (3, 25), (20, 3), (27, 6), (6, 2), (3, 10), (30, 10), (8, 26), (33, 11), (28, 15), (3, 30), (1, 1), (22, 28), (17, 32), (5, 21), (10, 25), (29, 28), (29, 15), (22, 12), (4, 34), (29, 18), (0, 34), (14, 29), (29, 10), (7, 11), (5, 18), (1, 11), (33, 16), (13, 23), (25, 21), (30, 2), (20, 26), (26, 13), (24, 0), (29, 0), (9, 24), (14, 32), (22, 15), (31, 6), (13, 20), (25, 34), (1, 13), (14, 25), (18, 13), (17, 9), (4, 17), (1, 6), (7, 24), (28, 18), (12, 22), (16, 11), (31, 12), (30, 18), (2, 2), (15, 0), (2, 13), (6, 14), (12, 34), (4, 9), (6, 12), (21, 5), (6, 17), (30, 15), (27, 28), (7, 20), (20, 27), (8, 14), (24, 31), (6, 1), (21, 8), (6, 20), (28, 31), (10, 31), (30, 9), (19, 17), (15, 22), (14, 31), (8, 3), (13, 29), (17, 15), (28, 8), (12, 29), (25, 12), (11, 17), (2, 1), (4, 8), (20, 21), (18, 7), (8, 11), (22, 26), (16, 14), (17, 1), (17, 29), (15, 21), (32, 0), (32, 32), (4, 14), (18, 23), (26, 21), (13, 7), (31, 3), (17, 13), (19, 6), (10, 6), (20, 2), (16, 13), (12, 2), (7, 17), (0, 7), (23, 32), (31, 13), (3, 2), (7, 29), (27, 27), (7, 23), (29, 26), (4, 10), (28, 9), (10, 22), (12, 12), (14, 22), (1, 19), (21, 29), (17, 22), (20, 31), (12, 31), (24, 29), (1, 21), (5, 5), (5, 26), (5, 29), (11, 4), (14, 8), (20, 18), (6, 4), (23, 33), (1, 20), (31, 22), (3, 26), (33, 12), (9, 18), (9, 34), (7, 34), (22, 9), (26, 25), (24, 25), (19, 30), (14, 3), (7, 25), (33, 23), (13, 11), (33, 9), (27, 7), (11, 5), (30, 19), (4, 13), (30, 31), (2, 11), (27, 11), (29, 13), (7, 2), (4, 6), (29, 19), (15, 32), (31, 31), (8, 22), (3, 9), (28, 21), (16, 30), (7, 19), (19, 21), (6, 22), (19, 25), (27, 22), (17, 28), (17, 31), (21, 20), (0, 13), (18, 3), (9, 25), (33, 22), (8, 7), (13, 24), (18, 17), (29, 4), (3, 13), (3, 19), (15, 3), (14, 13), (16, 31), (5, 4), (32, 17), (4, 7), (14, 2), (10, 8), (18, 26), (17, 2), (11, 33), (24, 30), (20, 6), (0, 25), (25, 33), (19, 11), (17, 16), (0, 17), (28, 5), (32, 9), (25, 32), (18, 22), (23, 7), (21, 22), (10, 3), (24, 20), (11, 12), (30, 20), (25, 23), (17, 19), (8, 19), (15, 9), (2, 22), (32, 2), (7, 21), (5, 25), (26, 34), (1, 10), (0, 16), (11, 6), (32, 15), (4, 20), (0, 22), (25, 25), (11, 2), (26, 20), (9, 26), (25, 9), (9, 23), (25, 1), (27, 25), (17, 26), (2, 17), (27, 15), (24, 4), (17, 8), (12, 6), (15, 8), (5, 17), (6, 24), (32, 4), (27, 4), (22, 30), (16, 8), (1, 31), (31, 19), (30, 32), (5, 34), (31, 32), (18, 6), (1, 33), (4, 11), (14, 5), (27, 12), (24, 23), (11, 29), (9, 2), (13, 9), (2, 21), (23, 2), (30, 23), (25, 18), (26, 7), (32, 1), (8, 13), (21, 24), (23, 8), (23, 10), (29, 23), (24, 1), (15, 14), (17, 21), (11, 20), (3, 20), (32, 8), (20, 20), (10, 28), (33, 33), (30, 26), (3, 34), (19, 32), (1, 12), (14, 6), (0, 27), (14, 15), (24, 26), (1, 32), (10, 14), (0, 28), (33, 26), (27, 13), (10, 10), (22, 25), (33, 21), (11, 10), (31, 5), (2, 9), (13, 8), (1, 27), (10, 1), (32, 25), (21, 17), (24, 6), (23, 0), (27, 24), (25, 29), (17, 6), (31, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752640", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 5), (17, 30), (0, 2), (15, 14), (27, 24), (8, 14), (30, 2), (9, 12), (29, 29), (28, 29), (7, 26), (21, 2), (9, 6), (2, 23), (30, 5), (6, 20), (14, 29), (23, 8), (29, 26), (5, 22), (5, 35), (27, 33), (13, 30), (29, 25), (24, 16), (12, 4), (16, 25), (10, 35), (23, 30), (33, 22), (33, 19), (6, 4), (18, 0), (33, 21), (6, 10), (4, 33), (26, 32), (8, 11), (17, 27), (17, 22), (28, 32), (27, 23), (18, 5), (7, 19), (19, 9), (21, 32), (7, 2), (27, 11), (23, 9), (5, 10), (22, 25), (5, 3), (17, 12), (2, 8), (27, 0), (21, 22), (28, 2), (15, 35), (4, 18), (22, 15), (18, 3), (11, 1), (33, 20), (23, 34), (6, 3), (7, 0), (0, 13), (22, 1), (1, 13), (26, 24), (10, 8), (1, 29), (2, 17), (3, 22), (14, 35), (24, 13), (19, 18), (16, 7), (28, 24), (1, 27), (31, 10), (31, 25), (21, 18), (15, 2), (25, 6), (27, 26), (23, 25), (3, 28), (12, 12), (28, 4), (29, 19), (10, 29), (10, 7), (3, 25), (3, 18), (21, 30), (32, 34), (22, 2), (32, 32), (5, 16), (23, 1), (7, 24), (22, 23), (29, 35), (20, 32), (26, 28), (19, 4), (11, 11), (27, 29), (12, 35), (15, 6), (10, 21), (10, 28), (10, 4), (18, 26), (24, 17), (1, 18), (17, 21), (15, 11), (9, 13), (22, 32), (26, 3), (11, 0), (0, 11), (32, 11), (9, 1), (15, 5), (17, 13), (25, 27), (4, 17), (33, 33), (21, 28), (20, 20), (9, 20), (13, 25), (17, 10), (5, 1), (20, 34), (21, 16), (15, 32), (6, 33), (3, 6), (5, 12), (12, 3), (28, 16), (1, 31), (9, 34), (0, 9), (4, 2), (32, 28), (11, 18), (8, 8), (4, 30), (33, 15), (22, 3), (32, 9), (24, 5), (27, 6), (0, 21), (0, 19), (27, 12), (2, 21), (31, 27), (23, 12), (22, 20), (7, 18), (23, 23), (14, 33), (14, 2), (17, 34), (4, 21), (4, 14), (10, 3), (9, 15), (24, 12), (11, 32), (5, 34), (9, 23), (19, 24), (15, 30), (31, 34), (17, 14), (9, 14), (13, 11), (16, 1), (31, 33), (5, 11), (4, 8), (7, 10), (16, 3), (18, 23), (6, 2), (0, 31), (14, 0), (14, 17), (26, 18), (11, 33), (26, 13), (33, 11), (30, 23), (10, 31), (1, 35), (31, 3), (2, 9), (11, 17), (33, 10), (4, 32), (10, 25), (19, 0), (19, 22), (12, 1), (14, 21), (8, 20), (13, 3), (24, 6), (1, 12), (20, 5), (3, 27), (13, 34), (24, 34), (26, 12), (5, 19), (25, 17), (32, 18), (25, 19), (20, 9), (25, 7), (26, 17), (1, 28), (6, 6), (10, 27), (4, 13), (25, 3), (25, 24), (8, 23), (11, 34), (5, 17), (0, 35), (0, 5), (2, 15), (13, 9), (10, 2), (4, 0), (16, 8), (31, 9), (12, 8), (29, 21), (8, 22), (29, 34), (1, 14), (14, 13), (13, 18), (32, 13), (11, 15), (19, 6), (23, 21), (25, 0), (1, 3), (29, 5), (17, 28), (29, 14), (27, 22), (19, 17), (33, 25), (15, 21), (27, 31), (5, 21), (23, 26), (27, 9), (6, 14), (6, 22), (24, 9), (25, 4), (9, 21), (13, 31), (22, 22), (12, 20), (12, 11), (8, 3), (15, 15), (25, 10), (7, 31), (11, 23), (1, 9), (5, 32), (16, 24), (25, 31), (25, 12), (19, 7), (0, 8), (24, 3), (14, 18), (14, 30), (26, 23), (18, 17), (15, 23), (3, 33), (6, 18), (2, 24), (10, 26), (32, 7), (23, 32), (23, 10), (16, 20), (31, 31), (27, 7), (29, 15), (12, 26), (32, 1), (16, 2), (7, 12), (21, 27), (2, 34), (19, 13), (4, 31), (11, 25), (33, 1), (2, 27), (5, 2), (2, 16), (9, 2), (4, 5), (32, 6), (30, 32), (12, 10), (4, 25), (32, 19), (23, 35), (15, 25), (15, 22), (15, 8), (12, 17), (30, 12), (19, 35), (15, 16), (16, 23), (18, 6), (23, 3), (26, 2), (8, 9), (0, 25), (24, 8), (17, 8), (26, 8), (9, 26), (9, 9), (31, 11), (30, 0), (6, 27), (15, 13), (6, 23), (22, 18), (15, 33), (13, 6), (2, 19), (18, 19), (30, 17), (26, 6), (16, 4), (32, 2), (31, 5), (26, 0), (22, 33), (10, 10), (17, 0), (18, 34), (2, 25), (28, 8), (15, 29), (33, 16), (14, 6), (13, 26), (33, 23), (8, 0), (13, 32), (15, 18), (10, 22), (32, 16), (26, 29), (9, 27), (12, 27), (19, 12), (5, 33), (3, 12), (4, 16), (1, 32), (33, 0), (13, 22), (12, 2), (1, 19), (24, 11), (12, 16), (30, 7), (4, 35), (14, 3), (16, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "931920", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), 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), (27, 23), (26, 27), (3, 1), (29, 27), (31, 12), (22, 16), (14, 11), (16, 32), (33, 5), (28, 27), (7, 30), (21, 34), (28, 13), (9, 2), (24, 27), (37, 18), (16, 26), (14, 13), (13, 15), (1, 21), (22, 9), (10, 35), (28, 25), (18, 30), (30, 20), (16, 16), (17, 26), (35, 19), (38, 22), (38, 30), (12, 17), (6, 28), (37, 21), (29, 20), (25, 2), (34, 15), (6, 14), (24, 33), (0, 30), (2, 19), (35, 30), (19, 20), (23, 0), (3, 19), (34, 30), (28, 17), (0, 21), (18, 31), (16, 10), (24, 1), (32, 29), (12, 3), (24, 6), (9, 16), (5, 30), (5, 16), (16, 4), (23, 30), (16, 1), (24, 29), (26, 25), (23, 11), (33, 34), (38, 32), (22, 27), (37, 12), (23, 21), (5, 32), (19, 24), (0, 12), (35, 9), (21, 19), (27, 13), (24, 20), (36, 4), (25, 25), (1, 0), (4, 26), (37, 24), (22, 3), (37, 20), (19, 26), (9, 1), (10, 8), (7, 7), (37, 31), (9, 22), (8, 23), (27, 24), (22, 1), (14, 30), (10, 13), (8, 2), (5, 26), (31, 6), (25, 30), (21, 17), (36, 6), (16, 0), (13, 32), (24, 4), (9, 4), (13, 22), (17, 14), (22, 6), (37, 25), (2, 15), (14, 16), (28, 18), (6, 4), (4, 8), (28, 24), (25, 28), (36, 16), (14, 28), (7, 15), (37, 28), (32, 6), (34, 24), (12, 0), (32, 3), (21, 33), (19, 5), (11, 10), (16, 2), (8, 21), (10, 30), (13, 28), (3, 32), (9, 10), (29, 2), (1, 18), (4, 17), (15, 18), (28, 29), (13, 33), (22, 5), (19, 13), (27, 12), (0, 32), (11, 4), (8, 32), (37, 9), (2, 29), (8, 26), (36, 32), (10, 14), (15, 19), (14, 23), (36, 11), (29, 5), (31, 26), (22, 13), (9, 17), (28, 2), (36, 23), (21, 4), (29, 13), (33, 29), (22, 21), (15, 35), (7, 20), (18, 33), (30, 7), (21, 20), (31, 32), (16, 19), (36, 13), (10, 7), (37, 3), (10, 2), (25, 10), (3, 9), (28, 11), (11, 6), (30, 28), (19, 35), (18, 23), (15, 24), (2, 27), (23, 6), (0, 31), (37, 30), (10, 12), (15, 4), (17, 18), (36, 29), (16, 11), (7, 4), (9, 20), (37, 23), (31, 23), (36, 30), (18, 8), (35, 29), (34, 9), (29, 14), (20, 3), (23, 18), (28, 0), (26, 12), (4, 3), (27, 19), (36, 28), (26, 28), (12, 5), (4, 29), (27, 14), (3, 0), (20, 0), (36, 17), (1, 6), (6, 25), (33, 15), (26, 7), (4, 25), (38, 7), (7, 23), (38, 29), (24, 15), (36, 15), (32, 27), (36, 34), (2, 20), (38, 2), (1, 4), (23, 27), (21, 23), (34, 8), (36, 12), (16, 31), (35, 7), (29, 22), (7, 1), (8, 17), (0, 28), (33, 8), (29, 19), (5, 35), (24, 5), (12, 12), (22, 2), (25, 21), (19, 4), (1, 30), (6, 13), (25, 35), (16, 25), (24, 28), (25, 33), (5, 29), (18, 28), (26, 3), (16, 18), (30, 9), (23, 26), (1, 3), (13, 2), (0, 22), (24, 30), (31, 29), (11, 3), (6, 35), (13, 1), (21, 7), (27, 26), (33, 26), (4, 23), (32, 5), (30, 26), (23, 9), (16, 27), (33, 21), (18, 7), (7, 18), (11, 29), (8, 5), (29, 21), (30, 2), (2, 10), (30, 8), (1, 8), (11, 11), (26, 26), (31, 7), (37, 6), (36, 24), (21, 26), (17, 12), (3, 20), (15, 5), (15, 30), (34, 11), (38, 14), (32, 23), (14, 1), (19, 7), (33, 9), (6, 34), (38, 26), (2, 24), (23, 33), (29, 35), (12, 23), (9, 0), (6, 8), (18, 22), (15, 11), (12, 26), (35, 12), (38, 19), (37, 13), (35, 16), (26, 32), (37, 16), (16, 14), (13, 27), (2, 14), (10, 28), (10, 25), (30, 29), (26, 16), (35, 32), (30, 13), (33, 3), (16, 7), (35, 17), (10, 19), (22, 7), (18, 14), (17, 23), (20, 30), (30, 6), (29, 25), (18, 5), (26, 30), (29, 15), (3, 30), (27, 35), (2, 12), (12, 33), (19, 19), (31, 34), (3, 24), (17, 21), (37, 5), (5, 0), (0, 33), (22, 30), (17, 24), (5, 34), (25, 13), (32, 16), (11, 25), (33, 6), (17, 22), (30, 0), (15, 16), (5, 19), (33, 0), (22, 12), (38, 9), (4, 2), (27, 8), (32, 11), (6, 18), (34, 12), (2, 2), (6, 22), (12, 22), (10, 24), (35, 24), (16, 15), (22, 29), (20, 19), (16, 13), (18, 24), (28, 10), (2, 1), (26, 6), (37, 26), (29, 24), (15, 29), (24, 26), (29, 18), (31, 33), (0, 8), (36, 14), (15, 25), (20, 1), (3, 16), (15, 27), (8, 0), (1, 13), (25, 34), (13, 31), (20, 2), (15, 0), (21, 5), (18, 10), (12, 10), (6, 5), (0, 18), (36, 27), (17, 30), (24, 25), (29, 9), (6, 2), (4, 7), (12, 13), (31, 5), (2, 18), (25, 18), (12, 24), (31, 8), (3, 35), (2, 7), (14, 6), (10, 27), (20, 4), (5, 25), (35, 35), (17, 7), (16, 8), (1, 28), (32, 34), (6, 3), (9, 30), (36, 35), (15, 2), (31, 15), (0, 35), (32, 13), (23, 3), (32, 24), (31, 3), (34, 3), (4, 6), (2, 26), (8, 34), (30, 12), (11, 30), (32, 9), (6, 32), (35, 3), (23, 10), (11, 35), (5, 23), (3, 11), (7, 29), (6, 23), (13, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "587250", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 34), (31, 26), (12, 2), (30, 35), (18, 34), (3, 10), (15, 21), (28, 12), (34, 18), (2, 1), (5, 8), (9, 13), (26, 28), (6, 33), (35, 18), (31, 10), (20, 23), (14, 5), (27, 15), (15, 15), (30, 6), (23, 30), (8, 32), (17, 3), (7, 16), (33, 23), (20, 33), (22, 29), (2, 26), (6, 10), (28, 23), (20, 32), (7, 32), (8, 29), (31, 11), (5, 34), (4, 17), (0, 4), (19, 23), (33, 32), (3, 16), (17, 0), (29, 28), (27, 11), (6, 35), (30, 15), (0, 35), (12, 7), (0, 18), (20, 11), (13, 31), (10, 15), (2, 33), (31, 25), (26, 17), (17, 31), (13, 13), (20, 4), (15, 25), (26, 20), (35, 15), (30, 0), (35, 3), (18, 25), (3, 29), (34, 3), (29, 11), (22, 23), (1, 11), (15, 27), (6, 6), (20, 10), (25, 10), (18, 30), (8, 19), (31, 18), (24, 16), (14, 3), (31, 30), (32, 13), (11, 30), (22, 26), (18, 17), (26, 16), (35, 24), (30, 23), (17, 32), (34, 22), (35, 27), (35, 0), (0, 10), (31, 23), (23, 11), (1, 24), (24, 9), (14, 24), (26, 24), (34, 29), (27, 30), (3, 25), (16, 9), (28, 6), (2, 24), (10, 5), (30, 1), (22, 20), (33, 31), (19, 28), (10, 17), (5, 30), (8, 30), (12, 16), (26, 15), (12, 11), (24, 6), (19, 31), (9, 3), (7, 14), (12, 3), (31, 17), (4, 21), (11, 22), (20, 28), (17, 19), (11, 19), (5, 17), (1, 20), (10, 7), (10, 19), (29, 3), (27, 1), (14, 7), (17, 28), (17, 10), (3, 35), (29, 35), (25, 9), (8, 15), (35, 34), (6, 19), (9, 0), (4, 11), (14, 11), (12, 28), (11, 11), (5, 7), (21, 32), (22, 16), (33, 1), (28, 17), (20, 21), (10, 18), (6, 14), (30, 18), (25, 27), (29, 15), (14, 6), (9, 20), (16, 35), (15, 30), (24, 12), (27, 25), (29, 24), (14, 17), (18, 0), (34, 23), (10, 33), (25, 12), (31, 15), (8, 13), (35, 25), (21, 8), (33, 17), (5, 1), (1, 31), (14, 14), (7, 18), (29, 18), (7, 29), (8, 4), (17, 22), (6, 9), (19, 2), (7, 9), (18, 22), (16, 31), (16, 21), (33, 21), (31, 22), (34, 16), (20, 13), (33, 5), (27, 5), (32, 19), (11, 5), (9, 26), (3, 12), (13, 18), (1, 12), (12, 34), (4, 20), (7, 21), (9, 7), (10, 32), (33, 22), (34, 14), (33, 11), (28, 19), (5, 18), (14, 9), (20, 5), (14, 26), (12, 4), (7, 20), (4, 10), (0, 14), (33, 15), (1, 19), (28, 27), (13, 16), (6, 17), (29, 25), (35, 8), (2, 29), (12, 8), (2, 6), (18, 21), (13, 21), (19, 26), (17, 23), (14, 8), (2, 22), (19, 21), (9, 28), (29, 30), (11, 33), (10, 24), (15, 32), (0, 12), (33, 6), (11, 25), (12, 33), (11, 21), (28, 28), (8, 28), (14, 16), (27, 35), (28, 22), (3, 23), (32, 34), (9, 35), (20, 9), (11, 24), (15, 13), (13, 30), (35, 16), (19, 15), (10, 23), (31, 28), (30, 31), (14, 20), (34, 9), (34, 17), (28, 18), (16, 16), (26, 31), (16, 12), (27, 0), (5, 14), (3, 3), (20, 17), (13, 2), (13, 19), (33, 20), (12, 10), (16, 2), (13, 32), (28, 10), (3, 19), (15, 10), (4, 5), (30, 22), (20, 30), (4, 2), (13, 12), (2, 35), (3, 20), (13, 1), (20, 26), (25, 29), (33, 13), (5, 26), (21, 25), (35, 23), (11, 27), (0, 28), (14, 28), (29, 16), (29, 27), (10, 8), (35, 10), (35, 19), (13, 20), (22, 19), (0, 6), (23, 13), (33, 14), (21, 17), (7, 26), (32, 1), (35, 5), (31, 1), (0, 8), (17, 21), (8, 22), (3, 2), (25, 8), (12, 31), (0, 26), (25, 3), (2, 25), (29, 0), (8, 6), (24, 25), (22, 3), (29, 1), (33, 10), (17, 25), (13, 11), (6, 28), (25, 25), (34, 0), (20, 15), (12, 24), (31, 13), (21, 29), (22, 4), (7, 15), (31, 24), (34, 33), (22, 2), (1, 14), (27, 29), (12, 13), (19, 29), (25, 31), (10, 35), (24, 13), (33, 2), (33, 30), (15, 7), (6, 21), (16, 20), (11, 0), (22, 17), (18, 2), (1, 22), (2, 3), (30, 32), (26, 21), (13, 8), (32, 12), (17, 20), (23, 17), (11, 8), (2, 2), (31, 12), (7, 6), (27, 21), (18, 9), (24, 19), (24, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "244640", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (35, 24), (30, 25), (12, 26), (21, 14), (35, 15), (0, 9), (27, 20), (7, 2), (32, 7), (36, 23), (19, 25), (17, 26), (34, 26), (31, 21), (9, 12), (22, 2), (23, 13), (23, 29), (8, 8), (17, 8), (21, 26), (19, 6), (5, 25), (1, 1), (12, 21), (30, 12), (21, 8), (26, 4), (22, 22), (4, 10), (27, 24), (18, 2), (24, 24), (14, 8), (35, 3), (30, 29), (24, 29), (11, 16), (24, 4), (7, 19), (7, 22), (33, 27), (8, 1), (11, 17), (23, 12), (28, 13), (13, 23), (7, 6), (9, 3), (3, 0), (34, 17), (30, 7), (9, 21), (3, 3), (34, 3), (0, 14), (23, 28), (33, 9), (11, 20), (16, 7), (12, 16), (31, 9), (24, 6), (18, 3), (6, 22), (29, 16), (22, 11), (21, 13), (30, 14), (7, 25), (8, 13), (24, 21), (22, 21), (26, 10), (22, 10), (32, 15), (31, 18), (18, 12), (3, 21), (28, 10), (13, 20), (6, 4), (1, 27), (20, 22), (31, 29), (19, 22), (1, 29), (27, 8), (3, 17), (31, 19), (30, 0), (17, 24), (22, 24), (14, 20), (35, 0), (6, 23), (16, 23), (19, 1), (33, 4), (27, 10), (22, 1), (12, 27), (2, 28), (24, 11), (18, 7), (34, 12), (12, 23), (8, 20), (19, 17), (35, 23), (5, 21), (27, 29), (12, 3), (32, 12), (5, 7), (5, 22), (31, 7), (10, 9), (1, 8), (26, 24), (32, 3), (14, 23), (0, 12), (26, 7), (2, 18), (36, 10), (29, 27), (36, 26), (4, 3), (30, 22), (14, 28), (19, 16), (19, 9), (36, 22), (0, 20), (14, 13), (2, 26), (24, 25), (13, 22), (22, 19), (12, 7), (3, 19), (12, 12), (9, 15), (24, 18), (31, 13), (20, 26), (2, 8), (8, 15), (18, 25), (10, 10), (11, 27), (27, 18), (21, 22), (21, 24), (0, 19), (20, 8), (27, 2), (19, 3), (15, 24), (30, 21), (10, 23), (35, 10), (8, 21), (32, 16), (30, 10), (5, 14), (30, 1), (6, 16), (15, 13), (18, 26), (22, 27), (16, 6), (4, 28), (36, 0), (4, 5), (31, 0), (16, 28), (2, 5), (29, 6), (31, 10), (13, 19), (29, 14), (13, 12), (32, 22), (9, 7), (18, 27), (20, 28), (11, 14), (28, 11), (16, 29), (11, 3), (27, 3), (16, 14), (8, 24), (11, 10), (15, 20), (4, 22), (22, 13), (27, 7), (25, 6), (2, 6), (6, 21), (34, 6), (16, 3), (5, 19), (17, 18), (3, 29), (15, 25), (5, 2), (33, 14), (21, 29), (34, 29), (29, 21), (36, 4), (3, 28), (30, 20), (26, 12), (1, 26), (9, 4), (13, 7), (5, 9), (11, 12), (34, 28), (4, 1), (20, 16), (32, 6), (27, 17), (6, 26), (9, 24), (23, 22), (25, 8), (26, 20), (10, 12), (3, 11), (36, 9), (32, 18), (32, 13), (20, 20), (4, 8), (22, 7), (29, 20), (19, 10), (24, 8), (12, 22), (3, 27), (16, 0), (25, 4), (8, 22), (30, 24), (18, 21), (35, 9), (0, 11), (25, 19), (28, 23), (4, 12), (36, 27), (16, 4), (5, 13), (16, 17), (12, 20), (5, 16), (28, 0), (8, 2), (36, 2), (19, 14), (32, 20), (11, 28), (3, 10), (33, 22), (15, 10), (14, 21), (29, 23), (26, 13), (19, 19), (12, 4), (28, 3), (2, 22), (19, 21), (35, 16), (27, 13), (23, 17), (23, 3), (6, 3), (33, 16), (16, 24), (16, 26), (1, 0), (13, 0), (27, 5), (24, 1), (14, 25), (2, 29), (3, 25), (19, 20), (34, 19), (4, 18), (22, 5), (32, 23), (23, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "435168", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), 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), (5, 32), (23, 1), (0, 4), (27, 27), (29, 4), (25, 6), (13, 3), (17, 23), (17, 20), (9, 26), (26, 2), (8, 30), (22, 27), (18, 20), (29, 6), (2, 7), (21, 16), (14, 16), (23, 7), (2, 33), (22, 24), (4, 1), (12, 30), (9, 16), (20, 32), (19, 16), (2, 6), (7, 19), (18, 1), (24, 15), (28, 8), (8, 32), (19, 32), (30, 27), (6, 13), (32, 2), (29, 25), (26, 21), (25, 1), (2, 27), (26, 11), (22, 25), (5, 25), (25, 22), (17, 8), (21, 32), (21, 27), (2, 20), (20, 28), (24, 23), (11, 0), (18, 22), (8, 0), (24, 24), (20, 10), (8, 26), (24, 12), (15, 15), (27, 12), (14, 15), (31, 1), (18, 32), (28, 1), (20, 27), (32, 0), (27, 0), (19, 9), (5, 9), (30, 16), (24, 9), (16, 15), (18, 30), (22, 10), (26, 22), (3, 30), (7, 30), (31, 0), (1, 13), (7, 4), (23, 13), (17, 2), (23, 20), (24, 33), (30, 18), (26, 4), (9, 10), (0, 23), (29, 12), (14, 2), (4, 13), (13, 14), (23, 0), (20, 1), (26, 28), (0, 20), (3, 32), (9, 13), (6, 28), (29, 10), (28, 18), (8, 12), (16, 1), (16, 11), (17, 22), (28, 7), (0, 33), (28, 10), (2, 31), (5, 29), (27, 20), (1, 27), (21, 22), (25, 33), (11, 10), (23, 17), (15, 0), (16, 28), (27, 19), (25, 13), (20, 26), (7, 3), (26, 25), (24, 10), (10, 21), (29, 9), (24, 32), (10, 29), (30, 33), (24, 27), (0, 32), (29, 20), (21, 18), (25, 11), (28, 20), (23, 32), (25, 12), (18, 2), (23, 12), (9, 17), (10, 3), (4, 21), (12, 14), (5, 11), (29, 33), (25, 15), (11, 22), (31, 14), (9, 4), (17, 16), (6, 27), (21, 0), (4, 16), (14, 8), (27, 6), (5, 33), (25, 18), (7, 32), (16, 26), (1, 18), (26, 18), (31, 18), (11, 16), (5, 16), (10, 16), (31, 30), (7, 18), (7, 13), (0, 31), (11, 31), (29, 8), (3, 28), (29, 21), (19, 8), (0, 8), (32, 9), (31, 9), (15, 21), (29, 26), (3, 8), (5, 1), (26, 20), (0, 6), (28, 26), (2, 29), (22, 5), (11, 20), (12, 1), (15, 16), (11, 33), (29, 2), (6, 25), (8, 25), (4, 33), (16, 31), (12, 17), (11, 32), (21, 28), (25, 2), (14, 33), (7, 12), (10, 32), (26, 14), (5, 18), (30, 25), (12, 20), (25, 20), (22, 17), (3, 6), (19, 22), (2, 32), (14, 3), (1, 24), (16, 3), (30, 9), (4, 32), (2, 3), (13, 21), (1, 19), (19, 14), (9, 23), (10, 11), (32, 31), (9, 15), (6, 3), (2, 23), (24, 6), (23, 8), (29, 28), (12, 2), (7, 7), (0, 19), (24, 13), (2, 30), (3, 20), (11, 15), (14, 5), (30, 23), (15, 7), (18, 33), (19, 24), (25, 9), (6, 14), (17, 25), (0, 24), (14, 29), (24, 28), (17, 4), (8, 17), (32, 25), (15, 5), (3, 27), (8, 19), (17, 11), (30, 22), (31, 4), (11, 30), (1, 10), (16, 20), (5, 21), (7, 0), (8, 7), (31, 22), (31, 6), (1, 26), (21, 12), (28, 4), (27, 15), (4, 11), (32, 5), (13, 6), (26, 33), (3, 11), (3, 16), (30, 0), (18, 11), (16, 5), (13, 12), (16, 21), (0, 22), (19, 3), (7, 31), (8, 16), (32, 30), (23, 30), (15, 6), (16, 4), (19, 15), (26, 19), (7, 29), (12, 26), (10, 4), (29, 3), (6, 26), (5, 7), (11, 21), (5, 19), (8, 11), (32, 17), (14, 17), (24, 3), (6, 4), (17, 7), (23, 16), (3, 24), (24, 4), (0, 30), (27, 29), (21, 14), (19, 6), (22, 19), (26, 3), (15, 22), (19, 7), (23, 24), (18, 23), (10, 18), (18, 21), (1, 0), (26, 5), (5, 22), (15, 3), (9, 33), (10, 31), (2, 17), (2, 4), (10, 25), (20, 3), (7, 27), (16, 16), (4, 27), (5, 13), (27, 8), (3, 23), (32, 27), (7, 15), (24, 20), (13, 17), (26, 29), (10, 14), (32, 13), (12, 19), (16, 32), (27, 33), (30, 3), (20, 15), (21, 17), (12, 21), (26, 31), (7, 2), (4, 25), (18, 27), (12, 15), (20, 22), (25, 5), (6, 6), (26, 7), (9, 22), (8, 22), (4, 4), (19, 33), (6, 12), (12, 16), (32, 3), (1, 14), (18, 12), (24, 31), (31, 26), (12, 10), (0, 29), (24, 26), (1, 25), (24, 17), (4, 30), (8, 10), (2, 22), (17, 19), (24, 16), (17, 9), (4, 18), (13, 19), (21, 33), (7, 24), (7, 26), (21, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14400", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 29), (23, 22), (10, 22), (0, 12), (23, 1), (3, 3), (23, 4), (22, 9), (29, 17), (23, 3), (2, 2), (28, 24), (26, 23), (18, 26), (14, 0), (19, 24), (10, 2), (22, 0), (11, 20), (13, 30), (26, 24), (17, 8), (28, 29), (12, 29), (9, 30), (16, 0), (24, 21), (14, 28), (28, 7), (27, 7), (15, 17), (14, 6), (5, 22), (21, 15), (0, 3), (25, 0), (8, 25), (16, 1), (11, 23), (9, 3), (1, 4), (29, 9), (7, 27), (7, 10), (17, 4), (11, 4), (8, 27), (16, 12), (5, 13), (8, 7), (30, 9), (2, 11), (10, 18), (24, 7), (20, 24), (10, 25), (14, 29), (15, 29), (7, 2), (3, 15), (3, 20), (4, 11), (12, 20), (8, 20), (11, 14), (21, 20), (2, 14), (17, 13), (29, 19), (22, 10), (7, 14), (15, 20), (11, 15), (22, 11), (2, 10), (12, 7), (27, 29), (30, 18), (26, 13), (11, 7), (7, 5), (13, 4), (0, 5), (5, 27), (26, 17), (30, 8), (25, 13), (1, 14), (11, 30), (2, 9), (24, 22), (22, 28), (17, 14), (21, 19), (23, 26), (14, 3), (5, 21), (0, 25), (15, 11), (26, 7), (2, 23), (19, 3), (25, 1), (28, 5), (24, 16), (2, 18), (30, 10), (9, 26), (1, 7), (8, 21), (10, 27), (12, 1), (5, 15), (24, 14), (13, 6), (26, 29), (23, 25), (4, 29), (22, 27), (18, 18), (13, 23), (29, 8), (3, 11), (28, 28), (21, 0), (20, 26), (22, 20), (28, 18), (30, 24), (12, 25), (22, 23), (19, 18), (10, 19), (14, 9), (13, 25), (28, 19), (2, 15), (15, 3), (1, 30), (10, 21), (0, 30), (30, 14), (6, 26), (17, 15), (20, 9), (11, 13), (24, 4), (13, 21), (17, 7), (4, 12), (24, 6), (13, 8), (29, 10), (21, 3), (6, 15), (0, 16), (25, 24), (5, 4), (7, 6), (18, 13), (9, 29), (2, 12), (7, 15), (3, 27), (19, 25), (17, 24), (27, 22), (30, 1), (5, 19), (8, 16), (27, 20), (25, 20), (1, 5), (8, 17), (8, 8), (20, 30), (22, 26), (5, 7), (1, 22), (1, 13), (5, 14), (8, 23), (23, 7), (2, 25), (9, 25), (25, 21), (21, 24), (29, 27), (3, 29), (13, 1), (30, 12), (20, 13), (23, 10), (4, 8), (6, 2), (2, 1), (1, 0), (25, 7), (28, 16), (28, 0), (23, 30), (20, 25), (29, 4), (24, 19), (27, 24), (27, 10), (17, 28), (21, 2), (21, 5), (9, 12), (19, 27), (25, 14), (15, 4), (3, 8), (15, 0), (26, 0), (27, 27), (8, 6), (14, 14), (0, 17), (0, 27), (6, 8), (27, 17), (15, 25), (6, 29), (21, 10), (20, 4), (1, 16), (5, 26), (12, 28), (16, 9), (20, 6), (9, 9), (28, 6), (10, 17), (10, 4), (14, 5), (28, 2), (17, 1), (26, 4), (27, 13), (20, 2), (28, 3), (8, 19), (24, 9), (1, 29), (13, 28), (20, 1), (30, 6), (24, 1), (10, 24), (26, 8), (9, 17), (21, 6), (27, 21), (12, 8), (4, 26), (18, 10), (22, 8), (11, 18), (4, 19), (13, 12), (6, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960336", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), 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), (10, 24), (1, 36), (13, 15), (31, 17), (27, 36), (2, 34), (8, 21), (26, 36), (25, 4), (17, 29), (6, 15), (3, 4), (10, 28), (31, 10), (15, 38), (3, 31), (0, 19), (10, 17), (4, 25), (12, 3), (12, 18), (33, 27), (15, 29), (31, 14), (9, 11), (4, 32), (0, 9), (7, 27), (26, 21), (2, 5), (24, 18), (21, 25), (5, 0), (0, 23), (31, 21), (31, 35), (7, 9), (9, 37), (11, 8), (27, 10), (30, 38), (5, 31), (2, 33), (2, 22), (28, 3), (1, 9), (1, 14), (12, 7), (30, 36), (3, 10), (27, 9), (14, 25), (23, 24), (0, 38), (29, 8), (29, 35), (6, 36), (28, 31), (16, 15), (1, 1), (2, 18), (26, 15), (29, 22), (1, 15), (15, 25), (2, 26), (27, 11), (3, 12), (20, 19), (26, 12), (33, 32), (16, 2), (15, 17), (3, 9), (11, 5), (26, 34), (30, 30), (7, 7), (12, 5), (17, 22), (8, 6), (18, 13), (24, 30), (0, 5), (29, 12), (4, 18), (33, 21), (2, 2), (0, 20), (24, 17), (0, 21), (1, 28), (17, 12), (19, 15), (3, 18), (30, 0), (30, 6), (10, 7), (33, 33), (17, 30), (21, 32), (7, 19), (11, 35), (9, 14), (6, 32), (1, 8), (20, 6), (2, 1), (13, 16), (7, 34), (18, 21), (32, 14), (15, 31), (8, 11), (25, 22), (23, 7), (32, 13), (27, 6), (1, 6), (7, 8), (22, 26), (17, 2), (27, 24), (5, 27), (17, 37), (11, 9), (27, 12), (20, 35), (18, 4), (17, 15), (27, 29), (33, 11), (20, 37), (30, 35), (30, 3), (23, 5), (23, 6), (20, 22), (9, 19), (19, 12), (18, 35), (0, 4), (19, 7), (21, 22), (31, 31), (20, 32), (31, 36), (15, 28), (4, 27), (22, 36), (7, 30), (25, 27), (6, 7), (28, 14), (2, 31), (15, 6), (0, 14), (26, 25), (25, 12), (22, 2), (12, 6), (31, 2), (0, 7), (33, 24), (9, 26), (21, 17), (20, 18), (22, 23), (18, 6), (8, 22), (28, 37), (26, 7), (25, 30), (6, 18), (11, 36), (12, 10), (29, 37), (2, 12), (10, 8), (19, 16), (18, 30), (22, 7), (27, 17), (3, 26), (32, 29), (33, 37), (33, 25), (19, 37), (9, 12), (20, 14), (24, 31), (5, 33), (1, 4), (27, 14), (17, 20), (24, 11), (9, 35), (31, 19), (5, 19), (24, 12), (23, 11), (26, 13), (5, 23), (10, 14), (6, 13), (18, 22), (2, 17), (4, 2), (11, 38), (19, 20), (24, 14), (9, 22), (30, 17), (18, 15), (4, 24), (3, 28), (28, 25), (3, 20), (12, 24), (28, 32), (33, 29), (2, 27), (9, 20), (4, 26), (7, 26), (12, 1), (12, 13), (21, 16), (14, 19), (0, 13), (25, 3), (21, 35), (6, 12), (24, 35), (13, 28), (17, 8), (24, 36), (23, 15), (6, 9), (11, 17), (21, 2), (22, 15), (32, 17), (14, 36), (22, 14), (31, 22), (3, 27), (13, 6), (16, 30), (21, 14), (1, 20), (19, 8), (13, 3), (17, 14), (23, 33), (7, 24), (2, 28), (29, 36), (0, 18), (33, 7), (31, 32), (16, 35), (15, 27), (5, 9), (30, 4), (10, 29), (21, 21), (19, 38), (8, 38), (13, 9), (20, 25), (33, 23), (30, 20), (24, 24), (6, 14), (17, 3), (19, 29), (18, 26), (1, 19), (26, 29), (30, 28), (8, 29), (26, 18), (7, 37), (26, 14), (27, 2), (4, 34), (29, 20), (25, 18), (4, 11), (8, 8), (8, 35), (4, 13), (33, 14), (5, 14), (28, 21), (9, 27), (7, 18), (2, 11), (20, 1), (25, 17), (19, 26), (21, 9), (14, 20), (15, 11), (10, 6), (22, 13), (12, 33), (28, 1), (20, 16), (2, 30), (11, 19), (33, 18), (4, 12), (4, 1), (25, 31), (6, 37), (0, 15), (19, 27), (15, 4), (19, 3), (23, 10), (23, 23), (8, 33), (31, 7), (5, 12), (26, 26), (26, 20), (28, 15), (15, 2), (2, 4), (31, 23), (16, 22), (14, 30), (19, 4), (27, 16), (0, 12), (3, 35), (21, 37), (8, 4), (13, 8), (33, 10), (18, 34), (31, 13), (14, 22), (8, 9), (2, 24), (22, 3), (10, 10), (7, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289872", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 32), (5, 6), (17, 27), (13, 6), (2, 9), (20, 9), (8, 4), (28, 18), (7, 28), (1, 28), (6, 24), (33, 20), (25, 15), (9, 8), (27, 4), (31, 2), (29, 29), (7, 11), (6, 35), (32, 17), (19, 6), (31, 32), (21, 32), (30, 28), (24, 9), (19, 19), (1, 17), (28, 21), (13, 5), (30, 5), (31, 9), (28, 36), (33, 1), (23, 14), (27, 33), (5, 9), (16, 20), (25, 6), (3, 1), (15, 35), (33, 15), (12, 14), (28, 2), (15, 31), (14, 14), (14, 4), (14, 33), (26, 9), (27, 22), (7, 9), (25, 26), (0, 6), (15, 28), (5, 4), (2, 12), (13, 31), (33, 13), (10, 7), (34, 16), (6, 12), (27, 5), (16, 31), (23, 16), (29, 21), (8, 7), (5, 30), (12, 1), (24, 36), (11, 13), (4, 13), (16, 21), (4, 5), (19, 1), (8, 14), (18, 25), (12, 28), (3, 36), (27, 19), (28, 7), (27, 13), (13, 21), (7, 27), (27, 1), (31, 27), (17, 31), (16, 22), (15, 33), (33, 34), (19, 20), (1, 31), (33, 5), (30, 1), (10, 25), (33, 0), (19, 26), (25, 9), (15, 36), (32, 31), (10, 0), (3, 16), (18, 10), (26, 20), (6, 11), (25, 34), (21, 16), (8, 22), (0, 11), (6, 13), (31, 7), (13, 25), (30, 31), (29, 27), (27, 16), (8, 21), (20, 32), (14, 21), (8, 34), (33, 11), (34, 14), (4, 33), (30, 23), (1, 21), (7, 36), (8, 20), (28, 25), (12, 17), (28, 9), (2, 32), (2, 14), (19, 34), (22, 26), (12, 11), (18, 14), (32, 16), (33, 26), (10, 29), (32, 19), (24, 0), (3, 6), (8, 28), (26, 18), (24, 29), (25, 27), (24, 34), (7, 24), (0, 16), (14, 23), (8, 23), (22, 19), (16, 16), (9, 24), (29, 36), (21, 24), (5, 14), (11, 34), (21, 18), (23, 21), (19, 16), (19, 3), (16, 33), (33, 2), (9, 11), (0, 22), (31, 28), (21, 11), (17, 29), (18, 11), (13, 3), (11, 3), (3, 5), (1, 15), (7, 21), (5, 31), (28, 33), (16, 19), (5, 1), (24, 3), (12, 31), (13, 30), (5, 19), (11, 19), (4, 3), (20, 21), (5, 2), (18, 16), (12, 29), (2, 19), (27, 18), (29, 34), (30, 2), (11, 23), (1, 1), (21, 35), (5, 7), (14, 25), (10, 32), (14, 28), (13, 15), (23, 25), (32, 24), (0, 15), (22, 23), (19, 14), (9, 34), (7, 35), (5, 24), (33, 4), (9, 14), (5, 26), (11, 7), (12, 34), (33, 22), (34, 34), (9, 23), (3, 19), (7, 5), (9, 36), (30, 12), (1, 9), (24, 15), (31, 30), (28, 30), (25, 13), (31, 19), (1, 22), (22, 14), (5, 22), (26, 35), (10, 13), (16, 28), (25, 35), (11, 4), (6, 31), (32, 34), (31, 36), (31, 6), (30, 32), (13, 12), (1, 6), (24, 1), (29, 14), (23, 0), (11, 28), (22, 4), (4, 18), (21, 17), (17, 21), (27, 32), (31, 12), (0, 18), (10, 27), (8, 9), (7, 32), (4, 9), (32, 21), (18, 0), (26, 31), (29, 3), (28, 11), (31, 20), (0, 8), (21, 27), (26, 24), (20, 28), (13, 2), (24, 31), (24, 6), (6, 6), (21, 29), (31, 10), (13, 8), (1, 18), (26, 33), (3, 15), (4, 20), (18, 20), (10, 17), (8, 26), (17, 34), (33, 8), (5, 17), (28, 27), (3, 20), (16, 7), (15, 15), (27, 24), (10, 23), (34, 6), (15, 8), (9, 13), (23, 36), (24, 18), (0, 14), (30, 18), (7, 23), (15, 22), (16, 5), (29, 13), (28, 26), (18, 36), (19, 2), (30, 10), (10, 19), (8, 8), (23, 20), (13, 7), (17, 10), (5, 25), (14, 29), (0, 2), (15, 21), (0, 13), (20, 33), (30, 9), (10, 11), (4, 0), (0, 20), (10, 18), (20, 19), (18, 17), (13, 24), (21, 20), (19, 8), (29, 10), (34, 24), (6, 1), (20, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866628", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 30), (12, 6), (21, 30), (22, 13), (12, 25), (19, 31), (28, 21), (27, 7), (9, 33), (12, 5), (22, 20), (19, 6), (12, 17), (5, 25), (11, 20), (3, 0), (8, 7), (1, 16), (26, 4), (29, 26), (8, 35), (21, 9), (28, 11), (0, 33), (4, 4), (5, 7), (27, 5), (29, 5), (1, 34), (23, 17), (16, 19), (23, 10), (3, 29), (19, 27), (1, 35), (26, 9), (28, 20), (12, 7), (3, 14), (29, 4), (13, 0), (29, 24), (5, 8), (12, 14), (20, 18), (10, 31), (14, 33), (24, 3), (26, 0), (1, 37), (11, 12), (8, 17), (23, 23), (19, 19), (23, 12), (21, 18), (7, 21), (13, 14), (3, 10), (27, 23), (9, 25), (15, 4), (4, 27), (22, 34), (9, 36), (19, 10), (8, 0), (13, 16), (22, 9), (9, 34), (25, 25), (22, 31), (19, 34), (13, 27), (4, 36), (9, 7), (13, 4), (23, 31), (28, 1), (28, 15), (29, 11), (6, 10), (22, 14), (27, 11), (3, 25), (23, 18), (15, 12), (11, 36), (0, 17), (15, 10), (20, 28), (26, 27), (15, 13), (19, 30), (25, 14), (21, 3), (4, 37), (23, 36), (18, 20), (29, 8), (9, 15), (23, 20), (21, 13), (29, 19), (7, 0), (16, 30), (26, 14), (3, 37), (4, 5), (26, 33), (21, 4), (18, 10), (24, 5), (9, 9), (1, 3), (21, 12), (4, 14), (26, 36), (5, 31), (28, 17), (10, 9), (11, 6), (28, 18), (10, 32), (27, 37), (13, 28), (23, 4), (18, 6), (28, 8), (11, 15), (17, 13), (24, 31), (17, 32), (14, 13), (28, 6), (27, 34), (17, 14), (24, 29), (3, 3), (3, 16), (18, 29), (11, 9), (8, 23), (19, 35), (1, 10), (3, 19), (24, 14), (18, 16), (27, 16), (19, 32), (4, 24), (24, 36), (28, 31), (7, 29), (20, 36), (21, 28), (4, 31), (3, 17), (2, 19), (6, 34), (27, 4), (13, 31), (0, 30), (1, 20), (27, 14), (18, 32), (28, 34), (10, 16), (18, 25), (26, 25), (15, 14), (23, 28), (22, 4), (18, 26), (2, 3), (6, 8), (20, 24), (21, 19), (28, 25), (21, 22), (3, 11), (17, 24), (10, 3), (18, 34), (27, 9), (10, 21), (22, 7), (19, 33), (2, 14), (5, 4), (28, 4), (26, 8), (11, 3), (13, 24), (22, 2), (3, 34), (1, 36), (1, 23), (18, 19), (0, 8), (24, 27), (8, 3), (13, 5), (10, 17), (17, 15), (17, 12), (12, 1), (15, 2), (15, 27), (11, 17), (29, 12), (10, 4), (6, 33), (20, 14), (15, 20), (3, 4), (0, 31), (20, 1), (5, 21), (27, 12), (15, 16), (2, 23), (0, 3), (12, 27), (1, 31), (24, 7), (10, 24), (1, 32), (24, 20), (25, 19), (18, 8), (0, 25), (2, 0), (16, 21), (27, 13), (6, 36), (14, 24), (1, 0), (5, 20), (9, 30), (5, 23), (6, 31), (4, 22), (17, 34), (1, 18), (20, 23), (2, 31), (16, 33), (21, 17), (1, 15), (18, 36), (8, 31), (10, 7), (21, 20), (24, 25), (2, 4), (5, 12), (0, 4), (20, 3), (9, 13), (29, 3), (7, 1), (17, 0), (21, 37), (5, 14), (9, 12), (0, 16), (7, 34), (26, 1), (14, 3), (14, 27), (27, 18), (12, 37), (8, 12), (3, 30), (14, 23), (20, 5), (1, 17), (29, 15), (28, 35), (8, 21), (5, 32), (14, 5), (8, 32), (6, 13), (0, 37), (14, 15), (11, 23), (9, 26), (14, 28), (29, 10), (1, 28), (2, 25), (13, 23), (1, 7), (10, 5), (24, 26), (13, 13), (23, 6), (13, 18), (24, 6), (25, 15), (19, 8), (20, 35), (26, 5), (16, 25), (15, 23), (2, 36), (12, 35), (5, 18), (15, 19), (13, 25), (5, 16), (6, 35), (16, 29), (25, 31), (22, 16), (17, 29), (11, 25), (21, 6), (10, 28), (17, 6), (23, 11), (15, 24), (12, 30), (10, 26), (25, 2), (6, 27), (7, 19), (13, 2), (25, 24), (7, 14), (15, 22), (22, 32), (20, 11), (3, 20), (26, 28), (19, 0), (9, 6), (3, 26), (2, 21), (16, 31), (23, 22), (0, 14), (16, 20), (17, 35), (16, 34), (0, 10), (17, 20), (25, 20), (19, 14)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "949824", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 14), (26, 11), (26, 19), (9, 2), (33, 16), (21, 25), (31, 14), (17, 31), (31, 5), (5, 23), (25, 25), (18, 28), (0, 11), (32, 5), (32, 19), (25, 1), (32, 13), (34, 12), (17, 1), (16, 29), (34, 24), (6, 14), (27, 3), (25, 22), (4, 25), (25, 24), (3, 17), (11, 0), (33, 18), (27, 16), (29, 23), (25, 12), (11, 10), (17, 11), (33, 7), (28, 27), (33, 0), (10, 27), (24, 23), (0, 19), (13, 9), (30, 8), (24, 30), (11, 30), (21, 3), (13, 19), (24, 17), (30, 25), (17, 25), (27, 1), (18, 26), (18, 24), (28, 23), (31, 18), (32, 4), (31, 23), (12, 23), (4, 30), (20, 23), (19, 24), (30, 31), (27, 4), (22, 6), (11, 9), (16, 17), (12, 0), (30, 26), (29, 11), (16, 4), (21, 6), (16, 25), (32, 29), (33, 20), (5, 31), (1, 21), (20, 9), (23, 23), (20, 3), (29, 1), (10, 2), (1, 17), (17, 0), (21, 31), (34, 26), (30, 5), (23, 15), (28, 7), (32, 28), (3, 6), (1, 26), (26, 7), (29, 6), (30, 28), (16, 30), (1, 9), (32, 6), (16, 22), (24, 18), (21, 4), (33, 23), (15, 24), (21, 13), (15, 31), (25, 5), (15, 2), (28, 19), (20, 16), (21, 16), (5, 0), (26, 27), (19, 25), (14, 1), (1, 8), (34, 3), (12, 19), (22, 25), (10, 15), (13, 24), (33, 11), (32, 25), (17, 20), (12, 27), (4, 13), (7, 4), (34, 30), (12, 9), (21, 17), (1, 1), (0, 15), (20, 19), (5, 29), (33, 21), (19, 8), (30, 0), (3, 15), (28, 20), (13, 26), (20, 21), (11, 3), (6, 2), (20, 6), (22, 10), (8, 20), (4, 0), (34, 14), (12, 22), (22, 29), (1, 19), (25, 15), (30, 14), (22, 8), (15, 27), (7, 5), (23, 7), (5, 9), (32, 21), (20, 26), (4, 14), (30, 1), (24, 4), (4, 9), (31, 21), (15, 20), (34, 13), (10, 24), (18, 11), (29, 31), (24, 5), (6, 18), (2, 10), (32, 14), (18, 8), (2, 3), (30, 9), (3, 12), (1, 0), (13, 13), (15, 29), (29, 12), (8, 14), (20, 5), (16, 27), (15, 0), (32, 3), (23, 31), (18, 1), (29, 0), (24, 2), (16, 24), (23, 25), (2, 7), (10, 26), (24, 26), (10, 23), (15, 22), (15, 9), (16, 14), (0, 12), (1, 30), (14, 20), (20, 28), (8, 28), (19, 6), (11, 29), (5, 6), (29, 18), (3, 10), (5, 26), (9, 30), (14, 29), (18, 6), (34, 20), (1, 23), (31, 25), (19, 20), (1, 28), (34, 5), (9, 17), (20, 11), (8, 6), (28, 28), (10, 12), (32, 8), (5, 1), (7, 6), (7, 22), (5, 16), (24, 14), (11, 15), (22, 5), (31, 22), (26, 28), (16, 10), (19, 3), (2, 2), (12, 21), (3, 18), (1, 27), (29, 21), (26, 22), (34, 19), (5, 20), (27, 5), (3, 4), (24, 29), (34, 23), (33, 27), (1, 16), (27, 20), (9, 10), (32, 26), (25, 20), (34, 29), (9, 21), (4, 22), (33, 2), (9, 3), (9, 25), (4, 15), (11, 1), (8, 16), (34, 1), (22, 16), (18, 16), (11, 22), (19, 21), (20, 18), (33, 22), (2, 29), (32, 27), (13, 16), (23, 0), (9, 18), (4, 16), (3, 14), (9, 12), (27, 13), (6, 26), (4, 29), (4, 2), (19, 18), (2, 24), (33, 25), (15, 1), (2, 9), (23, 14), (5, 17), (17, 22), (2, 23), (7, 8), (24, 19), (22, 9), (17, 3), (9, 23), (18, 12), (21, 1), (25, 14), (32, 24), (13, 7), (6, 7), (0, 16), (14, 12), (10, 25), (11, 26), (24, 11), (27, 19), (6, 31), (19, 16), (19, 2), (11, 12), (7, 24), (8, 15), (9, 29), (2, 0), (21, 21), (9, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705600", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 9), (16, 10), (20, 13), (21, 6), (23, 3), (21, 1), (22, 13), (18, 8), (32, 25), (23, 24), (16, 24), (27, 11), (28, 21), (7, 19), (19, 20), (23, 18), (31, 10), (13, 24), (22, 3), (26, 23), (18, 10), (4, 27), (24, 20), (28, 7), (2, 10), (1, 1), (4, 23), (31, 5), (32, 10), (29, 5), (15, 1), (8, 21), (9, 17), (15, 18), (18, 26), (31, 24), (7, 7), (23, 6), (18, 5), (24, 27), (1, 22), (29, 18), (2, 26), (12, 11), (1, 24), (7, 20), (28, 23), (22, 24), (18, 28), (22, 10), (28, 8), (12, 28), (6, 5), (31, 1), (19, 25), (15, 12), (10, 12), (3, 1), (25, 22), (17, 14), (25, 13), (24, 4), (18, 19), (1, 9), (21, 3), (15, 28), (13, 5), (5, 23), (3, 8), (0, 30), (15, 21), (8, 15), (30, 26), (4, 20), (10, 24), (15, 6), (31, 16), (2, 7), (27, 16), (14, 2), (30, 12), (10, 28), (10, 20), (9, 22), (16, 9), (5, 3), (15, 27), (17, 9), (10, 26), (25, 7), (2, 13), (25, 29), (9, 6), (5, 1), (26, 0), (27, 27), (19, 3), (20, 11), (30, 28), (15, 19), (6, 6), (7, 18), (29, 7), (24, 8), (6, 12), (27, 21), (0, 14), (21, 7), (2, 30), (16, 11), (6, 0), (3, 27), (3, 16), (4, 2), (3, 23), (7, 16), (24, 18), (23, 30), (20, 22), (25, 1), (17, 29), (31, 28), (17, 25), (15, 13), (24, 21), (31, 18), (17, 24), (1, 20), (31, 8), (13, 7), (27, 26), (14, 3), (17, 5), (28, 25), (16, 19), (6, 27), (29, 14), (9, 3), (19, 18), (8, 1), (11, 18), (16, 3), (17, 30), (0, 8), (31, 6), (1, 4), (11, 6), (13, 11), (17, 22), (32, 27), (22, 6), (8, 2), (26, 10), (31, 26), (8, 20), (12, 21), (19, 6), (16, 5), (26, 8), (9, 5), (26, 19), (22, 26), (3, 29), (16, 8), (16, 14), (3, 13), (8, 30), (18, 29), (32, 14), (0, 6), (21, 30), (22, 23), (24, 28), (28, 28), (18, 21), (22, 28), (3, 15), (12, 10), (7, 14), (18, 16), (31, 3), (11, 16), (26, 16), (2, 0), (8, 11), (27, 0), (0, 25), (11, 25), (28, 19), (29, 13), (26, 21), (29, 28), (23, 28), (20, 9), (25, 5), (15, 24), (11, 30), (11, 24), (28, 0), (22, 7), (29, 30), (3, 9), (8, 17), (1, 10), (14, 10), (6, 19), (27, 5), (12, 8), (10, 27), (9, 26), (24, 14), (8, 29), (22, 0), (9, 29), (24, 16), (1, 7), (15, 30), (30, 30), (14, 4), (29, 8), (13, 22), (22, 12), (14, 0), (8, 10), (11, 28), (17, 2), (9, 7), (23, 15), (21, 20), (12, 6), (2, 25), (8, 28), (1, 28), (13, 23), (11, 12), (11, 21), (32, 0), (7, 12), (4, 8), (29, 25), (12, 4), (29, 24), (26, 26), (19, 26), (16, 29), (32, 17), (4, 15), (25, 4), (20, 4), (28, 30), (31, 13), (18, 30), (20, 7), (5, 27), (21, 22), (24, 7), (23, 17), (20, 29), (20, 10), (11, 5), (11, 2), (21, 24), (12, 16), (30, 20), (5, 4), (23, 10), (30, 5), (23, 22), (26, 15), (1, 29), (7, 3), (11, 11), (5, 8), (18, 1), (23, 27), (0, 9), (18, 3), (20, 2), (21, 21), (29, 6), (6, 17), (28, 5), (19, 15), (32, 11), (4, 7), (16, 16), (16, 22), (26, 14), (14, 13), (13, 16), (15, 10), (3, 3), (6, 9), (1, 5), (25, 9), (8, 13), (12, 24), (6, 1), (2, 8), (32, 4), (27, 12), (27, 22), (31, 17), (0, 28), (2, 23), (25, 8), (3, 21), (26, 1), (17, 10), (6, 13), (19, 21), (9, 28), (26, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606528", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 16), (21, 9), (16, 27), (3, 10), (21, 36), (17, 31), (2, 6), (24, 20), (29, 13), (13, 23), (29, 10), (13, 26), (9, 6), (20, 27), (28, 29), (25, 9), (8, 27), (5, 19), (11, 9), (4, 0), (17, 8), (28, 8), (14, 15), (4, 24), (24, 11), (15, 37), (18, 4), (22, 10), (22, 35), (5, 25), (26, 35), (15, 20), (22, 2), (13, 32), (12, 22), (28, 36), (19, 17), (21, 22), (29, 18), (20, 21), (26, 19), (28, 15), (20, 37), (7, 7), (27, 7), (25, 18), (16, 29), (25, 32), (0, 31), (28, 21), (10, 17), (4, 20), (10, 13), (21, 26), (26, 24), (14, 18), (22, 17), (12, 31), (18, 0), (5, 17), (16, 32), (16, 16), (9, 4), (18, 13), (2, 34), (5, 31), (13, 12), (29, 5), (28, 32), (24, 12), (21, 7), (13, 29), (25, 5), (3, 21), (6, 11), (14, 1), (26, 14), (15, 3), (0, 29), (1, 11), (12, 21), (14, 29), (14, 36), (11, 6), (10, 29), (2, 35), (20, 6), (21, 12), (12, 30), (25, 11), (28, 3), (2, 32), (8, 31), (24, 29), (19, 20), (13, 14), (10, 19), (15, 18), (7, 18), (17, 16), (11, 29), (20, 28), (6, 12), (18, 37), (16, 26), (17, 30), (2, 24), (2, 37), (17, 29), (1, 19), (15, 14), (20, 36), (9, 30), (18, 26), (13, 36), (11, 35), (0, 12), (28, 14), (17, 23), (1, 6), (8, 23), (20, 34), (24, 15), (10, 2), (18, 34), (2, 20), (8, 1), (24, 36), (1, 2), (28, 7), (9, 10), (14, 35), (10, 31), (6, 25), (13, 5), (2, 5), (21, 24), (15, 1), (3, 32), (2, 15), (26, 29), (15, 35), (17, 32), (0, 9), (17, 9), (1, 30), (26, 16), (21, 21), (24, 3), (19, 34), (9, 9), (7, 6), (17, 36), (13, 1), (5, 13), (2, 22), (0, 33), (19, 11), (25, 33), (2, 7), (23, 35), (10, 11), (25, 23), (22, 6), (15, 22), (7, 0), (0, 10), (28, 37), (9, 21), (27, 9), (13, 16), (12, 37), (11, 11), (12, 11), (29, 21), (26, 31), (4, 21), (6, 5), (0, 16), (7, 2), (7, 11), (27, 16), (8, 17), (8, 4), (12, 25), (3, 15), (11, 25), (21, 0), (26, 32), (28, 2), (5, 7), (3, 34), (18, 18), (14, 32), (11, 2), (5, 36), (3, 14), (16, 11), (8, 0), (16, 34), (6, 2), (9, 24), (18, 11), (29, 30), (16, 33), (19, 30), (24, 16), (10, 23), (25, 21), (6, 14), (9, 23), (21, 4), (23, 13), (22, 11), (24, 33), (19, 12), (22, 36), (0, 5), (29, 11), (14, 17), (12, 32), (19, 32), (26, 2), (11, 10), (3, 17), (5, 12), (2, 11), (0, 15), (9, 13), (12, 23), (6, 29), (18, 12), (9, 5), (16, 15), (4, 1), (21, 34), (20, 26), (24, 30), (5, 11), (2, 1), (9, 25), (13, 17), (13, 3), (7, 36), (3, 29), (11, 30), (10, 14), (13, 19), (22, 1), (4, 2), (1, 14), (2, 33), (22, 31), (28, 1), (24, 28), (17, 20), (26, 8), (12, 36), (0, 20), (9, 17), (10, 37), (21, 13), (20, 9), (1, 32), (22, 27), (3, 25), (11, 5), (3, 23), (0, 11), (5, 21), (12, 27), (2, 14), (23, 15), (10, 16), (9, 3), (28, 34), (10, 21), (22, 15), (4, 10), (11, 21), (17, 24), (13, 34), (7, 19), (5, 3), (14, 2), (29, 33), (18, 21), (4, 16), (28, 24), (12, 33), (22, 14), (28, 31), (25, 6), (3, 36), (28, 17), (10, 3), (11, 23), (4, 35), (17, 18), (10, 6), (4, 34), (9, 20), (8, 37), (15, 30), (5, 26), (6, 33), (21, 17), (12, 24), (20, 4), (0, 7), (15, 11), (8, 25), (17, 17), (22, 34), (16, 31), (21, 1), (17, 34), (11, 7), (28, 5), (7, 29), (8, 18), (4, 28), (6, 8), (19, 0), (20, 25), (20, 16), (23, 30), (25, 29), (5, 27), (1, 28), (22, 22), (11, 31), (29, 9), (19, 5), (19, 26), (7, 22), (26, 25), (2, 17), (1, 24), (12, 20), (11, 24), (0, 14), (29, 0), (0, 28), (19, 19), (13, 10), (29, 28), (26, 22), (3, 13), (24, 27), (8, 29), (10, 10), (4, 15), (5, 28), (24, 1), (1, 36), (21, 8), (14, 26), (8, 14), (4, 19), (13, 20), (13, 9), (14, 21), (18, 16), (3, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "597114", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 6), (32, 14), (7, 9), (25, 6), (27, 13), (21, 10), (9, 4), (11, 22), (9, 34), (0, 19), (18, 15), (0, 35), (0, 21), (24, 20), (14, 6), (27, 0), (18, 26), (26, 5), (7, 28), (22, 15), (0, 12), (13, 17), (16, 0), (13, 6), (21, 20), (31, 18), (17, 9), (19, 34), (32, 18), (13, 33), (23, 23), (3, 25), (20, 11), (0, 33), (15, 3), (31, 8), (16, 11), (25, 24), (7, 3), (14, 19), (9, 19), (6, 5), (22, 17), (10, 0), (8, 17), (29, 35), (4, 27), (13, 1), (25, 28), (3, 29), (2, 35), (7, 11), (7, 22), (22, 21), (24, 7), (31, 12), (17, 8), (4, 25), (4, 29), (33, 17), (22, 12), (21, 21), (10, 6), (28, 9), (20, 1), (3, 17), (1, 33), (18, 5), (10, 12), (10, 22), (15, 21), (0, 1), (29, 1), (7, 32), (12, 0), (24, 32), (3, 9), (27, 19), (2, 29), (12, 19), (5, 19), (18, 34), (17, 6), (33, 1), (3, 10), (2, 22), (23, 15), (29, 20), (4, 13), (8, 28), (11, 2), (11, 12), (15, 31), (26, 20), (5, 22), (6, 23), (21, 35), (1, 17), (5, 28), (15, 18), (0, 24), (15, 12), (26, 15), (28, 29), (8, 30), (28, 17), (6, 10), (16, 28), (15, 23), (9, 21), (6, 9), (23, 0), (2, 2), (3, 14), (27, 6), (26, 16), (32, 12), (30, 35), (32, 24), (1, 35), (6, 8), (8, 19), (15, 7), (26, 32), (32, 27), (28, 1), (12, 7), (2, 34), (15, 8), (30, 12), (3, 4), (1, 7), (2, 15), (11, 15), (7, 0), (28, 6), (6, 1), (33, 34), (21, 30), (25, 30), (8, 9), (1, 10), (24, 25), (13, 34), (22, 2), (7, 6), (21, 8), (5, 18), (9, 20), (23, 3), (18, 29), (17, 31), (9, 26), (4, 10), (24, 9), (27, 33), (19, 29), (30, 31), (8, 32), (29, 9), (0, 17), (14, 12), (28, 31), (30, 6), (24, 30), (8, 27), (11, 23), (17, 22), (11, 5), (8, 16), (27, 23), (0, 15), (15, 6), (2, 7), (1, 16), (24, 2), (16, 12), (6, 13), (15, 1), (20, 0), (29, 19), (18, 6), (7, 10), (22, 31), (32, 6), (10, 9), (25, 25), (26, 14), (0, 5), (23, 22), (5, 8), (29, 30), (10, 26), (12, 22), (7, 8), (17, 15), (28, 25), (8, 0), (5, 2), (0, 3), (27, 11), (29, 16), (20, 32), (2, 8), (18, 19), (28, 0), (25, 7), (18, 22), (31, 13), (11, 31), (7, 2), (12, 12), (13, 22), (12, 13), (23, 20), (5, 29), (27, 29), (30, 29), (15, 26), (7, 5), (22, 3), (24, 18), (4, 3), (6, 21), (18, 7), (32, 19), (29, 2), (25, 8), (30, 22), (23, 17), (33, 7), (18, 11), (30, 0), (32, 21), (11, 34), (18, 18), (26, 3), (7, 25), (20, 14), (13, 27), (9, 23), (29, 24), (16, 7), (20, 25), (5, 4), (14, 8), (29, 10), (29, 14), (33, 3), (18, 3), (19, 3), (19, 23), (13, 12), (13, 9), (1, 24), (19, 20), (27, 7), (11, 16), (14, 21), (13, 15), (7, 29), (18, 31), (1, 12), (4, 0), (2, 18), (32, 16), (13, 28), (16, 31), (10, 29), (33, 13), (5, 16), (31, 31), (16, 34), (25, 11), (12, 15), (24, 22), (1, 31), (16, 4), (22, 7), (11, 3), (5, 21), (28, 22), (26, 19), (0, 31), (28, 4), (26, 8), (33, 10), (9, 2), (31, 11), (14, 0), (32, 23), (12, 3), (0, 6), (33, 12), (15, 5), (5, 30), (30, 27), (26, 26), (14, 25), (19, 13), (8, 3), (31, 16), (1, 26), (11, 13), (9, 18), (29, 11), (19, 24), (16, 35), (27, 27), (25, 32), (13, 24), (9, 12), (10, 21), (10, 13), (11, 6), (14, 10), (10, 4), (6, 11), (2, 25), (22, 19), (24, 35), (33, 33), (24, 3), (27, 35), (21, 18), (10, 2), (26, 29), (26, 28), (14, 26), (8, 21), (0, 9), (10, 33), (9, 7), (26, 10), (25, 19), (4, 17), (10, 30), (23, 18), (19, 9), (16, 9), (16, 8), (11, 32), (6, 31), (21, 29), (6, 33), (31, 21), (9, 15), (15, 22), (24, 5), (3, 28), (31, 17), (4, 20), (8, 33), (30, 16), (3, 27), (11, 26), (25, 9), (1, 32), (2, 5), (22, 9), (28, 3), (13, 0), (19, 4), (15, 20), (21, 17), (11, 7), (33, 22), (1, 15), (0, 25), (18, 23), (7, 1), (16, 16), (16, 24), (29, 33), (23, 13), (14, 28), (22, 28), (17, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404964", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (18, 7), (27, 10), (22, 24), (14, 36), (20, 23), (30, 21), (23, 17), (14, 33), (32, 32), (37, 5), (34, 1), (11, 27), (8, 5), (36, 11), (8, 34), (18, 18), (4, 35), (37, 9), (23, 18), (35, 21), (24, 9), (0, 13), (10, 2), (0, 32), (21, 29), (17, 0), (33, 7), (35, 10), (29, 15), (28, 24), (35, 2), (1, 34), (19, 0), (16, 4), (1, 22), (3, 20), (4, 4), (12, 26), (29, 17), (4, 34), (26, 12), (5, 13), (17, 2), (12, 13), (20, 2), (33, 10), (28, 26), (3, 23), (5, 4), (25, 6), (22, 36), (0, 22), (32, 21), (34, 8), (6, 25), (7, 18), (3, 8), (19, 23), (16, 25), (17, 19), (3, 26), (27, 36), (24, 1), (32, 11), (4, 33), (18, 21), (30, 10), (5, 28), (8, 13), (20, 31), (11, 2), (7, 30), (24, 11), (24, 32), (7, 11), (24, 21), (15, 14), (2, 30), (31, 10), (14, 13), (3, 35), (8, 0), (23, 7), (37, 4), (16, 0), (24, 18), (29, 19), (31, 15), (29, 3), (30, 25), (9, 26), (18, 11), (4, 31), (26, 28), (31, 3), (1, 23), (37, 35), (32, 24), (6, 12), (37, 21), (30, 5), (6, 34), (24, 29), (9, 30), (22, 25), (35, 7), (1, 10), (23, 32), (2, 13), (34, 5), (16, 18), (26, 11), (34, 18), (7, 13), (23, 0), (25, 12), (6, 8), (32, 14), (27, 31), (23, 16), (17, 12), (1, 28), (9, 32), (15, 18), (28, 20), (12, 23), (28, 16), (25, 25), (25, 7), (3, 11), (5, 31), (1, 19), (34, 2), (17, 24), (10, 8), (25, 32), (26, 32), (6, 27), (2, 23), (30, 13), (5, 7), (35, 20), (35, 6), (14, 31), (16, 8), (20, 33), (0, 36), (16, 16), (21, 4), (33, 15), (15, 4), (22, 34), (28, 5), (19, 28), (26, 0), (1, 8), (9, 27), (5, 5), (13, 20), (2, 4), (12, 9), (17, 14), (30, 32), (20, 12), (28, 8), (2, 12), (37, 18), (21, 22), (11, 1), (0, 11), (15, 26), (15, 19), (27, 17), (13, 14), (37, 13), (25, 20), (36, 24), (34, 22), (28, 12), (13, 27), (32, 18), (14, 21), (37, 30), (30, 18), (11, 6), (2, 36), (37, 2), (14, 25), (12, 15), (28, 15), (20, 3), (26, 1), (15, 31), (5, 9), (8, 8), (35, 15), (0, 15), (11, 15), (28, 18), (8, 29), (11, 9), (31, 20), (0, 35), (21, 8), (28, 33), (13, 10), (27, 3), (36, 28), (12, 7), (15, 13), (24, 8), (7, 10), (2, 6), (32, 17), (9, 11), (30, 29), (24, 0), (20, 27), (12, 5), (29, 25), (26, 14), (11, 0), (28, 7), (20, 34), (5, 8), (13, 35), (23, 5), (8, 22), (37, 28), (11, 35), (16, 35), (22, 21), (30, 36), (6, 5), (17, 18), (7, 1), (5, 36), (35, 36), (11, 26), (16, 12), (2, 22), (34, 24), (9, 13), (5, 26), (21, 13), (2, 27), (1, 16), (16, 28), (20, 1), (17, 3), (4, 7), (14, 32), (13, 22), (28, 25), (0, 18), (25, 26), (6, 16), (29, 18), (35, 0), (32, 22), (14, 9), (12, 3), (21, 17), (12, 10), (4, 26), (23, 3), (6, 17), (28, 2), (36, 8), (27, 21), (29, 33), (4, 10), (5, 30), (31, 13), (9, 12), (0, 30), (33, 0), (3, 19), (0, 23), (30, 27), (37, 16), (29, 26), (21, 35), (1, 35), (19, 32), (17, 28), (12, 22), (1, 0), (19, 21), (9, 6), (7, 20), (37, 24), (11, 21), (5, 17), (24, 26), (12, 34), (13, 1), (13, 13), (32, 33), (18, 10), (16, 2), (12, 36), (21, 23), (12, 29), (9, 17), (3, 36), (20, 24), (19, 14), (33, 14), (26, 22), (17, 22), (1, 7), (1, 21), (32, 6), (20, 15), (27, 26), (31, 22), (23, 28), (1, 20), (33, 5), (4, 30), (22, 22), (28, 27), (16, 13), (21, 36), (26, 33), (32, 27), (37, 12), (20, 11), (9, 28), (11, 22), (20, 20), (29, 12), (9, 4), (16, 27), (33, 30), (23, 25), (10, 1), (36, 0), (22, 0), (36, 10), (31, 17), (18, 22), (26, 9), (13, 32), (28, 36), (21, 24), (22, 35), (34, 3), (14, 16), (20, 9), (31, 2), (19, 6), (23, 24), (33, 8), (1, 4), (2, 19), (6, 28), (8, 7), (21, 3), (3, 12), (12, 18), (13, 9), (22, 16), (9, 10), (6, 4), (9, 8), (7, 12), (17, 21), (19, 17), (17, 16), (8, 3), (22, 12), (12, 11), (26, 19), (10, 4), (35, 1), (15, 27), (5, 34), (15, 2), (5, 35), (36, 19), (9, 18), (6, 11), (23, 14), (35, 30), (19, 34), (9, 5), (21, 7), (4, 18), (14, 14), (13, 12), (20, 26), (12, 14), (17, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "951678", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), 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), (6, 28), (38, 1), (13, 2), (10, 25), (36, 9), (1, 11), (37, 10), (0, 12), (12, 4), (22, 31), (31, 4), (8, 12), (5, 28), (6, 16), (19, 2), (14, 31), (27, 16), (14, 27), (19, 6), (25, 25), (28, 21), (34, 14), (1, 6), (22, 2), (35, 5), (3, 18), (24, 6), (17, 2), (11, 6), (27, 31), (34, 3), (3, 16), (10, 29), (5, 20), (6, 24), (3, 11), (14, 3), (8, 18), (27, 9), (31, 15), (16, 10), (35, 4), (12, 31), (26, 28), (2, 4), (29, 2), (5, 29), (36, 21), (26, 27), (9, 30), (20, 15), (31, 1), (13, 12), (4, 17), (20, 4), (33, 23), (10, 18), (33, 1), (4, 22), (28, 9), (21, 8), (8, 14), (5, 0), (16, 26), (7, 10), (29, 8), (23, 26), (35, 14), (38, 9), (20, 23), (29, 16), (4, 27), (23, 5), (2, 26), (28, 3), (23, 6), (36, 5), (32, 11), (0, 22), (21, 27), (4, 11), (10, 19), (30, 29), (6, 2), (6, 31), (11, 27), (30, 16), (38, 23), (17, 7), (12, 1), (13, 8), (35, 21), (20, 27), (18, 6), (24, 1), (34, 25), (26, 21), (7, 31), (27, 7), (15, 16), (2, 15), (1, 31), (19, 31), (33, 12), (11, 11), (18, 7), (22, 25), (12, 14), (4, 24), (21, 9), (14, 25), (29, 18), (28, 23), (31, 5), (0, 23), (19, 25), (23, 31), (7, 29), (32, 23), (29, 5), (24, 20), (4, 21), (38, 25), (35, 20), (28, 18), (37, 8), (36, 12), (24, 11), (34, 24), (38, 13), (5, 7), (30, 4), (6, 9), (2, 3), (13, 25), (18, 18), (15, 27), (31, 12), (12, 0), (13, 13), (0, 20), (2, 17), (19, 18), (5, 24), (14, 0), (4, 12), (34, 30), (36, 0), (8, 28), (2, 8), (38, 28), (14, 16), (36, 16), (19, 10), (7, 12), (28, 5), (23, 27), (10, 30), (0, 6), (36, 15), (19, 12), (12, 27), (12, 10), (19, 1), (18, 19), (6, 10), (30, 10), (11, 30), (6, 6), (28, 11), (3, 4), (9, 16), (36, 20), (27, 22), (14, 15), (8, 2), (15, 20), (18, 28), (28, 19), (7, 22), (2, 11), (13, 9), (33, 26), (17, 30), (17, 4), (12, 23), (11, 28), (3, 8), (25, 15), (27, 6), (23, 8), (31, 25), (27, 3), (18, 4), (7, 8), (22, 17), (11, 21), (32, 25), (38, 18), (2, 12), (33, 29), (15, 21), (4, 9), (16, 31), (18, 17), (9, 24), (33, 16), (4, 0), (11, 31), (2, 16), (31, 31), (18, 30), (38, 26), (15, 12), (4, 14), (27, 11), (32, 18), (16, 29), (19, 21), (24, 2), (19, 7), (8, 23), (8, 11), (29, 24), (32, 3), (6, 4), (37, 4), (22, 12), (28, 28), (4, 1), (38, 7), (1, 9), (22, 19), (0, 3), (0, 25), (9, 4), (21, 7), (0, 26), (13, 17), (1, 26), (20, 25), (10, 5), (22, 28), (3, 21), (9, 10), (28, 24), (1, 17), (37, 5), (11, 8), (1, 28), (3, 22), (21, 11), (25, 0), (29, 6), (25, 19), (9, 5), (3, 6), (36, 14), (15, 1), (10, 22), (22, 24), (32, 5), (16, 17), (16, 23), (17, 26), (20, 1), (37, 27), (5, 22), (31, 27), (1, 20), (34, 26), (24, 21), (11, 5), (10, 21), (27, 12), (11, 12), (5, 26), (13, 31), (37, 0), (20, 21), (31, 13), (18, 14), (15, 31), (21, 14), (3, 29), (5, 23), (15, 25), (5, 3), (26, 9), (38, 6), (4, 18), (27, 5), (0, 9), (38, 19), (12, 21), (26, 25), (37, 11), (29, 13), (2, 27), (13, 28), (29, 1), (14, 24), (0, 18), (32, 7), (18, 27), (1, 16), (32, 26), (14, 13), (24, 18), (15, 23), (4, 2), (16, 27), (22, 27), (4, 23), (38, 22), (17, 10), (21, 3), (28, 10), (35, 29), (36, 24), (13, 22), (31, 10), (6, 8), (15, 26), (11, 17), (4, 4), (30, 7), (10, 10), (5, 11), (32, 21), (16, 18), (36, 19), (15, 22), (21, 6), (5, 17), (26, 20), (1, 29), (13, 1), (27, 14), (4, 29), (20, 20), (36, 29), (24, 4), (16, 9), (23, 14), (33, 5), (21, 26), (31, 26), (22, 21), (26, 8), (21, 17), (32, 2), (16, 21), (14, 6), (36, 17), (22, 9), (24, 12), (35, 23), (1, 14), (17, 31), (1, 8), (26, 6), (7, 28), (4, 28), (11, 19), (17, 27), (22, 15), (14, 1), (27, 24), (13, 21), (8, 24), (14, 22), (31, 16), (38, 29), (15, 28), (32, 19), (10, 6), (5, 15), (19, 13), (18, 23), (13, 11), (37, 1), (25, 16), (36, 31), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "637296", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 0), (17, 17), (32, 15), (2, 0), (5, 32), (1, 14), (16, 2), (13, 19), (4, 7), (20, 29), (14, 22), (27, 4), (4, 30), (33, 10), (21, 16), (24, 30), (10, 34), (1, 33), (8, 33), (4, 24), (2, 5), (22, 23), (26, 18), (14, 23), (29, 29), (13, 5), (37, 7), (2, 20), (2, 33), (17, 26), (22, 28), (35, 10), (19, 1), (3, 29), (4, 31), (15, 13), (28, 6), (8, 28), (19, 34), (26, 0), (34, 34), (7, 31), (5, 1), (31, 29), (7, 0), (5, 22), (5, 17), (30, 0), (23, 30), (1, 30), (15, 15), (12, 1), (37, 0), (14, 19), (27, 3), (24, 25), (9, 23), (19, 14), (36, 20), (23, 19), (35, 17), (2, 16), (33, 18), (35, 7), (36, 6), (29, 23), (8, 11), (21, 14), (25, 17), (28, 15), (5, 7), (29, 8), (30, 24), (19, 9), (20, 5), (35, 8), (7, 27), (34, 32), (15, 19), (10, 20), (33, 4), (24, 2), (37, 17), (12, 14), (1, 8), (20, 34), (32, 12), (16, 28), (6, 0), (35, 12), (28, 7), (36, 7), (24, 21), (27, 19), (12, 34), (2, 22), (16, 13), (33, 19), (9, 9), (22, 1), (12, 29), (18, 16), (2, 12), (20, 25), (22, 5), (25, 2), (5, 2), (16, 14), (11, 20), (15, 2), (9, 32), (8, 17), (28, 9), (37, 14), (23, 18), (6, 7), (29, 27), (13, 17), (26, 9), (28, 11), (16, 26), (29, 22), (38, 12), (38, 24), (23, 20), (17, 12), (15, 8), (32, 22), (18, 0), (22, 3), (2, 26), (25, 30), (20, 26), (11, 34), (31, 34), (17, 23), (33, 11), (32, 4), (30, 7), (33, 21), (7, 30), (15, 21), (32, 17), (9, 3), (9, 26), (5, 8), (16, 22), (7, 13), (32, 19), (17, 2), (27, 33), (38, 13), (12, 15), (23, 14), (12, 10), (14, 12), (28, 18), (35, 13), (16, 31), (11, 32), (38, 11), (24, 14), (2, 2), (26, 10), (7, 10), (21, 17), (10, 19), (2, 7), (29, 30), (5, 33), (3, 19), (32, 27), (28, 3), (32, 9), (11, 13), (23, 15), (23, 10), (24, 3), (3, 30), (31, 8), (4, 15), (37, 18), (37, 31), (7, 25), (10, 21), (9, 8), (13, 2), (10, 14), (8, 24), (20, 31), (11, 26), (18, 19), (25, 19), (0, 4), (34, 17), (29, 24), (20, 15), (31, 0), (22, 26), (8, 13), (1, 11), (15, 33), (22, 2), (19, 6), (14, 20), (33, 28), (9, 11), (4, 2), (6, 30), (7, 16), (20, 13), (21, 29), (1, 32), (22, 34), (17, 31), (12, 11), (23, 25), (17, 32), (2, 28), (23, 3), (17, 6), (29, 19), (14, 15), (33, 23), (36, 24), (28, 4), (34, 4), (38, 30), (34, 25), (28, 20), (1, 26), (0, 29), (37, 34), (7, 23), (3, 31), (12, 8), (38, 23), (29, 10), (3, 18), (14, 11), (15, 12), (38, 29), (33, 31), (14, 9), (31, 32), (9, 25), (5, 27), (31, 23), (22, 20), (12, 27), (7, 26), (38, 9), (9, 33), (13, 28), (15, 1), (6, 23), (29, 14), (31, 22), (0, 3), (5, 30), (38, 14), (14, 8), (8, 23), (3, 23), (10, 29), (31, 33), (10, 3), (33, 17), (21, 5), (16, 18), (13, 23), (37, 5), (21, 15), (26, 7), (31, 16), (18, 12), (10, 11), (15, 6), (4, 8), (18, 30), (10, 27), (27, 20), (27, 2), (7, 12), (30, 3), (9, 20), (23, 34), (17, 18), (27, 23), (38, 20), (37, 21), (22, 18), (18, 31), (35, 3), (19, 27), (18, 15), (14, 26), (28, 13), (38, 6), (29, 11), (25, 8), (14, 24), (21, 23), (10, 4), (18, 34), (13, 9), (21, 25), (8, 14), (8, 15), (14, 28), (7, 34), (28, 19), (13, 1), (36, 32), (34, 27), (16, 11), (34, 14), (2, 13), (25, 25), (13, 7), (29, 25), (20, 11), (25, 24), (13, 22), (36, 23), (22, 13), (16, 30), (12, 28), (13, 10), (8, 8), (2, 1), (10, 0), (21, 26), (27, 34), (2, 6), (5, 4), (12, 3), (23, 21), (37, 4), (20, 0), (18, 4), (33, 2), (27, 0), (2, 9), (29, 12), (11, 6), (4, 25), (0, 28), (9, 16), (15, 31), (25, 3), (6, 15), (6, 1), (11, 17), (8, 26), (27, 12), (1, 21), (14, 29), (25, 12), (8, 10), (33, 26), (34, 20), (26, 26), (20, 4), (3, 10), (25, 11), (36, 26), (25, 23), (36, 14), (25, 27), (4, 0), (5, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "352512", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 18), (5, 3), (32, 16), (6, 8), (23, 3), (18, 6), (31, 9), (11, 21), (31, 11), (22, 20), (16, 18), (0, 1), (15, 35), (24, 33), (29, 2), (28, 11), (12, 34), (13, 5), (29, 33), (22, 15), (21, 12), (11, 12), (14, 31), (7, 25), (20, 14), (19, 14), (24, 15), (29, 0), (1, 10), (26, 15), (16, 25), (22, 29), (6, 23), (29, 13), (4, 16), (9, 20), (6, 16), (5, 4), (20, 15), (33, 0), (10, 24), (26, 25), (2, 35), (6, 20), (14, 7), (27, 7), (21, 9), (1, 34), (16, 0), (0, 31), (19, 21), (29, 3), (18, 7), (29, 32), (33, 18), (1, 13), (4, 28), (9, 26), (24, 18), (1, 26), (3, 16), (19, 24), (21, 6), (5, 1), (3, 32), (32, 32), (16, 23), (24, 17), (8, 18), (31, 30), (9, 3), (10, 18), (16, 15), (22, 31), (32, 11), (23, 8), (7, 16), (32, 27), (24, 21), (31, 4), (11, 6), (17, 24), (16, 31), (18, 33), (8, 10), (17, 10), (31, 12), (26, 29), (9, 9), (5, 13), (32, 3), (15, 23), (25, 32), (17, 21), (9, 32), (0, 34), (27, 21), (18, 24), (30, 16), (28, 16), (18, 20), (21, 28), (16, 22), (9, 15), (0, 3), (32, 25), (25, 10), (30, 10), (11, 23), (5, 34), (9, 19), (21, 35), (1, 25), (17, 30), (15, 11), (5, 17), (28, 24), (33, 1), (1, 19), (17, 4), (16, 10), (23, 13), (2, 20), (18, 23), (32, 26), (3, 25), (21, 22), (27, 0), (22, 18), (32, 15), (22, 4), (19, 8), (13, 19), (10, 2), (30, 12), (13, 4), (14, 30), (11, 17), (8, 14), (15, 13), (7, 18), (11, 34), (0, 27), (3, 24), (7, 22), (2, 12), (21, 18), (26, 13), (7, 32), (33, 25), (23, 6), (7, 27), (1, 30), (22, 21), (3, 19), (16, 4), (3, 22), (21, 4), (2, 16), (16, 6), (33, 14), (17, 31), (12, 12), (18, 15), (0, 22), (31, 20), (25, 7), (0, 25), (4, 1), (8, 16), (13, 27), (1, 14), (8, 13), (26, 11), (5, 2), (25, 25), (1, 6), (28, 19), (3, 34), (21, 3), (31, 21), (28, 32), (5, 7), (22, 11), (1, 16), (3, 31), (7, 1), (29, 8), (11, 5), (19, 17), (25, 27), (29, 23), (0, 21), (6, 25), (24, 30), (4, 10), (1, 4), (32, 2), (27, 29), (4, 22), (9, 7), (0, 2), (32, 31), (9, 16), (20, 33), (12, 1), (7, 14), (5, 32), (25, 12), (8, 8), (16, 11), (6, 35), (29, 31), (8, 31), (19, 16), (30, 23), (18, 30), (17, 25), (19, 22), (23, 33), (33, 3), (22, 5), (15, 26), (25, 2), (1, 35), (6, 32), (21, 13), (31, 1), (27, 4), (32, 19), (33, 9), (32, 34), (27, 1), (27, 24), (25, 20), (22, 6), (26, 3), (0, 17), (2, 33), (15, 16), (24, 26), (18, 0), (13, 32), (22, 27), (3, 29), (19, 6), (27, 13), (4, 26), (16, 14), (19, 3), (14, 28), (12, 32), (26, 9), (21, 19), (21, 34), (11, 0), (2, 15), (13, 24), (24, 23), (19, 26), (12, 21), (16, 20), (27, 9), (24, 7), (7, 5), (3, 35), (33, 22), (12, 4), (17, 8), (29, 1), (10, 35), (9, 13), (17, 15), (10, 33), (27, 10), (7, 17), (21, 27), (19, 5), (11, 7), (21, 2), (1, 7), (17, 5), (25, 23), (23, 7), (29, 9), (33, 6), (22, 25), (9, 35), (9, 34), (10, 9), (33, 16), (1, 31), (5, 33), (2, 11), (3, 1), (3, 8), (27, 30), (1, 8), (22, 23), (15, 28), (30, 17), (30, 28), (31, 7), (31, 10), (16, 3), (18, 1), (24, 13), (30, 35), (10, 25), (15, 2), (28, 33), (22, 7), (2, 4), (26, 0), (3, 26), (2, 25), (0, 10), (14, 24), (31, 22), (6, 26), (4, 25), (24, 6), (23, 31), (32, 6), (28, 28), (27, 28), (5, 30), (17, 20), (17, 27), (15, 25), (20, 34), (17, 1), (7, 31), (7, 21), (5, 9), (6, 13), (9, 31), (20, 8), (28, 0), (28, 2), (10, 11), (27, 33), (6, 19), (8, 33), (4, 35), (30, 22), (30, 20), (5, 14), (17, 7), (28, 15), (11, 15), (31, 25), (6, 12), (26, 10), (11, 14), (17, 6), (30, 26), (4, 33), (33, 17), (10, 19), (27, 16), (14, 35), (24, 3), (15, 1), (0, 4), (14, 18), (25, 3), (5, 29), (22, 8), (21, 5), (3, 17), (13, 15), (14, 5), (18, 28), (20, 24), (9, 0), (29, 24), (28, 7), (9, 17), (19, 28), (0, 5), (0, 33), (32, 13), (21, 31), (7, 8), (2, 13), (6, 2), (24, 19), (8, 11), (2, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "630000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 27), (25, 21), (18, 19), (16, 34), (20, 37), (21, 28), (28, 6), (6, 5), (17, 4), (19, 14), (23, 25), (5, 18), (22, 10), (18, 0), (5, 22), (11, 9), (0, 21), (6, 32), (30, 11), (9, 13), (3, 6), (13, 14), (25, 33), (12, 9), (23, 7), (16, 12), (4, 16), (30, 22), (26, 10), (18, 21), (3, 18), (23, 37), (21, 24), (24, 15), (30, 23), (25, 37), (0, 26), (8, 31), (15, 16), (2, 29), (10, 24), (15, 36), (27, 19), (25, 14), (4, 27), (3, 35), (7, 8), (2, 25), (8, 13), (26, 29), (11, 5), (24, 36), (17, 9), (3, 19), (12, 37), (20, 21), (19, 2), (19, 11), (23, 26), (7, 31), (8, 8), (9, 18), (11, 31), (15, 0), (20, 33), (28, 8), (9, 10), (29, 36), (8, 35), (9, 6), (14, 33), (1, 25), (1, 30), (15, 8), (14, 11), (16, 16), (8, 16), (28, 7), (28, 34), (25, 32), (12, 0), (20, 5), (18, 29), (21, 32), (3, 22), (5, 9), (12, 25), (2, 17), (15, 10), (5, 16), (20, 11), (2, 19), (23, 6), (9, 20), (9, 35), (23, 34), (19, 22), (16, 10), (29, 11), (1, 7), (25, 5), (10, 19), (8, 36), (25, 24), (12, 24), (7, 17), (26, 16), (29, 17), (6, 12), (10, 18), (14, 21), (24, 27), (27, 1), (30, 6), (19, 33), (3, 24), (21, 27), (9, 36), (4, 20), (3, 31), (19, 35), (29, 33), (27, 3), (21, 9), (9, 3), (17, 33), (2, 12), (4, 25), (6, 7), (3, 33), (14, 8), (0, 30), (13, 23), (7, 15), (26, 4), (16, 6), (12, 10), (3, 14), (14, 7), (24, 8), (8, 17), (24, 17), (4, 34), (8, 11), (6, 22), (9, 9), (6, 13), (14, 1), (29, 24), (12, 6), (14, 17), (9, 31), (12, 12), (27, 21), (8, 20), (24, 0), (20, 1), (25, 1), (4, 18), (22, 4), (26, 36), (12, 21), (1, 28), (10, 28), (22, 28), (30, 14), (27, 10), (1, 37), (20, 2), (20, 24), (9, 19), (29, 14), (11, 12), (1, 16), (28, 37), (11, 32), (13, 31), (29, 18), (7, 24), (23, 2), (7, 23), (18, 3), (3, 32), (10, 36), (29, 31), (10, 31), (0, 9), (11, 36), (2, 28), (7, 20), (29, 0), (17, 18), (10, 6), (24, 29), (18, 16), (14, 12), (22, 6), (26, 27), (8, 19), (28, 28), (27, 15), (4, 7), (20, 0), (5, 25), (9, 16), (28, 12), (21, 6), (8, 37), (22, 14), (11, 27), (22, 23), (17, 1), (1, 24), (22, 25), (4, 5), (2, 18), (20, 26), (8, 33), (29, 8), (12, 29), (20, 27), (4, 29), (17, 8), (8, 34), (30, 13), (16, 19), (22, 31), (30, 0), (6, 19), (0, 15), (7, 0), (5, 21), (8, 6), (30, 30), (11, 19), (26, 31), (30, 28), (15, 34), (7, 12), (18, 24), (11, 10), (6, 14), (8, 12), (16, 15), (21, 20), (7, 16), (13, 15), (12, 19), (28, 16), (10, 26), (30, 20), (20, 36), (19, 24), (25, 11), (17, 28), (8, 15), (7, 18), (17, 26), (17, 31), (29, 28), (24, 26), (18, 31), (5, 19), (23, 3), (18, 28), (7, 3), (26, 5), (24, 12), (27, 28), (18, 35), (18, 14), (0, 33), (25, 6), (15, 19), (4, 13), (19, 32), (15, 11), (18, 10), (6, 33), (2, 20), (21, 23), (10, 7), (16, 31), (11, 29), (20, 13), (24, 28), (26, 32), (23, 4), (3, 7), (28, 10), (14, 36), (15, 22), (13, 30), (7, 7), (5, 20), (3, 23), (13, 11), (18, 26), (4, 14), (27, 4), (14, 0), (10, 4), (4, 1), (1, 34), (13, 22), (24, 10), (28, 0), (6, 30), (8, 22), (19, 23), (22, 11), (26, 35), (1, 23), (11, 0), (30, 17), (26, 26), (18, 33), (15, 28), (20, 3), (9, 27), (10, 14), (12, 13), (19, 9), (2, 27), (21, 2), (21, 10), (2, 23), (24, 34), (11, 6), (16, 22), (3, 8), (10, 27), (16, 11), (25, 8), (13, 27), (25, 10), (0, 14), (21, 35), (27, 24), (26, 13), (19, 13), (2, 36), (25, 20), (18, 25), (24, 35), (27, 16), (18, 11), (13, 19), (27, 25), (12, 36), (29, 10), (6, 2), (26, 22), (11, 18), (3, 30), (15, 2), (17, 11), (22, 33), (3, 25), (28, 13), (13, 26), (22, 32), (2, 31), (25, 22), (10, 23), (3, 3), (9, 34), (19, 3), (2, 4), (13, 7), (19, 28), (18, 36), (14, 9), (30, 8), (5, 13), (15, 35), (10, 0), (12, 20), (30, 19), (18, 4), (4, 24), (25, 31), (15, 26), (18, 30), (9, 22), (17, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259840", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 15), (6, 35), (26, 33), (30, 32), (28, 0), (5, 2), (3, 7), (22, 30), (21, 10), (37, 23), (29, 0), (32, 3), (26, 27), (35, 8), (17, 8), (18, 32), (16, 2), (9, 28), (11, 25), (24, 24), (15, 17), (12, 26), (15, 8), (25, 34), (20, 2), (8, 0), (6, 20), (31, 10), (10, 18), (3, 24), (10, 3), (12, 8), (12, 36), (9, 31), (38, 34), (9, 0), (14, 31), (2, 18), (10, 1), (26, 8), (22, 37), (31, 7), (0, 28), (1, 26), (24, 12), (9, 24), (19, 34), (12, 6), (16, 1), (33, 34), (5, 1), (18, 27), (38, 29), (28, 16), (34, 28), (23, 34), (31, 6), (17, 16), (30, 17), (13, 33), (30, 5), (28, 4), (26, 3), (30, 13), (2, 34), (11, 11), (8, 13), (18, 5), (38, 33), (18, 25), (8, 11), (26, 1), (37, 22), (18, 21), (1, 23), (5, 8), (2, 36), (28, 11), (15, 23), 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(2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631800", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), 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), (2, 9), (22, 34), (35, 26), (23, 23), (34, 9), (18, 34), (15, 18), (26, 25), (26, 3), (30, 1), (12, 5), (22, 8), (2, 32), (20, 7), (15, 32), (21, 34), (28, 11), (18, 9), (17, 30), (27, 12), (23, 8), (32, 7), (31, 19), (34, 32), (11, 7), (15, 28), (5, 2), (18, 0), (27, 20), (7, 14), (32, 14), (36, 24), (30, 7), (9, 15), (25, 30), (5, 20), (5, 9), (26, 23), (15, 19), (9, 5), (20, 10), (1, 3), (6, 12), (31, 25), (13, 4), (2, 13), (18, 1), (32, 16), (36, 11), (34, 28), (22, 18), (8, 7), (32, 3), (1, 12), (32, 13), (22, 3), (18, 11), (24, 1), (31, 14), (27, 23), (2, 34), (35, 32), (30, 9), (13, 14), (14, 27), (31, 16), (13, 13), (10, 33), (20, 6), (13, 30), (9, 21), (6, 3), (26, 21), (17, 5), (35, 9), (20, 30), (33, 0), (27, 9), (24, 11), (26, 34), (30, 19), (26, 7), (24, 16), (35, 19), (6, 13), (25, 29), (5, 26), (7, 17), (16, 24), (19, 15), (2, 17), (25, 10), (10, 6), (16, 1), (10, 26), (31, 9), (15, 11), (20, 9), (36, 28), (35, 3), (33, 28), (1, 1), (11, 19), (13, 23), (3, 3), (20, 22), (24, 9), (5, 30), (19, 31), (7, 7), (12, 15), (36, 17), (7, 32), (15, 0), (17, 34), (29, 9), (2, 7), (25, 0), (21, 13), (35, 30), (19, 0), (12, 3), (32, 22), (11, 8), (15, 24), (16, 21), (28, 32), (24, 22), (32, 26), (10, 3), (9, 31), (11, 14), (0, 2), (21, 17), (3, 13), (23, 11), (25, 8), (7, 29), (14, 5), (24, 15), (11, 27), (31, 32), (21, 8), (36, 0), (5, 28), (6, 15), (35, 13), (17, 21), (35, 29), (33, 14), (33, 31), (22, 12), (24, 0), (19, 26), (9, 30), (11, 3), (8, 8), (8, 30), (23, 10), (32, 27), (28, 4), (36, 4), (32, 10), (28, 5), (20, 14), (24, 26), (16, 10), (0, 7), (1, 23), (6, 11), (23, 18), (36, 3), (24, 4), (12, 14), (34, 11), (13, 33), (19, 8), (29, 34), (35, 15), (16, 6), (29, 22), (2, 33), (21, 9), (6, 17), (33, 10), (15, 9), (12, 2), (19, 32), (29, 19), (23, 1), (17, 29), (5, 29), (15, 13), (35, 27), (16, 11), (8, 29), (5, 13), (23, 16), (30, 27), (29, 24), (20, 32), (29, 3), (9, 26), (21, 23), (14, 33), (4, 14), (12, 25), (17, 22), (0, 32), (2, 8), (16, 19), (29, 2), (6, 2), (9, 14), (19, 28), (8, 12), (15, 5), (10, 19), (27, 18), (33, 12), (23, 26), (8, 5), (1, 21), (23, 5), (29, 12), (27, 32), (25, 25), (28, 18), (19, 7), (0, 20), (20, 26), (33, 18), (36, 21), (3, 29), (14, 14), (28, 23), (36, 31), (20, 19), (24, 14), (35, 12), (25, 33), (19, 21), (11, 20), (18, 30), (35, 10), (25, 20), (5, 10), (30, 18), (34, 6), (22, 20), (10, 34), (24, 2), (23, 27), (15, 6), (35, 14), (1, 7), (32, 30), (29, 29), (10, 14), (6, 14), (27, 25), (19, 14), (6, 19), (26, 19), (9, 23), (30, 25), (14, 7), (8, 25), (19, 17), (4, 31), (9, 7), (5, 23), (10, 25), (10, 0), (17, 20), (18, 25), (6, 28), (36, 32), (14, 10), (5, 32), (20, 24), (9, 18), (11, 33), (31, 31), (26, 16), (11, 18), (34, 12), (4, 10), (34, 8), (29, 5), (27, 27), (24, 5), (27, 10), (28, 16), (6, 6), (17, 13), (25, 32), (20, 18), (22, 14), (30, 16), (36, 22), (23, 28), (16, 23), (21, 27), (5, 22), (35, 7), (18, 26), (33, 22), (7, 27), (1, 6), (28, 22), (9, 13), (15, 27), (22, 28), (32, 20), (22, 4), (32, 4), (23, 22), (3, 0), (33, 32), (21, 12), (33, 1), (30, 15), (9, 16), (15, 16), (16, 30), (30, 13), (29, 4), (32, 17), (36, 13), (2, 6), (17, 9), (19, 16), (29, 7), (27, 22), (14, 3), (15, 14), (5, 21), (17, 10), (13, 22), (4, 11), (2, 18), (1, 13), (14, 22), (10, 32), (8, 6), (11, 32), (18, 31), (27, 8), (17, 28), (8, 21), (29, 0), (3, 28), (34, 27), (32, 8), (9, 19), (17, 18), (9, 9), (17, 24), (16, 5), (31, 10), (11, 12), (30, 0), (12, 31), (24, 10), (34, 19), (26, 5), (31, 0), (18, 24), (19, 12), (21, 32), (1, 22), (31, 21), (20, 5), (8, 9), (7, 5), (30, 8), (22, 32), (25, 12), (25, 7), (28, 6), (33, 29), (10, 10), (11, 25), (7, 21), (26, 15), (8, 15), (26, 28), (19, 34), (29, 25), (12, 30), (21, 30), (13, 7), (22, 26), (27, 13), (14, 13), (0, 34), (34, 4), (24, 19), (22, 19), (7, 0), (21, 3), (27, 33), (22, 17), (3, 9), (29, 30), (15, 21), (10, 1), (35, 34), (24, 32), (10, 15), (26, 18), (21, 28), (5, 17), (29, 6), (24, 21), (18, 4), (20, 13), (11, 10), (11, 34), (32, 5), (34, 15), (0, 1), (20, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "912384", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 21), (1, 23), (1, 6), (31, 16), (7, 20), (5, 10), (1, 28), (31, 14), (11, 10), (19, 6), (28, 21), (26, 22), (18, 15), (23, 6), (0, 8), (10, 26), (17, 3), (6, 0), (0, 26), (25, 26), (26, 23), (22, 27), (18, 27), (22, 26), (26, 30), (9, 21), (21, 22), (26, 17), (8, 0), (0, 7), (19, 15), (24, 30), (20, 16), (8, 29), (17, 1), (3, 21), (20, 27), (10, 8), (21, 28), (11, 0), (5, 24), (32, 9), (23, 0), (23, 3), (14, 11), (33, 28), (4, 17), (29, 17), (19, 13), (14, 30), (13, 22), (29, 11), (33, 23), (7, 31), (28, 19), (7, 11), (9, 0), (20, 17), (13, 20), (10, 21), (9, 7), (29, 0), (29, 31), (22, 19), (23, 30), (26, 3), (14, 14), (12, 15), (21, 8), (26, 13), (23, 31), (5, 15), (33, 22), (24, 17), (7, 8), (30, 24), (3, 15), (0, 11), (24, 18), (6, 17), (25, 13), (23, 21), (0, 13), (20, 23), (5, 29), (10, 2), (31, 22), (7, 25), (28, 11), (27, 25), (27, 22), (28, 18), (8, 22), (15, 10), (16, 17), (21, 25), (24, 28), (30, 31), (32, 28), (11, 29), (19, 31), (32, 25), (9, 2), (15, 27), (25, 2), (8, 3), (4, 2), (25, 21), (14, 9), (28, 28), (15, 7), (5, 19), (9, 14), (32, 2), (3, 31), (9, 24), (15, 23), (10, 16), (17, 24), (28, 17), (5, 5), (30, 14), (25, 15), (18, 26), (23, 16), (4, 23), (23, 24), (31, 24), (21, 27), (32, 7), (8, 19), (9, 1), (1, 14), (4, 0), (27, 18), (26, 25), (23, 5), (33, 7), (12, 28), (32, 11), (30, 6), (2, 25), (1, 21), (31, 21), (15, 14), (14, 12), (11, 23), (24, 19), (32, 26), (28, 23), (29, 30), (18, 18), (20, 8), (6, 19), (1, 8), (31, 20), (18, 20), (22, 16), (4, 22), (13, 4), (16, 14), (10, 0), (1, 12), (9, 11), (7, 22), (6, 28), (15, 0), (16, 20), (5, 28), (24, 16), (12, 30), (27, 9), (10, 23), (17, 21), (30, 28), (12, 10), (1, 30), (32, 21), (16, 15), (3, 3), (12, 17), (27, 5), (9, 29), (21, 1), (19, 25), (9, 9), (16, 10), (20, 5), (3, 13), (27, 21), (10, 9), (6, 13), (23, 7), (10, 17), (2, 14), (22, 28), (13, 18), (15, 29), (8, 11), (25, 24), (2, 31), (0, 10), (32, 3), (7, 9), (28, 3), (30, 5), (23, 23), (27, 15), (15, 11), (27, 6), (24, 12), (5, 18), (17, 27), (30, 10), (11, 3), (7, 26), (15, 26), (31, 18), (0, 14), (6, 30), (13, 31), (11, 18), (8, 13), (0, 5), (10, 30), (32, 8), (29, 27), (32, 10), (14, 6), (12, 31), (25, 20), (23, 14), (28, 24), (13, 3), (3, 9), (20, 31), (0, 24), (20, 0), (13, 12), (10, 7), (24, 29), (33, 4), (20, 2), (21, 14), (28, 16), (4, 27), (32, 23), (30, 13), (25, 6), (25, 19), (3, 19), (12, 11), (15, 24), (33, 14), (23, 17), (18, 28), (6, 4), (29, 5), (12, 0), (4, 11), (13, 16), (14, 21), (12, 7), (6, 3), (13, 8), (0, 20), (8, 23), (20, 1), (22, 8), (13, 17), (27, 27), (23, 20), (21, 20), (4, 7), (25, 29), (5, 7), (17, 28), (7, 7), (12, 22), (16, 16), (1, 0), (33, 15), (2, 9), (8, 25), (23, 11), (14, 0), (11, 22), (14, 8), (33, 24), (7, 29), (2, 8), (18, 21), (14, 15), (5, 21), (3, 14), (0, 27), (11, 17), (5, 27), (4, 24), (16, 23), (23, 27), (6, 5), (2, 24), (32, 5), (14, 5), (12, 23), (22, 11), (21, 31), (18, 3), (6, 29), (4, 28), (13, 23), (0, 22), (3, 22), (6, 16), (31, 23), (21, 4), (10, 31), (30, 20), (19, 17), (6, 31), (9, 10), (17, 10), (13, 10), (28, 6), (17, 23), (17, 2), (18, 7), (27, 19), (19, 5), (16, 21), (7, 4), (2, 26), (5, 9), (8, 21), (18, 0), (21, 18), (31, 25), (14, 25), (8, 26), (24, 5), (25, 8), (2, 23), (2, 3), (29, 23), (32, 15), (33, 3), (8, 7), (7, 23), (3, 27), (12, 12), (2, 1), (18, 1), (19, 28), (3, 30), (15, 1), (1, 25), (30, 11), (33, 29), (9, 27), (26, 2), (13, 21), (8, 1), (23, 29), (14, 23), (17, 6), (33, 13), (27, 13), (20, 29), (2, 18), (20, 22), (28, 12), (14, 17), (10, 29), (30, 3), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "866560", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), 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), (18, 29), (18, 36), (28, 9), (23, 0), (27, 17), (31, 6), (5, 29), (19, 20), (0, 2), (19, 29), (6, 29), (23, 15), (9, 34), (2, 26), (13, 7), (10, 13), (9, 31), (24, 36), (16, 1), (13, 18), (2, 16), (20, 4), (30, 8), (7, 24), (25, 14), (22, 25), (22, 27), (22, 8), (3, 10), (28, 22), (24, 18), (1, 26), (21, 29), (19, 37), (22, 16), (28, 33), (13, 21), (4, 22), (13, 13), (13, 19), (2, 5), (30, 18), (22, 22), (31, 12), (13, 3), (25, 37), (1, 11), (7, 6), (27, 35), (9, 0), (30, 16), (13, 20), (17, 0), (21, 5), (15, 25), (18, 16), (4, 36), (29, 6), (29, 13), (25, 36), (31, 30), (8, 21), (26, 9), (27, 29), (19, 38), (22, 9), (3, 23), (28, 6), (11, 11), (3, 13), (6, 22), (31, 17), (19, 6), (13, 30), (4, 14), (8, 19), (2, 32), (19, 0), (10, 24), (15, 35), (11, 0), (29, 24), (2, 18), (22, 18), (2, 6), (22, 10), (10, 35), (24, 35), (16, 24), (5, 14), (11, 38), (15, 24), (25, 31), (18, 7), (1, 5), (24, 30), (23, 18), (27, 9), (3, 30), (8, 23), (8, 38), (4, 2), (13, 5), (26, 23), (10, 2), (0, 3), (6, 38), (31, 0), (9, 14), (30, 0), (22, 34), (27, 38), (4, 20), (4, 35), (0, 31), (11, 28), (19, 26), (3, 8), (20, 7), (15, 10), (19, 8), (29, 22), (10, 16), (11, 24), (2, 37), (17, 15), (22, 7), (1, 1), (30, 38), (27, 16), (0, 32), (1, 22), (24, 17), (2, 3), (4, 32), (7, 20), (5, 19), (31, 20), (24, 33), (1, 16), (24, 11), (14, 9), (11, 35), (7, 13), (11, 3), (20, 22), (3, 6), (23, 7), (10, 28), (20, 38), (8, 35), (23, 14), (27, 6), (12, 20), (9, 28), (4, 26), (22, 4), (28, 21), (30, 25), (7, 19), (23, 23), (7, 29), (4, 38), (5, 5), (8, 36), (14, 12), (16, 37), (28, 1), (25, 3), (27, 36), (30, 5), (18, 30), (21, 22), (27, 33), (4, 7), (8, 27), (29, 14), (9, 16), (12, 12), (11, 18), (16, 31), (23, 5), (7, 32), (12, 37), (8, 0), (27, 23), (8, 31), (3, 25), (5, 7), (30, 10), (5, 2), (22, 37), (17, 1), (12, 26), (13, 34), (30, 7), (18, 26), (22, 11), (24, 28), (1, 29), (28, 13), (20, 3), (24, 0), (20, 35), (12, 32), (4, 1), (19, 28), (3, 27), (14, 35), (6, 6), (21, 10), (26, 17), (29, 0), (31, 4), (31, 16), (9, 30), (29, 7), (18, 31), (31, 11), (6, 4), (23, 37), (4, 21), (24, 9), (10, 22), (22, 33), (26, 13), (12, 18), (17, 24), (24, 5), (21, 14), (26, 33), (29, 2), (15, 31), (30, 15), (15, 37), (6, 5), (0, 28), (5, 10), (14, 29), (7, 35), (11, 7), (10, 19), (26, 25), (2, 15), (3, 36), (22, 1), (21, 35), (29, 19), (21, 31), (14, 15), (18, 14), (30, 13), (5, 24), (1, 23), (29, 35), (21, 37), (7, 4), (6, 10), (11, 10), (6, 17), (8, 26), (1, 36), (1, 38), (2, 24), (17, 22), (11, 9), (30, 24), (0, 38), (0, 13), (10, 30), (26, 8), (19, 33), (23, 12), (7, 5), (1, 20), (9, 15), (14, 34), (31, 7), (15, 28), (30, 19), (30, 17), (8, 7), (13, 28), (30, 4), (28, 27), (30, 6), (4, 29), (3, 37), (12, 10), (24, 32), (16, 13), (30, 11), (27, 10), (5, 33), (13, 16), (19, 18), (31, 21), (5, 32), (23, 22), (29, 36), (16, 35), (14, 7), (14, 2), (1, 35), (16, 3), (10, 17), (25, 0), (7, 34), (4, 3), (20, 18), (16, 26), (9, 5), (29, 5), (4, 5), (14, 18), (14, 8), (19, 15), (14, 14), (12, 23), (9, 29), (7, 16), (2, 27), (14, 28), (20, 8), (7, 38), (4, 4), (18, 18), (10, 36), (8, 1), (18, 12), (7, 14), (7, 23), (1, 33), (14, 20), (21, 27), (9, 18), (0, 27), (28, 16), (6, 26), (10, 18), (6, 13), (3, 35), (28, 37), (1, 24), (19, 23), (16, 11), (4, 9), (0, 26), (26, 34), (1, 21), (1, 2), (25, 25), (21, 34), (31, 19), (24, 25), (4, 23), (21, 30), (10, 9), (13, 36), (26, 5), (31, 28), (12, 9), (17, 9), (19, 1), (18, 20), (6, 19), (10, 37), (23, 11), (22, 14), (0, 22), (18, 17), (23, 8), (28, 5), (24, 4), (24, 26), (13, 24), (27, 24), (31, 25), (16, 9), (13, 33), (20, 29), (12, 13), (9, 25), (4, 24), (7, 3), (6, 14), (2, 33), (26, 22), (0, 15), (26, 26), (2, 9), (11, 5), (6, 24), (28, 0), (28, 28), (12, 19), (31, 1), (23, 36), (23, 2), (14, 37), (28, 23), (5, 15), (29, 37), (2, 31), (30, 32), (29, 10), (24, 16), (23, 28), (5, 8), (11, 1), (1, 28), (30, 27), (18, 22), (24, 37), (26, 31), (9, 17), (29, 26), (27, 7), (0, 5), (13, 27), (6, 12), (29, 9), (26, 18), (27, 18), (12, 0), (27, 1), (18, 38), (8, 22), (22, 20), (9, 13), (28, 36), (31, 36), (24, 24), (20, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "556800", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 23), (21, 11), (27, 10), (22, 29), (30, 17), (38, 12), (17, 7), (9, 15), (21, 12), (12, 22), (11, 4), (11, 22), (34, 17), (12, 26), (24, 2), (13, 12), (6, 13), (29, 8), (12, 4), (5, 10), (9, 11), (23, 25), (23, 11), (2, 8), (10, 12), (22, 4), (23, 22), (2, 0), (29, 5), (35, 0), (3, 7), (24, 21), (27, 26), (19, 29), (34, 13), (8, 4), (33, 25), (33, 28), (26, 24), (35, 3), (24, 29), (24, 13), (5, 23), (20, 18), (20, 0), (13, 14), (14, 16), (11, 20), (4, 12), (4, 4), (19, 25), (28, 21), (7, 25), (24, 4), (7, 3), (6, 11), (32, 25), (35, 9), (30, 7), (0, 19), (24, 19), (26, 2), (12, 3), (36, 24), (18, 17), (24, 3), (25, 5), (8, 21), (35, 14), (27, 22), (31, 1), (3, 21), (26, 12), (25, 22), (31, 17), (38, 15), (33, 3), (36, 1), (32, 4), (15, 24), (1, 16), (8, 8), (4, 2), (29, 3), (6, 15), (1, 22), (14, 25), (10, 1), (32, 23), (22, 15), (33, 26), (24, 6), (22, 27), (16, 4), (17, 1), (36, 18), (5, 2), (1, 2), (4, 21), (15, 3), (11, 12), (27, 1), (9, 27), (3, 15), (34, 29), (14, 13), (6, 7), (38, 1), (2, 26), (12, 27), (28, 16), (16, 11), (9, 24), (37, 18), (32, 22), (14, 4), (9, 2), (18, 11), (15, 12), (28, 26), (20, 6), (28, 29), (6, 16), (34, 6), (1, 28), (29, 23), (14, 19), (18, 16), (7, 18), (36, 7), (30, 16), (10, 13), (4, 22), (25, 29), (31, 10), (21, 3), (24, 24), (14, 17), (13, 13), (4, 17), (17, 21), (3, 18), (36, 5), (2, 13), (2, 14), (22, 12), (22, 13), (32, 1), (22, 18), (36, 16), (8, 17), (8, 9), (27, 5), (3, 9), (30, 6), (17, 27), (28, 14), (11, 7), (38, 4), (18, 29), (31, 29), (1, 25), (24, 14), (5, 0), (10, 25), (33, 20), (30, 9), (1, 26), (1, 9), (29, 22), (8, 27), (38, 21), (34, 4), (29, 26), (17, 29), (20, 8), (17, 14), (10, 3), (31, 28), (31, 8), (24, 12), (30, 12), (34, 10), (14, 21), (0, 22), (26, 9), (19, 14), (15, 22), (21, 26), (36, 26), (5, 19), (3, 19), (23, 1), (37, 11), (8, 15), (16, 28), (11, 17), (25, 4), (7, 20), (22, 24), (29, 4), (10, 23), (1, 20), (30, 18), (25, 18), (13, 23), (36, 19), (20, 29), (32, 13), (36, 15), (32, 18), (9, 25), (19, 16), (29, 14), (29, 17), (18, 8), (2, 6), (8, 10), (26, 5), (23, 28), (3, 10), (34, 11), (38, 0), (30, 15), (7, 11), (8, 13), (12, 12), (30, 5), (26, 10), (35, 6), (38, 26), (13, 20), (28, 2), (8, 12), (5, 5), (33, 5), (38, 25), (23, 2), (24, 26), (0, 6), (31, 3), (34, 7), (27, 4), (32, 7), (35, 27), (35, 26), (9, 17), (3, 1), (11, 0), (23, 21), (23, 18), (31, 6), (8, 26), (8, 19), (34, 12), (37, 4), (35, 1), (14, 8), (2, 15), (22, 28), (16, 27), (6, 10), (12, 24), (21, 16), (30, 27), (33, 2), (38, 19), (4, 18), (7, 22), (26, 17), (19, 2), (3, 5), (20, 24), (25, 12), (19, 4), (28, 0), (36, 28), (20, 3), (2, 19), (19, 11), (23, 16), (11, 13), (10, 6), (16, 13), (7, 17), (4, 0), (28, 23), (18, 2), (20, 4), (5, 28), (21, 13), (37, 20), (29, 28), (33, 14), (0, 1), (7, 24), (3, 17), (31, 11), (32, 8), (7, 7), (21, 18), (31, 23), (37, 28), (24, 11), (21, 29), (3, 16), (9, 28), (26, 18), (19, 19), (19, 1), (22, 16), (7, 14), (1, 13), (15, 29), (13, 0), (8, 24), (10, 5), (9, 6), (35, 10), (36, 6), (25, 1), (37, 1), (3, 26), (20, 27), (32, 20), (20, 25), (32, 28), (18, 3), (6, 1), (9, 29), (19, 9), (34, 25), (1, 21), (26, 14), (18, 14), (10, 26), (25, 19), (8, 23), (8, 29), (18, 28), (8, 22), (28, 27), (16, 20), (19, 22), (2, 7), (22, 7), (22, 22), (14, 12), (11, 23), (7, 21), (18, 27), (1, 17), (2, 17), (15, 4), (2, 29), (17, 22), (9, 8), (6, 14), (27, 24), (15, 0), (20, 20), (7, 4), (0, 2), (21, 0), (31, 13), (25, 27), (19, 21), (15, 20), (35, 12), (27, 0), (12, 20), (10, 16), (16, 26), (36, 3), (37, 8), (34, 24), (11, 5), (6, 17), (22, 0), (10, 14), (27, 20), (4, 15), (11, 19), (30, 25), (20, 26), (13, 5), (25, 7), (0, 29), (10, 29), (35, 20), (19, 18), (6, 6), (37, 10), (19, 28), (25, 10), (6, 3), (33, 27), (21, 4), (28, 20), (32, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "139360", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 38), (23, 29), (21, 27), (17, 38), (6, 5), (11, 30), (15, 11), (26, 33), (12, 9), (0, 35), (9, 18), (26, 24), (21, 23), (12, 18), (25, 7), (5, 8), (15, 3), (22, 30), (27, 9), (25, 13), (16, 0), (8, 15), (10, 20), (4, 8), (29, 15), (18, 21), (14, 14), (21, 31), (3, 19), (17, 19), (14, 21), (3, 14), (11, 22), (31, 22), (5, 34), (25, 21), (7, 3), (16, 1), (27, 36), (2, 15), (13, 35), (25, 3), (4, 25), (24, 8), (30, 16), (0, 32), (10, 24), (7, 34), (17, 34), (23, 1), (24, 7), (8, 16), (13, 5), (0, 13), (13, 14), (11, 27), (13, 20), (18, 32), (18, 19), (8, 29), (9, 17), (14, 28), (14, 5), (11, 2), (18, 20), (2, 34), (14, 12), (28, 34), (19, 3), (7, 31), (4, 22), (8, 7), (24, 0), (18, 27), (25, 35), (2, 27), (7, 1), (1, 5), (11, 20), (4, 31), (0, 36), (14, 25), (30, 26), (15, 18), (2, 16), (7, 30), (20, 30), (15, 10), (4, 15), (13, 24), (16, 24), (7, 5), (10, 6), (26, 11), (24, 24), (16, 6), (21, 37), (5, 13), (8, 10), (2, 5), (4, 36), (26, 13), (6, 31), (31, 8), (14, 32), (25, 20), (15, 19), (9, 13), (4, 9), (31, 27), (18, 29), (12, 0), (22, 34), (9, 19), (0, 14), (11, 33), (13, 18), (2, 31), (30, 0), (23, 7), (22, 10), (7, 8), (28, 24), (23, 28), (9, 35), (15, 33), (1, 21), (30, 36), (20, 23), (13, 26), (22, 4), (12, 31), (22, 23), (30, 38), (4, 29), (30, 21), (10, 32), (2, 23), (19, 38), (14, 9), (8, 31), (7, 15), (6, 17), (22, 26), (10, 7), (31, 13), (16, 36), (15, 29), (19, 1), (7, 32), (16, 15), (25, 5), (13, 33), (25, 16), (27, 7), (22, 2), (7, 17), (23, 36), (22, 11), (2, 7), (13, 21), (3, 33), (17, 31), (23, 4), (19, 20), (30, 29), (1, 30), (20, 4), (12, 16), (17, 36), (15, 38), (16, 31), (17, 17), (4, 5), (13, 8), (25, 34), (23, 14), (8, 35), (17, 22), (14, 3), (24, 1), (4, 34), (3, 3), (28, 26), (26, 17), (3, 16), (8, 9), (0, 31), (4, 28), (7, 29), (30, 7), (24, 34), (30, 4), (22, 9), (7, 6), (5, 31), (27, 27), (29, 26), (10, 35), (0, 16), (1, 27), (28, 14), (7, 33), (11, 15), (26, 15), (1, 29), (22, 8), (1, 19), (2, 9), (9, 30), (20, 0), (6, 12), (18, 8), (8, 38), (2, 12), (1, 1), (30, 11), (3, 28), (4, 20), (15, 4), (27, 25), (9, 24), (2, 33), (29, 16), (29, 20), (25, 32), (15, 1), (19, 32), (28, 4), (28, 20), (18, 33), (14, 33), (9, 38), (18, 24), (7, 20), (19, 28), (10, 28), (1, 34), (29, 29), (18, 5), (9, 12), (30, 14), (0, 6), (4, 13), (20, 17), (19, 21), (27, 4), (16, 7), (28, 29), (23, 35), (20, 31), (22, 37), (28, 33), (7, 13), (30, 19), (6, 35), (26, 29), (12, 19), (30, 2), (1, 26), (2, 35), (9, 23), (26, 38), (0, 22), (16, 9), (0, 38), (12, 25), (1, 14), (7, 14), (4, 4), (31, 12), (3, 7), (11, 38), (2, 29), (2, 24), (27, 2), (23, 17), (10, 15), (8, 11), (4, 21), (18, 16), (10, 19), (29, 22), (27, 8), (0, 30), (4, 38), (13, 1), (30, 30), (3, 36), (24, 29), (21, 4), (8, 20), (3, 20), (20, 29), (20, 35), (15, 37), (29, 5), (26, 34), (26, 20), (1, 20), (23, 25), (31, 3), (30, 20), (23, 6), (20, 21), (29, 21), (9, 29), (31, 7), (6, 19), (19, 8), (5, 2), (10, 22), (23, 27), (21, 24), (2, 30), (3, 32), (27, 26), (2, 6), (4, 35), (18, 31), (4, 7), (23, 19), (18, 2), (17, 9), (14, 26), (10, 27), (14, 11), (8, 14), (10, 25), (19, 17), (10, 10), (0, 2), (5, 9), (3, 4), (23, 12), (1, 24), (3, 11), (5, 7), (14, 36), (24, 25), (0, 34), (20, 20), (21, 17), (24, 12), (16, 13), (31, 26), (5, 0), (26, 16), (5, 10), (3, 27), (29, 33), (15, 23), (25, 27), (4, 18), (4, 30), (28, 27), (1, 33), (20, 16), (25, 22), (9, 10), (2, 8), (22, 31), (14, 24), (31, 20), (12, 13), (16, 26), (17, 20), (0, 12), (0, 15), (21, 21), (30, 15), (24, 31), (31, 32), (12, 34), (31, 1), (1, 9), (17, 14), (23, 20), (23, 18), (17, 26), (31, 18), (3, 1), (22, 0), (12, 36), (5, 16), (7, 9), (14, 19), (1, 28), (0, 5), (20, 32), (18, 3), (11, 24), (4, 1), (5, 18), (21, 30), (16, 34), (19, 12), (15, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507780", "dataset": "MATH"}
{"messages": [{"content": "In a 35x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 32), 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), (3, 30), (3, 22), (22, 6), (15, 30), (3, 17), (25, 22), (25, 9), (33, 9), (22, 23), (34, 22), (13, 25), (27, 20), (9, 1), (24, 18), (34, 3), (6, 29), (12, 15), (29, 25), (11, 9), (22, 26), (33, 27), (0, 21), (7, 0), (8, 1), (28, 19), (1, 16), (12, 2), (29, 2), (15, 14), (19, 27), (17, 29), (11, 27), (23, 22), (30, 31), (10, 17), (19, 4), (17, 16), (18, 26), (13, 32), (20, 5), (21, 20), (17, 13), (26, 25), (15, 7), (30, 24), (6, 14), (17, 23), (3, 8), (0, 25), (15, 9), (9, 27), (33, 7), (0, 4), (33, 11), (14, 29), (0, 30), (4, 26), (14, 25), (18, 29), (20, 24), (20, 9), (1, 1), (11, 12), (15, 8), (26, 22), (16, 9), (18, 19), (6, 4), (0, 1), (22, 15), (31, 15), (4, 18), (6, 25), (30, 6), (2, 28), (10, 22), (32, 13), (24, 19), (27, 8), (7, 15), (34, 26), (33, 22), (22, 21), (11, 0), (27, 30), (0, 11), (10, 26), (11, 18), (9, 5), (3, 9), (31, 8), (3, 23), (22, 24), (14, 10), (0, 10), (28, 16), (21, 12), (21, 11), (17, 26), (11, 28), (11, 4), (29, 32), (16, 10), (11, 10), (17, 22), (16, 25), (18, 32), (31, 12), (17, 4), (30, 12), (2, 23), (30, 23), (32, 25), (1, 7), (12, 20), (22, 30), (29, 28), (34, 29), (12, 14), (5, 26), (13, 5), (16, 3), (33, 3), (24, 30), (30, 5), (24, 4), (10, 11), (1, 11), (22, 14), (23, 3), (7, 17), (5, 1), (32, 7), (34, 6), (16, 22), (14, 15), (31, 25), (16, 32), (22, 7), (15, 22), (23, 5), (25, 11), (6, 1), (30, 11), (24, 12), (16, 4), (30, 15), (30, 9), (31, 4), (24, 5), (22, 28), (22, 13), (32, 23), (6, 12), (0, 3), (15, 12), (17, 21), (8, 9), (28, 32), (21, 4), (33, 31), (31, 13), (3, 32), (21, 3), (5, 27), (9, 15), (22, 0), (26, 31), (18, 6), (13, 14), (13, 0), (7, 2), (4, 17), (27, 32), (23, 23), (16, 16), (26, 30), (23, 0), (28, 0), (20, 10), (17, 5), (16, 30), (27, 26), (20, 32), (23, 4), (24, 1), (19, 3), (31, 6), (10, 29), (26, 15), (1, 6), (25, 2), (21, 6), (28, 5), (12, 13), (19, 29), (28, 8), (10, 10), (29, 27), (8, 27), (27, 2), (4, 8), (31, 21), (14, 8), (29, 18), (33, 24), (26, 26), (25, 24), (32, 31), (10, 3), (13, 3), (25, 21), (7, 25), (7, 22), (16, 20), (3, 26), (7, 7), (28, 22), (9, 9), (20, 17), (18, 14), (26, 12), (10, 21), (16, 28), (31, 26), (26, 11), (17, 0), (27, 3), (0, 18), (29, 16), (15, 2), (30, 28), (15, 32), (33, 10), (4, 12), (17, 10), (27, 23), (23, 12), (8, 11), (6, 8), (17, 8), (1, 22), (31, 18), (7, 10), (21, 13), (28, 28), (24, 6), (17, 6), (11, 3), (26, 7), (18, 17), (33, 25), (13, 19), (18, 27), (9, 3), (27, 29), (9, 16), (2, 19), (30, 1), (21, 10), (8, 6), (10, 14), (33, 16), (17, 14), (7, 32), (10, 6), (25, 30), (34, 5), (34, 11), (34, 10), (31, 20), (28, 15), (30, 0), (17, 3), (26, 28), (21, 26), (8, 23), (30, 8), (9, 14), (22, 2), (28, 2), (15, 3), (1, 13), (1, 24), (27, 27), (2, 8), (16, 21), (31, 23), (20, 28), (34, 31), (13, 30), (3, 2), (4, 14), (6, 21), (27, 21), (27, 13), (0, 12), (4, 21), (24, 32), (9, 11), (13, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867776", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 20), (33, 14), (7, 3), (18, 0), (19, 9), (1, 13), (2, 8), (24, 30), (18, 6), (4, 7), (36, 25), (30, 1), (23, 30), (20, 7), (20, 5), (25, 5), (19, 1), (27, 8), (13, 12), (22, 8), (29, 27), (4, 27), (14, 31), (31, 0), (15, 0), (32, 26), (31, 30), (17, 22), (19, 23), (12, 25), (7, 15), (5, 13), (8, 28), (1, 12), (30, 3), (3, 28), (37, 12), (36, 11), (27, 29), (1, 8), (4, 6), (6, 8), (7, 18), (33, 26), (11, 13), (19, 8), (36, 30), (28, 31), (25, 9), (37, 9), (30, 14), (1, 10), (29, 26), (15, 9), (34, 15), (15, 3), (32, 10), (4, 12), (5, 30), (37, 16), (29, 11), (2, 13), (0, 3), (34, 9), (15, 18), (21, 30), (27, 26), (34, 8), (19, 26), (37, 5), (29, 5), (18, 25), (13, 21), (30, 22), (6, 5), (30, 21), (11, 2), (26, 10), (16, 20), (31, 18), (18, 12), (32, 3), (9, 31), (25, 19), (19, 25), (19, 6), (9, 18), (1, 30), (20, 4), (33, 1), (37, 23), (27, 14), (30, 24), (0, 2), (32, 25), (3, 24), (4, 9), (9, 16), (24, 29), (1, 29), (17, 13), (15, 19), (13, 27), (5, 8), (23, 6), (6, 20), (23, 20), (15, 26), (14, 17), (32, 16), (26, 20), (37, 30), (28, 32), (20, 1), (0, 18), (17, 31), (20, 23), (21, 25), (20, 29), (26, 22), (16, 29), (9, 30), (2, 23), (1, 17), (2, 16), (37, 6), (14, 19), (33, 12), (7, 19), (6, 12), (6, 6), (7, 21), (10, 30), (12, 20), (8, 31), (11, 30), (24, 6), (3, 22), (6, 7), (5, 16), (19, 7), (24, 1), (33, 30), (22, 20), (26, 6), (7, 29), (15, 22), (9, 23), (13, 29), (30, 31), (36, 20), (21, 13), (8, 14), (27, 28), (28, 27), (25, 32), (21, 26), (33, 25), (29, 0), (12, 10), (11, 15), (9, 20), (26, 31), (20, 9), (29, 6), (17, 5), (18, 21), (26, 5), (20, 19), (30, 17), (9, 28), (14, 20), (36, 17), (5, 9), (22, 9), (10, 4), (15, 24), (17, 10), (20, 12), (34, 23), (10, 12), (23, 1), (30, 10), (20, 26), (21, 1), (8, 4), (8, 26), (34, 7), (32, 6), (6, 0), (31, 25), (23, 14), (20, 14), (1, 16), (1, 24), (6, 13), (37, 15), (28, 20), (9, 27), (21, 27), (37, 24), (28, 10), (5, 28), (19, 29), (18, 31), (35, 12), (15, 23), (35, 15), (2, 32), (16, 25), (14, 27), (13, 24), (14, 12), (16, 8), (6, 3), (21, 18), (13, 13), (13, 28), (24, 8), (21, 28), (24, 16), (24, 27), (22, 17), (16, 24), (17, 15), (17, 26), (17, 21), (23, 18), (1, 25), (27, 9), (10, 13), (37, 22), (30, 11), (29, 28), (6, 24), (14, 9), (7, 6), (35, 16), (26, 19), (36, 14), (16, 12), (3, 13), (3, 30), (34, 26), (13, 9), (6, 19), (36, 21), (0, 29), (14, 32), (24, 10), (25, 7), (5, 17), (27, 16), (12, 14), (28, 28), (29, 23), (24, 19), (27, 2), (5, 2), (32, 22), (37, 2), (26, 32), (37, 29), (36, 0), (6, 21), (25, 27), (31, 27), (13, 4), (0, 32), (5, 6), (10, 21), (21, 4), (2, 30), (1, 4), (4, 18), (36, 15), (28, 2), (6, 22), (32, 5), (17, 16), (8, 24), (15, 6), (24, 32), (33, 6), (14, 8), (5, 22), (17, 18), (1, 28), (31, 29), (24, 11), (27, 11), (8, 2), (24, 25), (23, 10), (21, 19), (33, 15), (4, 5), (6, 2), (37, 8), (9, 9), (5, 23), (21, 16), (10, 19), (9, 25), (18, 22), (9, 21), (19, 21), (17, 27), (34, 11), (17, 0), (21, 22), (7, 11), (23, 29), (20, 16), (13, 32), (16, 7), (0, 31), (32, 19), (21, 29), (35, 13), (8, 13), (35, 19), (23, 25), (25, 15), (0, 13), (3, 8), (4, 22), (29, 20), (2, 29), (28, 5), (2, 18), (8, 15), (17, 19), (13, 0), (17, 23), (10, 1), (18, 4), (35, 6), (9, 10), (22, 1), (30, 30), (16, 10), (34, 14), (33, 3), (32, 13), (36, 29), (28, 18), (32, 28), (14, 5), (13, 26), (9, 6), (14, 6), (1, 20), (22, 2), (35, 7), (22, 6), (37, 25), (33, 20), (35, 4), (24, 24), (0, 19), (18, 17), (20, 17), (37, 26), (20, 24), (15, 21), (5, 15), (21, 2), (24, 31), (11, 18), (13, 31), (7, 22), (26, 21), (31, 22), (20, 11), (34, 27), (25, 6), (4, 4), (23, 17), (4, 32), (29, 12), (6, 23), (26, 3), (3, 4), (30, 20), (6, 30), (22, 13), (7, 20), (11, 27), (29, 29), (30, 9), (29, 31), (35, 21), (12, 22), (9, 24), (22, 23), (25, 1), (35, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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), (4, 10), (18, 6), (19, 30), (13, 26), (6, 8), (15, 25), (28, 5), (8, 23), (1, 20), (13, 7), (0, 17), (11, 27), (7, 18), (27, 7), (0, 18), (21, 15), (25, 17), (4, 4), (7, 20), (9, 8), (24, 10), (14, 11), (25, 18), (5, 19), (18, 11), (30, 35), (13, 23), (10, 12), (11, 21), (3, 6), (27, 26), (11, 20), (27, 4), (20, 22), (0, 21), (18, 29), (6, 31), (22, 24), (12, 13), (26, 2), (25, 23), (8, 24), (27, 32), (18, 8), (13, 13), (6, 3), (23, 19), (6, 19), (3, 10), (0, 26), (13, 20), (3, 17), (14, 15), (21, 3), (13, 18), (6, 14), (17, 12), (13, 30), (1, 15), (15, 6), (4, 23), (26, 24), (10, 6), (23, 25), (2, 31), (23, 30), (23, 3), (10, 26), (19, 35), (26, 14), (7, 15), (18, 10), (1, 9), (11, 8), (18, 9), (18, 14), (8, 26), (6, 27), (30, 4), (1, 0), (16, 19), (20, 21), (19, 15), (7, 34), (1, 5), (7, 32), (20, 36), (23, 32), (14, 21), (25, 29), (10, 14), (29, 30), (9, 26), (16, 23), (27, 5), (21, 21), (17, 29), (1, 19), (13, 33), (12, 20), (8, 11), (24, 14), (1, 6), (23, 8), (18, 18), (7, 22), (24, 23), (7, 29), (23, 34), (18, 34), (12, 35), (16, 10), (19, 32), (15, 20), (7, 7), (4, 13), (21, 17), (29, 3), (2, 13), (10, 29), (26, 1), (3, 31), (21, 20), (11, 25), (30, 19), (8, 10), (8, 9), (26, 36), (13, 28), (12, 33), (29, 14), (6, 21), (0, 3), (27, 18), (2, 11), (13, 27), (11, 4), (10, 2), (28, 26), (29, 23), (14, 28), (5, 17), (30, 22), (22, 36), (11, 6), (30, 24), (18, 2), (2, 34), (20, 2), (11, 35), (14, 10), (6, 15), (25, 19), (17, 28), (28, 33), (11, 19), (18, 30), (9, 33), (19, 29), (0, 28), (27, 17), (28, 9), (4, 2), (30, 18), (21, 35), (8, 22), (3, 34), (9, 10), (2, 12), (30, 12), (8, 6), (3, 16), (18, 16), (15, 2), (13, 2), (28, 17), (10, 4), (30, 15), (8, 30), (5, 34), (5, 28), (26, 30), (22, 15), (27, 31), (12, 17), (25, 6), (4, 33), (9, 7), (17, 32), (15, 7), (11, 3), (26, 28), (25, 11), (20, 12), (21, 7), (1, 8), (9, 20), (27, 10), (16, 11), (15, 11), (17, 26), (8, 3), (18, 12), (16, 31), (6, 30), (24, 34), (24, 22), (0, 7), (11, 31), (14, 6), (10, 30), (5, 14), (13, 4), (0, 27), (26, 8), (12, 34), (8, 36), (24, 17), (24, 21), (14, 0), (4, 34), (14, 23), (19, 27), (7, 26), (5, 1), (3, 14), (3, 20), (30, 17), (27, 24), (18, 25), (2, 25), (18, 26), (11, 26), (5, 8), (2, 16), (25, 7), (19, 26), (23, 20), (10, 35), (26, 7), (1, 22), (1, 17), (10, 33), (8, 7), (5, 10), (23, 35), (30, 8), (12, 12), (10, 22), (23, 22), (3, 26), (26, 11), (11, 36), (14, 16), (20, 6), (24, 19), (18, 13), (21, 29), (13, 1), (6, 33), (19, 21), (16, 3), (16, 15), (12, 1), (3, 8), (28, 11), (12, 36), (23, 11), (22, 23), (25, 21), (18, 0), (21, 36), (6, 1), (27, 2), (28, 6), (7, 3), (17, 33), (19, 5), (16, 27), (16, 25), (0, 23), (14, 18), (12, 10), (7, 31), (26, 19), (19, 1), (15, 17), (19, 20), (24, 25), (10, 16), (0, 4), (1, 14), (0, 13), (20, 34), (8, 33), (16, 7), (21, 16), (2, 5), (2, 3), (7, 11), (19, 16), (2, 6), (26, 23), (11, 1), (19, 10), (1, 3), (1, 35), (1, 13), (29, 28), (23, 4), (22, 9), (1, 33), (9, 13), (24, 26), (23, 26), (6, 4), (23, 29), (25, 33), (10, 3), (13, 6), (0, 2), (6, 10), (17, 3), (19, 31), (3, 23), (25, 26), (29, 8), (0, 33), (6, 25), (9, 27), (18, 36), (28, 12), (24, 16), (23, 7), (22, 14), (5, 27), (19, 0), (10, 13), (21, 30), (14, 34), (14, 31), (8, 4), (2, 4), (4, 19), (30, 30), (28, 0), (30, 29), (30, 1), (15, 4), (13, 22), (6, 24), (10, 25), (11, 11), (3, 28), (29, 2), (26, 35), (17, 31), (18, 23), (2, 36), (20, 19), (21, 28), (6, 23), (21, 10), (21, 6), (24, 30), (24, 33), (19, 13), (27, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "745200", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 0), (11, 21), (6, 2), (34, 16), (30, 25), (15, 14), (0, 34), (20, 19), (8, 9), (33, 9), (15, 28), (30, 5), (10, 24), (6, 5), (24, 6), (15, 3), (24, 32), (13, 36), (16, 28), (10, 29), (37, 24), (14, 2), (6, 25), (25, 34), (5, 32), (9, 1), (23, 18), (34, 11), (33, 32), (8, 10), (14, 5), (29, 37), (14, 3), (5, 35), (8, 3), (12, 33), (1, 29), (24, 8), (34, 35), (16, 4), (32, 18), (37, 0), (37, 35), (11, 32), (5, 25), (26, 29), (2, 8), (30, 20), (17, 7), (14, 29), (28, 19), (18, 8), (21, 23), (15, 16), (10, 17), (6, 20), (2, 21), (28, 31), (11, 11), (20, 25), (33, 15), (36, 7), (3, 31), (27, 17), (36, 22), (10, 27), (29, 2), (19, 26), (25, 19), (24, 12), (13, 20), (14, 27), (33, 12), (33, 2), (33, 11), (4, 16), (15, 36), (32, 8), (17, 19), (34, 24), (1, 6), (35, 4), (37, 10), (33, 13), (6, 14), (11, 1), (2, 1), (18, 17), (17, 2), (29, 16), (22, 35), (2, 25), (20, 20), (8, 33), (36, 28), (13, 12), (33, 27), (20, 13), (37, 15), (27, 3), (1, 21), (11, 33), (2, 29), (31, 32), (29, 18), (32, 28), (37, 30), (22, 15), (25, 14), (1, 37), (24, 31), (4, 4), (12, 18), (25, 0), (30, 21), (14, 26), (26, 30), (13, 5), (35, 3), (16, 7), (6, 22), (21, 27), (16, 16), (11, 26), (30, 29), (6, 24), (38, 11), (13, 23), (21, 34), (34, 7), (30, 3), (35, 35), (13, 11), (28, 4), (30, 19), (30, 28), (29, 6), (3, 32), (0, 10), (15, 5), (25, 7), (23, 30), (14, 31), (10, 30), (28, 12), (20, 37), (28, 33), (7, 26), (31, 13), (25, 1), (4, 6), (18, 21), (2, 6), (17, 20), (17, 28), (31, 11), (32, 11), (3, 3), (8, 25), (21, 32), (10, 34), (32, 30), (22, 1), (5, 27), (13, 21), (18, 27), (24, 37), (20, 35), (8, 0), (11, 37), (31, 27), (16, 32), (32, 36), (8, 14), (34, 26), (24, 13), (33, 31), (22, 5), (34, 17), (5, 16), (24, 30), (9, 24), (14, 16), (11, 23), (24, 5), (16, 6), (36, 31), (30, 36), (7, 13), (7, 14), (15, 13), (12, 27), (25, 29), (2, 22), (10, 3), (13, 4), (1, 4), (4, 7), (8, 15), (23, 1), (15, 19), (11, 12), (30, 12), (5, 20), (31, 26), (17, 13), (24, 28), (19, 15), (30, 32), (36, 1), (31, 7), (12, 19), (25, 18), (26, 24), (26, 35), (1, 23), (3, 29), (4, 19), (6, 7), (21, 3), (27, 12), (25, 32), (30, 18), (9, 30), (32, 1), (1, 16), (9, 29), (25, 22), (30, 10), (35, 34), (31, 30), (5, 1), (21, 29), (19, 29), (18, 13), (34, 5), (38, 3), (29, 36), (36, 20), (31, 4), (20, 3), (23, 5), (15, 29), (12, 16), (17, 10), (13, 27), (25, 2), (2, 13), (15, 35), (5, 0), (16, 35), (13, 25), (29, 5), (1, 10), (26, 31), (9, 4), (19, 5), (22, 19), (38, 21), (13, 14), (25, 35), (27, 23), (13, 17), (5, 23), (7, 1), (4, 25), (28, 13), (34, 25), (10, 37), (24, 9), (12, 12), (34, 2), (8, 23), (37, 1), (14, 34), (27, 9), (4, 20), (0, 12), (15, 20), (13, 8), (29, 7), (13, 24), (29, 23), (16, 26), (3, 16), (16, 22), (21, 19), (16, 17), (0, 33), (3, 12), (38, 25), (10, 8), (8, 5), (21, 2), (8, 13), (30, 9), (35, 30), (2, 2), (33, 25), (11, 20), (21, 36), (9, 32), (26, 10), (31, 6), (6, 8), (3, 4), (25, 8), (11, 36), (23, 23), (17, 27), (34, 21), (0, 4), (20, 8), (27, 8), (7, 19), (2, 23), (35, 2), (34, 1), (5, 10), (5, 28), (23, 10), (4, 28), (15, 22), (5, 2), (18, 32), (37, 21), (25, 30), (36, 4), (10, 4), (4, 27), (4, 32), (21, 16), (27, 28), (26, 4), (14, 25), (20, 28), (13, 10), (15, 6), (28, 25), (21, 6), (7, 15), (36, 10), (4, 30), (32, 19), (16, 21), (29, 28), (26, 6), (19, 36), (4, 1), (12, 3), (30, 34), (12, 24), (12, 22), (18, 15), (17, 12), (37, 6), (11, 13), (15, 24), (26, 18), (31, 17), (24, 24), (6, 37), (5, 14), (29, 29), (28, 3), (33, 36), (13, 32), (4, 34), (14, 14), (21, 20), (16, 24), (25, 25), (9, 11), (38, 7), (2, 36), (34, 0), (6, 36), (21, 25), (27, 25), (7, 30), (5, 8), (20, 29), (16, 20), (15, 27), (0, 23), (2, 11), (32, 9), (19, 31), (6, 6), (38, 24), (15, 26), (3, 34), (21, 24), (3, 26), (22, 2), (19, 12), (6, 17), (36, 35), (27, 0), (5, 4), (4, 14), (37, 13), (14, 7), (32, 5), (3, 0), (8, 20), (9, 23), (3, 15), (2, 20), (29, 30), (38, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "391680", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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), (10, 22), (19, 14), (6, 23), (5, 7), (19, 28), (24, 3), (4, 19), (27, 34), (26, 22), (23, 10), (0, 30), (28, 8), (6, 16), (20, 30), (17, 2), (19, 25), (7, 21), (16, 10), (17, 21), (10, 5), (12, 34), (10, 6), (11, 16), (11, 8), (5, 0), (21, 25), (1, 3), (25, 20), (23, 11), (27, 18), (2, 4), (26, 2), (1, 29), (18, 7), (9, 2), (25, 25), (14, 18), (21, 23), (12, 19), (2, 1), (23, 33), (9, 17), (25, 27), (13, 22), (15, 3), (1, 31), (24, 28), (23, 15), (9, 16), (0, 27), (29, 19), (14, 27), (2, 22), (10, 3), (26, 9), (3, 19), (14, 5), (16, 0), (8, 22), (24, 13), (28, 18), (3, 15), (6, 33), (0, 31), (24, 23), (9, 6), (27, 19), (13, 31), (17, 20), (20, 3), (18, 9), (20, 21), (16, 17), (1, 14), (20, 17), (6, 20), (0, 11), (2, 28), (8, 26), (25, 29), (23, 23), (8, 16), (17, 13), (23, 16), (3, 7), (4, 18), (12, 17), (5, 25), (23, 9), (19, 16), (15, 17), (17, 3), (12, 11), (24, 6), (19, 2), (3, 18), (15, 31), (0, 33), (25, 30), (19, 33), (29, 30), (19, 20), (10, 0), (17, 5), (21, 10), (2, 14), (29, 29), (1, 15), (5, 29), (21, 18), (21, 16), (9, 1), (29, 22), (16, 29), (6, 10), (27, 21), (25, 1), (20, 32), (7, 24), (0, 10), (14, 7), (16, 16), (13, 13), (7, 10), (11, 14), (25, 34), (11, 33), (17, 17), (22, 13), (8, 23), (28, 3), (27, 4), (17, 10), (25, 9), (18, 34), (16, 21), (11, 18), (21, 30), (24, 24), (13, 3), (27, 2), (2, 3), (25, 23), (1, 18), (25, 17), (24, 5), (9, 18), (3, 13), (8, 4), (4, 11), (26, 5), (10, 25), (6, 1), (4, 30), (19, 26), (9, 31), (23, 34), (24, 7), (20, 6), (1, 28), (8, 34), (10, 13), (0, 8), (29, 17), (12, 8), (12, 5), (18, 22), (27, 8), (13, 9), (2, 26), (15, 24), (7, 3), (17, 1), (15, 7), (21, 29), (25, 24), (10, 8), (23, 29), (18, 18), (11, 2), (27, 32), (5, 21), (22, 18), (12, 16), (18, 13), (3, 24), (6, 0), (3, 34), (15, 6), (23, 8), (29, 11), (4, 29), (4, 9), (4, 4), (4, 2), (5, 1), (16, 12), (25, 26), (9, 4), (16, 11), (25, 4), (11, 23), (13, 15), (27, 0), (3, 26), (19, 31), (5, 9), (4, 0), (22, 0), (3, 22), (14, 31), (21, 6), (2, 17), (10, 4), (25, 32), (10, 23), (4, 24), (7, 1), (0, 17), (28, 22), (0, 29), (27, 31), (17, 23), (1, 2), (6, 15), (9, 27), (13, 21), (22, 23), (22, 2), (29, 31), (28, 25), (21, 27), (6, 32), (20, 22), (17, 25), (18, 19), (18, 2), (12, 26), (20, 11), (13, 6), (20, 5), (25, 19), (23, 18), (19, 4), (5, 27), (12, 0), (27, 9), (14, 26), (16, 9), (8, 17), (1, 0), (1, 21), (27, 17), (4, 28), (11, 3), (17, 9), (29, 18), (3, 9), (14, 33), (22, 7), (0, 32), (25, 33), (8, 8), (27, 23), (23, 6), (10, 18), (29, 21), (7, 2), (16, 15), (28, 10), (7, 8), (19, 17), (14, 29), (15, 25), (27, 25), (14, 8), (15, 28), (7, 31), (9, 3), (14, 4), (12, 14), (29, 25), (2, 9), (15, 30), (19, 18), (18, 4), (21, 26), (17, 32), (9, 34), (19, 15), (22, 12), (2, 20), (27, 28), (0, 25), (10, 12), (16, 6), (15, 19), (10, 17), (7, 33), (18, 8), (9, 26), (23, 17), (0, 18), (22, 21), (11, 1), (16, 3), (23, 31), (17, 22), (17, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "521280", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 27), (27, 15), (18, 23), (11, 20), (22, 17), (4, 10), (19, 20), (7, 5), (6, 17), (19, 5), (6, 11), (11, 26), (27, 34), (7, 3), (2, 35), (10, 32), (6, 19), (5, 24), (3, 18), (19, 26), (5, 26), (29, 16), (12, 3), (1, 12), (20, 28), (28, 7), (24, 29), (24, 9), (11, 28), (13, 17), (25, 32), (14, 5), (25, 35), (17, 11), (9, 6), (28, 10), (19, 2), (5, 3), (30, 29), (27, 22), (27, 29), (15, 24), (22, 29), (0, 29), (20, 34), (17, 24), (20, 19), (6, 23), (18, 24), (7, 19), (25, 9), (17, 14), (1, 16), (9, 19), (20, 32), (16, 16), (6, 12), (18, 3), (28, 18), (8, 12), (1, 3), (5, 32), (17, 8), (4, 5), (5, 8), (9, 4), (25, 4), (20, 27), (29, 18), (20, 6), (7, 27), (28, 30), (27, 27), (30, 5), (18, 32), (9, 12), (4, 35), (16, 3), (14, 16), (2, 3), (18, 28), (26, 30), (12, 27), (30, 1), (0, 22), (26, 25), (15, 33), (21, 11), (17, 22), (2, 27), (25, 23), (12, 34), (2, 9), (23, 10), (14, 32), (28, 33), (20, 33), (28, 4), (30, 11), (20, 9), (14, 6), (13, 26), (5, 18), (7, 23), (13, 10), (8, 4), (17, 21), (15, 13), (9, 1), (3, 33), (8, 31), (15, 31), (1, 29), (6, 13), (19, 4), (3, 11), (28, 5), (13, 6), (10, 15), (19, 8), (25, 12), (9, 26), (1, 27), (29, 27), (3, 24), (15, 27), (26, 21), (3, 20), (0, 27), (1, 14), (10, 1), (1, 35), (4, 25), (0, 8), (16, 27), (3, 3), (21, 12), (22, 4), (27, 1), (21, 27), (26, 18), (18, 35), (22, 0), (23, 18), (10, 30), (10, 6), (15, 6), (18, 15), (2, 8), (12, 7), (10, 7), (19, 35), (17, 15), (29, 3), (27, 10), (6, 22), (22, 16), (3, 30), (2, 34), (1, 30), (25, 21), (10, 29), (4, 24), (20, 3), (8, 35), (0, 33), (10, 22), (13, 31), (12, 30), (17, 17), (9, 32), (12, 9), (6, 15), (0, 13), (12, 12), (16, 21), (29, 4), (22, 21), (20, 23), (25, 22), (6, 24), (3, 29), (6, 29), (9, 33), (13, 16), (0, 4), (0, 7), (5, 33), (9, 10), (16, 5), (6, 14), (18, 22), (30, 18), (21, 29), (4, 8), (22, 7), (16, 28), (13, 7), (15, 16), (27, 33), (21, 33), (21, 17), (13, 4), (21, 19), (4, 31), (5, 15), (15, 1), (5, 12), (14, 27), (25, 19), (17, 25), (14, 35), (21, 0), (5, 20), (21, 10), (15, 15), (23, 1), (7, 34), (30, 14), (29, 22), (19, 7), (28, 16), (5, 14), (18, 9), (13, 3), (27, 20), (28, 19), (29, 10), (15, 10), (24, 21), (25, 2), (8, 11), (25, 30), (12, 22), (21, 23), (12, 28), (23, 3), (19, 31), (3, 13), (23, 34), (12, 23), (22, 25), (18, 10), (5, 27), (0, 15), (1, 11), (7, 11), (27, 25), (4, 18), (9, 23), (6, 28), (13, 30), (19, 15), (30, 28), (17, 26), (13, 19), (29, 14), (1, 20), (16, 9), (19, 28), (0, 1), (11, 25), (26, 32), (16, 24), (17, 12), (7, 29), (5, 2), (8, 25), (0, 17), (14, 33), (26, 33), (8, 8), (2, 29), (27, 19), (7, 16), (29, 21), (29, 0), (9, 35), (10, 10), (25, 28), (0, 32), (7, 2), (19, 13), (11, 12), (5, 6), (4, 1), (4, 33), (2, 28), (8, 17), (25, 33), (25, 17), (15, 4), (11, 4), (23, 17), (21, 26), (19, 33), (17, 34), (29, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112560", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 19), (2, 3), (10, 26), (21, 10), (20, 8), (10, 0), (23, 3), (12, 30), (26, 0), (6, 16), (32, 30), (26, 4), (30, 33), (2, 6), (31, 12), (12, 31), (32, 15), (25, 35), (11, 34), (22, 4), (31, 29), (19, 9), (8, 14), (12, 25), (19, 32), (21, 7), (21, 11), (21, 17), (11, 5), (22, 33), (30, 20), (6, 26), (6, 34), (30, 26), (3, 4), (19, 16), (4, 8), (1, 12), (3, 2), (23, 15), (9, 4), (16, 11), (28, 27), (5, 0), (2, 19), (7, 20), (18, 35), (7, 18), (22, 30), (16, 3), (4, 34), (3, 32), (14, 5), (4, 15), (33, 29), (31, 5), (29, 12), (15, 18), (3, 0), (12, 3), (1, 6), (8, 8), (15, 2), (24, 2), (22, 12), (25, 7), (4, 21), (33, 13), (2, 26), (31, 16), (32, 32), (19, 5), (30, 22), (9, 7), (27, 8), (22, 17), (7, 12), (14, 35), (5, 22), (11, 30), (19, 29), (10, 19), (15, 23), (23, 22), (26, 25), (13, 30), (2, 32), (17, 0), (24, 12), (13, 0), (28, 10), (7, 11), (14, 17), (20, 30), (17, 18), (19, 1), (1, 29), (24, 16), (28, 23), (14, 30), (28, 32), (25, 34), (28, 29), (20, 7), (5, 12), (2, 27), (14, 4), (30, 11), (3, 9), (20, 25), (5, 2), (10, 17), (29, 30), (31, 27), (22, 11), (28, 1), (7, 16), (23, 24), (27, 15), (12, 29), (3, 12), (5, 28), (0, 14), (30, 3), (27, 5), (11, 0), (30, 30), (26, 19), (7, 0), (9, 21), (13, 33), (4, 28), (7, 33), (24, 9), (18, 25), (24, 35), (7, 23), (13, 4), (20, 34), (28, 28), (5, 26), (21, 32), (23, 19), (11, 29), (14, 24), (28, 34), (15, 15), (12, 6), (26, 24), (22, 0), (11, 13), (16, 6), (17, 12), (24, 18), (23, 35), (6, 20), (16, 34), (0, 9), (24, 23), (8, 35), (33, 25), (25, 8), (0, 24), (6, 29), (13, 8), (23, 2), (3, 11), (17, 4), (20, 26), (18, 16), (15, 5), (16, 9), (11, 14), (23, 9), (22, 15), (2, 25), (29, 10), (11, 12), (5, 32), (12, 33), (31, 15), (9, 26), (26, 33), (5, 35), (11, 28), (30, 27), (31, 10), (15, 7), (1, 7), (26, 3), (6, 15), (13, 23), (4, 2), (20, 0), (15, 1), (10, 32), (5, 4), (0, 23), (3, 33), (29, 8), (0, 32), (16, 14), (28, 3), (19, 35), (1, 34), (12, 17), (1, 9), (1, 4), (28, 22), (29, 15), (7, 22), (8, 20), (23, 5), (11, 3), (8, 16), (31, 20), (6, 33), (27, 19), (23, 8), (29, 22), (13, 7), (30, 23), (9, 23), (1, 24), (20, 21), (11, 21), (24, 32), (13, 26), (13, 11), (31, 6), (33, 14), (10, 4), (22, 13), (15, 34), (0, 27), (6, 23), (19, 8), (15, 26), (25, 26), (4, 10), (2, 17), (0, 1), (29, 23), (21, 28), (9, 31), (4, 3), (12, 14), (9, 22), (15, 10), (5, 30), (7, 15), (5, 18), (6, 31), (17, 22), (29, 4), (2, 13), (30, 6), (27, 30), (3, 21), (29, 34), (27, 6), (33, 22), (31, 33), (16, 26), (2, 31), (22, 6), (28, 11), (25, 25), (32, 26), (13, 21), (1, 18), (9, 30), (18, 4), (28, 7), (20, 11), (0, 22), (21, 22), (13, 10), (12, 24), (3, 18), (24, 34), (18, 3), (7, 28), (25, 19), (28, 21), (15, 27), (23, 31), (10, 27), (5, 21), (27, 13), (33, 15), (14, 21), (21, 19), (22, 9), (11, 17), (27, 7), (4, 29), (18, 7), (31, 7), (24, 30), (2, 4), (14, 32), (28, 0), (19, 28), (12, 16), (19, 0), (2, 34), (8, 4), (11, 10), (11, 19), (9, 29), (32, 21), (29, 9), (16, 28), (16, 25), (19, 12), (19, 10), (11, 24), (32, 2), (26, 7), (13, 27), (27, 0), (20, 4), (29, 24), (22, 34), (3, 34), (6, 14), (6, 21), (14, 19), (26, 28), (0, 3), (30, 32), (3, 26), (16, 20), (15, 24), (30, 8), (32, 25), (26, 2), (29, 2), (32, 3), (17, 13), (25, 2), (30, 24), (32, 13), (15, 17), (11, 4), (25, 23), (22, 1), (8, 5), (14, 16), (2, 21), (19, 15), (5, 29), (31, 4), (10, 34), (6, 13), (18, 0), (23, 32), (10, 10), (10, 25), (21, 4), (27, 20), (30, 16), (18, 15), (1, 22), (8, 28), (25, 15), (6, 12), (6, 18), (9, 6), (30, 0), (28, 17), (1, 25), (10, 13), (19, 17), (32, 22), (32, 12), (26, 29), (22, 32), (20, 20), (3, 22), (16, 2), (29, 31), (26, 20), (22, 24), (26, 23), (14, 3), (24, 4), (14, 33), (13, 19), (17, 30), (11, 22), (30, 2), (3, 10), (29, 26), (3, 27), (30, 14), (28, 2), (27, 3), (0, 13), (7, 31), (7, 14), (25, 11), (26, 27), (28, 15), (29, 18), (23, 23), (20, 5), (28, 4), (23, 14), (7, 7), (5, 17), (22, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "437360", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 5), (28, 22), (38, 7), (31, 18), (26, 20), (10, 35), (7, 12), (4, 33), (33, 13), (1, 14), (4, 11), (21, 15), (21, 20), (21, 34), (27, 15), (1, 11), (24, 25), (33, 33), (34, 6), (29, 12), (23, 19), (29, 13), (4, 0), (5, 5), (6, 23), (23, 4), (36, 20), (15, 9), (19, 6), (31, 17), (30, 7), (33, 29), (7, 6), (21, 36), (5, 1), (19, 20), (8, 14), (9, 14), (24, 20), (21, 30), (20, 34), (28, 14), (35, 24), (17, 22), (32, 32), (22, 24), (24, 7), (18, 0), (6, 14), (11, 7), (28, 20), (1, 12), (23, 36), (31, 15), (37, 29), (18, 5), (13, 33), (11, 24), (16, 34), (25, 23), (19, 12), (27, 19), (20, 29), (9, 31), (2, 23), (38, 32), (5, 7), (9, 11), (2, 7), (2, 13), (35, 31), (4, 21), (0, 11), (2, 11), (34, 31), (31, 7), (37, 17), (7, 33), (4, 14), (0, 37), (30, 28), (37, 22), (0, 22), (18, 10), (8, 9), (16, 9), (36, 8), (25, 19), (14, 37), (38, 23), (15, 20), (4, 20), (13, 30), (3, 13), (1, 17), (25, 4), (4, 24), (0, 15), (6, 7), (12, 5), (36, 7), (23, 34), (14, 2), (38, 11), (34, 28), (3, 29), (34, 7), (11, 27), (32, 26), (5, 22), (29, 16), (14, 6), (24, 10), (37, 1), (29, 21), (11, 6), (31, 35), (29, 1), (32, 8), (34, 22), (26, 23), (17, 13), (24, 9), (0, 18), (9, 29), (31, 32), (4, 31), (36, 5), (33, 15), (36, 1), (18, 17), (15, 33), (4, 26), (34, 2), (26, 6), (18, 11), (34, 11), (3, 17), (27, 29), (22, 12), (18, 3), (38, 0), (25, 7), (25, 24), (18, 23), (19, 4), (12, 11), (7, 3), (22, 15), (9, 17), (10, 12), (21, 13), (22, 6), (3, 15), (5, 29), (11, 15), (34, 37), (24, 27), (32, 31), (23, 30), (11, 3), (27, 2), (34, 26), (17, 16), (30, 16), (14, 3), (38, 15), (28, 6), (19, 7), (29, 11), (11, 30), (7, 4), (31, 1), (26, 1), (8, 34), (27, 30), (26, 15), (25, 33), (31, 2), (29, 34), (25, 6), (15, 24), (18, 27), (5, 13), (10, 5), (20, 15), (38, 34), (2, 17), (11, 13), (8, 36), (14, 11), (12, 12), (31, 19), (10, 27), (15, 1), (30, 14), (21, 29), (21, 6), (4, 7), (2, 14), (19, 17), (34, 5), (11, 23), (1, 25), (15, 13), (36, 36), (3, 35), (38, 20), (24, 5), (33, 3), (36, 34), (2, 3), (10, 19), (37, 36), (28, 21), (8, 2), (29, 4), (32, 2), (0, 30), (26, 17), (3, 4), (18, 22), (37, 32), (3, 6), (25, 8), (37, 26), (31, 9), (6, 19), (9, 0), (10, 25), (35, 35), (22, 23), (34, 33), (24, 18), (17, 12), (30, 34), (29, 30), (3, 22), (38, 22), (34, 17), (14, 32), (28, 0), (1, 30), (5, 6), (37, 34), (6, 18), (34, 18), (23, 33), (13, 28), (19, 25), (22, 19), (3, 11), (8, 28), (2, 22), (11, 1), (18, 7), (35, 26), (5, 30), (27, 11), (25, 21), (0, 27), (9, 4), (5, 37), (10, 11), (24, 6), (10, 36), (4, 22), (21, 23), (15, 34), (17, 23), (15, 25), (24, 30), (6, 9), (8, 19), (30, 32), (34, 27), (13, 37), (29, 32), (18, 19), (24, 29), (3, 20), (32, 3), (13, 18), (37, 4), (12, 22), (33, 30), (34, 25), (8, 35), (33, 8), (22, 32), (16, 3), (34, 13), (13, 3), (33, 27), (12, 2), (20, 1), (4, 13), (24, 24), (8, 11), (35, 21), (27, 17), (38, 3), (36, 25), (32, 4), (25, 25), (1, 4), (8, 31), (13, 12), (28, 27), (15, 4), (16, 26), (0, 5), (34, 14), (5, 27), (24, 17), (35, 30), (36, 10), (22, 26), (18, 2), (16, 28), (32, 33), (25, 18), (27, 31), (37, 14), (1, 6), (34, 23), (24, 19), (10, 1), (14, 13), (26, 0), (24, 37), (21, 31), (20, 7), (29, 37), (14, 5), (18, 35), (10, 21), (33, 11), (23, 3), (30, 4), (20, 16), (19, 11), (3, 5), (1, 3), (20, 0), (7, 30), (37, 8), (4, 12), (4, 2), (32, 25), (22, 0), (12, 24), (15, 31), (0, 23), (3, 31), (38, 1), (31, 8), (3, 25), (22, 8), (14, 25), (38, 2), (21, 25), (27, 18), (31, 25), (26, 19), (12, 35), (24, 1), (8, 24), (21, 18), (13, 25), (0, 28), (16, 37), (17, 6), (22, 18), (5, 9), (5, 24), (7, 16), (9, 7), (22, 2), (19, 19), (23, 31), (23, 1), (26, 30), (35, 19), (33, 1), (13, 15), (25, 30), (7, 17), (17, 29), (28, 25), (11, 2), (1, 28), (21, 5), (35, 1), (34, 30), (33, 20), (36, 29), (9, 6), (35, 33), (10, 28), (14, 20), (3, 9), (28, 15), (14, 23), (24, 8), (30, 0), (17, 2), (2, 2), (1, 16), (11, 16), (37, 20), (8, 15), (15, 8), (16, 32), (27, 13), (32, 0), (24, 12), (30, 10), (21, 28), (23, 9), (38, 30), (34, 34), (3, 37), (33, 16), (1, 34), (21, 21), (31, 12), (16, 2), (33, 25), (6, 20), (2, 15), (12, 33), (20, 37), (31, 5), (30, 11), (33, 12), (15, 6), (10, 9), (38, 26), (26, 9), (22, 30), (17, 33), (27, 3), (17, 4), (18, 16), (0, 13), (31, 16), (0, 7), (26, 14), (28, 4), (22, 36), (26, 7), (32, 28), (15, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "470712", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 33), (8, 16), (25, 2), (5, 12), (12, 5), (9, 15), (13, 25), (20, 18), (8, 20), (15, 14), (12, 1), (24, 3), (25, 20), (26, 32), (10, 26), (18, 18), (7, 2), (12, 35), (33, 6), (10, 33), (27, 29), (25, 10), (20, 30), (20, 36), (16, 29), (29, 8), (17, 15), (22, 16), (3, 1), (15, 12), (0, 21), (13, 14), (15, 15), (31, 12), (15, 34), (29, 33), (24, 25), (8, 23), (22, 21), (17, 35), (26, 31), (11, 5), (19, 8), (7, 26), (1, 12), (19, 14), (8, 3), (0, 30), (8, 4), (7, 14), (9, 16), (31, 15), (7, 35), (21, 8), (19, 33), (26, 27), (33, 28), (7, 10), (19, 34), (28, 27), (32, 24), (25, 35), (12, 34), (4, 36), (14, 3), (1, 23), (20, 11), (13, 5), (24, 31), (22, 26), (12, 24), (8, 19), (2, 23), (4, 29), (29, 19), (3, 14), (30, 28), (7, 36), (31, 29), (24, 10), (9, 14), (26, 23), (5, 25), (7, 8), (32, 15), (17, 31), (26, 11), (27, 9), (6, 12), (31, 7), (20, 9), (7, 23), (20, 21), (1, 33), (1, 20), (27, 8), (15, 2), (18, 29), (13, 32), (22, 8), (24, 4), (25, 13), (20, 23), (12, 23), (17, 11), (26, 2), (22, 28), (16, 26), (20, 2), (26, 6), (12, 19), (10, 11), (6, 31), (29, 6), (19, 29), (5, 33), (1, 1), (9, 22), (16, 5), (28, 10), (6, 14), (8, 0), (16, 28), (1, 24), (7, 17), (13, 18), (30, 15), (5, 29), (33, 19), (27, 32), (14, 11), (27, 21), (2, 2), (21, 23), (7, 12), (24, 19), (17, 10), (2, 19), (7, 13), (0, 6), (20, 34), (10, 19), (12, 29), (2, 6), (0, 11), (24, 28), (32, 1), (20, 32), (30, 17), (4, 16), (18, 24), (19, 21), (24, 9), (4, 19), (2, 10), (10, 27), (26, 4), (21, 1), (8, 1), (11, 28), (20, 8), (26, 35), (21, 32), (12, 12), (4, 14), (11, 21), (13, 3), (25, 30), (3, 22), (24, 27), (16, 35), (7, 15), (17, 3), (29, 13), (17, 1), (5, 8), (0, 9), (32, 23), (23, 5), (27, 27), (27, 25), (1, 35), (7, 3), (31, 18), (11, 6), (12, 7), (12, 8), (27, 15), (18, 20), (1, 16), (31, 34), (24, 22), (33, 32), (19, 11), (14, 10), (7, 16), (24, 26), (3, 20), (15, 31), (22, 14), (30, 16), (25, 17), (29, 20), (29, 32), (31, 14), (14, 4), (13, 20), (6, 26), (25, 18), (16, 9), (3, 8), (23, 10), (20, 3), (25, 26), (5, 23), (26, 34), (13, 15), (22, 7), (7, 20), (15, 28), (28, 5), (30, 29), (13, 16), (6, 36), (26, 30), (17, 24), (19, 1), (11, 7), (23, 23), (10, 10), (24, 29), (5, 6), (27, 36), (4, 15), (11, 13), (26, 14), (8, 11), (30, 12), (4, 32), (13, 24), (12, 22), (5, 21), (32, 10), (1, 11), (32, 8), (5, 11), (32, 21), (23, 15), (1, 26), (23, 6), (30, 25), (21, 16), (17, 14), (21, 7), (9, 11), (24, 24), (29, 35), (0, 12), (14, 19), (16, 33), (7, 32), (28, 33), (26, 28), (1, 29), (33, 18), (10, 15), (29, 30), (33, 10), (5, 17), (22, 22), (28, 9), (29, 24), (11, 17), (24, 16), (32, 6), (33, 26), (8, 32), (5, 35), (6, 3), (12, 15), (29, 23), (1, 3), (31, 10), (31, 2), (4, 17), (25, 4), (2, 5), (29, 3), (11, 2), (23, 16), (31, 21), (10, 16), (25, 11), (31, 4), (21, 36), (26, 16), (18, 15), (25, 3), (19, 6), (27, 3), (23, 22), (3, 32), (15, 7), (2, 34), (22, 25), (16, 13), (16, 7), (30, 33), (12, 16), (1, 27), (8, 24), (14, 32), (23, 1), (10, 36), (6, 24), (8, 9), (15, 22), (27, 14), (9, 13), (0, 4), (26, 29), (11, 30), (14, 22), (13, 1), (27, 12), (18, 30), (24, 30), (11, 35), (15, 17), (21, 29), (4, 24), (3, 26), (28, 2), (18, 28), (18, 33), (7, 7), (3, 25), (25, 33), (26, 21), (17, 20), (3, 16), (4, 35), (5, 4), (3, 34), (32, 36), (12, 3), (2, 30), (28, 21), (18, 13), (20, 1), (23, 13), (25, 15), (0, 16), (0, 10), (5, 30), (25, 28), (10, 9), (19, 17), (31, 13), (26, 7), (11, 26), (32, 0), (18, 2), (3, 36), (7, 9), (19, 22), (15, 25), (15, 36), (29, 2), (2, 9), (7, 18), (14, 20), (18, 27), (31, 16), (18, 21), (5, 7), (30, 0), (24, 0), (13, 23), (6, 34), (21, 6), (19, 4), (27, 19), (17, 32), (17, 9), (17, 4), (24, 35), (33, 14), (15, 23), (5, 26), (23, 0), (0, 15), (12, 33), (21, 26), (23, 21), (28, 26), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "588720", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), 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), (26, 15), (6, 3), (32, 9), (11, 20), (32, 18), (15, 0), (10, 11), (23, 26), (23, 27), (19, 3), (13, 0), (28, 11), (7, 29), (10, 17), (25, 16), (31, 12), (16, 17), (9, 28), (13, 17), (2, 1), (33, 8), (19, 16), (1, 3), (36, 13), (31, 29), (21, 15), (13, 21), (15, 1), (22, 19), (32, 28), (20, 28), (16, 31), (34, 7), (3, 20), (4, 27), (0, 10), (11, 30), (24, 18), (30, 26), (34, 10), (5, 9), (12, 9), (30, 10), (20, 25), (30, 20), (2, 0), (30, 2), (13, 27), (30, 1), (36, 25), (35, 31), (0, 4), (19, 1), (24, 24), (2, 31), (34, 8), (29, 25), (1, 18), (9, 23), (15, 29), (33, 5), (4, 29), (23, 19), (9, 5), (8, 17), (4, 16), (35, 20), (33, 2), (5, 21), (20, 27), (35, 7), (14, 17), (27, 8), (31, 26), (14, 29), (25, 13), (4, 1), (21, 24), (3, 21), (10, 18), (11, 19), (24, 5), (31, 4), (11, 12), (20, 1), (15, 30), (35, 13), (12, 16), (12, 7), (26, 30), (3, 19), (6, 5), (19, 15), (24, 1), (13, 5), (23, 18), (4, 23), (1, 23), (4, 17), (1, 17), (24, 7), (19, 22), (6, 2), (23, 2), (35, 12), (15, 3), (21, 7), (21, 10), (14, 10), (24, 26), (35, 28), (31, 21), (31, 19), (15, 19), (33, 20), (36, 24), (17, 28), (26, 26), (2, 19), (28, 23), (4, 14), (1, 11), (22, 29), (13, 7), (13, 12), (35, 5), (27, 30), (22, 10), (36, 3), (16, 23), (1, 19), (24, 9), (0, 29), (5, 10), (12, 29), (9, 19), (33, 14), (25, 19), (14, 26), (7, 30), (23, 31), (9, 30), (5, 19), (12, 4), (32, 6), (21, 12), (24, 4), (9, 27), (36, 28), (28, 21), (29, 18), (31, 13), (1, 22), (28, 22), (22, 2), (27, 2), (6, 31), (21, 6), (13, 15), (28, 16), (33, 19), (1, 27), (32, 15), (1, 25), (7, 13), (17, 6), (2, 5), (23, 7), (18, 25), (26, 0), (19, 8), (6, 0), (23, 20), (28, 10), (9, 0), (19, 7), (25, 17), (11, 25), (36, 4), (33, 15), (16, 4), (10, 21), (8, 31), (4, 13), (6, 18), (4, 19), (25, 5), (18, 10), (34, 22), (28, 14), (10, 25), (0, 9), (33, 25), (3, 4), (11, 11), (33, 9), (24, 22), (14, 11), (27, 16), (33, 1), (16, 27), (27, 25), (27, 17), (33, 24), (19, 30), (2, 29), (1, 28), (16, 30), (5, 1), (21, 16), (35, 11), (3, 18), (34, 27), (33, 6), (20, 16), (3, 6), (20, 22), (36, 16), (3, 0), (14, 25), (2, 22), (19, 11), (26, 12), (9, 26), (21, 9), (12, 12), (8, 4), (14, 19), (27, 22), (25, 29), (29, 5), (16, 28), (25, 23), (12, 6), (15, 12), (11, 1), (16, 16), (27, 21), (18, 20), (21, 4), (33, 10), (28, 30), (28, 9), (30, 8), (22, 16), (20, 2), (1, 14), (27, 7), (0, 2), (32, 16), (22, 30), (27, 26), (21, 27), (21, 11), (35, 10), (4, 28), (15, 9), (11, 27), (20, 23), (30, 0), (34, 28), (17, 26), (9, 11), (30, 28), (30, 23), (0, 25), (25, 18), (9, 10), (15, 10), (1, 0), (26, 10), (22, 11), (24, 15), (1, 20), (12, 27), (26, 23), (22, 0), (3, 25), (34, 26), (8, 6), (27, 14), (34, 12), (34, 19), (18, 15), (28, 19), (24, 17), (32, 2), (11, 31), (35, 29), (20, 30), (7, 4), (34, 0), (34, 2), (5, 16), (31, 22), (7, 28), (10, 13), (17, 12), (0, 5), (1, 9), (13, 26), (20, 13), (20, 5), (18, 17), (0, 31), (26, 22), (16, 8), (29, 8), (6, 20), (13, 11), (27, 11), (30, 30), (21, 25), (31, 9), (15, 16), (8, 12), (9, 14), (14, 1), (8, 30), (22, 3), (28, 28), (13, 19), (1, 24), (16, 1), (25, 11), (13, 23), (2, 13), (10, 12), (20, 12), (28, 0), (5, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "985608", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), 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), (29, 33), (11, 16), (26, 32), (13, 6), (15, 26), (15, 20), (34, 11), (33, 4), (20, 13), (17, 28), (1, 35), (29, 1), (27, 30), (37, 9), (6, 29), (2, 27), (5, 20), (1, 31), (9, 23), (25, 11), (14, 29), (3, 6), (30, 15), (28, 21), (12, 2), (36, 28), (7, 17), (15, 13), (30, 14), (10, 25), (14, 27), (36, 7), (27, 21), (31, 20), (12, 10), (25, 8), (4, 6), (28, 2), (29, 12), (14, 22), (11, 25), (23, 25), (28, 19), (35, 5), (31, 19), (13, 34), (1, 2), (28, 17), (3, 5), (20, 18), (14, 24), (37, 6), (14, 16), (17, 20), (25, 13), (8, 31), (15, 14), (15, 7), (30, 24), (29, 19), (21, 17), (20, 10), (23, 27), (1, 30), (10, 32), (30, 13), (33, 29), (19, 10), (16, 22), (27, 22), (25, 29), (18, 19), (21, 23), (23, 3), (1, 11), (12, 5), (18, 15), (9, 17), (9, 16), (19, 27), (33, 18), (24, 30), (27, 26), (5, 27), (36, 8), (26, 2), (9, 9), (23, 12), (12, 28), (18, 27), (29, 2), (22, 24), (7, 3), (2, 8), (35, 10), (6, 7), (2, 17), (28, 1), (15, 31), (30, 35), (23, 33), (14, 1), (36, 32), (14, 33), (32, 28), (5, 13), (8, 8), (2, 22), (27, 14), (23, 26), (33, 24), (29, 25), (28, 25), (19, 30), (22, 7), (32, 12), (24, 3), (27, 11), (0, 13), (2, 20), (3, 28), (20, 9), (17, 9), (32, 27), (14, 17), (6, 10), (16, 3), (1, 7), (31, 34), (34, 4), (9, 3), (18, 30), (4, 0), (3, 27), (36, 13), (27, 9), (26, 29), (23, 22), (19, 7), (14, 15), (36, 33), (30, 30), (10, 28), (11, 29), (25, 22), (35, 28), (12, 1), (14, 14), (26, 3), (21, 8), (25, 27), (34, 13), (19, 6), (3, 2), (13, 1), (29, 15), (10, 14), (9, 31), (2, 12), (20, 28), (8, 5), (28, 4), (17, 19), (37, 29), (2, 16), (35, 19), (5, 22), (14, 25), (14, 35), (37, 28), (17, 8), (11, 12), (2, 21), (37, 20), (9, 25), (8, 4), (19, 24), (12, 25), (13, 10), (1, 3), (8, 3), (34, 12), (18, 21), (30, 22), (13, 24), (36, 6), (4, 22), (23, 6), (35, 33), (20, 6), (5, 16), (22, 18), (3, 15), (24, 2), (35, 8), (30, 0), (32, 30), (29, 20), (29, 27), (4, 20), (9, 21), (9, 6), (5, 11), (5, 12), (35, 18), (6, 25), (30, 1), (33, 7), (18, 24), (24, 11), (3, 8), (25, 15), (29, 18), (25, 23), (14, 3), (33, 2), (10, 4), (15, 28), (37, 34), (36, 25), (5, 24), (21, 30), (7, 32), (4, 19), (32, 29), (9, 7), (30, 20), (24, 29), (5, 23), (9, 1), (15, 22), (5, 3), (10, 1), (25, 25), (13, 0), (26, 27), (2, 35), (17, 7), (24, 9), (18, 17), (21, 25), (22, 20), (36, 29), (37, 21), (13, 8), (32, 13), (14, 9), (6, 33), (13, 22), (37, 8), (14, 8), (19, 20), (4, 29), (31, 9), (2, 7), (5, 29), (25, 32), (31, 14), (2, 9), (0, 30), (23, 35), (22, 6), (7, 23), (25, 35), (36, 15), (29, 16), (7, 16), (6, 6), (15, 23), (15, 8), (36, 30), (16, 4), (3, 9), (23, 17), (2, 19), (10, 2), (29, 4), (0, 23), (4, 16), (32, 19), (31, 30), (17, 5), (30, 21), (7, 24), (35, 24), (31, 15), (1, 4), (22, 17), (32, 3), (4, 25), (14, 5), (10, 29), (32, 25), (24, 4), (29, 10), (23, 34), (13, 28), (16, 9), (16, 7), (30, 34), (32, 7), (26, 22), (24, 8), (19, 32), (33, 8), (5, 25), (33, 28), (31, 33), (3, 12), (21, 5), (31, 8), (31, 35), (8, 32), (8, 26), (26, 25), (0, 4), (6, 9), (30, 10), (0, 29), (27, 1), (12, 26), (32, 0), (29, 32), (20, 30), (36, 11), (31, 0), (36, 22), (18, 14), (8, 24), (28, 9), (34, 0), (30, 4), (26, 26), (23, 21), (8, 16), (26, 17), (19, 16), (4, 9), (24, 22), (33, 26), (20, 22), (11, 26), (14, 34), (28, 5), (14, 7), (5, 14), (28, 22), (12, 12), (34, 22), (19, 5), (18, 25), (20, 7), (6, 22), (32, 20), (28, 24), (33, 3), (30, 28), (16, 34), (36, 17), (31, 22), (25, 31), (18, 16), (25, 18), (1, 16), (13, 20), (27, 8), (31, 4), (31, 25), (7, 12), (27, 12), (20, 23), (11, 19), (37, 2), (22, 9), (9, 0), (2, 24), (29, 5), (23, 18), (2, 26), (0, 15), (12, 6), (13, 25), (15, 24), (1, 23), (0, 17), (32, 21), (21, 32), (1, 17), (2, 2), (6, 31), (23, 29), (28, 27), (6, 20), (21, 19), (24, 10), (19, 2), (16, 1), (7, 10), (35, 13), (34, 29), (22, 19), (15, 3), (24, 33), (28, 26), (19, 23), (2, 1), (31, 12), (14, 12), (0, 18), (7, 19), (34, 17), (1, 28), (28, 34), (5, 8), (35, 3), (11, 15), (10, 24), (8, 25), (24, 31), (4, 18), (37, 13), (0, 12), (10, 22), (37, 0), (16, 18), (20, 14), (26, 0), (14, 32), (35, 1), (10, 12), (13, 4), (19, 17), (31, 10), (34, 16), (25, 14), (32, 2), (0, 14), (8, 15), (0, 16), (1, 18), (32, 11), (21, 31), (28, 14), (26, 30), (17, 35), (5, 19), (34, 2), (21, 26), (24, 5), (13, 19), (21, 12), (7, 1), (8, 17), (8, 28), (0, 10), (19, 14), (5, 30), (3, 23), (20, 5), (24, 0), (33, 10), (34, 23), (1, 33), (28, 20), (28, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284400", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 29), (22, 0), (23, 25), (28, 17), (14, 9), (18, 20), (18, 11), (1, 21), (21, 8), (14, 1), (2, 9), (11, 23), (23, 28), (13, 18), (15, 28), (24, 28), (12, 15), (24, 13), (7, 18), (1, 28), (6, 11), (30, 23), (13, 27), (20, 19), (17, 0), (5, 9), (10, 3), (5, 16), (20, 21), (1, 8), (19, 5), (8, 27), (25, 27), (3, 19), (20, 23), (25, 15), (3, 3), (22, 22), (30, 9), (23, 1), (9, 15), (4, 22), (8, 25), (4, 14), (13, 28), (31, 3), (29, 2), (0, 10), (7, 6), (22, 16), (10, 20), (24, 19), (28, 26), (11, 16), (11, 6), (15, 14), (29, 5), (12, 3), (18, 17), (26, 22), (22, 3), (4, 19), (7, 3), (31, 2), (2, 21), (23, 19), (29, 13), (30, 12), (9, 25), (27, 10), (21, 21), (18, 2), (0, 2), (29, 27), (25, 5), (0, 24), (14, 12), (17, 3), (7, 15), (7, 22), (16, 15), (3, 14), (13, 7), (23, 29), (16, 0), (15, 8), (21, 0), (0, 28), (16, 17), (15, 29), (7, 11), (20, 9), (3, 9), (6, 7), (6, 19), (27, 23), (28, 19), (5, 26), (11, 15), (12, 4), (6, 25), (18, 28), (18, 13), (22, 10), (2, 29), (25, 25), (27, 27), (28, 5), (29, 29), (6, 1), (30, 25), (1, 10), (7, 5), (4, 7), (4, 1), (18, 6), (30, 7), (17, 5), (5, 17), (11, 22), (11, 14), (26, 15), (30, 21), (16, 1), (8, 28), (29, 22), (2, 2), (11, 4), (1, 18), (25, 24), (9, 8), (0, 22), (27, 19), (2, 25), (25, 20), (6, 21), (6, 24), (28, 22), (9, 23), (19, 29), (14, 6), (0, 27), (26, 2), (25, 10), (15, 12), (11, 26), (28, 7), (26, 27), (11, 7), (9, 10), (8, 23), (25, 8), (17, 7), (19, 4), (15, 15), (1, 16), (16, 16), (30, 13), (26, 24), (7, 21), (7, 14), (20, 20), (31, 10), (3, 8), (17, 13), (11, 5), (15, 22), (17, 16), (28, 6), (7, 26), (27, 25), (29, 15), (1, 13), (11, 19), (2, 1), (29, 3), (2, 14), (17, 8), (25, 13), (29, 25), (1, 24), (15, 5), (1, 29), (4, 29), (24, 10), (3, 27), (22, 12), (24, 7), (29, 17), (14, 21), (16, 13), (5, 22), (17, 11), (28, 0), (1, 20), (18, 27), (19, 25), (0, 25), (13, 19), (27, 14), (0, 17), (26, 11), (20, 13), (22, 21), (18, 3), (7, 20), (12, 18), (27, 28), (6, 22), (11, 0), (19, 8), (9, 22), (15, 26), (2, 5), (14, 24), (21, 14), (2, 7), (0, 16), (22, 2), (26, 0), (27, 8), (17, 1), (22, 20), (17, 9), (21, 12), (5, 6), (17, 24), (22, 4), (23, 20), (17, 21), (3, 15), (8, 12), (4, 16), (28, 18), (10, 18), (16, 10), (19, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507348", "dataset": "MATH"}
{"messages": [{"content": "In a 39x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 30), (2, 26), (1, 2), (29, 12), (5, 18), (5, 0), (0, 19), (13, 14), (7, 23), (37, 28), (0, 24), (21, 2), (0, 22), (35, 10), (16, 11), (3, 27), (17, 11), (23, 19), (14, 26), (36, 25), (4, 0), (23, 23), (9, 22), (29, 5), (22, 22), (11, 5), (10, 15), (12, 13), (24, 19), (19, 25), (27, 17), (9, 20), (22, 32), (31, 22), (30, 10), (7, 2), (32, 18), (9, 25), (11, 35), (3, 2), (19, 12), (15, 6), (22, 4), (0, 21), (30, 33), (4, 19), (13, 8), (14, 3), (14, 4), (19, 0), (28, 3), (37, 27), (19, 29), (7, 32), (32, 30), (34, 16), (38, 19), (19, 26), (38, 4), (26, 27), (19, 2), (29, 22), (26, 6), (6, 24), (26, 22), (14, 20), (29, 25), (4, 6), (16, 15), (17, 8), (36, 6), (8, 17), (33, 1), (24, 32), (10, 22), (30, 15), (27, 20), (35, 4), (21, 27), (15, 25), (3, 4), (12, 15), (8, 3), (8, 28), (15, 18), (32, 12), (32, 28), (16, 21), (20, 11), (4, 29), (14, 23), (2, 21), (23, 27), (38, 32), (28, 27), (34, 12), (20, 13), (1, 26), (18, 31), (32, 26), (15, 9), (33, 23), (4, 1), (4, 21), (5, 32), (21, 13), (22, 19), (31, 34), (5, 1), (26, 2), (22, 8), (8, 12), (33, 25), (1, 31), (23, 24), (38, 16), (6, 32), (32, 16), (3, 28), (33, 7), (6, 31), (24, 10), (35, 16), (13, 23), (20, 19), (18, 25), (4, 3), (32, 20), (8, 24), (4, 20), (10, 4), (35, 29), (37, 30), (2, 20), (32, 32), (7, 5), (16, 19), (12, 23), (25, 1), (36, 15), (38, 23), (34, 29), (8, 0), (20, 29), (23, 17), (35, 24), (23, 12), (4, 30), (13, 9), (31, 13), (6, 22), (0, 35), (25, 4), (15, 20), (8, 1), (35, 34), (9, 32), (8, 14), (22, 3), (5, 27), (0, 29), (12, 10), (32, 6), (17, 28), (9, 9), (9, 8), (10, 21), (1, 10), (15, 12), (18, 7), (4, 32), (9, 2), (24, 2), (37, 11), (8, 7), (15, 28), (27, 6), (19, 32), (26, 31), (36, 14), (31, 32), (28, 21), (22, 10), (23, 2), (22, 35), (19, 27), (36, 11), (30, 13), (11, 31), (7, 8), (38, 25), (35, 2), (33, 6), (36, 13), (23, 8), (38, 33), (16, 32), (7, 30), (16, 22), (29, 18), (2, 15), (23, 29), (19, 3), (36, 24), (32, 7), (11, 11), (13, 7), (5, 14), (35, 14), (28, 20), (7, 1), (29, 19), (15, 31), (25, 0), (5, 5), (36, 0), (19, 23), (11, 23), (19, 15), (37, 3), (32, 24), (15, 33), (16, 23), (8, 23), (35, 32), (36, 10), (2, 2), (19, 6), (6, 17), (14, 15), (27, 10), (38, 12), (20, 25), (19, 20), (36, 3), (13, 21), (22, 15), (11, 34), (36, 20), (32, 29), (28, 30), (12, 28), (5, 10), (30, 3), (32, 35), (37, 19), (22, 31), (23, 3), (6, 6), (27, 28), (34, 19), (6, 15), (31, 29), (3, 17), (15, 32), (20, 23), (4, 18), (18, 24), (0, 34), (30, 30), (34, 22), (29, 2), (38, 22), (34, 20), (2, 16), (12, 1), (15, 14), (20, 2), (30, 35), (11, 25), (6, 18), (13, 25), (30, 25), (1, 16), (23, 10), (21, 4), (16, 20), (12, 24), (34, 10), (9, 17), (37, 23), (35, 5), (4, 31), (23, 18), (29, 15), (26, 29), (12, 16), (7, 31), (0, 26), (31, 2), (0, 15), (8, 9), (3, 20), (37, 2), (20, 6), (15, 11), (12, 2), (7, 0), (0, 30), (31, 0), (28, 16), (27, 2), (36, 23), (10, 27), (22, 30), (0, 4), (19, 21), (14, 9), (18, 20), (36, 7), (27, 23), (34, 1), (4, 5), (9, 31), (33, 32), (22, 34), (32, 33), (6, 28), (23, 28), (27, 5), (15, 7), (2, 25), (13, 34), (33, 35), (12, 22), (21, 23), (0, 28), (10, 8), (12, 21), (12, 32), (35, 0), (26, 11), (24, 6), (34, 0), (37, 35), (11, 29), (28, 5), (17, 7), (2, 3), (11, 24), (14, 30), (27, 16), (37, 10), (9, 18), (18, 11), (38, 3), (28, 9), (11, 21), (9, 11), (14, 11), (10, 9), (1, 18), (6, 35), (12, 33), (27, 15), (18, 18), (34, 6), (7, 28), (0, 5), (38, 31), (27, 25), (14, 25), (32, 19), (24, 0), (33, 27), (11, 1), (14, 31), (37, 9), (25, 27), (18, 0), (32, 21), (19, 17), (26, 7), (36, 30), (1, 29), (31, 4), (2, 11), (20, 9), (25, 22), (8, 35), (24, 24), (1, 27), (28, 14), (30, 23), (33, 12), (1, 19), (29, 16), (33, 34), (37, 21), (17, 31), (32, 14), (22, 33), (13, 13), (28, 28), (17, 1), (10, 0), (35, 28), (26, 26), (3, 6), (23, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "970200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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), (21, 8), (9, 33), (29, 16), (20, 11), (16, 19), (28, 4), (0, 28), (25, 20), (3, 27), (2, 27), (20, 22), (0, 34), (13, 3), (12, 24), (9, 19), (6, 24), (28, 33), (0, 5), (23, 2), (21, 19), (20, 10), (2, 22), (24, 27), (20, 19), (16, 1), (22, 23), (4, 30), (8, 5), (18, 9), (17, 16), (14, 22), (8, 2), (11, 19), (25, 15), (16, 29), (3, 2), (5, 22), (29, 28), (14, 27), (8, 17), (28, 27), (12, 2), (26, 10), (7, 0), (11, 22), (11, 15), (13, 30), (6, 13), (17, 8), (25, 22), (12, 29), (21, 7), (15, 26), (15, 1), (29, 7), (6, 5), (6, 23), (9, 25), (12, 31), (27, 0), (18, 24), (11, 18), (11, 27), (7, 5), (20, 27), (3, 5), (20, 25), (29, 5), (2, 16), (17, 28), (3, 11), (28, 19), (5, 15), (16, 18), (17, 9), (9, 2), (10, 17), (29, 12), (19, 23), (9, 0), (8, 18), (22, 3), (4, 6), (24, 10), (29, 18), (11, 17), (12, 8), (22, 22), (0, 14), (6, 18), (25, 34), (17, 12), (29, 1), (19, 8), (0, 20), (28, 32), (18, 34), (8, 7), (22, 20), (2, 30), (22, 6), (23, 17), (16, 33), (8, 27), (21, 23), (23, 10), (21, 0), (27, 27), (11, 9), (1, 8), (16, 32), (12, 23), (1, 6), (1, 28), (17, 30), (14, 4), (27, 13), (16, 27), (3, 1), (19, 31), (21, 33), (13, 12), (12, 1), (7, 3), (14, 2), (0, 12), (22, 15), (11, 13), (10, 27), (26, 4), (4, 20), (10, 3), (20, 23), (26, 1), (6, 9), (9, 18), (27, 20), (15, 14), (16, 11), (20, 31), (4, 27), (18, 16), (5, 6), (5, 3), (3, 4), (5, 30), (6, 16), (18, 2), (26, 26), (28, 5), (16, 21), (26, 28), (5, 17), (5, 24), (21, 25), (27, 14), (24, 13), (19, 26), (27, 22), (28, 7), (18, 12), (15, 24), (21, 12), (18, 14), (25, 27), (10, 21), (9, 11), (8, 19), (12, 19), (12, 20), (15, 27), (23, 4), (26, 33), (17, 22), (14, 23), (0, 33), (9, 24), (1, 33), (3, 24), (0, 27), (8, 10), (24, 3), (4, 0), (17, 15), (9, 16), (15, 20), (21, 24), (25, 0), (17, 29), (4, 12), (3, 7), (6, 28), (13, 20), (27, 28), (14, 14), (3, 18), (19, 14), (13, 27), (2, 14), (7, 34), (3, 33), (16, 14), (20, 15), (1, 14), (0, 29), (11, 31), (22, 29), (6, 30), (5, 21), (20, 33), (12, 0), (27, 31), (18, 32), (29, 26), (8, 3), (9, 22), (9, 15), (27, 24), (4, 8), (5, 1), (19, 21), (7, 26), (5, 2), (24, 29), (14, 1), (29, 8), (0, 23), (11, 6), (10, 13), (18, 31), (14, 29), (28, 11), (26, 29), (19, 15), (11, 12), (1, 15), (27, 32), (29, 13), (17, 1), (27, 25), (21, 29), (25, 12), (12, 26), (22, 11), (17, 19), (5, 13), (6, 34), (23, 20), (2, 28), (0, 8), (17, 7), (7, 29), (19, 12), (20, 8), (10, 30), (2, 4), (14, 20), (17, 33), (12, 9), (28, 8), (10, 9), (3, 9), (7, 17), (1, 20), (26, 17), (8, 15), (23, 33), (25, 17), (16, 10), (12, 16), (29, 2), (28, 28), (22, 0), (29, 27), (29, 20), (21, 2), (24, 28), (8, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "729400", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 18), (7, 3), (11, 0), (3, 23), (13, 19), (4, 22), (31, 0), (27, 17), (1, 30), (14, 1), (6, 1), (30, 0), (15, 4), (23, 31), (19, 12), (15, 30), (0, 17), (20, 20), (2, 23), (6, 23), (11, 27), (18, 19), (25, 3), (26, 19), (13, 20), (24, 23), (14, 5), (11, 5), (25, 12), (10, 28), (26, 21), (9, 23), (27, 4), (20, 10), (25, 14), (4, 23), (1, 20), (4, 4), (22, 22), (5, 20), (9, 5), (32, 6), (14, 6), (4, 8), (24, 26), (17, 14), (30, 15), (8, 0), (21, 26), (30, 30), (17, 5), (20, 2), (28, 31), (10, 0), (23, 8), (16, 26), (27, 31), (1, 24), (28, 4), (22, 25), (15, 25), (15, 18), (24, 30), (26, 6), (30, 12), (6, 16), (6, 20), (28, 11), (11, 7), (1, 17), (24, 5), (19, 10), (29, 7), (31, 27), (33, 5), (31, 28), (26, 24), (18, 28), (11, 10), (23, 21), (28, 22), (6, 31), (14, 30), (11, 29), (0, 30), (12, 25), (2, 12), (18, 14), (21, 21), (27, 23), (31, 4), (18, 5), (10, 3), (4, 7), (10, 15), (10, 21), (10, 20), (9, 2), (8, 9), (30, 19), (5, 30), (28, 0), (22, 24), (19, 4), (27, 25), (29, 0), (33, 16), (11, 31), (16, 8), (24, 6), (9, 17), (4, 24), (12, 12), (4, 6), (22, 1), (15, 31), (3, 22), (5, 19), (21, 29), (31, 21), (9, 16), (19, 8), (14, 15), (10, 7), (12, 24), (6, 17), (24, 13), (0, 20), (18, 21), (3, 20), (29, 1), (17, 27), (6, 5), (2, 18), (14, 24), (19, 3), (9, 22), (19, 11), (23, 19), (31, 20), (24, 15), (19, 0), (31, 5), (29, 8), (2, 31), (18, 22), (2, 14), (10, 30), (10, 26), (21, 14), (32, 22), (8, 11), (8, 23), (8, 1), (19, 13), (9, 20), (12, 11), (31, 7), (23, 10), (29, 14), (5, 3), (24, 24), (3, 27), (13, 14), (27, 21), (0, 4), (28, 10), (15, 20), (4, 12), (5, 23), (11, 9), (22, 26), (17, 15), (23, 16), (3, 10), (20, 26), (24, 4), (0, 1), (9, 25), (24, 8), (32, 19), (8, 14), (26, 9), (8, 13), (20, 13), (0, 10), (5, 11), (2, 6), (17, 8), (31, 14), (2, 7), (24, 29), (2, 22), (10, 24), (31, 1), (17, 16), (18, 17), (19, 21), (7, 25), (2, 11), (29, 22), (18, 29), (13, 9), (6, 2), (21, 17), (29, 15), (20, 1), (5, 14), (4, 3), (23, 12), (8, 7), (31, 19), (30, 24), (24, 14), (32, 1), (3, 31), (5, 8), (33, 9), (31, 22), (33, 15), (28, 1), (24, 27), (13, 31), (8, 19), (22, 16), (27, 15), (3, 5), (13, 29), (26, 15), (2, 5), (6, 21), (26, 8), (28, 25), (26, 27), (19, 5), (22, 20), (19, 2), (33, 26), (6, 9), (0, 3), (23, 9), (15, 7), (26, 4), (8, 25), (23, 27), (23, 23), (3, 30), (17, 29), (17, 28), (13, 8), (33, 17), (29, 10), (15, 1), (29, 27), (6, 10), (10, 19), (25, 20), (2, 2), (32, 30), (33, 7), (4, 26), (16, 10), (26, 5), (4, 1), (15, 0), (23, 25), (0, 21), (17, 0), (26, 0), (7, 13), (16, 28), (31, 13), (16, 20), (12, 13), (33, 24), (32, 14), (12, 4), (29, 3), (9, 31), (33, 1), (33, 19), (27, 10), (5, 26), (5, 1), (1, 14), (31, 9), (15, 14), (2, 4), (32, 16), (13, 0), (22, 5), (31, 2), (6, 4), (21, 28), (17, 2), (17, 30), (24, 18), (20, 19), (24, 7), (10, 10), (5, 4), (32, 29), (31, 10), (24, 9), (32, 8), (6, 11), (29, 23), (21, 13), (16, 14), (31, 6), (28, 24), (16, 5), (11, 2), (26, 26), (27, 27), (8, 10), (33, 28), (14, 12), (13, 15), (30, 14), (10, 31), (29, 26), (22, 12), (16, 29), (25, 26), (15, 12), (30, 8), (11, 11), (19, 23), (9, 6), (0, 16), (27, 5), (33, 25), (33, 30), (20, 16), (6, 14), (13, 27), (2, 29), (28, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "811620", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), 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, 2), (6, 9), (26, 17), (4, 3), (22, 28), (30, 21), (3, 10), (33, 8), (13, 6), (16, 3), (6, 4), (27, 26), (19, 23), (6, 18), (17, 25), (7, 21), (5, 22), (0, 1), (29, 6), (12, 1), (31, 8), (7, 18), (16, 25), (29, 18), (16, 23), (12, 6), (1, 12), (24, 5), (26, 22), (2, 23), (3, 0), (17, 14), (32, 19), (24, 18), (1, 16), (12, 16), (4, 10), (3, 1), (29, 1), (27, 29), (26, 1), (14, 17), (12, 10), (15, 0), (27, 18), (23, 3), (15, 24), (10, 5), (15, 13), (0, 3), (24, 6), (9, 9), (21, 10), (6, 14), (28, 3), (10, 13), (30, 6), (22, 8), (7, 7), (11, 26), (15, 18), (29, 12), (9, 1), (33, 26), (13, 26), (0, 25), (25, 24), (33, 13), (7, 5), (8, 26), (33, 9), (10, 1), (27, 12), (7, 16), (10, 28), (24, 17), (24, 21), (15, 28), (24, 23), (31, 9), (22, 24), (12, 7), (31, 18), (13, 20), (7, 10), (9, 5), (14, 21), (8, 7), (22, 19), (33, 24), (6, 10), (21, 2), (23, 25), (13, 9), (30, 12), (24, 4), (2, 9), (2, 25), (12, 25), (11, 28), (1, 25), (27, 13), (11, 2), (30, 17), (19, 18), (17, 13), (21, 15), (0, 18), (4, 26), (30, 27), (4, 14), (9, 13), (17, 21), (21, 12), (27, 2), (23, 7), (28, 25), (33, 11), (14, 7), (28, 29), (14, 8), (15, 6), (19, 7), (21, 25), (10, 3), (16, 22), (9, 22), (33, 22), (24, 3), (22, 14), (1, 28), (8, 0), (8, 28), (21, 17), (31, 25), (33, 20), (7, 13), (3, 12), (27, 9), (9, 15), (6, 17), (15, 12), (0, 20), (29, 8), (23, 18), (25, 23), (22, 5), (28, 26), (31, 6), (26, 3), (7, 4), (30, 14), (15, 8), (12, 14), (32, 18), (28, 22), (13, 1), (5, 26), (14, 27), (19, 20), (8, 2), (7, 15), (17, 0), (15, 26), (30, 15), (27, 28), (14, 25), (5, 15), (23, 9), (17, 26), (27, 19), (9, 6), (25, 16), (0, 23), (20, 4), (32, 8), (17, 3), (26, 20), (16, 6), (29, 13), (14, 29), (17, 23), (20, 2), (26, 11), (16, 9), (5, 29), (0, 10), (27, 17), (8, 5), (33, 17), (11, 7), (21, 23), (19, 11), (1, 10), (2, 15), (29, 22), (27, 3), (8, 19), (30, 19), (6, 11), (22, 9), (8, 18), (11, 16), (4, 4), (4, 16), (33, 28), (28, 14), (25, 13), (32, 12), (17, 2), (4, 15), (29, 0), (24, 10), (11, 3), (2, 28), (2, 8), (18, 7), (14, 11), (30, 18), (27, 25), (26, 5), (4, 22), (3, 25), (12, 21), (10, 21), (21, 0), (17, 29), (14, 4), (2, 13), (4, 1), (23, 22), (9, 19), (25, 27), (23, 16), (32, 13), (24, 11), (11, 21), (28, 4), (11, 13), (15, 21), (26, 19), (1, 5), (18, 26), (0, 6), (20, 0), (5, 12), (28, 18), (30, 23), (13, 8), (25, 5), (13, 15), (4, 24), (10, 22), (14, 14), (14, 3), (20, 25), (1, 15), (11, 1), (9, 11), (6, 28), (26, 27), (23, 28), (30, 11), (25, 1), (25, 4), (16, 15), (12, 17), (3, 26), (5, 0), (12, 3), (28, 27), (31, 12), (11, 4), (4, 11), (16, 14), (18, 10), (27, 5), (14, 15), (32, 22), (11, 0), (22, 17), (6, 25), (10, 25), (19, 14), (18, 14), (32, 11), (5, 1), (28, 10), (31, 3), (3, 23), (4, 19), (28, 1), (21, 14), (26, 23), (20, 22), (3, 19), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "825792", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 24), (20, 22), (6, 22), (9, 7), (25, 13), (15, 11), (0, 12), (1, 4), (27, 3), (13, 15), (36, 7), (2, 6), (9, 1), (25, 5), (32, 7), (32, 24), (10, 2), (19, 23), (8, 4), (13, 22), (2, 10), (15, 9), (1, 11), (7, 14), (5, 30), (15, 10), (16, 2), (5, 23), (11, 21), (5, 16), (13, 25), (25, 3), (6, 2), (9, 30), (33, 15), (36, 3), (29, 6), (10, 27), (4, 17), (2, 20), (10, 16), (3, 8), (32, 25), (21, 19), (24, 11), (36, 22), (30, 30), (29, 22), (14, 22), (7, 21), (23, 28), (2, 0), (27, 6), (35, 24), (35, 1), (23, 10), (24, 14), (7, 25), (32, 9), (26, 21), (4, 24), (17, 11), (24, 8), (8, 16), (31, 18), (30, 26), (5, 8), (9, 22), (11, 17), (17, 15), (1, 29), (15, 26), (16, 29), (16, 23), (8, 26), (21, 13), (25, 11), (26, 8), (5, 20), (0, 13), (21, 30), (5, 3), (13, 13), (8, 3), (19, 8), (32, 1), (7, 18), (34, 25), (7, 9), (31, 14), (7, 11), (22, 23), (16, 11), (35, 23), (16, 15), (15, 13), (29, 19), (9, 12), (34, 0), (18, 14), (26, 24), (35, 10), (11, 15), (14, 0), (12, 20), (22, 24), (21, 5), (29, 25), (33, 9), (21, 4), (17, 4), (24, 0), (18, 6), (29, 3), (20, 2), (10, 23), (36, 0), (27, 9), (31, 29), (7, 12), (24, 25), (2, 21), (0, 6), (0, 19), (16, 22), (19, 19), (10, 6), (21, 7), (12, 12), (13, 24), (18, 10), (2, 28), (12, 25), (29, 15), (3, 26), (7, 2), (28, 27), (15, 19), (29, 28), (15, 23), (35, 14), (16, 24), (15, 30), (3, 23), (0, 14), (23, 20), (32, 19), (11, 14), (19, 15), (27, 24), (28, 19), (4, 25), (29, 11), (11, 29), (31, 2), (34, 2), (31, 8), (4, 0), (30, 12), (11, 18), (27, 7), (27, 16), (11, 11), (7, 0), (29, 12), (17, 13), (1, 8), (13, 18), (23, 16), (18, 9), (19, 12), (34, 20), (30, 19), (30, 3), (2, 24), (20, 10), (14, 26), (34, 4), (21, 9), (32, 21), (28, 23), (3, 24), (3, 14), (11, 16), (1, 21), (31, 19), (5, 25), (0, 15), (20, 26), (6, 3), (27, 0), (1, 23), (14, 8), (19, 13), (13, 27), (21, 11), (25, 18), (30, 7), (34, 29), (12, 7), (14, 15), (18, 27), (35, 13), (28, 8), (32, 30), (16, 6), (19, 0), (3, 19), (10, 4), (2, 7), (32, 0), (10, 7), (30, 20), (18, 30), (20, 5), (13, 19), (12, 14), (36, 29), (34, 27), (15, 25), (12, 27), (23, 14), (6, 11), (2, 30), (28, 24), (25, 24), (4, 3), (28, 2), (13, 0), (29, 23), (4, 9), (24, 28), (14, 9), (3, 9), (25, 20), (14, 5), (36, 18), (18, 20), (21, 18), (6, 28), (17, 5), (21, 25), (12, 5), (15, 4), (30, 15), (8, 25), (8, 10), (32, 5), (17, 24), (11, 20), (0, 9), (30, 28), (0, 20), (24, 23), (30, 14), (4, 4), (29, 17), (21, 21), (30, 9), (3, 25), (22, 25), (2, 1), (21, 3), (23, 4), (15, 16), (15, 29), (8, 9), (7, 20), (24, 29), (25, 30), (22, 5), (28, 11), (0, 5), (0, 18), (29, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254520", "dataset": "MATH"}
{"messages": [{"content": "In a 33x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 28), (8, 19), (20, 1), (6, 4), (10, 15), (20, 6), (17, 31), (11, 3), (25, 28), (12, 18), (22, 26), (6, 16), (27, 30), (17, 4), (31, 10), (26, 21), (12, 16), (9, 23), (7, 27), (20, 2), (7, 30), (15, 31), (4, 30), (20, 30), (13, 7), (11, 4), (14, 16), (12, 1), (19, 22), (22, 2), (28, 22), (26, 9), (8, 18), (2, 5), (20, 31), (31, 3), (26, 25), (7, 32), (17, 2), (24, 26), (13, 30), (24, 7), (22, 28), (15, 8), (7, 17), (7, 0), (2, 21), (26, 10), (22, 20), (2, 16), (22, 25), (17, 23), (20, 5), (2, 30), (28, 17), (28, 20), (28, 4), (16, 23), (28, 15), (20, 3), (30, 17), (24, 21), (11, 24), (13, 17), (10, 27), (10, 3), (20, 21), (23, 18), (10, 31), (2, 8), (28, 28), (18, 8), (32, 26), (9, 5), (18, 29), (29, 28), (7, 19), (25, 1), (30, 20), (24, 12), (30, 18), (5, 8), (22, 12), (17, 32), (19, 5), (6, 27), (11, 12), (12, 8), (16, 2), (4, 13), (29, 21), (23, 29), (18, 18), (31, 4), (4, 18), (24, 19), (14, 22), (26, 18), (5, 23), (28, 11), (5, 1), (28, 3), (23, 20), (18, 2), (14, 13), (4, 1), (12, 29), (17, 9), (15, 7), (31, 17), (14, 14), (31, 6), (23, 2), (9, 3), (11, 15), (4, 4), (24, 25), (32, 17), (7, 20), (15, 12), (2, 24), (8, 27), (8, 25), (14, 3), (11, 14), (3, 13), (25, 7), (21, 7), (30, 8), (0, 18), (10, 8), (9, 29), (6, 25), (29, 9), (3, 26), (8, 17), (27, 18), (3, 15), (2, 32), (19, 15), (4, 10), (31, 1), (25, 10), (9, 15), (6, 17), (13, 1), (19, 11), (21, 13), (29, 22), (17, 30), (23, 25), (18, 1), (19, 26), (13, 11), (30, 24), (20, 17), (4, 21), (17, 22), (20, 4), (10, 25), (9, 28), (25, 12), (4, 31), (26, 24), (30, 15), (6, 2), (26, 28), (24, 6), (6, 9), (3, 21), (31, 12), (30, 6), (9, 8), (18, 17), (12, 26), (5, 4), (15, 28), (8, 10), (6, 19), (23, 26), (12, 20), (13, 8), (10, 21), (15, 16), (31, 19), (23, 14), (12, 6), (26, 4), (16, 30), (7, 10), (14, 1), (17, 29), (16, 21), (17, 0), (32, 2), (26, 13), (28, 0), (19, 13), (16, 9), (27, 24), (10, 7), (21, 12), (32, 6), (11, 0), (5, 6), (20, 24), (32, 30), (3, 4), (14, 17), (4, 11), (32, 7), (30, 12), (0, 8), (1, 9), (2, 1), (8, 2), (0, 9), (17, 5), (18, 15), (6, 14), (9, 27), (3, 32), (30, 23), (28, 18), (30, 10), (14, 32), (25, 5), (14, 5), (28, 6), (20, 16), (18, 22), (27, 29), (20, 15), (16, 13), (10, 18), (8, 8), (10, 29), (14, 31), (29, 7), (26, 5), (5, 17), (22, 7), (5, 10), (18, 14), (21, 11), (26, 15), (29, 15), (25, 30), (11, 22), (21, 21), (5, 11), (15, 29), (20, 23), (26, 17), (4, 22), (12, 4), (4, 17), (19, 0), (27, 32), (25, 18), (9, 21), (17, 27), (13, 19), (19, 9), (20, 9), (18, 10), (29, 10), (24, 32), (8, 31), (19, 28), (15, 22), (1, 4), (13, 27), (16, 27), (8, 13), (7, 1), (22, 30), (6, 26), (12, 23), (6, 32), (31, 15), (28, 32), (22, 32), (14, 12), (7, 2), (29, 23), (1, 2), (29, 6), (29, 31), (27, 22), (16, 8), (19, 31), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369600", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 21), (10, 28), (21, 6), (4, 5), (24, 13), (11, 13), (5, 3), (23, 2), (1, 8), (2, 9), (11, 24), (27, 6), (13, 12), (10, 23), (13, 26), (20, 24), (29, 5), (21, 21), (4, 16), (14, 17), (3, 13), (18, 30), (29, 2), (9, 4), (10, 3), (10, 21), (16, 29), (29, 6), (26, 24), (1, 11), (24, 3), (6, 11), (28, 7), (11, 20), (16, 4), (25, 1), (22, 24), (2, 20), (30, 25), (5, 4), (29, 11), (25, 4), (11, 2), (30, 20), (26, 29), (15, 30), (10, 30), (2, 21), (25, 24), (5, 7), (28, 14), (1, 3), (19, 24), (30, 13), (24, 5), (6, 15), (8, 21), (23, 3), (13, 1), (1, 13), (22, 10), (18, 5), (20, 16), (28, 2), (10, 29), (1, 21), (9, 3), (18, 3), (18, 27), (15, 0), (14, 27), (5, 12), (6, 0), (26, 5), (4, 12), (6, 17), (21, 28), (1, 27), (10, 27), (8, 26), (5, 23), (25, 27), (19, 15), (17, 5), (0, 18), (13, 4), (29, 15), (23, 9), (16, 22), (16, 30), (24, 30), (8, 4), (27, 13), (6, 14), (1, 25), (9, 12), (5, 24), (8, 15), (17, 27), (5, 10), (17, 11), (3, 12), (3, 29), (8, 8), (14, 15), (25, 2), (7, 20), (25, 7), (2, 27), (4, 9), (12, 0), (2, 13), (12, 21), (0, 17), (11, 28), (29, 20), (1, 17), (1, 26), (6, 10), (27, 23), (12, 22), (24, 29), (0, 5), (20, 0), (24, 8), (3, 28), (14, 3), (28, 19), (17, 9), (1, 6), (20, 30), (17, 12), (14, 28), (19, 11), (15, 21), (29, 21), (0, 15), (26, 26), (4, 13), (9, 9), (0, 8), (28, 29), (10, 18), (9, 30), (13, 20), (26, 8), (21, 8), (4, 28), (9, 22), (15, 25), (22, 13), (10, 14), (14, 4), (15, 19), (23, 8), (24, 4), (9, 19), (25, 10), (7, 8), (0, 23), (17, 20), (27, 8), (25, 12), (21, 10), (28, 30), (12, 12), (15, 27), (3, 11), (19, 22), (23, 6), (2, 2), (23, 16), (1, 9), (21, 22), (16, 0), (2, 8), (26, 2), (26, 4), (19, 10), (3, 5), (6, 9), (28, 18), (26, 21), (10, 5), (19, 19), (13, 30), (8, 9), (29, 10), (25, 22), (20, 1), (13, 11), (3, 30), (23, 1), (25, 5), (5, 29), (17, 24), (10, 9), (20, 21), (9, 18), (21, 17), (14, 6), (20, 28), (30, 0), (9, 2), (2, 25), (19, 13), (24, 17), (21, 13), (11, 4), (23, 21), (24, 10), (4, 15), (20, 12), (11, 30), (17, 22), (7, 24), (2, 16), (18, 9), (18, 16), (12, 4), (16, 17), (18, 28), (3, 18), (18, 14), (26, 25), (25, 30), (4, 4), (18, 10), (0, 25), (16, 25), (16, 23), (6, 12), (4, 10), (16, 11), (7, 29), (2, 3), (28, 12), (19, 8), (9, 21), (12, 8), (4, 24), (8, 1), (13, 14), (9, 15), (11, 10), (10, 15), (9, 0), (14, 5), (5, 28), (6, 3), (15, 18), (11, 14), (1, 15), (28, 25), (7, 1), (20, 23), (29, 9), (23, 10), (27, 20), (24, 0), (28, 16), (3, 9), (18, 15), (7, 7), (12, 1), (21, 30), (4, 8), (9, 28), (4, 22), (10, 7), (27, 9), (22, 5), (15, 20), (20, 5), (8, 10), (3, 4), (19, 30), (30, 9), (5, 14), (20, 6), (22, 27), (17, 23), (10, 12), (3, 27), (30, 27), (17, 2), (11, 3), (25, 19), (4, 27), (21, 7), (16, 8), (23, 15), (9, 13), (13, 25), (9, 16), (1, 16), (12, 17), (14, 12), (26, 0), (25, 18), (8, 5), (20, 22), (30, 17), (2, 29), (13, 6), (28, 27), (2, 15), (1, 10), (2, 7), (8, 16), (3, 20), (28, 13), (7, 28), (29, 13), (14, 11), (27, 26), (25, 29), (0, 10), (18, 1), (7, 3), (26, 15), (8, 27), (14, 21), (27, 30), (19, 20), (20, 8), (8, 13), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551040", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 2), (19, 5), (18, 16), (0, 25), (28, 6), (26, 29), (8, 10), (18, 32), (9, 35), (10, 34), (15, 5), (19, 21), (16, 26), (29, 16), (25, 33), (23, 11), (18, 7), (8, 5), (30, 12), (12, 12), (34, 30), (5, 28), (32, 33), (27, 31), (4, 20), (18, 34), (33, 28), (34, 28), (33, 29), (30, 19), (13, 26), (21, 4), (33, 31), (7, 17), (25, 5), (21, 32), (19, 9), (17, 27), (33, 1), (30, 17), (7, 36), (25, 16), (30, 3), (8, 8), (29, 36), (17, 4), (20, 30), (17, 14), (2, 36), (1, 23), (27, 4), (30, 9), (6, 8), (28, 25), (16, 36), (22, 32), (15, 23), (17, 15), (29, 12), (20, 9), (17, 37), (2, 25), (33, 30), (12, 31), (17, 11), (4, 32), (34, 15), (12, 14), (19, 20), (1, 22), (7, 9), (24, 15), (25, 23), (30, 31), (11, 12), (31, 34), (31, 2), (28, 16), (13, 29), (18, 33), (10, 33), (28, 14), (15, 24), (32, 20), (20, 14), (12, 23), (12, 36), (26, 17), (7, 34), (12, 4), (26, 19), (7, 13), (0, 10), (4, 0), (27, 5), (25, 4), (19, 30), (22, 31), (5, 29), (20, 31), (5, 18), (24, 37), (34, 5), (6, 27), (32, 7), (0, 13), (3, 34), (12, 22), (7, 37), (0, 37), (6, 16), (28, 29), (31, 36), (20, 18), (16, 14), (5, 35), (12, 32), (21, 22), (27, 15), (23, 27), (11, 28), (1, 34), (23, 14), (17, 12), (11, 31), (5, 20), (9, 17), (32, 2), (10, 5), (19, 4), (8, 37), (12, 17), (15, 10), (16, 4), (8, 3), (16, 21), (26, 30), (0, 27), (22, 15), (24, 0), (27, 28), (26, 7), (8, 4), (8, 36), (15, 7), (17, 7), (3, 24), (27, 35), (21, 35), (5, 15), (14, 33), (14, 21), (11, 8), (24, 8), (31, 25), (30, 8), (28, 34), (22, 24), (16, 35), (28, 7), (22, 13), (15, 18), (15, 31), (30, 7), (6, 12), (30, 22), (13, 30), (33, 16), (0, 12), (1, 33), (6, 28), (32, 14), (6, 33), (6, 31), (13, 25), (33, 2), (2, 31), (2, 26), (5, 1), (1, 5), (5, 9), (21, 15), (2, 28), (25, 11), (16, 24), (17, 0), (20, 37), (18, 28), (22, 8), (11, 16), (19, 10), (1, 18), (27, 23), (2, 32), (0, 29), (10, 10), (31, 21), (21, 30), (5, 23), (4, 30), (29, 27), (30, 28), (11, 1), (1, 32), (12, 29), (15, 17), (8, 24), (14, 17), (15, 28), (32, 16), (32, 25), (23, 32), (3, 9), (27, 2), (11, 3), (8, 21), (13, 24), (11, 19), (30, 32), (26, 25), (20, 29), (12, 35), (10, 20), (31, 30), (10, 21), (27, 9), (16, 20), (4, 9), (7, 26), (29, 5), (29, 1), (18, 30), (32, 9), (16, 17), (32, 28), (22, 25), (23, 35), (33, 8), (24, 30), (20, 10), (18, 19), (23, 30), (23, 28), (1, 16), (12, 5), (23, 33), (16, 0), (34, 2), (7, 31), (20, 3), (21, 24), (22, 20), (25, 9), (20, 15), (2, 3), (7, 1), (13, 6), (31, 17), (14, 37), (19, 12), (4, 2), (34, 10), (14, 35), (17, 33), (26, 18), (31, 1), (22, 37), (33, 5), (14, 16), (23, 18), (31, 4), (18, 8), (31, 9), (26, 3), (13, 1), (31, 6), (26, 16), (13, 0), (7, 19), (3, 35), (23, 26), (24, 5), (32, 18), (12, 1), (26, 12), (22, 5), (0, 21), (4, 15), (11, 11), (21, 29), (11, 13), (6, 4), (2, 9), (16, 2), (28, 17), (32, 27), (15, 12), (23, 23), (34, 27), (29, 32), (29, 9), (6, 25), (19, 24), (24, 31), (28, 31), (4, 25), (22, 26), (20, 8), (7, 22), (0, 35), (32, 12), (26, 36), (17, 32), (7, 6), (7, 29), (1, 1), (11, 6), (3, 1), (20, 13), (12, 34), (33, 7), (30, 34), (2, 22), (28, 27), (26, 4), (27, 10), (2, 8), (14, 14), (8, 18), (29, 23), (10, 6), (18, 23), (7, 21), (28, 22), (19, 18), (15, 30), (27, 24), (33, 18), (0, 26), (1, 8), (8, 23), (12, 15), (16, 25), (18, 11), (1, 24), (33, 20), (31, 15), (12, 9), (4, 12), (28, 33), (34, 33), (5, 6), (14, 28), (33, 37), (4, 11), (7, 30), (32, 26), (34, 35), (12, 18), (23, 4), (10, 27), (2, 16), (28, 1), (13, 10), (2, 35), (7, 18), (31, 11), (14, 24), (11, 20), (19, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225216", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 10), (4, 12), (9, 10), (20, 35), (6, 35), (27, 1), (25, 4), (21, 34), (17, 17), (18, 17), (22, 7), (11, 21), (4, 13), (5, 4), (28, 4), (23, 5), (0, 35), (31, 17), (16, 11), (11, 8), (11, 17), (15, 27), (29, 14), (4, 34), (24, 7), (24, 12), (20, 20), (28, 5), (31, 21), (20, 4), (4, 20), (7, 31), (4, 6), (2, 17), (2, 16), (25, 12), (23, 16), (4, 4), (21, 2), (32, 7), (29, 16), (3, 22), (32, 32), (12, 34), (13, 9), (25, 0), (5, 3), (5, 24), (27, 24), (17, 8), (15, 35), (4, 29), (14, 19), (12, 5), (4, 32), (2, 29), (19, 16), (23, 27), (9, 15), (28, 1), (20, 2), (26, 25), (30, 28), (2, 2), (29, 8), (0, 20), (6, 19), (2, 35), (24, 9), (26, 11), (5, 12), (11, 2), (26, 33), (3, 2), (24, 22), (24, 0), (10, 17), (8, 0), (15, 0), (18, 6), (25, 30), (17, 0), (17, 29), (28, 15), (19, 22), (3, 16), (17, 5), (8, 2), (12, 7), (32, 4), (2, 3), (23, 34), (17, 7), (15, 31), (25, 6), (1, 10), (29, 24), (21, 18), (1, 3), (3, 10), (6, 22), (8, 8), (32, 1), (18, 35), (22, 28), (6, 18), (6, 27), (4, 33), (21, 24), (11, 29), (21, 16), (28, 0), (3, 3), (30, 0), (16, 31), (11, 35), (6, 4), (15, 21), (5, 30), (3, 26), (30, 24), (5, 22), (23, 20), (30, 13), (31, 22), (16, 34), (6, 29), (20, 17), (14, 34), (7, 27), (12, 35), (26, 21), (29, 7), (1, 11), (12, 15), (19, 5), (3, 30), (9, 31), (12, 16), (20, 28), (9, 11), (22, 21), (7, 33), (20, 8), (5, 21), (27, 5), (18, 33), (24, 28), (6, 33), (28, 6), (21, 10), (16, 17), (1, 33), (4, 23), (30, 1), (19, 34), (23, 18), (21, 6), (10, 20), (11, 28), (23, 3), (0, 1), (24, 2), (28, 17), (12, 28), (16, 29), (18, 14), (31, 4), (25, 35), (22, 13), (21, 14), (8, 24), (15, 12), (5, 2), (29, 29), (4, 22), (10, 1), (10, 12), (22, 31), (15, 33), (6, 12), (26, 20), (4, 16), (0, 6), (17, 33), (17, 3), (8, 7), (29, 19), (3, 32), (23, 28), (19, 9), (14, 27), (26, 16), (4, 28), (29, 21), (0, 27), (21, 27), (23, 0), (8, 14), (12, 27), (13, 33), (18, 29), (2, 26), (31, 23), (19, 0), (26, 28), (32, 34), (21, 1), (8, 5), (4, 8), (20, 25), (21, 21), (25, 19), (9, 26), (8, 35), (32, 11), (28, 14), (0, 10), (26, 8), (32, 8), (7, 11), (22, 4), (0, 16), (18, 31), (13, 32), (19, 26), (22, 34), (15, 2), (29, 11), (25, 11), (7, 20), (15, 3), (26, 12), (9, 5), (2, 11), (8, 27), (14, 3), (7, 19), (25, 31), (24, 21), (0, 2), (14, 1), (21, 28), (4, 7), (15, 30), (13, 22), (2, 25), (13, 31), (32, 23), (15, 32), (26, 18), (17, 23), (2, 23), (18, 19), (0, 31), (28, 28), (11, 33), (26, 13), (10, 29), (27, 27), (17, 16), (12, 18), (20, 15), (24, 6), (12, 23), (30, 26), (13, 19), (17, 19), (17, 11), (1, 28), (22, 11), (18, 11), (19, 14), (28, 18), (11, 19), (3, 31), (22, 16), (17, 25), (11, 22), (24, 11), (10, 4), (11, 24), (8, 16), (1, 1), (28, 19), (1, 24), (2, 13), (16, 27), (8, 18), (16, 30), (1, 31), (23, 29), (1, 30), (27, 11), (4, 18), (10, 14), (27, 2), (7, 6), (10, 15), (3, 6), (31, 27), (20, 13), (0, 9), (10, 8), (18, 22), (31, 20), (13, 16), (30, 20), (11, 34), (22, 1), (14, 14), (7, 0), (3, 34), (17, 35), (32, 9), (4, 26), (18, 27), (3, 23), (17, 32), (9, 29), (6, 0), (6, 5), (30, 19), (30, 6), (23, 25), (12, 3), (7, 22), (9, 18), (32, 19), (26, 32), (13, 18), (29, 12), (11, 12), (25, 33), (29, 31), (7, 34), (27, 12), (27, 14), (21, 13), (16, 32), (6, 15), (17, 9), (1, 20), (18, 25), (28, 26), (31, 3), (18, 4), (27, 34), (1, 32), (12, 12), (3, 7), (31, 13), (7, 10), (13, 6), (16, 19), (9, 19), (21, 15), (12, 20), (6, 34), (20, 7), (32, 14), (16, 16), (11, 6), (17, 15), (20, 22), (10, 31), (16, 7), (11, 27), (25, 5), (10, 27), (23, 17), (21, 20), (32, 17), (6, 3), (19, 12), (15, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892064", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), 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), (19, 25), (1, 10), (4, 12), (31, 16), (7, 9), (1, 31), (28, 6), (16, 2), (6, 24), (10, 3), (28, 8), (5, 2), (20, 26), (25, 26), (34, 11), (32, 1), (6, 19), (9, 19), (34, 22), (11, 0), (19, 6), (21, 18), (15, 11), (19, 17), (24, 29), (26, 26), (14, 12), (16, 0), (25, 16), (19, 0), (4, 25), (19, 13), (18, 2), (3, 22), (30, 26), (34, 14), (18, 29), (30, 27), (9, 24), (6, 27), (29, 13), (12, 13), (7, 0), (30, 13), (8, 13), (26, 16), (13, 22), (4, 17), (2, 22), (5, 28), (5, 1), (1, 11), (4, 23), (29, 20), (19, 4), (15, 23), (26, 9), (10, 29), (25, 20), (28, 30), (32, 25), (8, 25), (11, 19), (14, 6), (0, 10), (29, 14), (20, 0), (23, 31), (9, 2), (10, 26), (17, 6), (20, 2), (19, 2), (12, 5), (28, 7), (18, 20), (7, 20), (18, 8), (22, 23), (25, 15), (12, 15), (2, 9), (18, 17), (11, 14), (9, 1), (31, 29), (12, 16), (22, 5), (11, 10), (23, 14), (17, 25), (6, 21), (21, 1), (30, 22), (16, 3), (3, 10), (18, 24), (0, 2), (21, 13), (7, 31), (13, 28), (12, 17), (26, 4), (27, 22), (15, 17), (14, 29), (28, 20), (23, 5), (26, 21), (21, 30), (3, 16), (29, 12), (17, 9), (3, 24), (8, 7), (5, 29), (20, 16), (22, 17), (0, 6), (13, 31), (7, 2), (3, 11), (25, 25), (10, 21), (24, 0), (23, 2), (6, 22), (24, 7), (15, 22), (34, 17), (33, 10), (25, 19), (17, 31), (30, 20), (2, 30), (24, 8), (28, 17), (1, 14), (19, 8), (12, 6), (1, 9), (18, 31), (28, 5), (10, 9), (17, 23), (16, 8), (30, 16), (4, 11), (33, 14), (28, 4), (12, 30), (0, 22), (13, 0), (22, 10), (32, 2), (8, 27), (9, 14), (21, 12), (20, 3), (31, 31), (28, 11), (7, 4), (25, 28), (29, 9), (12, 20), (31, 26), (11, 27), (20, 15), (5, 9), (2, 26), (29, 16), (0, 21), (34, 25), (25, 17), (22, 1), (18, 9), (25, 29), (25, 4), (9, 31), (12, 10), (29, 24), (8, 0), (8, 14), (19, 16), (15, 8), (25, 14), (6, 14), (31, 11), (9, 10), (23, 16), (2, 4), (15, 12), (7, 5), (30, 28), (1, 21), (23, 10), (25, 21), (6, 1), (9, 16), (31, 0), (20, 9), (3, 26), (14, 22), (2, 6), (12, 27), (3, 25), (20, 22), (18, 12), (14, 21), (21, 3), (23, 28), (28, 10), (30, 10), (17, 19), (16, 29), (3, 5), (33, 6), (34, 0), (13, 11), (26, 5), (1, 20), (23, 27), (3, 12), (9, 28), (31, 12), (18, 18), (4, 1), (31, 10), (22, 25), (11, 3), (15, 30), (33, 13), (7, 14), (13, 3), (27, 10), (17, 11), (14, 1), (30, 2), (9, 29), (16, 6), (29, 28), (11, 2), (31, 22), (6, 20), (10, 22), (3, 7), (7, 19), (21, 9), (22, 18), (28, 2), (32, 19), (5, 17), (21, 27), (27, 11), (18, 16), (19, 19), (8, 15), (32, 28), (19, 1), (34, 2), (32, 4), (34, 7), (33, 5), (4, 15), (24, 10), (34, 1), (32, 5), (31, 6), (26, 30), (30, 4), (0, 7), (21, 16), (11, 4), (33, 22), (2, 20), (27, 30), (0, 18), (28, 23), (20, 17), (34, 16), (0, 25), (13, 10), (22, 20), (5, 11), (13, 12), (22, 7), (20, 7), (15, 13), (3, 20), (10, 6), (32, 17), (5, 14), (30, 23), (20, 8), (8, 31), (12, 28), (23, 8), (17, 15), (31, 15), (21, 17), (23, 30), (26, 15), (9, 26), (8, 19), (14, 31), (2, 29), (20, 13), (5, 5), (18, 6), (7, 24), (2, 28), (14, 20), (15, 6), (4, 3), (18, 5), (21, 22), (34, 15), (24, 3), (11, 9), (31, 19), (33, 16), (4, 24), (6, 3), (8, 24), (5, 6), (12, 25), (16, 17), (1, 24), (20, 14), (2, 0), (14, 7), (30, 1), (12, 2), (34, 9), (5, 18), (13, 21), (25, 31), (0, 11), (16, 11), (17, 3), (4, 2), (24, 25), (3, 23), (5, 24), (2, 3), (7, 15), (33, 20), (23, 11), (12, 24), (8, 23), (34, 4), (13, 17), (11, 26), (13, 26), (6, 26), (27, 15), (11, 31), (33, 8), (11, 17), (34, 20), (25, 24), (3, 21), (22, 29), (0, 16), (29, 21), (34, 30), (4, 20), (32, 22), (17, 13), (3, 15), (23, 17), (26, 10), (13, 27), (4, 8), (3, 8), (28, 9), (3, 9), (16, 21), (21, 28), (30, 25), (33, 3), (31, 1), (28, 26), (10, 5), (14, 28), (17, 7), (16, 16), (1, 7), (21, 20), (20, 31), (6, 9), (9, 5), (16, 7), (1, 13), (33, 9), (19, 11), (18, 19), (20, 24), (17, 4), (22, 9), (31, 13), (11, 24), (34, 29), (1, 19), (23, 25), (33, 0), (19, 14), (10, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "729648", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), 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), (15, 22), (21, 25), (10, 4), (17, 7), (20, 3), (14, 3), (3, 11), (7, 3), (7, 26), (22, 38), (28, 36), (12, 37), (24, 9), (14, 2), (2, 18), (27, 28), (21, 16), (18, 26), (26, 6), (5, 1), (0, 13), (29, 34), (9, 9), (29, 33), (29, 17), (6, 8), (10, 24), (12, 33), (25, 19), (25, 34), (16, 38), (5, 35), (20, 11), (10, 14), (11, 24), (14, 4), (16, 35), (9, 1), (10, 0), (21, 8), (2, 5), (1, 30), (25, 29), (18, 0), (25, 15), (10, 1), (12, 8), (9, 14), (2, 28), (9, 37), (2, 26), (29, 25), (25, 1), (5, 17), (5, 9), (29, 37), (27, 3), (15, 9), (9, 25), (4, 29), (8, 35), (18, 31), (25, 36), (3, 8), (17, 28), (11, 12), (4, 17), (0, 14), (1, 18), (27, 35), (6, 3), (14, 1), (0, 22), (20, 1), (23, 25), (11, 31), (25, 7), (21, 13), (4, 37), (13, 32), (7, 10), (8, 7), (0, 4), (13, 27), (2, 23), (3, 4), (11, 27), (23, 10), (25, 3), (12, 19), (28, 29), (22, 17), (3, 30), (24, 0), (19, 27), (9, 18), (28, 23), (9, 20), (10, 17), (19, 32), (1, 12), (4, 38), (3, 10), (11, 9), (0, 15), (19, 34), (23, 14), (18, 23), (7, 22), (14, 8), (9, 23), (14, 33), (5, 20), (22, 26), (2, 35), (23, 17), (21, 0), (22, 25), (15, 5), (7, 31), (6, 19), (0, 32), (11, 2), (28, 4), (0, 30), (9, 13), (14, 15), (19, 8), (24, 20), (3, 0), (1, 34), (21, 10), (7, 34), (8, 34), (12, 16), (25, 23), (20, 21), (5, 14), (21, 26), (22, 24), (7, 30), (28, 16), (8, 26), (9, 5), (23, 33), (24, 6), (28, 9), (15, 32), (17, 29), (26, 2), (2, 1), (27, 30), (6, 22), (19, 38), (22, 22), (22, 32), (11, 26), (22, 2), (20, 33), (23, 27), (15, 25), (22, 11), (5, 31), (28, 8), (12, 30), (2, 33), (20, 10), (27, 27), (3, 23), (12, 13), (10, 6), (26, 16), (3, 1), (26, 0), (10, 3), (26, 20), (24, 15), (17, 38), (0, 9), (0, 7), (24, 35), (22, 29), (15, 7), (24, 4), (16, 5), (20, 30), (2, 34), (29, 32), (19, 6), (3, 9), (24, 25), (5, 32), (25, 17), (11, 36), (17, 22), (23, 13), (16, 29), (15, 3), (12, 36), (26, 29), (0, 21), (11, 13), (16, 9), (9, 16), (24, 5), (1, 26), (25, 9), (8, 36), (4, 30), (14, 32), (6, 14), (0, 29), (3, 34), (26, 8), (23, 30), (21, 34), (27, 25), (16, 8), (25, 8), (19, 20), (27, 8), (29, 5), (12, 38), (15, 1), (20, 28), (20, 18), (27, 11), (23, 0), (8, 29), (19, 14), (18, 9), (15, 38), (19, 24), (2, 29), (9, 3), (4, 22), (10, 19), (15, 24), (11, 1), (2, 6), (24, 16), (21, 31), (5, 24), (9, 2), (25, 38), (7, 2), (25, 4), (8, 38), (6, 18), (8, 3), (24, 12), (2, 12), (17, 12), (17, 16), (16, 1), (26, 17), (6, 37), (29, 3), (6, 31), (13, 9), (16, 22), (26, 19), (5, 33), (15, 21), (23, 19), (9, 0), (24, 37), (20, 36), (3, 18), (18, 33), (27, 6), (11, 35), (8, 20), (16, 18), (1, 29), (18, 36), (1, 23), (3, 14), (21, 12), (22, 1), (28, 26), (1, 22), (8, 37), (17, 31), (8, 28), (8, 27), (25, 31), (12, 4), (26, 7), (12, 9), (2, 25), (4, 9), (4, 23), (1, 20), (18, 19), (13, 15), (24, 24), (26, 21), (27, 9), (1, 25), (10, 21), (28, 30), (25, 16), (10, 38), (18, 13), (8, 22), (2, 3), (11, 20), (26, 24), (29, 24), (21, 14), (15, 12), (20, 0), (24, 22), (19, 35), (13, 36), (8, 4), (17, 14), (7, 35), (2, 2), (18, 22), (22, 14), (6, 15), (29, 13), (7, 18), (16, 34), (12, 35), (16, 14), (5, 36), (25, 18), (16, 24), (24, 30)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900000", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), 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), (30, 0), (30, 23), (3, 13), (22, 32), (15, 11), (22, 17), (26, 24), (12, 5), (1, 31), (6, 17), (25, 0), (8, 14), (17, 33), (16, 18), (12, 24), (18, 5), (5, 14), (5, 28), (29, 19), (7, 9), (11, 19), (9, 7), (13, 17), (11, 21), (21, 19), (1, 0), (19, 13), (0, 26), (6, 13), (3, 15), (8, 7), (21, 11), (2, 8), (24, 19), (16, 12), (6, 5), (29, 24), (15, 1), (11, 8), (10, 27), (22, 10), (8, 0), (25, 18), (7, 8), (6, 22), (25, 9), (0, 20), (0, 18), (5, 17), (26, 10), (4, 33), (11, 11), (22, 1), (27, 31), (15, 14), (10, 2), (10, 8), (17, 18), (15, 22), (3, 29), (16, 26), (24, 7), (2, 10), (29, 21), (16, 31), (13, 23), (29, 3), (21, 12), (22, 14), (20, 25), (23, 26), (20, 16), (0, 13), (10, 20), (0, 12), (30, 6), (27, 3), (26, 17), (1, 23), (16, 32), (16, 2), (30, 10), (26, 13), (1, 19), (29, 4), (6, 33), (2, 13), (2, 22), (23, 9), (9, 0), (30, 13), (10, 12), (25, 7), (23, 28), (28, 5), (5, 23), (17, 20), (13, 2), (14, 11), (16, 6), (16, 10), (19, 9), (30, 30), (1, 17), (9, 21), (7, 4), (15, 19), (10, 32), (29, 30), (2, 1), (8, 16), (20, 26), (28, 19), (7, 30), (4, 14), (1, 26), (7, 24), (23, 5), (24, 26), (23, 10), (4, 21), (21, 30), (8, 2), (26, 14), (6, 4), (13, 29), (5, 2), (22, 15), (30, 11), (20, 7), (22, 16), (13, 11), (18, 33), (18, 14), (6, 6), (5, 32), (19, 27), (4, 4), (2, 29), (4, 30), (24, 0), (1, 16), (21, 5), (22, 13), (2, 30), (20, 32), (30, 3), (10, 18), (2, 11), (24, 25), (31, 27), (14, 22), (31, 2), (25, 31), (12, 3), (11, 26), (7, 7), (12, 29), (4, 22), (29, 29), (8, 29), (6, 26), (20, 17), (31, 5), (11, 31), (1, 11), (28, 6), (11, 28), (12, 20), (2, 23), (12, 11), (3, 7), (1, 9), (23, 25), (24, 28), (9, 27), (5, 8), (21, 18), (25, 19), (23, 14), (11, 23), (7, 0), (2, 12), (25, 1), (24, 1), (30, 24), (13, 0), (13, 9), (20, 13), (2, 24), (19, 10), (16, 30), (1, 27), (4, 28), (3, 9), (4, 20), (25, 17), (27, 29), (8, 9), (13, 16), (26, 26), (20, 0), (9, 31), (22, 31), (3, 19), (9, 30), (26, 18), (3, 18), (22, 9), (18, 12), (15, 7), (8, 26), (8, 4), (5, 13), (8, 8), (17, 12), (1, 24), (23, 13), (26, 28), (22, 5), (30, 15), (23, 15), (4, 32), (31, 19), (23, 0), (10, 10), (22, 19), (24, 29), (3, 20), (21, 1), (15, 16), (0, 32), (29, 2), (6, 7), (4, 8), (1, 30), (2, 25), (11, 25), (25, 20), (17, 22), (14, 18), (26, 32), (0, 8), (20, 23), (5, 21), (14, 6), (13, 8), (29, 14), (9, 32), (6, 28), (14, 3), (29, 8), (23, 24), (10, 30), (12, 2), (31, 28), (13, 27), (16, 22), (11, 4), (31, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "567000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 29), (25, 0), (24, 14), (13, 13), (21, 27), (10, 24), (16, 14), (25, 12), (6, 21), (30, 11), (8, 9), (3, 8), (15, 3), (15, 14), (7, 12), (22, 24), (7, 6), (8, 4), (20, 28), (4, 4), (23, 4), (0, 19), (11, 8), (7, 30), (24, 16), (25, 15), (6, 28), (7, 27), (22, 29), (23, 21), (16, 25), (14, 19), (30, 14), (27, 5), (25, 13), (20, 21), (1, 23), (1, 28), (0, 13), (30, 26), (1, 27), (21, 29), (3, 6), (23, 3), (22, 11), (14, 3), (14, 15), (22, 22), (17, 31), (29, 14), (1, 2), (11, 5), (19, 21), (7, 25), (9, 28), (23, 13), (23, 2), (27, 2), (9, 22), (15, 23), (23, 24), (19, 27), (26, 19), (6, 1), (14, 25), (7, 14), (20, 20), (6, 0), (1, 21), (27, 21), (13, 1), (22, 18), (3, 10), (3, 13), (22, 3), (11, 12), (9, 26), (14, 30), (9, 24), (15, 13), (0, 31), (2, 7), (14, 18), (10, 14), (10, 21), (4, 27), (22, 19), (16, 15), (12, 0), (24, 9), (7, 9), (5, 1), (19, 4), (19, 17), (4, 22), (8, 12), (25, 26), (15, 10), (4, 0), (23, 27), (7, 13), (23, 10), (9, 5), (25, 23), (24, 2), (12, 22), (1, 19), (2, 30), (13, 9), (8, 22), (0, 12), (26, 15), (25, 7), (4, 21), (25, 6), (10, 3), (11, 4), (18, 31), (15, 21), (13, 16), (8, 16), (16, 10), (12, 30), (20, 30), (21, 3), (20, 13), (21, 23), (1, 3), (21, 14), (11, 19), (7, 20), (26, 4), (25, 14), (24, 24), (6, 7), (29, 7), (15, 9), (30, 3), (16, 17), (22, 12), (13, 29), (6, 9), (17, 23), (9, 17), (23, 17), (30, 20), (23, 5), (19, 1), (9, 7), (29, 5), (22, 7), (9, 6), (6, 15), (23, 28), (9, 3), (14, 9), (17, 14), (26, 29), (17, 5), (8, 28), (26, 17), (21, 22), (29, 15), (7, 19), (17, 2), (30, 18), (10, 22), (25, 25), (15, 29), (4, 13), (25, 27), (2, 22), (2, 8), (0, 15), (27, 22), (11, 25), (6, 2), (3, 3), (3, 4), (15, 26), (9, 19), (6, 18), (28, 22), (8, 8), (18, 13), (24, 20), (8, 25), (15, 24), (5, 14), (3, 16), (30, 1), (16, 5), (12, 19), (8, 30), (21, 2), (11, 24), (17, 7), (1, 24), (25, 18), (22, 16), (2, 21), (18, 20), (27, 20), (30, 19), (27, 12), (16, 23), (26, 1), (12, 31), (1, 15), (6, 16), (4, 28), (14, 12), (0, 17), (16, 26), (10, 8), (6, 30), (30, 2), (4, 10), (3, 19), (10, 6), (19, 28), (10, 11), (7, 16), (2, 9), (22, 30), (10, 9), (16, 2), (9, 18), (2, 11), (5, 9), (2, 1), (10, 12), (12, 25), (2, 3), (26, 14), (5, 2), (3, 24), (9, 1), (24, 10), (19, 3), (29, 23), (26, 7), (16, 22), (26, 12), (19, 8), (25, 5), (7, 21), (11, 17), (5, 5), (20, 31), (18, 2), (18, 21), (3, 9), (9, 21), (1, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369720", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (15, 28), (25, 27), (11, 26), (32, 3), (9, 15), (20, 18), (24, 14), (13, 12), (2, 6), (13, 31), (8, 29), (25, 26), (32, 16), (18, 20), (32, 12), (23, 17), (2, 14), (33, 6), (21, 18), (19, 5), (5, 27), (23, 18), (17, 25), (2, 5), (27, 31), (27, 5), (23, 3), (17, 30), (33, 13), (7, 1), (32, 26), (32, 9), (25, 14), (7, 31), (34, 8), (23, 6), (24, 10), (18, 8), (20, 16), (19, 8), (10, 32), (15, 8), (6, 24), (20, 24), (18, 16), (32, 28), (22, 9), (29, 28), (10, 27), (1, 7), (28, 19), (24, 0), (3, 0), (25, 15), (14, 10), (16, 11), (33, 26), (20, 30), (31, 31), (11, 0), (24, 16), (12, 16), (34, 1), (35, 15), (33, 2), (28, 30), (12, 12), (2, 4), (19, 10), (5, 24), (20, 23), (25, 28), (34, 12), (31, 20), (6, 5), (9, 19), (35, 26), (16, 28), (26, 17), (25, 9), (32, 15), (22, 7), (32, 10), (31, 7), (13, 30), (6, 18), (20, 12), (6, 8), (18, 14), (12, 6), (21, 15), (11, 12), (0, 26), (32, 6), (12, 22), (6, 28), (30, 13), (29, 7), (22, 15), (33, 21), (26, 22), (20, 3), (32, 4), (12, 0), (13, 21), (6, 15), (27, 10), (34, 4), (34, 9), (30, 28), (6, 26), (4, 27), (30, 18), (26, 27), (27, 27), (2, 25), (27, 14), (11, 30), (3, 18), (19, 21), (19, 14), (7, 14), (21, 26), (4, 25), (30, 9), (6, 11), (26, 8), (17, 19), (5, 30), (18, 27), (21, 0), (30, 31), (12, 9), (4, 11), (24, 17), (5, 22), (29, 26), (15, 26), (7, 2), (10, 15), (10, 16), (1, 32), (6, 12), (8, 17), (9, 28), (0, 12), (24, 12), (3, 25), (31, 18), (16, 29), (8, 14), (11, 14), (26, 9), (25, 17), (15, 20), (22, 13), (13, 7), (16, 1), (5, 7), (12, 18), (19, 28), (6, 23), (2, 10), (32, 24), (12, 7), (27, 22), (1, 23), (18, 30), (20, 5), (20, 32), (34, 29), (12, 28), (22, 11), (24, 4), (3, 20), (10, 10), (23, 27), (14, 3), (25, 1), (23, 14), (23, 25), (34, 30), (18, 2), (33, 15), (12, 24), (11, 23), (0, 28), (19, 26), (33, 23), (25, 2), (19, 20), (32, 32), (9, 20), (13, 9), (7, 13), (19, 27), (24, 3), (2, 7), (30, 3), (12, 23), (11, 21), (29, 3), (17, 2), (28, 8), (17, 23), (24, 11), (27, 3), (23, 5), (15, 3), (13, 3), (24, 13), (15, 14), (30, 7), (8, 9), (17, 10), (17, 16), (35, 13), (10, 20), (34, 28), (26, 18), (26, 7), (6, 9), (21, 31), (27, 13), (9, 31), (27, 0), (18, 4), (32, 30), (12, 26), (35, 9), (31, 30), (21, 2), (32, 7), (6, 7), (3, 8), (20, 22), (35, 10), (13, 11), (21, 6), (31, 22), (30, 4), (35, 31), (8, 30), (32, 25), (15, 21), (14, 25), (6, 2), (4, 4), (10, 25), (1, 10), (24, 9), (29, 30), (23, 31), (1, 6), (22, 19), (7, 7), (1, 11), (34, 13), (7, 32), (32, 27), (1, 8), (21, 24), (26, 24), (16, 22), (1, 25), (17, 15), (32, 18), (7, 15), (9, 0), (10, 19), (5, 21), (10, 4), (0, 19), (12, 14), (3, 32), (23, 28), (34, 25), (18, 22), (17, 3), (1, 18), (14, 8), (16, 13), (28, 2), (35, 17), (23, 16), (7, 24), (20, 27), (2, 23), (8, 12), (30, 17), (19, 32), (4, 14), (13, 13), (6, 17), (31, 8), (17, 29), (11, 20), (25, 5), (7, 5), (26, 6), (3, 31), (3, 15), (28, 21), (10, 18), (26, 26), (4, 13), (1, 19), (30, 1), (32, 23), (29, 12), (15, 15), (25, 20), (29, 22), (24, 18), (28, 32), (22, 27), (17, 32), (0, 25), (5, 18), (10, 28), (27, 4), (28, 7), (11, 32), (26, 10), (22, 22), (2, 2), (20, 11), (35, 6), (21, 8), (35, 27), (28, 5), (31, 6), (23, 4), (2, 19), (22, 17), (22, 5), (16, 21), (23, 8), (21, 27), (23, 20), (22, 0), (0, 10), (8, 23), (10, 30), (8, 20), (18, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306860", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), 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), (16, 4), (21, 13), (7, 10), (19, 16), (22, 0), (20, 7), (29, 30), (8, 15), (9, 3), (9, 12), (38, 17), (31, 29), (18, 4), (16, 19), (30, 13), (0, 2), (9, 14), (11, 13), (9, 23), (19, 6), (3, 5), (30, 17), (33, 3), (21, 19), (25, 31), (26, 30), (14, 21), (19, 12), (29, 9), (27, 1), (26, 9), (32, 4), (35, 13), (23, 26), (8, 19), (35, 14), (11, 4), (2, 24), (17, 24), (16, 15), (3, 28), (8, 2), (9, 17), (31, 30), (32, 23), (5, 11), (19, 9), (9, 20), (37, 8), (18, 19), (13, 4), (4, 9), (17, 3), (25, 13), (16, 31), (7, 17), (35, 11), (2, 22), (35, 28), (32, 1), (34, 15), (4, 0), (3, 26), (31, 2), (21, 1), (34, 28), (16, 5), (6, 19), (14, 9), (7, 4), (35, 27), (23, 7), (28, 10), (35, 16), (11, 0), (23, 18), (13, 26), (11, 30), (21, 24), (38, 16), (23, 15), (7, 9), (32, 20), (10, 7), (27, 17), (18, 31), (28, 22), (23, 13), (19, 5), (17, 10), (37, 5), (10, 1), (37, 1), (13, 14), (20, 16), (30, 27), (14, 16), (21, 28), (21, 16), (11, 24), (22, 32), (6, 15), (35, 0), (28, 28), (24, 2), (5, 27), (26, 16), (33, 12), (30, 16), (4, 4), (24, 9), (15, 13), (34, 27), (3, 30), (37, 32), (29, 12), (10, 22), (32, 18), (15, 29), (27, 16), (1, 31), (0, 21), (15, 8), (18, 6), (19, 25), (13, 32), (1, 26), (20, 1), (15, 24), (3, 15), (29, 1), (25, 23), (23, 29), (25, 29), (15, 25), (4, 25), (10, 26), (0, 20), (28, 17), (5, 0), (21, 8), (25, 17), (30, 10), (27, 5), (37, 28), (20, 6), (35, 21), (4, 8), (22, 28), (20, 25), (13, 30), (1, 21), (3, 24), (10, 27), (38, 21), (23, 20), (29, 11), (21, 30), (21, 26), (30, 3), (35, 7), (15, 5), (14, 0), (0, 19), (17, 25), (24, 3), (18, 7), (29, 32), (23, 12), (3, 31), (7, 30), (8, 13), (31, 7), (26, 5), (0, 18), (7, 3), (20, 30), (35, 4), (20, 14), (22, 4), (14, 29), (18, 15), (9, 13), (26, 8), (30, 25), (29, 26), (35, 10), (12, 26), (2, 26), (23, 25), (21, 15), (1, 13), (14, 12), (30, 14), (23, 6), (22, 30), (26, 28), (22, 9), (4, 19), (4, 30), (24, 26), (33, 4), (1, 20), (0, 5), (25, 24), (2, 18), (20, 17), (28, 19), (28, 6), (12, 13), (34, 8), (11, 25), (8, 31), (16, 16), (4, 11), (16, 1), (16, 18), (21, 11), (4, 29), (29, 5), (35, 12), (8, 25), (7, 22), (27, 4), (17, 29), (27, 9), (17, 21), (12, 14), (17, 18), (32, 28), (2, 3), (33, 7), (38, 18), (0, 4), (16, 30), (6, 17), (34, 17), (36, 21), (9, 25), (35, 30), (25, 27), (35, 22), (14, 20), (1, 3), (34, 23), (36, 4), (6, 18), (2, 10), (3, 0), (8, 6), (25, 6), (13, 10), (37, 25), (31, 8), (19, 32), (6, 1), (25, 2), (24, 22), (20, 12), (35, 20), (29, 20), (16, 3), (38, 28), (16, 32), (10, 4), (33, 13), (1, 0), (9, 1), (22, 31), (2, 4), (37, 11), (9, 28), (37, 26), (37, 21), (29, 27), (35, 15), (24, 8), (1, 11), (23, 28), (12, 15), (18, 25), (0, 7), (9, 5), (18, 30), (7, 23), (4, 1), (28, 1), (0, 11), (28, 7), (20, 29), (13, 12), (10, 19), (14, 3), (5, 21), (16, 8), (31, 10), (21, 3), (2, 21), (26, 25), (8, 11), (24, 11), (29, 6), (21, 6), (22, 11), (5, 12), (21, 20), (11, 12), (32, 2), (12, 7), (13, 20), (30, 15), (26, 21), (5, 8), (31, 12), (24, 21), (20, 27), (31, 32), (13, 0), (5, 23), (3, 11), (28, 29), (5, 26), (32, 10), (30, 24), (18, 23), (8, 17), (5, 7), (36, 27), (36, 3), (4, 10), (32, 32), (17, 1), (9, 21), (23, 16), (26, 18), (38, 1), (30, 26), (25, 12), (2, 8), (26, 0), (38, 6), (25, 4), (2, 27), (29, 15), (18, 20), (28, 16), (5, 6), (15, 27), (28, 15), (24, 16), (9, 10), (30, 30), (12, 32), (17, 9), (36, 11), (4, 14), (36, 24), (6, 22), (26, 12), (27, 26), (7, 21), (9, 29), (3, 32), (31, 3), (31, 28), (2, 20), (13, 23), (37, 23), (14, 14), (25, 19), (30, 23), (26, 2), (33, 14), (21, 21), (6, 26), (16, 17), (12, 27), (34, 13), (23, 32), (7, 11), (11, 8), (15, 11), (36, 22), (36, 0), (21, 17), (31, 22), (24, 17), (0, 31), (32, 8), (0, 12), (27, 31), (5, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "474768", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 12), (28, 32), (5, 22), (26, 17), (18, 6), (11, 14), (14, 9), (31, 30), (7, 14), (3, 11), (10, 16), (30, 30), (22, 3), (28, 13), (7, 17), (25, 12), (1, 32), (22, 35), (19, 17), (31, 33), (13, 36), (1, 16), (0, 26), (31, 11), (30, 18), (7, 13), (23, 19), (3, 21), (13, 7), (6, 6), (14, 31), (21, 20), (1, 1), (5, 30), (29, 12), (17, 24), (1, 25), (23, 3), (2, 33), (13, 35), (1, 22), (17, 9), (31, 13), (25, 31), (3, 15), (6, 9), (10, 13), (5, 8), (11, 8), (5, 33), (5, 7), (15, 22), (20, 0), (28, 11), (1, 3), (9, 20), (27, 11), (9, 8), (1, 2), (5, 2), (21, 18), (20, 2), (1, 13), (7, 35), (3, 10), (28, 8), (20, 24), (23, 2), (0, 7), (0, 19), (3, 22), (23, 16), (4, 2), (7, 8), (24, 18), (3, 7), (18, 4), (15, 32), (18, 31), (31, 7), (7, 25), (10, 29), (3, 8), (8, 30), (11, 30), (17, 28), (28, 1), (20, 23), (31, 21), (10, 19), (3, 5), (21, 12), (21, 4), (20, 16), (27, 22), (24, 0), (17, 7), (10, 11), (16, 19), (1, 5), (9, 24), (5, 34), (6, 13), (21, 21), (18, 35), (22, 36), (3, 34), (20, 22), (17, 34), (7, 18), (20, 28), (26, 26), (0, 23), (21, 23), (25, 24), (24, 13), (18, 1), (3, 36), (10, 32), (14, 13), (12, 31), (21, 14), (27, 34), (14, 29), (4, 24), (7, 19), (21, 5), (30, 10), (18, 25), (19, 1), (14, 33), (31, 28), (26, 25), (21, 17), (10, 0), (8, 23), (16, 23), (0, 4), (9, 1), (14, 18), (30, 7), (25, 8), (19, 26), (11, 25), (1, 8), (11, 2), (15, 33), (5, 0), (13, 18), (7, 27), (31, 5), (18, 15), (6, 26), (6, 17), (15, 30), (20, 20), (28, 23), (17, 10), (19, 12), (9, 2), (17, 25), (25, 2), (20, 15), (15, 28), (30, 29), (28, 0), (23, 15), (30, 14), (28, 6), (19, 2), (4, 28), (28, 4), (17, 11), (29, 34), (4, 13), (1, 7), (0, 33), (31, 17), (27, 21), (26, 11), (25, 32), (3, 6), (22, 32), (21, 30), (15, 0), (21, 3), (8, 25), (24, 27), (2, 22), (4, 29), (19, 18), (13, 13), (4, 4), (11, 35), (5, 28), (6, 3), (20, 11), (2, 23), (9, 25), (1, 9), (4, 17), (24, 12), (10, 36), (25, 5), (5, 23), (24, 35), (3, 29), (7, 12), (21, 11), (3, 19), (22, 34), (14, 28), (12, 29), (11, 7), (17, 21), (8, 15), (13, 14), (19, 11), (1, 27), (22, 26), (14, 12), (19, 9), (7, 36), (10, 4), (9, 29), (31, 8), (2, 15), (13, 23), (6, 27), (24, 21), (19, 10), (3, 4), (29, 35), (26, 29), (20, 4), (9, 13), (19, 22), (17, 31), (24, 3), (14, 23), (15, 5), (18, 11), (4, 15), (8, 16), (10, 5), (4, 14), (1, 26), (26, 1), (28, 14), (2, 25), (28, 29), (26, 34), (21, 29), (10, 9), (4, 22), (12, 22), (29, 24), (25, 23), (14, 34), (13, 4), (17, 13), (3, 1), (6, 10), (3, 31), (3, 24), (6, 34), (2, 18), (11, 29), (20, 17), (23, 8), (1, 23), (8, 20), (16, 28), (4, 8), (22, 9), (1, 35), (5, 18), (7, 34), (30, 1), (23, 11), (10, 35), (1, 21), (20, 32), (23, 29), (1, 33), (30, 33), (13, 12), (1, 6), (12, 33), (0, 1), (13, 10), (22, 29), (25, 4), (13, 1), (29, 13), (26, 32), (14, 19), (9, 0), (15, 29), (6, 1), (1, 14), (12, 16), (13, 27), (14, 20), (28, 22), (25, 19), (18, 20), (9, 7), (17, 36), (2, 28), (2, 6), (17, 12), (8, 36), (12, 2), (13, 26), (0, 35), (16, 0), (9, 5), (26, 27), (28, 7), (2, 32), (11, 1), (20, 29), (8, 3), (30, 17), (4, 25), (12, 11), (28, 25), (26, 28), (16, 25), (27, 3), (9, 12), (22, 31), (4, 26), (29, 14), (6, 4), (24, 33), (19, 32), (10, 28), (15, 31), (11, 33), (2, 35), (28, 27), (0, 12), (14, 24), (24, 16), (28, 26), (11, 3), (11, 27), (24, 32), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "534528", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (2, 32), (8, 17), (25, 3), (4, 6), (29, 5), (0, 21), (9, 7), (24, 10), (4, 1), (28, 5), (9, 8), (18, 9), (5, 3), (10, 7), (21, 10), (4, 11), (20, 10), (19, 9), (21, 2), (20, 1), (29, 10), (28, 4), (7, 15), (23, 20), (8, 33), (29, 26), (6, 25), (2, 23), (32, 32), (25, 5), (32, 27), (11, 18), (25, 2), (3, 8), (2, 29), (11, 12), (30, 13), (6, 14), (0, 32), (17, 24), (16, 34), (30, 6), (6, 5), (0, 11), (0, 16), (33, 2), (3, 21), (16, 0), (20, 11), (21, 30), (15, 19), (10, 1), (15, 33), (22, 11), (1, 18), (4, 26), (5, 15), (23, 17), (18, 28), (31, 2), (8, 26), (16, 8), (25, 31), (0, 14), (4, 18), (29, 31), (31, 33), (30, 2), (15, 25), (33, 10), (25, 9), (25, 23), (15, 31), (23, 8), (13, 25), (24, 16), (0, 25), (3, 34), (6, 33), (27, 17), (13, 18), (8, 21), (14, 1), (34, 8), (17, 19), (26, 22), (27, 1), (17, 30), (6, 7), (12, 19), (10, 3), (26, 27), (15, 28), (14, 13), (18, 8), (29, 9), (30, 20), (28, 1), (3, 16), (2, 26), (0, 20), (30, 18), (27, 28), (7, 1), (10, 18), (32, 10), (22, 2), (7, 31), (22, 12), (1, 16), (14, 15), (18, 20), (4, 22), (13, 1), (23, 4), (7, 8), (12, 24), (26, 16), (23, 0), (22, 21), (3, 20), (28, 32), (27, 11), (4, 5), (8, 19), (18, 25), (33, 6), (27, 24), (10, 31), (6, 6), (20, 22), (0, 3), (27, 6), (11, 26), (10, 6), (33, 9), (7, 32), (24, 34), (19, 26), (11, 32), (11, 33), (5, 24), (16, 2), (16, 26), (16, 28), (30, 29), (12, 27), (10, 10), (33, 34), (25, 4), (4, 25), (27, 27), (5, 1), (24, 1), (4, 10), (4, 21), (24, 24), (20, 16), (25, 34), (0, 12), (26, 31), (35, 30), (30, 33), (5, 2), (3, 10), (17, 0), (12, 22), (3, 26), (32, 19), (9, 28), (18, 2), (23, 27), (7, 28), (6, 34), (16, 24), (28, 17), (18, 12), (16, 20), (5, 0), (26, 4), (11, 6), (28, 27), (15, 7), (35, 23), (8, 31), (17, 12), (23, 1), (17, 26), (10, 27), (27, 8), (21, 12), (28, 29), (22, 15), (1, 26), (13, 22), (2, 19), (5, 31), (21, 25), (21, 17), (14, 4), (12, 25), (12, 26), (29, 28), (11, 27), (10, 32), (29, 19), (35, 29), (6, 30), (30, 9), (3, 14), (31, 5), (25, 19), (21, 0), (3, 27), (12, 21), (8, 18), (33, 14), (6, 16), (0, 4), (35, 11), (10, 24), (26, 29), (32, 34), (12, 30), (22, 19), (12, 33), (5, 5), (24, 23), (25, 29), (18, 11), (3, 2), (29, 7), (10, 19), (1, 4), (32, 7), (29, 25), (7, 5), (25, 1), (3, 7), (20, 4), (32, 25), (33, 24), (22, 18), (19, 34), (29, 4), (6, 3), (33, 23), (30, 0), (5, 25), (23, 12), (18, 14), (8, 4), (15, 13), (15, 15), (12, 32), (22, 23), (24, 15), (1, 32), (24, 30), (34, 32), (17, 32), (19, 27), (0, 19), (23, 19), (2, 22), (16, 10), (26, 33), (27, 9), (13, 31), (28, 13), (6, 15), (12, 4), (31, 34), (0, 26), (30, 7), (16, 19), (13, 21), (24, 17), (15, 2), (14, 8), (26, 15), (6, 31), (2, 16), (19, 29), (26, 20), (31, 1), (26, 21), (12, 23), (1, 12), (32, 29), (4, 14), (13, 14), (32, 15), (20, 33), (20, 0), (35, 21), (21, 4), (6, 2), (4, 30), (16, 18), (14, 17), (16, 23), (3, 30), (7, 24), (31, 0), (26, 3), (21, 21), (10, 29), (11, 9), (25, 17), (17, 33), (10, 16), (25, 30), (20, 24), (29, 30), (10, 9), (27, 20), (26, 26), (26, 12), (30, 28), (1, 2), (9, 33), (12, 7), (13, 6), (24, 28), (26, 13), (20, 9), (3, 28), (0, 10), (31, 4), (13, 0), (34, 7), (15, 17), (0, 34), (20, 7), (9, 3), (3, 3), (33, 12), (6, 11), (28, 3), (10, 2), (9, 22), (26, 0), (31, 3), (1, 29), (35, 0), (29, 16), (12, 2), (35, 4), (35, 8), (21, 3), (34, 1), (6, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "511560", "dataset": "MATH"}
{"messages": [{"content": "In a 33x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 37), 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), (2, 1), (0, 2), (21, 37), (5, 32), (0, 34), (13, 17), (20, 7), (26, 29), (20, 34), (15, 16), (19, 8), (32, 19), (12, 33), (16, 20), (27, 33), (8, 16), (7, 9), (14, 2), (11, 3), (8, 11), (4, 4), (5, 6), (32, 14), (28, 17), (12, 1), (19, 0), (18, 22), (11, 26), (21, 25), (21, 36), (2, 7), (30, 35), (23, 1), (18, 4), (2, 11), (20, 35), (19, 27), (18, 28), (12, 35), (25, 16), (16, 32), (24, 14), (19, 25), (16, 14), (27, 16), (0, 33), (12, 24), (30, 4), (26, 13), (20, 4), (0, 13), (32, 10), (1, 27), (7, 23), (26, 27), (6, 10), (17, 13), (32, 17), (14, 13), (20, 32), (24, 23), (8, 22), (5, 14), (14, 16), (10, 13), (11, 21), (17, 32), (26, 33), (22, 6), (11, 8), (8, 27), (32, 11), (17, 19), (11, 2), (9, 0), (0, 17), (4, 7), (3, 29), (21, 10), (12, 20), (15, 5), (28, 37), (13, 22), (0, 4), (5, 23), (29, 26), (31, 12), (16, 3), (23, 33), (26, 36), (18, 31), (24, 2), (5, 1), (29, 21), (28, 25), (3, 14), (29, 24), (25, 30), (11, 18), (20, 16), (2, 28), (32, 15), (23, 22), (27, 21), (21, 21), (12, 16), (1, 28), (7, 6), (20, 14), (7, 35), (28, 36), (8, 24), (16, 35), (21, 14), (10, 17), (27, 9), (31, 29), (12, 32), (20, 12), (15, 3), (17, 28), (3, 13), (13, 21), (13, 15), (19, 12), (20, 19), (8, 35), (19, 21), (30, 32), (18, 18), (1, 25), (5, 27), (27, 18), (9, 22), (3, 2), (6, 31), (23, 32), (19, 32), (15, 10), (14, 17), (5, 33), (16, 22), (8, 5), (4, 31), (8, 23), (30, 30), (21, 1), (3, 5), (26, 9), (2, 30), (18, 10), (4, 34), (6, 16), (4, 25), (24, 19), (30, 25), (13, 34), (21, 2), (8, 21), (13, 13), (27, 6), (2, 36), (32, 5), (5, 2), (28, 34), (7, 3), (27, 23), (21, 18), (6, 20), (24, 3), (27, 19), (5, 17), (24, 7), (29, 17), (9, 33), (11, 27), (9, 18), (15, 20), (28, 12), (31, 37), (7, 30), (19, 29), (13, 26), (3, 15), (12, 22), (4, 27), (26, 35), (19, 15), (11, 16), (17, 31), (12, 34), (28, 22), (17, 2), (17, 18), (5, 25), (26, 10), (11, 33), (1, 8), (32, 0), (11, 24), (26, 17), (31, 1), (21, 12), (20, 30), (4, 24), (10, 1), (13, 19), (22, 29), (31, 14), (8, 37), (24, 32), (2, 20), (3, 12), (21, 3), (15, 32), (7, 31), (1, 7), (24, 6), (3, 22), (29, 19), (21, 33), (8, 31), (23, 2), (15, 11), (1, 26), (0, 7), (22, 14), (7, 4), (20, 15), (14, 37), (13, 29), (13, 11), (16, 6), (4, 19), (22, 15), (15, 21), (13, 16), (32, 16), (31, 17), (23, 28), (4, 16), (4, 30), (31, 15), (5, 28), (14, 25), (16, 18), (10, 12), (26, 24), (10, 14), (27, 5), (23, 10), (28, 10), (30, 34), (5, 16), (1, 18), (20, 21), (29, 37), (32, 35), (10, 27), (25, 3), (11, 20), (30, 24), (11, 10), (23, 27), (26, 19), (28, 13), (3, 32), (20, 17), (15, 18), (21, 24), (4, 28), (14, 11), (32, 33), (6, 7), (10, 20), (25, 24), (22, 11), (19, 36), (28, 14), (3, 6), (10, 29), (21, 6), (22, 18), (31, 31), (10, 25), (6, 12), (2, 2), (24, 0), (13, 8), (20, 13), (0, 14), (20, 29), (7, 0), (23, 37), (18, 6), (20, 11), (30, 18), (16, 9), (6, 4), (14, 27), (7, 28), (9, 24), (6, 33), (28, 20), (32, 8), (28, 29), (5, 19), (12, 15), (16, 5), (13, 4), (7, 19), (9, 1), (2, 23), (13, 32), (8, 1), (25, 15), (1, 30), (9, 19), (3, 9), (13, 33), (0, 21), (9, 2), (27, 8), (15, 8), (0, 26), (13, 5), (7, 20), (14, 26), (4, 13), (29, 7), (5, 11), (11, 4), (18, 13), (9, 27), (11, 34), (28, 21), (27, 4), (27, 29), (5, 8), (13, 2), (6, 36), (9, 35), (27, 0), (31, 5), (29, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "994194", "dataset": "MATH"}
{"messages": [{"content": "In a 32x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 36), 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), (29, 14), (12, 23), (29, 13), (20, 16), (23, 22), (3, 3), (25, 34), (12, 11), (19, 2), (24, 22), (26, 15), (20, 21), (12, 5), (24, 0), (25, 33), (9, 13), (23, 15), (31, 28), (19, 6), (25, 18), (2, 7), (26, 17), (8, 34), (8, 25), (28, 28), (6, 7), (26, 25), (14, 35), (24, 16), (5, 9), (16, 1), (27, 16), (25, 16), (4, 21), (14, 22), (3, 34), (17, 17), (29, 28), (15, 17), (21, 6), (11, 23), (4, 23), (26, 10), (15, 7), (5, 27), (5, 13), (21, 30), (18, 16), (25, 22), (11, 9), (30, 30), (16, 31), (21, 7), (13, 25), (28, 10), (26, 14), (10, 26), (4, 22), (16, 8), (30, 29), (15, 16), (1, 24), (2, 1), (28, 8), (15, 36), (10, 35), (2, 33), (29, 23), (11, 36), (14, 18), (16, 6), (30, 15), (3, 28), (19, 4), (17, 2), (6, 2), (12, 16), (29, 32), (28, 35), (5, 1), (10, 33), (26, 33), (14, 25), (9, 11), (16, 10), (26, 7), (9, 33), (8, 9), (14, 28), (27, 4), (3, 6), (7, 18), (31, 30), (4, 4), (9, 24), (11, 27), (4, 31), (13, 6), (5, 29), (10, 34), (12, 34), (2, 20), (0, 20), (20, 3), (10, 13), (28, 29), (26, 11), (30, 12), (9, 30), (13, 29), (11, 29), (17, 15), (18, 11), (14, 1), (27, 14), (5, 0), (23, 27), (1, 13), (31, 8), (21, 0), (28, 3), (16, 13), (0, 35), (5, 24), (17, 32), (16, 17), (23, 2), (27, 30), (7, 29), (11, 30), (26, 0), (30, 35), (9, 8), (11, 19), (23, 6), (6, 26), (25, 8), (1, 6), (17, 27), (7, 4), (0, 9), (29, 25), (1, 9), (28, 21), (16, 15), (19, 16), (15, 13), (7, 28), (2, 12), (4, 35), (17, 30), (3, 13), (11, 14), (3, 1), (19, 36), (10, 10), (20, 31), (14, 33), (29, 17), (7, 33), (17, 36), (15, 34), (10, 21), (31, 22), (0, 16), (26, 19), (27, 24), (11, 35), (13, 28), (30, 21), (8, 4), (18, 10), (22, 3), (7, 36), (18, 3), (20, 12), (28, 31), (28, 1), (19, 21), (19, 24), (24, 1), (12, 2), (0, 6), (15, 11), (9, 27), (5, 20), (26, 22), (1, 14), (20, 5), (24, 10), (26, 18), (6, 20), (19, 0), (20, 22), (8, 17), (20, 6), (17, 8), (0, 21), (17, 13), (29, 8), (23, 11), (25, 12), (7, 2), (16, 21), (23, 28), (16, 32), (8, 14), (6, 34), (7, 5), (1, 25), (14, 21), (27, 20), (23, 36), (31, 24), (31, 4), (26, 26), (20, 14), (4, 16), (15, 1), (0, 7), (16, 3), (13, 17), (17, 18), (30, 1), (21, 36), (31, 14), (2, 32), (23, 7), (3, 30), (28, 22), (21, 35), (28, 26), (0, 33), (21, 11), (1, 28), (19, 29), (29, 27), (17, 23), (18, 19), (19, 22), (2, 24), (25, 20), (17, 9), (13, 36), (30, 8), (30, 32), (5, 4), (26, 32), (20, 28), (12, 22), (30, 0), (16, 34), (24, 25), (15, 0), (16, 26), (5, 28), (14, 23), (24, 24), (18, 9), (10, 36), (27, 23), (26, 16), (12, 15), (3, 25), (2, 8), (9, 28), (11, 2), (17, 28), (7, 32), (13, 21), (20, 19), (18, 8), (14, 4), (23, 29), (17, 10), (10, 7), (27, 21), (15, 6), (17, 14), (28, 14), (29, 7), (11, 28), (16, 20), (1, 29), (23, 17), (29, 24), (3, 17), (31, 15), (2, 18), (2, 36), (23, 16), (15, 24), (12, 13), (6, 27), (1, 21), (26, 13), (27, 9), (15, 22), (23, 10), (2, 30), (22, 36), (22, 35), (22, 17), (1, 17), (6, 24), (13, 0), (23, 21), (24, 9), (9, 17), (14, 0), (6, 28), (24, 27), (10, 32), (6, 18), (28, 30), (17, 25), (15, 35), (24, 14), (27, 25), (0, 3), (25, 31), (20, 18), (3, 20), (24, 17), (7, 15), (5, 34), (17, 24), (21, 27), (8, 5), (24, 6), (6, 32), (16, 35), (3, 18), (30, 27), (2, 26), (28, 9), (16, 18), (1, 3), (16, 0), (2, 5), (23, 12), (24, 23), (10, 15), (24, 36), (13, 9), (24, 8), (3, 15), (5, 33), (15, 4), (30, 20), (31, 20), (1, 12), (19, 1), (9, 21), (23, 26), (15, 33), (5, 32), (6, 16), (4, 25), (13, 12), (8, 11), (6, 36), (29, 21), (21, 26), (14, 2), (8, 18), (5, 23), (20, 17), (31, 26), (6, 21), (4, 33), (22, 19), (19, 28), (1, 7), (20, 1), (4, 30), (9, 36), (8, 0), (28, 32), (22, 16), (6, 35), (19, 32), (11, 26), (20, 34), (18, 5), (23, 4), (31, 13), (9, 16), (1, 33), (14, 13), (12, 19), (29, 12), (10, 0), (18, 21), (30, 4), (26, 21), (6, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349596", "dataset": "MATH"}
{"messages": [{"content": "In a 36x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 30), 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), (14, 28), (35, 7), (0, 5), (29, 0), (24, 26), (6, 15), (25, 11), (12, 14), (19, 7), (1, 8), (18, 28), (22, 13), (1, 23), (6, 29), (3, 18), (34, 5), (13, 13), (9, 26), (16, 26), (13, 23), (21, 14), (18, 12), (27, 14), (6, 30), (29, 28), (18, 13), (13, 4), (5, 3), (2, 13), (20, 7), (19, 17), (34, 22), (31, 6), (9, 10), (10, 5), (18, 26), (6, 5), (20, 20), (22, 7), (11, 14), (33, 6), (24, 6), (22, 4), (2, 23), (3, 12), (16, 28), (22, 14), (0, 28), (30, 26), (23, 14), (24, 18), (25, 5), (1, 21), (28, 24), (25, 1), (25, 18), (1, 22), (18, 2), (7, 6), (15, 13), (18, 9), (33, 17), (33, 25), (31, 7), (29, 1), (2, 16), (29, 8), (14, 8), (17, 18), (15, 16), (4, 8), (4, 2), (15, 17), (31, 11), (19, 16), (23, 10), (28, 27), (11, 11), (1, 14), (8, 12), (11, 22), (29, 17), (14, 0), (15, 4), (17, 19), (6, 20), (21, 27), (2, 20), (15, 22), (25, 27), (2, 26), (3, 13), (11, 28), (8, 1), (22, 0), (30, 25), (14, 7), (34, 24), (16, 20), (8, 27), (28, 18), (20, 9), (10, 15), (0, 6), (19, 8), (13, 14), (14, 10), (10, 4), (22, 29), (12, 20), (28, 7), (2, 19), (2, 11), (35, 29), (25, 3), (26, 19), (10, 1), (20, 27), (7, 18), (11, 10), (26, 26), (32, 19), (16, 23), (4, 30), (13, 0), (7, 5), (10, 20), (14, 3), (2, 3), (4, 19), (8, 28), (32, 14), (35, 19), (4, 6), (27, 4), (20, 26), (15, 30), (33, 24), (10, 2), (9, 25), (13, 20), (18, 20), (28, 0), (1, 28), (0, 14), (3, 17), (8, 29), (24, 22), (2, 10), (31, 18), (5, 28), (14, 21), (13, 29), (28, 8), (33, 19), (20, 29), (19, 30), (27, 9), (24, 2), (4, 17), (5, 4), (1, 30), (8, 6), (19, 6), (1, 4), (34, 14), (7, 19), (12, 15), (24, 15), (9, 9), (14, 22), (28, 30), (30, 9), (2, 8), (5, 24), (12, 22), (11, 26), (3, 8), (12, 6), (21, 18), (2, 24), (6, 10), (29, 18), (23, 25), (22, 26), (13, 2), (23, 13), (30, 3), (9, 14), (27, 28), (9, 1), (28, 22), (30, 1), (16, 2), (33, 1), (6, 21), (31, 24), (17, 15), (8, 4), (19, 13), (35, 22), (13, 17), (4, 14), (14, 4), (16, 16), (17, 3), (10, 26), (34, 15), (30, 12), (22, 20), (32, 22), (30, 22), (29, 7), (10, 11), (26, 28), (18, 24), (10, 27), (24, 21), (31, 1), (17, 16), (4, 11), (0, 17), (22, 11), (15, 2), (13, 21), (4, 20), (30, 27), (24, 24), (30, 28), (6, 7), (35, 20), (22, 1), (1, 16), (5, 2), (6, 25), (20, 17), (22, 22), (35, 11), (25, 10), (23, 24), (17, 29), (8, 0), (1, 0), (34, 19), (7, 4), (25, 23), (24, 20), (21, 22), (8, 23), (22, 6), (29, 21), (27, 0), (1, 2), (33, 2), (31, 3), (28, 3), (13, 1), (30, 24), (11, 30), (31, 26), (2, 29), (26, 20), (15, 26), (8, 26), (16, 19), (22, 16), (12, 10), (22, 30), (31, 23), (12, 29), (0, 26), (9, 29), (34, 18), (14, 16), (13, 8), (23, 29), (25, 0), (22, 15), (24, 0), (16, 9), (35, 5), (4, 9), (21, 4), (20, 10), (22, 8), (29, 4), (32, 0), (12, 7), (23, 2), (2, 22), (16, 3), (16, 10), (25, 25), (9, 11), (9, 21), (17, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417816", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), 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, 31), (11, 24), (15, 30), (10, 5), (16, 32), (23, 25), (30, 32), (11, 35), (9, 12), (18, 29), (5, 7), (25, 2), (16, 21), (18, 6), (4, 13), (19, 20), (29, 4), (27, 17), (18, 18), (5, 30), (24, 14), (13, 31), (26, 30), (25, 0), (22, 13), (7, 5), (14, 18), (21, 5), (27, 29), (6, 10), (27, 22), (21, 31), (19, 7), (23, 34), (20, 36), (10, 17), (26, 26), (6, 6), (8, 20), (28, 17), (10, 34), (30, 27), (1, 13), (18, 20), (1, 27), (13, 21), (26, 24), (20, 20), (17, 30), (24, 25), (24, 36), (9, 16), (29, 30), (27, 32), (15, 9), (21, 0), (12, 36), (2, 29), (27, 14), (17, 23), (4, 27), (24, 7), (0, 36), (3, 13), (12, 8), (29, 18), (5, 19), (8, 35), (6, 15), (18, 21), (10, 1), (29, 23), (8, 13), (22, 0), (24, 29), (23, 7), (22, 3), (1, 32), (4, 16), (1, 22), (9, 3), (21, 16), (0, 16), (6, 26), (5, 16), (20, 35), (28, 0), (11, 14), (8, 33), (20, 17), (25, 22), (19, 11), (29, 8), (1, 8), (30, 3), (10, 36), (30, 14), (20, 6), (14, 25), (5, 12), (27, 21), (10, 19), (14, 3), (20, 21), (4, 3), (7, 13), (14, 1), (10, 23), (17, 2), (2, 34), (18, 27), (22, 1), (20, 9), (6, 32), (16, 36), (15, 10), (2, 1), (18, 32), (12, 33), (7, 18), (30, 10), (28, 33), (16, 24), (30, 18), (11, 4), (29, 5), (16, 7), (3, 18), (20, 23), (0, 25), (10, 8), (16, 10), (7, 30), (15, 12), (0, 22), (6, 20), (15, 1), (12, 3), (16, 33), (23, 33), (28, 20), (23, 36), (9, 5), (9, 26), (10, 14), (5, 9), (22, 4), (23, 13), (9, 36), (28, 4), (26, 36), (10, 11), (5, 6), (26, 27), (1, 25), (29, 19), (18, 17), (26, 34), (7, 14), (20, 22), (19, 9), (17, 18), (5, 27), (14, 31), (30, 22), (19, 21), (8, 14), (25, 31), (0, 34), (14, 20), (13, 36), (24, 22), (18, 15), (8, 27), (2, 21), (13, 20), (29, 12), (13, 22), (2, 30), (4, 26), (23, 24), (13, 8), (27, 30), (17, 27), (26, 13), (22, 7), (7, 35), (30, 35), (29, 1), (2, 8), (6, 27), (24, 13), (29, 6), (15, 27), (23, 28), (26, 35), (2, 0), (18, 5), (22, 30), (19, 36), (9, 18), (17, 29), (2, 11), (5, 11), (9, 30), (7, 12), (10, 6), (17, 16), (4, 22), (10, 12), (13, 2), (12, 13), (29, 2), (2, 17), (27, 9), (5, 29), (15, 32), (5, 33), (14, 19), (7, 4), (1, 0), (5, 21), (6, 13), (18, 11), (26, 21), (16, 30), (12, 31), (0, 14), (28, 10), (23, 5), (10, 25), (26, 10), (3, 26), (30, 16), (27, 19), (24, 31), (3, 8), (23, 31), (27, 36), (19, 2), (0, 29), (23, 35), (19, 26), (22, 22), (26, 11), (12, 22), (10, 13), (0, 19), (2, 9), (4, 1), (8, 18), (29, 20), (14, 2), (21, 10), (10, 22), (30, 13), (1, 9), (19, 8), (16, 20), (17, 34), (17, 7), (9, 8), (13, 26), (15, 17), (30, 24), (23, 3), (28, 30), (21, 15), (20, 12), (2, 33), (16, 27), (3, 32), (30, 26), (18, 9), (19, 30), (4, 34), (21, 6), (28, 23), (26, 16), (10, 15), (14, 30), (21, 26), (14, 27), (8, 28), (16, 15), (8, 30), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 29), 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), (29, 29), (12, 12), (0, 3), (4, 24), (14, 14), (31, 25), (32, 19), (1, 13), (13, 4), (12, 9), (26, 19), (28, 3), (30, 22), (13, 13), (26, 14), (34, 21), (7, 18), (5, 15), (8, 17), (25, 14), (14, 16), (9, 12), (29, 2), (22, 14), (10, 23), (23, 10), (14, 6), (22, 18), (19, 18), (7, 27), (15, 15), (22, 22), (25, 28), (2, 24), (33, 6), (14, 20), (31, 15), (19, 12), (13, 9), (34, 12), (18, 13), (18, 19), (22, 9), (28, 25), (14, 12), (28, 16), (9, 28), (15, 28), (23, 28), (15, 12), (4, 27), (19, 2), (30, 12), (10, 2), (21, 0), (21, 9), (28, 9), (32, 15), (14, 11), (12, 15), (25, 20), (11, 24), (14, 13), (29, 13), (27, 5), (33, 19), (22, 27), (16, 25), (10, 11), (9, 8), (16, 13), (17, 12), (20, 0), (25, 18), (8, 27), (6, 21), (4, 25), (6, 9), (30, 1), (5, 10), (21, 4), (26, 26), (24, 16), (24, 21), (28, 13), (22, 13), (11, 0), (18, 7), (3, 0), (8, 4), (3, 3), (31, 10), (26, 10), (5, 28), (15, 11), (14, 2), (24, 9), (30, 7), (33, 17), (9, 19), (28, 27), (4, 22), (19, 3), (22, 5), (2, 23), (4, 12), (1, 1), (24, 24), (30, 5), (4, 9), (6, 1), (13, 25), (20, 3), (14, 24), (12, 1), (26, 20), (18, 5), (17, 21), (26, 25), (0, 27), (28, 8), (7, 25), (18, 0), (28, 21), (17, 15), (1, 18), (30, 9), (21, 10), (11, 29), (11, 5), (28, 5), (29, 17), (27, 1), (19, 24), (26, 4), (4, 28), (32, 23), (1, 23), (16, 22), (29, 24), (25, 15), (12, 18), (6, 18), (13, 21), (0, 4), (33, 2), (13, 3), (33, 12), (31, 20), (16, 29), (1, 22), (14, 19), (8, 5), (34, 11), (26, 6), (5, 29), (24, 11), (19, 14), (34, 7), (21, 27), (30, 6), (14, 21), (8, 13), (28, 24), (1, 4), (20, 24), (18, 8), (5, 12), (12, 14), (9, 5), (33, 25), (5, 18), (32, 14), (2, 21), (4, 4), (33, 26), (0, 22), (16, 3), (28, 11), (6, 26), (15, 17), (22, 26), (24, 14), (2, 14), (20, 2), (26, 2), (18, 4), (34, 17), (16, 11), (17, 25), (9, 27), (32, 0), (8, 14), (0, 29), (22, 17), (27, 26), (5, 20), (0, 26), (28, 28), (3, 20), (20, 5), (18, 12), (31, 0), (33, 10), (20, 18), (3, 15), (24, 27), (19, 20), (22, 3), (17, 14), (3, 18), (16, 7), (19, 25), (5, 13), (23, 26), (1, 11), (30, 8), (22, 0), (32, 26), (20, 9), (2, 28), (33, 23), (30, 21), (14, 28), (30, 27), (25, 17), (14, 4), (23, 7), (20, 7), (30, 2), (32, 20), (8, 26), (33, 9), (30, 10), (32, 10), (11, 2), (29, 9), (22, 12), (28, 2), (19, 0), (23, 27), (16, 26), (31, 9), (6, 16), (12, 24), (33, 28), (6, 24), (15, 1), (2, 13), (5, 8), (2, 7), (23, 3), (20, 1), (26, 27), (3, 22), (23, 17), (24, 6), (15, 27), (29, 3), (28, 10), (26, 24), (8, 9), (10, 10), (19, 23), (22, 21), (21, 13), (1, 9), (3, 1), (12, 16), (32, 17), (25, 26), (11, 20), (17, 19), (33, 14), (12, 27), (16, 19), (23, 15), (31, 17), (13, 12), (17, 23), (12, 5), (31, 22), (1, 27), (3, 10), (1, 26), (12, 29), (0, 13), (34, 23), (26, 11), (28, 22), (23, 23), (13, 19), (8, 29), (16, 8), (4, 15), (5, 27), (5, 11), (7, 20), (1, 2), (17, 29), (24, 12), (28, 17), (11, 6), (1, 16), (1, 3), (6, 6), (30, 28), (3, 16), (31, 23), (14, 22), (16, 2), (11, 21), (11, 27), (28, 4), (34, 19), (27, 21), (32, 29), (7, 7), (16, 12), (19, 16), (9, 2), (20, 20), (0, 19), (25, 12), (11, 11), (5, 26), (26, 7), (12, 26), (14, 10), (1, 14), (30, 4), (27, 20), (31, 21), (30, 14), (8, 20), (7, 26), (0, 11), (11, 1), (12, 17), (0, 2), (26, 8), (0, 21), (18, 24), (16, 27), (21, 2), (0, 25), (1, 6), (16, 17), (13, 22), (6, 7), (31, 8), (20, 25), (25, 8), (17, 17), (18, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895488", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), 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), (12, 24), (16, 5), (5, 12), (26, 11), (22, 32), (27, 1), (16, 26), (19, 15), (28, 31), (2, 1), (27, 14), (2, 32), (5, 1), (2, 28), (21, 30), (20, 16), (2, 16), (15, 7), (1, 33), (27, 5), (22, 20), (10, 31), (24, 16), (12, 9), (14, 4), (3, 9), (19, 13), (19, 12), (32, 25), (26, 16), (0, 9), (4, 10), (20, 19), (9, 24), (7, 4), (4, 12), (10, 15), (27, 0), (7, 22), (18, 0), (31, 12), (1, 29), (19, 11), (21, 33), (23, 33), (9, 7), (24, 4), (19, 14), (20, 34), (27, 9), (16, 16), (1, 1), (30, 19), (17, 1), (0, 7), (4, 28), (15, 4), (20, 10), (11, 5), (9, 33), (31, 24), (15, 23), (19, 1), (30, 29), (27, 12), (13, 1), (23, 9), (7, 0), (12, 26), (10, 24), (7, 26), (33, 20), (7, 18), (13, 16), (32, 11), (28, 9), (32, 3), (0, 28), (2, 20), (31, 0), (16, 32), (6, 27), (14, 6), (15, 16), (32, 21), (2, 15), (27, 10), (4, 16), (21, 22), (3, 30), (29, 32), (5, 28), (4, 15), (33, 4), (11, 34), (3, 2), (18, 2), (17, 31), (32, 9), (23, 14), (11, 33), (0, 13), (33, 25), (17, 18), (31, 9), (21, 10), (18, 6), (18, 22), (19, 25), (10, 7), (12, 0), (20, 27), (27, 2), (16, 11), (24, 12), (25, 34), (30, 31), (25, 30), (6, 17), (16, 21), (19, 29), (23, 4), (3, 10), (21, 23), (32, 17), (9, 13), (12, 25), (32, 5), (21, 18), (13, 12), (26, 29), (19, 17), (12, 8), (9, 4), (8, 9), (15, 25), (19, 4), (15, 17), (27, 6), (10, 25), (14, 17), (21, 25), (13, 31), (9, 23), (2, 12), (7, 30), (29, 16), (24, 24), (23, 31), (21, 5), (15, 3), (26, 24), (7, 20), (25, 27), (25, 8), (6, 5), (6, 7), (17, 0), (1, 18), (0, 29), (10, 9), (22, 11), (15, 27), (12, 13), (28, 14), (13, 27), (12, 5), (14, 19), (30, 6), (19, 23), (0, 3), (26, 22), (6, 19), (7, 5), (24, 10), (20, 26), (23, 5), (3, 15), (25, 0), (19, 20), (0, 31), (1, 24), (10, 34), (28, 29), (11, 7), (26, 7), (22, 19), (25, 3), (19, 28), (31, 20), (6, 30), (32, 34), (9, 9), (6, 15), (19, 6), (30, 24), (10, 30), (13, 21), (4, 21), (30, 13), (27, 23), (8, 11), (1, 20), (25, 14), (14, 13), (10, 20), (1, 12), (29, 13), (11, 27), (14, 22), (4, 25), (5, 33), (31, 30), (7, 2), (12, 1), (25, 16), (20, 32), (7, 7), (1, 28), (27, 26), (27, 17), (15, 26), (3, 0), (19, 18), (1, 6), (33, 21), (15, 15), (1, 0), (32, 7), (17, 15), (7, 13), (0, 32), (20, 23), (20, 9), (11, 11), (1, 17), (29, 31), (8, 2), (22, 30), (22, 3), (8, 5), (2, 26), (2, 10), (17, 23), (1, 23), (23, 18), (7, 15), (13, 29), (31, 26), (33, 6), (10, 13), (26, 4), (13, 3), (16, 2), (22, 22), (0, 15), (25, 5), (3, 8), (9, 34), (14, 34), (30, 3), (25, 28), (12, 2), (18, 19), (11, 12), (0, 24), (2, 6), (9, 18), (1, 32), (26, 6), (22, 5), (18, 5), (27, 25), (12, 17), (2, 27), (29, 1), (24, 7), (11, 9), (5, 10), (2, 14), (16, 19), (16, 33), (10, 28), (22, 0), (18, 14), (6, 23), (28, 27), (29, 3), (27, 27), (6, 13), (24, 8), (0, 25), (30, 14), (26, 0), (21, 11), (17, 24), (1, 7), (31, 27), (11, 23), (21, 2), (17, 11), (28, 1), (6, 18), (7, 1), (6, 8), (14, 18), (10, 11), (33, 10), (10, 16), (32, 1), (33, 27), (26, 21), (9, 14), (21, 3), (15, 12), (20, 6), (31, 6), (16, 9), (27, 16), (19, 5), (6, 10), (3, 5), (28, 19), (28, 20), (26, 34), (28, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872960", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 32), (1, 30), (15, 8), (25, 33), (5, 26), (3, 31), (8, 4), (17, 6), (6, 11), (32, 23), (6, 2), (0, 31), (7, 1), (17, 21), (28, 17), (19, 6), (15, 7), (1, 1), (27, 24), (2, 5), (24, 19), (7, 19), (27, 30), (14, 14), (21, 9), (28, 7), (2, 7), (11, 6), (18, 2), (8, 33), (23, 21), (29, 13), (29, 0), (14, 12), (13, 31), (12, 22), (17, 22), (19, 16), (32, 2), (8, 28), (12, 12), (9, 21), (17, 26), (25, 6), (1, 17), (5, 22), (1, 6), (13, 30), (27, 21), (6, 21), (13, 5), (13, 26), (29, 14), (21, 7), (27, 11), (24, 4), (20, 19), (10, 23), (25, 20), (23, 8), (15, 15), (26, 34), (23, 23), (8, 24), (13, 23), (32, 32), (31, 2), (20, 18), (32, 1), (20, 23), (13, 20), (25, 36), (14, 27), (29, 29), (28, 23), (23, 33), (33, 25), (23, 30), (4, 21), (12, 23), (0, 33), (17, 33), (32, 22), (15, 24), (28, 34), (15, 31), (14, 32), (15, 23), (1, 23), (11, 33), (31, 6), (8, 25), (22, 34), (3, 32), (33, 0), (21, 18), (15, 37), (4, 9), (0, 12), (12, 17), (2, 23), (8, 21), (5, 20), (11, 25), (26, 31), (17, 19), (31, 18), (2, 27), (21, 1), (23, 12), (19, 4), (5, 33), (21, 6), (22, 33), (13, 1), (15, 13), (26, 12), (33, 32), (20, 11), (24, 18), (8, 6), (29, 12), (3, 3), (9, 12), (8, 7), (1, 35), (6, 10), (5, 11), (11, 32), (11, 9), (10, 33), (19, 32), (2, 20), (15, 6), (18, 23), (26, 2), (12, 10), (7, 27), (14, 33), (2, 2), (11, 10), (10, 7), (22, 15), (0, 14), (32, 12), (18, 6), (9, 20), (13, 32), (17, 12), (25, 26), (21, 11), (32, 15), (20, 12), (16, 29), (21, 35), (22, 19), (12, 21), (6, 37), (12, 37), (29, 37), (7, 14), (32, 30), (22, 3), (33, 14), (30, 33), (28, 33), (5, 36), (7, 10), (31, 15), (10, 19), (9, 14), (15, 1), (18, 1), (22, 8), (5, 0), (27, 12), (28, 35), (32, 16), (33, 31), (17, 15), (4, 5), (23, 29), (21, 31), (30, 2), (1, 9), (4, 34), (15, 33), (14, 15), (27, 4), (2, 36), (2, 34), (14, 18), (8, 17), (30, 15), (16, 4), (15, 16), (27, 20), (4, 14), (29, 5), (12, 16), (5, 2), (19, 27), (4, 7), (24, 7), (1, 19), (10, 12), (31, 24), (7, 30), (11, 35), (22, 16), (24, 22), (3, 6), (14, 30), (17, 28), (6, 9), (13, 22), (26, 4), (27, 25), (31, 31), (1, 11), (23, 10), (11, 13), (14, 25), (9, 31), (13, 35), (32, 25), (10, 22), (4, 33), (6, 25), (11, 12), (33, 28), (11, 15), (28, 19), (30, 24), (2, 26), (27, 13), (22, 9), (29, 36), (7, 28), (7, 22), (9, 34), (33, 34), (0, 32), (23, 25), (10, 28), (1, 12), (21, 25), (10, 26), (18, 19), (20, 2), (3, 34), (7, 29), (11, 36), (4, 35), (17, 34), (9, 35), (29, 31), (2, 3), (10, 20), (18, 14), (4, 25), (2, 25), (2, 32), (26, 5), (13, 9), (5, 8), (31, 22), (21, 37), (7, 20), (29, 27), (23, 32), (25, 17), (6, 36), (19, 12), (9, 18), (16, 3), (17, 35), (22, 27), (27, 26), (18, 32), (26, 17), (13, 18), (26, 28), (17, 37), (28, 1), (7, 26), (27, 23), (25, 31), (10, 3), (9, 29), (10, 37), (15, 26), (27, 3), (0, 28), (4, 36), (1, 18), (22, 0), (23, 11), (26, 15), (14, 29), (9, 3), (31, 37), (17, 1), (30, 18), (28, 20), (9, 5), (14, 17), (5, 13), (28, 9), (24, 9), (25, 28), (16, 19), (23, 17), (16, 10), (21, 3), (10, 11), (13, 17), (12, 33), (21, 8), (3, 30), (30, 26), (0, 11), (9, 15), (2, 9), (33, 13), (25, 4), (14, 8), (10, 25), (15, 9), (11, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3960", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 23), (10, 34), (27, 15), (9, 32), (8, 26), (16, 24), (12, 24), (12, 6), (3, 27), (12, 0), (23, 12), (19, 9), (2, 25), (26, 11), (25, 9), (1, 34), (18, 0), (4, 18), (14, 18), (16, 10), (31, 34), (27, 17), (17, 32), (7, 1), (17, 14), (29, 9), (32, 18), (14, 2), (13, 15), (18, 13), (4, 21), (12, 11), (29, 6), (32, 22), (5, 23), (21, 24), (3, 17), (1, 16), (0, 16), (14, 16), (15, 34), (25, 19), (18, 6), (20, 28), (22, 1), (23, 19), (34, 22), (4, 29), (26, 23), (22, 30), (3, 13), (3, 14), (9, 8), (11, 21), (14, 23), (8, 12), (3, 32), (33, 7), (23, 3), (33, 33), (15, 4), (10, 20), (14, 31), (7, 12), (17, 12), (16, 28), (29, 8), (18, 14), (15, 31), (3, 7), (15, 1), (34, 6), (15, 30), (11, 31), (30, 19), (7, 22), (14, 15), (2, 16), (31, 4), (25, 17), (33, 24), (3, 19), (4, 28), (25, 7), (21, 7), (18, 4), (19, 26), (17, 31), (5, 11), (5, 28), (33, 22), (16, 4), (27, 26), (12, 21), (1, 32), (19, 31), (23, 30), (8, 30), (24, 18), (13, 6), (24, 1), (34, 15), (3, 1), (3, 18), (14, 9), (27, 1), (4, 1), (34, 7), (33, 17), (1, 13), (34, 9), (18, 16), (28, 6), (2, 29), (13, 11), (10, 24), (31, 5), (33, 11), (16, 30), (4, 10), (11, 10), (5, 30), (24, 21), (27, 24), (17, 23), (10, 9), (6, 6), (4, 11), (14, 0), (19, 12), (10, 1), (27, 4), (19, 3), (32, 25), (30, 29), (22, 26), (31, 17), (32, 7), (23, 14), (27, 34), (16, 19), (11, 27), (27, 9), (16, 5), (14, 30), (5, 29), (30, 35), (31, 16), (7, 5), (23, 15), (5, 27), (26, 18), (18, 28), (19, 11), (10, 32), (7, 15), (12, 12), (30, 15), (5, 34), (12, 17), (3, 0), (23, 5), (24, 31), (13, 8), (7, 25), (10, 10), (31, 26), (29, 1), (5, 1), (4, 15), (32, 9), (14, 34), (1, 14), (30, 4), (0, 20), (22, 7), (0, 23), (17, 0), (18, 32), (20, 7), (2, 35), (27, 27), (34, 3), (9, 5), (11, 13), (22, 27), (14, 19), (17, 30), (12, 5), (6, 7), (26, 28), (29, 32), (19, 24), (30, 7), (9, 11), (13, 4), (6, 32), (1, 9), (21, 26), (32, 0), (26, 30), (4, 32), (21, 6), (9, 31), (4, 33), (18, 30), (19, 14), (31, 0), (30, 32), (5, 7), (2, 22), (29, 30), (8, 5), (23, 8), (27, 5), (9, 7), (14, 13), (3, 2), (12, 2), (4, 5), (26, 3), (25, 16), (1, 28), (2, 2), (13, 23), (17, 13), (32, 26), (21, 15), (24, 4), (15, 26), (1, 10), (22, 4), (6, 15), (4, 31), (34, 16), (33, 4), (19, 27), (27, 11), (6, 26), (18, 8), (0, 11), (14, 21), (15, 35), (33, 31), (32, 4), (9, 1), (4, 25), (12, 29), (9, 23), (21, 21), (28, 7), (3, 12), (31, 12), (13, 20), (25, 3), (32, 10), (33, 18), (2, 6), (31, 22), (30, 11), (22, 12), (5, 6), (29, 19), (7, 32), (26, 10), (12, 28), (1, 22), (26, 34), (0, 33), (18, 18), (17, 29), (22, 17), (8, 15), (16, 21), (9, 16), (25, 10), (22, 10), (28, 13), (13, 29), (28, 15), (1, 5), (19, 2), (14, 12), (19, 5), (31, 31), (15, 8), (2, 27), (14, 24), (24, 2), (6, 10), (16, 12), (31, 27), (17, 25), (19, 20), (25, 20), (15, 23), (6, 18), (21, 1), (25, 28), (30, 20), (4, 0), (33, 12), (17, 34), (29, 29), (21, 34), (1, 12), (8, 7), (13, 5), (12, 9), (22, 23), (9, 30), (28, 5), (8, 21), (34, 0), (21, 13), (25, 6), (6, 31), (22, 20), (7, 27), (18, 1), (33, 2), (5, 25), (2, 13), (25, 12), (21, 16), (17, 21), (8, 31), (4, 2), (0, 29), (14, 14), (2, 10), (34, 1), (7, 16), (19, 16), (22, 5), (9, 15), (24, 3), (26, 29), (4, 13), (16, 29), (26, 8), (20, 31), (7, 19), (20, 15), (3, 28), (30, 10), (23, 4), (22, 34), (31, 25), (13, 34), (17, 35), (32, 11), (7, 4), (0, 35), (7, 21), (29, 20), (14, 22), (28, 26), (9, 29), (11, 24), (17, 8), (25, 30), (24, 22), (10, 19), (14, 35), (29, 21), (20, 6), (28, 11), (23, 24), (20, 34), (25, 34), (7, 28), (15, 12), (13, 19), (9, 13), (25, 11), (23, 16), (7, 13), (7, 30), (15, 2), (0, 12), (21, 5), (16, 20), (20, 17), (8, 22), (28, 34), (27, 0), (0, 1), (20, 2), (14, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "641784", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 27), (34, 30), (20, 5), (35, 16), (26, 1), (27, 16), (19, 26), (35, 12), (24, 24), (3, 23), (38, 10), (11, 13), (7, 29), (33, 28), (33, 23), (33, 29), (30, 14), (37, 19), (9, 2), (8, 22), (7, 1), (21, 0), (14, 15), (16, 19), (8, 30), (17, 15), (5, 26), (26, 20), (33, 2), (15, 18), (11, 16), (33, 11), (5, 6), (1, 32), (13, 3), (37, 20), (4, 32), (23, 4), (28, 18), (1, 10), (19, 24), (34, 0), (34, 3), (12, 18), (10, 28), (26, 22), (38, 3), (7, 7), (30, 22), (38, 20), (18, 25), (20, 6), (22, 6), (18, 28), (14, 7), (23, 9), (28, 28), (17, 13), (30, 5), (13, 22), (24, 22), (18, 9), (13, 27), (3, 14), (17, 17), (12, 26), (4, 19), (36, 19), (27, 13), (12, 0), (22, 30), (36, 20), (14, 12), (28, 16), (26, 8), (14, 27), (34, 4), (0, 10), (14, 23), (17, 19), (25, 21), (20, 32), (29, 12), (6, 4), (36, 12), (14, 10), (31, 29), (6, 8), (22, 14), (9, 26), (19, 1), (6, 29), (24, 19), (25, 1), (21, 26), (33, 21), (3, 8), (37, 4), (29, 21), (13, 16), (10, 3), (17, 14), (9, 27), (29, 3), (15, 28), (30, 4), (3, 21), (5, 19), (20, 19), (0, 17), (7, 8), (15, 24), (22, 7), (16, 17), (9, 31), (20, 24), (35, 20), (6, 19), (1, 25), (18, 30), (7, 0), (11, 31), (29, 9), (15, 5), (37, 31), (27, 3), (29, 17), (38, 7), (20, 26), (25, 29), (23, 19), (5, 28), (36, 9), (16, 0), (31, 32), (4, 7), (28, 14), (13, 14), (27, 18), (12, 20), (26, 12), (22, 21), (28, 26), (38, 14), (12, 6), (17, 5), (20, 16), (11, 28), (10, 31), (12, 30), (12, 1), (30, 29), (11, 11), (3, 13), (25, 27), (22, 4), (4, 17), (25, 8), (1, 20), (15, 17), (10, 1), (36, 15), (22, 24), (23, 10), (18, 17), (37, 24), (21, 27), (2, 9), (7, 15), (2, 8), (33, 31), (24, 12), (3, 10), (29, 20), (9, 11), (17, 1), (8, 13), (3, 28), (16, 9), (2, 17), (18, 18), (1, 2), (25, 6), (12, 10), (18, 1), (21, 7), (35, 7), (9, 7), (24, 1), (26, 13), (4, 15), (24, 25), (4, 2), (1, 17), (7, 3), (18, 6), (0, 4), (23, 13), (34, 2), (16, 24), (37, 11), (22, 16), (14, 14), (31, 14), (22, 31), (10, 14), (34, 16), (17, 22), (38, 13), (17, 16), (35, 26), (7, 12), (2, 0), (9, 32), (7, 9), (16, 7), (31, 28), (14, 3), (19, 23), (0, 9), (25, 22), (3, 9), (32, 19), (38, 26), (24, 27), (17, 25), (5, 1), (6, 22), (23, 11), (21, 1), (28, 30), (19, 17), (11, 26), (32, 3), (4, 26), (2, 10), (5, 12), (12, 32), (8, 4), (8, 0), (19, 13), (34, 19), (19, 27), (6, 15), (28, 8), (20, 13), (23, 16), (38, 5), (32, 28), (32, 23), (31, 27), (24, 29), (18, 2), (3, 1), (0, 5), (1, 9), (34, 10), (4, 9), (21, 3), (34, 26), (25, 19), (29, 26), (0, 3), (29, 18), (17, 4), (38, 31), (2, 28), (17, 9), (32, 31), (6, 18), (5, 11), (13, 9), (6, 27), (18, 19), (6, 26), (22, 11), (8, 12), (24, 4), (11, 24), (20, 12), (11, 25), (14, 17), (9, 20), (10, 26), (32, 5), (21, 15), (32, 7), (21, 10), (10, 17), (20, 25), (7, 13), (18, 7), (8, 2), (26, 10), (12, 11), (15, 32), (34, 14), (37, 3), (25, 7), (28, 6), (20, 10), (21, 25), (7, 4), (9, 3), (5, 9), (32, 0), (25, 26), (37, 2), (31, 5), (28, 5), (20, 14), (29, 2), (37, 17), (29, 31), (3, 15), (11, 30), (10, 6), (14, 13), (38, 27), (11, 27), (18, 32), (38, 0), (33, 5), (32, 2), (35, 1), (13, 31), (30, 23), (8, 16), (2, 6), (22, 19), (28, 22), (1, 7), (25, 23), (5, 14), (4, 31), (26, 2), (21, 24), (34, 12), (31, 26), (24, 17), (8, 31), (9, 21), (16, 1), (18, 26), (12, 23), (30, 16), (0, 14), (2, 19), (22, 23), (0, 25), (27, 15), (20, 9), (1, 0), (38, 2), (3, 11), (35, 30), (1, 26), (8, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380640", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 11), (23, 16), (19, 19), (18, 9), (3, 24), (0, 18), (29, 28), (13, 2), (30, 13), (10, 25), (21, 15), (26, 5), (12, 19), (17, 30), (23, 10), (11, 18), (14, 0), (14, 1), (22, 3), (5, 12), (11, 14), (24, 21), (6, 13), (2, 16), (6, 28), (14, 15), (16, 4), (25, 2), (16, 21), (12, 16), (1, 6), (27, 19), (4, 6), (25, 22), (29, 12), (9, 22), (23, 1), (7, 18), (26, 14), (18, 21), (28, 28), (27, 20), (23, 26), (1, 15), (21, 17), (8, 2), (21, 5), (22, 27), (2, 4), (7, 21), (11, 30), (5, 3), (20, 29), (5, 9), (13, 18), (19, 29), (17, 5), (0, 3), (2, 2), (16, 9), (29, 19), (16, 1), (0, 24), (11, 13), (4, 1), (19, 23), (8, 9), (16, 18), (8, 0), (9, 7), (22, 2), (19, 14), (17, 11), (25, 19), (25, 12), (19, 4), (3, 26), (0, 11), (22, 20), (17, 4), (30, 15), (12, 26), (17, 8), (18, 23), (19, 28), (28, 25), (4, 20), (19, 11), (30, 25), (8, 14), (12, 3), (10, 26), (4, 27), (17, 12), (9, 0), (17, 19), (24, 5), (15, 21), (4, 16), (0, 1), (23, 7), (7, 12), (11, 10), (8, 10), (14, 23), (23, 12), (29, 2), (25, 4), (18, 30), (15, 8), (6, 30), (22, 8), (20, 20), (8, 1), (29, 6), (11, 22), (27, 2), (15, 2), (24, 0), (22, 29), (23, 5), (29, 17), (6, 16), (17, 0), (1, 14), (3, 0), (20, 2), (7, 8), (26, 17), (29, 29), (11, 21), (8, 24), (17, 24), (5, 24), (18, 22), (29, 9), (5, 4), (21, 1), (8, 30), (6, 4), (5, 6), (9, 13), (22, 26), (4, 10), (22, 10), (30, 4), (10, 12), (22, 19), (19, 18), (1, 13), (26, 3), (25, 16), (14, 21), (23, 0), (6, 0), (29, 4), (19, 15), (17, 1), (28, 30), (5, 5), (27, 26), (2, 24), (23, 2), (16, 17), (16, 20), (7, 26), (21, 4), (17, 9), (16, 13), (6, 20), (25, 6), (15, 12), (17, 17), (21, 10), (27, 5), (29, 11), (28, 4), (7, 11), (0, 19), (24, 3), (4, 14), (13, 3), (19, 10), (30, 3), (28, 18), (7, 28), (13, 4), (15, 15), (27, 30), (17, 18), (17, 16), (21, 0), (11, 29), (13, 21), (21, 29), (30, 12), (8, 28), (9, 30), (14, 8), (23, 4), (29, 7), (22, 0), (1, 30), (2, 10), (11, 9), (1, 10), (29, 21), (28, 6), (30, 14), (26, 7), (22, 16), (13, 13), (2, 22), (6, 11), (21, 18), (2, 26), (10, 30), (14, 20), (4, 11), (0, 9), (30, 6), (25, 9), (24, 25), (29, 25), (20, 25), (24, 11), (16, 24), (13, 22), (20, 0), (19, 26), (17, 14), (5, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "165078", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), 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), (0, 15), (26, 24), (12, 15), (31, 19), (31, 6), (16, 18), (25, 5), (11, 29), (3, 2), (18, 9), (14, 24), (25, 30), (20, 29), (27, 27), (27, 22), (4, 38), (20, 9), (23, 22), (12, 4), (14, 2), (6, 37), (29, 33), (23, 33), (14, 28), (27, 31), (19, 37), (11, 15), (15, 8), (10, 34), (27, 1), (18, 3), (22, 2), (2, 32), (32, 33), (3, 1), (2, 15), (16, 30), (7, 34), (4, 9), (7, 12), (14, 13), (10, 19), (21, 33), (4, 7), (12, 13), (14, 26), (9, 34), (4, 6), (4, 15), (11, 11), (16, 1), (20, 10), (19, 20), (15, 29), (0, 2), (28, 16), (28, 5), (19, 26), (29, 16), (9, 26), (9, 15), (24, 35), (23, 2), (8, 2), (2, 6), (15, 16), (4, 17), (24, 25), (29, 30), (33, 3), (0, 32), (10, 12), (8, 13), (24, 6), (20, 22), (31, 21), (26, 35), (29, 31), (15, 31), (12, 0), (11, 18), (3, 0), (22, 34), (5, 29), (5, 6), (18, 27), (8, 38), (15, 34), (16, 2), (5, 11), (5, 20), (32, 21), (10, 21), (27, 6), (16, 12), (9, 7), (32, 5), (17, 32), (9, 35), (12, 38), (4, 8), (8, 6), (16, 24), (25, 16), (11, 21), (25, 17), (5, 18), (22, 33), (18, 31), (17, 30), (7, 5), (4, 13), (6, 0), (31, 14), (2, 26), (11, 33), (5, 12), (25, 33), (31, 28), (10, 30), (15, 4), (27, 14), (17, 22), (18, 8), (11, 38), (18, 30), (29, 7), (8, 3), (33, 31), (5, 36), (15, 0), (2, 22), (22, 16), (28, 23), (6, 22), (2, 10), (20, 37), (11, 24), (30, 5), (28, 12), (3, 35), (28, 24), (9, 30), (7, 25), (22, 17), (22, 0), (15, 38), (5, 0), (4, 22), (32, 20), (30, 35), (14, 17), (32, 2), (19, 0), (32, 7), (2, 18), (21, 3), (1, 36), (13, 36), (10, 35), (33, 5), (28, 15), (5, 35), (11, 7), (31, 24), (23, 9), (30, 33), (20, 18), (8, 36), (2, 38), (17, 16), (9, 5), (16, 4), (23, 17), (16, 5), (6, 26), (5, 13), (17, 7), (6, 3), (5, 4), (29, 22), (31, 35), (26, 14), (30, 23), (22, 6), (24, 18), (8, 11), (7, 32), (2, 17), (3, 9), (21, 10), (31, 23), (20, 16), (2, 33), (16, 9), (3, 36), (7, 2), (3, 24), (13, 16), (21, 5), (7, 22), (14, 18), (7, 27), (14, 15), (32, 32), (6, 34), (23, 36), (0, 37), (11, 30), (12, 14), (0, 10), (5, 3), (11, 25), (3, 4), (33, 15), (22, 38), (30, 29), (16, 19), (14, 11), (3, 28), (16, 15), (12, 6), (19, 4), (4, 26), (11, 34), (6, 13), (5, 37), (22, 5), (10, 27), (10, 23), (2, 21), (29, 17), (15, 35), (30, 32), (12, 7), (26, 7), (21, 14), (30, 38), (12, 3), (32, 9), (1, 16), (3, 6), (25, 2), (3, 29), (22, 10), (20, 14), (8, 30), (29, 35), (3, 33), (18, 15), (30, 4), (8, 9), (29, 36), (23, 6), (7, 4), (21, 7), (0, 22), (23, 26), (6, 6), (25, 1), (2, 36), (21, 11), (22, 7), (4, 16), (21, 34), (6, 24), (21, 29), (24, 34), (18, 29), (31, 3), (21, 30), (7, 18), (30, 21), (21, 9), (8, 33), (10, 6), (30, 14), (13, 33), (2, 7), (11, 1), (16, 20), (1, 23), (5, 15), (15, 24), (4, 30), (5, 7), (29, 9), (4, 5), (33, 29), (5, 17), (7, 6), (7, 11), (17, 8), (24, 20), (1, 32), (18, 22), (0, 6), (15, 23), (14, 34), (32, 3), (7, 16), (30, 3), (25, 18), (18, 5), (32, 31), (33, 36), (31, 32), (31, 10), (33, 32), (27, 3), (8, 27), (2, 0), (13, 14), (24, 21), (0, 13), (14, 9), (29, 5), (29, 27), (31, 11), (22, 15), (16, 37), (4, 11), (19, 9), (9, 28), (23, 31), (19, 28), (20, 30), (4, 4), (12, 21), (4, 0), (9, 23), (2, 9), (13, 10), (33, 26), (17, 13), (21, 36), (17, 6), (8, 12), (6, 32), (31, 20), (2, 30), (22, 26), (3, 13), (10, 16), (2, 37), (17, 38), (10, 32), (11, 26), (12, 22), (8, 20), (16, 11), (17, 14), (31, 25), (11, 16), (4, 24), (33, 6), (28, 27), (3, 18), (5, 22), (14, 10), (16, 38), (1, 38), (21, 37), (20, 17), (18, 25), (17, 36), (0, 24), (16, 25), (4, 27), (17, 18), (10, 18), (8, 14), (0, 28), (21, 15), (16, 26), (13, 4), (1, 31), (29, 14), (31, 31), (13, 12), (31, 0), (11, 4), (24, 2), (3, 37), (1, 22), (33, 33), (24, 5), (6, 38), (9, 19), (27, 24), (8, 16), (0, 16), (26, 3), (15, 2), (14, 29), (27, 38), (12, 32), (28, 7), (16, 21), (19, 1), (21, 23), (29, 21), (25, 20), (32, 30), (17, 33), (5, 30), (24, 10), (24, 36), (1, 26), (22, 18), (12, 23), (5, 34), (26, 27), (28, 32), (6, 18), (14, 33), (20, 1), (7, 20), (1, 20), (7, 21), (30, 10), (8, 5), (23, 27), (20, 8), (27, 16), (28, 22), (31, 34), (21, 26), (11, 32), (5, 25), (10, 22), (25, 31), (31, 17), (12, 2), (20, 28), (32, 35), (32, 38)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "710592", "dataset": "MATH"}
{"messages": [{"content": "In a 33x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (13, 2), (17, 14), (15, 0), (24, 25), (1, 4), (4, 15), (25, 18), (6, 6), (16, 11), (17, 9), (12, 10), (4, 24), (11, 12), (6, 29), (23, 18), (1, 13), (17, 23), (24, 14), (18, 21), (22, 8), (23, 21), (19, 8), (16, 14), (6, 20), (20, 30), (18, 27), (0, 11), (22, 3), (17, 10), (13, 1), (19, 18), (16, 19), (7, 13), (9, 19), (11, 17), (15, 10), (30, 30), (7, 25), (1, 12), (25, 29), (3, 30), (24, 16), (12, 18), (9, 11), (24, 4), (2, 16), (23, 4), (0, 19), (26, 9), (4, 18), (13, 14), (20, 7), (8, 14), (27, 27), (24, 17), (25, 20), (32, 7), (7, 3), (2, 9), (30, 4), (18, 31), (30, 20), (28, 14), (31, 24), (32, 29), (5, 1), (24, 27), (0, 24), (3, 14), (18, 9), (3, 11), (29, 19), (21, 19), (8, 27), (22, 16), (7, 2), (24, 29), (14, 31), (18, 5), (31, 21), (31, 9), (9, 30), (10, 22), (17, 26), (4, 6), (7, 17), (5, 3), (20, 16), (14, 5), (0, 21), (14, 3), (5, 9), (19, 11), (28, 5), (10, 12), (28, 21), (28, 20), (30, 28), (27, 22), (14, 7), (8, 15), (2, 25), (0, 10), (12, 15), (30, 1), (12, 20), (5, 18), (21, 3), (18, 12), (18, 17), (31, 17), (0, 17), (5, 0), (15, 9), (20, 5), (16, 8), (16, 30), (24, 12), (15, 26), (9, 10), (0, 29), (16, 21), (6, 19), (7, 28), (13, 27), (10, 15), (5, 8), (16, 29), (30, 29), (24, 9), (5, 2), (5, 31), (26, 0), (24, 28), (16, 27), (32, 10), (18, 24), (3, 29), (8, 13), (15, 21), (29, 8), (20, 31), (29, 24), (1, 9), (5, 5), (27, 11), (23, 27), (1, 30), (6, 28), (6, 16), (2, 5), (15, 12), (31, 13), (29, 12), (27, 13), (21, 10), (22, 10), (13, 15), (6, 1), (12, 21), (31, 1), (15, 20), (14, 24), (13, 31), (12, 29), (20, 6), (12, 0), (19, 26), (7, 22), (30, 8), (15, 24), (31, 0), (9, 24), (21, 29), (23, 30), (16, 15), (4, 4), (8, 9), (4, 20), (14, 28), (26, 31), (18, 3), (32, 12), (25, 24), (19, 17), (11, 13), (0, 15), (19, 28), (4, 14), (21, 15), (26, 20), (6, 26), (20, 13), (30, 7), (20, 18), (17, 17), (26, 26), (23, 15), (16, 24), (24, 23), (15, 31), (21, 13), (23, 3), (9, 23), (11, 16), (22, 23), (31, 11), (22, 12), (6, 8), (12, 7), (30, 9), (15, 16), (25, 3), (16, 16), (15, 11), (23, 25), (17, 21), (12, 19), (17, 0), (17, 24), (31, 10), (10, 30), (6, 4), (19, 5), (2, 3), (5, 27), (12, 27), (13, 10), (32, 28), (2, 20), (16, 23), (0, 12), (0, 1), (9, 20), (15, 17), (2, 1), (21, 21), (26, 19), (32, 0), (11, 30), (32, 27), (28, 18), (11, 2), (17, 20), (12, 8), (30, 25), (11, 1), (22, 2), (9, 13), (13, 26), (31, 18), (25, 7), (29, 31), (13, 12), (10, 18), (19, 6), (25, 4), (9, 5), (23, 23), (24, 1), (29, 28), (23, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "663552", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), 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, 32), (1, 3), (3, 8), (21, 11), (20, 9), (19, 4), (28, 13), (9, 25), (10, 7), (33, 8), (15, 5), (30, 28), (4, 23), (19, 1), (13, 26), (32, 13), (30, 10), (18, 15), (33, 19), (11, 3), (1, 21), (1, 14), (8, 25), (1, 11), (15, 19), (24, 0), (28, 1), (4, 20), (23, 10), (2, 31), (11, 21), (27, 2), (11, 29), (14, 7), (0, 25), (33, 26), (11, 26), (36, 13), (27, 31), (2, 32), (26, 30), (32, 21), (33, 5), (18, 20), (29, 28), (0, 31), (16, 17), (6, 8), (1, 12), (29, 5), (18, 29), (22, 8), (8, 26), (26, 28), (20, 2), (33, 1), (14, 9), (0, 22), (21, 6), (12, 27), (13, 32), (6, 6), (30, 32), (36, 8), (6, 0), (5, 31), (20, 15), (35, 23), (27, 26), (33, 11), (17, 18), (7, 9), (21, 16), (33, 32), (24, 10), (27, 8), (31, 3), (36, 4), (30, 29), (3, 18), (14, 28), (33, 30), (9, 18), (35, 7), (33, 21), (4, 8), (18, 25), (36, 15), (25, 27), (14, 20), (30, 12), (6, 2), (35, 8), (1, 26), (12, 30), (12, 1), (10, 30), (16, 14), (10, 25), (5, 23), (27, 1), (21, 21), (35, 13), (31, 22), (26, 13), (29, 15), (3, 23), (14, 3), (24, 4), (9, 17), (27, 20), (34, 8), (0, 14), (13, 1), (11, 9), (35, 19), (7, 6), (21, 9), (11, 11), (12, 15), (9, 22), (2, 26), (17, 23), (3, 32), (36, 0), (2, 30), (30, 11), (11, 28), (5, 27), (21, 20), (13, 4), (4, 13), (33, 22), (6, 7), (19, 0), (22, 25), (9, 20), (2, 22), (35, 4), (30, 2), (36, 26), (17, 31), (17, 9), (1, 28), (5, 10), (20, 11), (32, 32), (28, 17), (16, 18), (20, 27), (20, 29), (31, 24), (6, 19), (3, 26), (33, 23), (34, 21), (19, 28), (9, 7), (1, 27), (28, 21), (33, 6), (24, 29), (16, 24), (26, 31), (3, 21), (36, 7), (16, 23), (12, 13), (12, 8), (18, 12), (23, 4), (29, 29), (15, 16), (24, 28), (15, 32), (19, 31), (35, 9), (36, 12), (21, 24), (14, 31), (18, 19), (30, 0), (21, 13), (3, 12), (29, 20), (9, 24), (30, 8), (10, 22), (34, 26), (11, 27), (11, 5), (12, 22), (12, 18), (29, 3), (2, 18), (19, 11), (20, 0), (12, 7), (19, 29), (14, 23), (22, 14), (20, 20), (4, 25), (20, 1), (17, 14), (36, 17), (32, 26), (21, 28), (0, 19), (19, 12), (22, 22), (24, 13), (7, 32), (16, 13), (10, 13), (7, 31), (17, 16), (30, 4), (4, 26), (8, 21), (15, 17), (10, 12), (23, 1), (25, 16), (2, 4), (19, 24), (34, 25), (5, 18), (7, 17), (2, 14), (4, 27), (24, 18), (4, 14), (24, 12), (12, 5), (0, 17), (0, 21), (23, 17), (23, 20), (10, 16), (24, 3), (6, 29), (31, 14), (13, 28), (17, 17), (20, 21), (2, 27), (30, 16), (32, 28), (30, 14), (8, 20), (2, 19), (31, 28), (16, 21), (1, 9), (7, 23), (28, 5), (13, 29), (36, 31), (26, 8), (25, 6), (3, 9), (17, 26), (27, 19), (26, 29), (11, 7), (28, 27), (16, 16), (5, 5), (36, 29), (32, 7), (10, 20), (8, 18), (17, 29), (27, 21), (11, 12), (28, 16), (16, 26), (10, 15), (11, 16), (34, 18), (16, 30), (5, 26), (1, 0), (34, 0), (31, 16), (15, 22), (32, 5), (7, 26), (0, 10), (9, 5), (19, 9), (32, 31), (29, 21), (7, 14), (14, 25), (1, 15), (16, 15), (22, 7), (13, 21), (15, 12), (16, 7), (1, 5), (19, 3), (3, 27), (0, 24), (6, 31), (17, 25), (24, 14), (6, 32), (0, 6), (7, 5), (27, 25), (5, 17), (10, 19), (22, 28), (21, 12), (22, 0), (6, 11), (33, 7), (24, 30), (25, 29), (17, 22), (35, 25), (28, 11), (13, 10), (16, 10), (10, 11), (7, 19), (23, 29), (7, 8), (8, 30), (23, 5), (0, 16), (1, 17), (30, 20), (7, 20), (25, 1), (19, 2), (31, 29), (12, 23), (23, 28), (19, 27), (20, 30), (33, 25), (14, 0), (26, 3), (27, 27), (11, 24), (19, 5), (18, 30), (24, 23), (12, 21), (27, 29), (0, 23), (16, 32), (17, 11), (26, 10), (28, 26), (27, 18), (18, 9), (29, 7), (26, 20), (11, 14), (14, 4), (35, 15), (6, 22), (32, 4), (1, 24), (34, 6), (34, 24), (3, 7), (13, 31), (13, 25), (8, 29), (27, 23), (25, 5), (34, 32), (5, 11), (33, 18), (10, 26), (23, 32), (8, 16), (30, 26), (9, 6), (24, 25), (29, 31), (16, 29), (27, 3), (4, 6), (2, 25), (5, 32), (9, 1), (25, 28), (23, 25), (7, 22), (5, 6), (19, 21), (4, 1), (12, 4), (0, 5), (8, 31), (26, 21), (0, 30), (20, 4), (11, 4), (23, 0), (31, 20), (4, 15), (12, 26), (16, 22), (31, 9), (3, 29), (5, 7), (29, 10), (15, 28), (11, 25), (28, 6), (16, 9), (7, 15), (35, 28), (6, 27), (31, 30), (2, 10), (34, 7), (24, 21), (6, 24), (10, 10), (14, 27), (14, 2), (30, 18), (25, 12), (30, 17), (33, 14), (20, 31), (36, 6), (35, 26), (22, 29), (18, 16), (12, 29), (3, 0), (1, 1), (32, 16), (24, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "757422", "dataset": "MATH"}
{"messages": [{"content": "In a 30x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 23), (7, 28), (18, 13), (0, 16), (25, 10), (21, 3), (15, 18), (5, 22), (12, 13), (16, 29), (22, 16), (20, 14), (15, 7), (9, 18), (15, 25), (7, 24), (18, 6), (9, 12), (3, 19), (6, 1), (6, 29), (13, 13), (10, 27), (0, 10), (5, 7), (1, 29), (6, 17), (29, 10), (2, 25), (28, 0), (17, 14), (13, 5), (25, 17), (28, 24), (19, 21), (29, 0), (12, 22), (28, 29), (10, 5), (9, 25), (9, 3), (6, 20), (2, 16), (27, 25), (16, 3), (20, 26), (22, 26), (5, 29), (2, 28), (18, 21), (9, 8), (17, 8), (19, 20), (17, 29), (8, 27), (6, 27), (20, 1), (25, 18), (1, 23), (7, 29), (25, 20), (3, 17), (20, 20), (25, 12), (21, 27), (26, 3), (10, 21), (24, 29), (9, 28), (17, 25), (3, 27), (4, 7), (24, 0), (5, 21), (16, 28), (21, 12), (22, 19), (16, 8), (22, 28), (1, 26), (10, 24), (1, 7), (0, 22), (16, 30), (22, 14), (27, 29), (15, 17), (21, 25), (26, 7), (13, 17), (20, 24), (10, 12), (27, 4), (5, 1), (17, 28), (29, 27), (3, 22), (2, 4), (13, 4), (1, 2), (7, 10), (5, 9), (25, 26), (22, 27), (1, 27), (25, 9), (8, 3), (14, 15), (14, 10), (8, 11), (2, 24), (25, 3), (13, 0), (1, 9), (7, 3), (6, 30), (13, 14), (5, 30), (22, 0), (19, 19), (14, 1), (2, 21), (12, 19), (5, 5), (29, 12), (5, 15), (13, 20), (14, 24), (5, 11), (9, 11), (6, 19), (14, 20), (4, 14), (19, 30), (2, 15), (26, 21), (2, 26), (25, 24), (17, 7), (10, 10), (29, 1), (3, 13), (12, 8), (25, 7), (6, 7), (5, 8), (6, 0), (27, 8), (6, 3), (7, 20), (12, 11), (3, 24), (26, 23), (10, 26), (18, 17), (11, 6), (17, 22), (20, 25), (25, 28), (6, 24), (2, 17), (7, 0), (24, 10), (24, 12), (20, 10), (26, 4), (18, 24), (17, 12), (15, 3), (23, 23), (10, 30), (22, 23), (22, 10), (1, 4), (19, 25), (9, 9), (29, 20), (25, 1), (15, 26), (26, 19), (0, 3), (11, 7), (20, 18), (21, 29), (26, 5), (2, 1), (3, 2), (3, 5), (24, 1), (19, 24), (24, 19), (12, 9), (6, 15), (15, 4), (8, 1), (9, 29), (22, 18), (21, 23), (25, 6), (4, 9), (10, 9), (22, 11), (9, 27), (13, 1), (7, 26), (27, 7), (2, 13), (12, 0), (10, 17), (9, 10), (13, 7), (6, 11), (19, 23), (2, 29), (6, 5), (3, 25), (24, 4), (8, 9), (24, 9), (12, 1), (15, 14), (6, 9), (0, 4), (4, 8), (5, 20), (14, 8), (4, 26), (28, 12), (6, 22), (21, 8), (24, 13), (18, 19), (23, 0), (26, 20), (22, 8), (14, 22), (8, 8), (13, 15), (25, 0), (21, 6), (25, 2), (28, 7), (26, 16), (9, 16), (8, 28), (26, 25), (9, 13), (2, 9), (25, 15), (2, 20), (1, 24), (18, 4), (21, 22), (24, 17), (5, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114984", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 18), (28, 32), (4, 21), (27, 5), (18, 8), (29, 11), (22, 33), (30, 25), (12, 32), (31, 33), (5, 5), (31, 16), (2, 7), (1, 29), (6, 7), (6, 26), (34, 12), (16, 29), (21, 23), (19, 21), (21, 33), (27, 31), (19, 4), (25, 7), (30, 27), (10, 24), (1, 10), (32, 5), (1, 17), (16, 16), (8, 14), (31, 5), (10, 7), (31, 31), (32, 34), (32, 8), (33, 17), (33, 30), (5, 31), (30, 20), (19, 26), (11, 23), (30, 3), (6, 3), (21, 16), (19, 33), (8, 34), (19, 6), (4, 28), (22, 18), (32, 9), (34, 20), (29, 18), (12, 5), (12, 19), (31, 29), (10, 12), (7, 29), (20, 17), (1, 12), (32, 18), (25, 15), (9, 33), (17, 21), (32, 15), (23, 1), (23, 20), (24, 16), (18, 13), (2, 2), (32, 33), (12, 9), (28, 5), (23, 28), (17, 0), (9, 2), (6, 21), (9, 17), (25, 10), (28, 33), (19, 12), (17, 28), (9, 30), (12, 29), (25, 33), (1, 27), (29, 25), (13, 25), (33, 26), (9, 15), (19, 30), (33, 24), (10, 32), (21, 25), (33, 20), (7, 7), (21, 30), (14, 27), (22, 14), (31, 10), (30, 13), (9, 1), (13, 16), (28, 22), (29, 17), (9, 9), (20, 18), (18, 5), (3, 0), (3, 25), (4, 17), (28, 1), (5, 22), (11, 13), (21, 20), (8, 18), (26, 8), (1, 15), (20, 2), (18, 4), (14, 15), (29, 23), (21, 10), (31, 0), (31, 23), (29, 20), (24, 10), (15, 11), (3, 10), (29, 1), (19, 19), (23, 16), (15, 33), (23, 21), (14, 29), (24, 27), (5, 19), (24, 20), (6, 13), (24, 26), (32, 10), (20, 30), (30, 14), (18, 27), (23, 27), (23, 22), (32, 25), (0, 26), (8, 27), (2, 3), (17, 26), (9, 0), (11, 15), (4, 27), (20, 5), (28, 26), (29, 22), (15, 12), (6, 15), (29, 10), (9, 8), (20, 23), (26, 26), (31, 13), (10, 33), (0, 28), (22, 9), (10, 26), (29, 9), (11, 28), (28, 27), (10, 28), (16, 21), (0, 20), (22, 7), (0, 27), (16, 2), (9, 14), (17, 15), (15, 27), (7, 18), (7, 14), (28, 2), (24, 32), (29, 19), (29, 15), (13, 15), (10, 3), (18, 31), (30, 15), (4, 15), (28, 9), (7, 24), (27, 19), (16, 11), (26, 15), (13, 13), (30, 16), (6, 0), (7, 27), (0, 4), (7, 22), (5, 30), (8, 23), (2, 9), (32, 11), (31, 20), (15, 21), (3, 31), (25, 23), (23, 14), (29, 16), (23, 24), (33, 28), (12, 21), (23, 19), (14, 30), (26, 9), (34, 15), (29, 8), (27, 23), (10, 11), (9, 3), (10, 19), (24, 29), (18, 0), (5, 9), (2, 6), (11, 21), (14, 31), (27, 28), (34, 17), (14, 1), (22, 24), (4, 8), (34, 3), (12, 0), (11, 24), (8, 2), (33, 13), (24, 9), (21, 17), (22, 5), (23, 7), (2, 29), (15, 13), (5, 10), (14, 22), (0, 29), (25, 26), (1, 25), (28, 31), (5, 4), (34, 6), (31, 22), (24, 5), (18, 34), (2, 15), (30, 7), (15, 24), (13, 7), (10, 17), (10, 21), (5, 28), (16, 33), (20, 9), (7, 8), (4, 9), (14, 12), (27, 22), (9, 26), (5, 26), (20, 13), (30, 8), (22, 12), (2, 20), (15, 4), (30, 6), (8, 30), (5, 32), (3, 17), (13, 8), (4, 12), (17, 18), (30, 33), (15, 20), (6, 23), (11, 8), (7, 15), (12, 3), (27, 3), (4, 19), (14, 19), (33, 23), (19, 7), (12, 17), (6, 22), (18, 25), (30, 0), (13, 30), (24, 7), (28, 20), (16, 19), (34, 32), (25, 29), (27, 12), (23, 33), (28, 19), (6, 27), (33, 1), (3, 22), (33, 18), (34, 24), (33, 16), (24, 19), (7, 19), (8, 31), (19, 15), (8, 15), (14, 25), (20, 29), (5, 13), (28, 25), (8, 11), (13, 17), (5, 15), (21, 15), (13, 19), (19, 20), (23, 13), (16, 26), (3, 1), (12, 14), (16, 1), (18, 24), (18, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "377280", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 32), (13, 5), (4, 8), (12, 10), (14, 10), (29, 25), (29, 5), (6, 9), (0, 6), (13, 29), (25, 3), (23, 34), (21, 21), (20, 26), (27, 31), (10, 23), (21, 27), (7, 29), (21, 8), (8, 26), (4, 26), (19, 33), (21, 0), (27, 25), (7, 8), (18, 21), (10, 34), (20, 24), (10, 6), (10, 12), (20, 20), (12, 33), (28, 20), (25, 2), (3, 12), (18, 13), (3, 0), (1, 18), (4, 11), (18, 9), (1, 20), (24, 7), (22, 17), (18, 26), (28, 6), (16, 11), (5, 5), (1, 23), (13, 11), (24, 32), (2, 26), (25, 0), (18, 34), (20, 32), (5, 19), (4, 18), (18, 25), (27, 3), (7, 13), (3, 19), (4, 12), (5, 25), (13, 27), (13, 28), (23, 31), (5, 26), (26, 32), (6, 1), (28, 17), (3, 17), (1, 8), (27, 11), (13, 1), (3, 28), (0, 32), (7, 0), (4, 27), (25, 24), (26, 24), (1, 11), (18, 31), (29, 4), (3, 26), (3, 13), (4, 7), (20, 34), (1, 26), (3, 2), (12, 25), (13, 26), (0, 28), (9, 33), (24, 22), (10, 27), (22, 7), (7, 21), (25, 10), (15, 22), (17, 25), (7, 31), (19, 24), (3, 14), (29, 30), (14, 28), (13, 8), (24, 29), (8, 4), (13, 18), (25, 29), (21, 1), (1, 17), (13, 6), (4, 29), (19, 26), (15, 30), (24, 33), (0, 33), (17, 14), (25, 17), (11, 9), (2, 4), (14, 0), (15, 11), (21, 7), (29, 12), (29, 11), (28, 14), (1, 2), (22, 25), (4, 4), (16, 14), (24, 30), (7, 32), (16, 15), (10, 31), (20, 5), (11, 11), (27, 22), (0, 21), (10, 29), (1, 16), (20, 33), (24, 23), (4, 1), (0, 34), (11, 13), (24, 11), (26, 18), (17, 27), (17, 15), (23, 19), (7, 14), (15, 33), (13, 33), (27, 18), (29, 20), (18, 15), (2, 27), (3, 22), (23, 10), (10, 3), (8, 19), (0, 26), (8, 2), (13, 4), (10, 19), (25, 9), (5, 15), (14, 5), (5, 32), (5, 10), (26, 19), (21, 33), (0, 30), (14, 25), (7, 17), (19, 16), (2, 23), (23, 26), (17, 34), (11, 8), (18, 4), (9, 11), (19, 6), (11, 5), (9, 23), (0, 1), (16, 2), (17, 0), (3, 34), (12, 26), (27, 5), (22, 23), (11, 30), (8, 17), (28, 0), (11, 10), (11, 26), (10, 21), (25, 1), (15, 2), (10, 32), (1, 3), (2, 16), (20, 23), (9, 17), (4, 24), (26, 15), (29, 0), (10, 14), (23, 11), (23, 0), (9, 32), (16, 6), (13, 17), (15, 27), (23, 20), (14, 24), (23, 5), (28, 5), (7, 15), (14, 19), (13, 30), (18, 11), (25, 26), (24, 0), (2, 19), (19, 9), (5, 2), (27, 1), (1, 27), (25, 20), (15, 28), (22, 27), (1, 29), (4, 32), (9, 30), (11, 19), (19, 32), (29, 21), (16, 17), (14, 29), (15, 34), (23, 30), (10, 8), (2, 12), (22, 22), (17, 22), (17, 6), (21, 23), (18, 19), (5, 28), (11, 25), (11, 3), (1, 28), (19, 31), (6, 27), (23, 17), (23, 13), (9, 7), (26, 26), (13, 7), (23, 32), (18, 17), (29, 19), (18, 27), (24, 14), (3, 7), (13, 16), (28, 26), (6, 33), (1, 13), (23, 15), (20, 6), (12, 7), (2, 20), (18, 10), (22, 4), (5, 7), (28, 1), (9, 19), (17, 20), (2, 33), (29, 18), (20, 12), (26, 13), (4, 30), (13, 25), (6, 5), (10, 11), (21, 13), (11, 0), (2, 5), (24, 24), (9, 1), (24, 20), (16, 23), (20, 17), (8, 30), (21, 25), (1, 9), (4, 5), (22, 21), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "423360", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 31), (23, 13), (1, 31), (9, 31), (16, 29), (20, 30), (2, 33), (11, 33), (31, 4), (13, 18), (8, 1), (23, 26), (4, 33), (11, 23), (33, 14), (15, 18), (16, 32), (12, 20), (33, 30), (22, 31), (2, 4), (32, 21), (7, 32), (21, 24), (17, 28), (28, 27), (29, 34), (8, 37), (3, 33), (8, 18), (1, 16), (32, 37), (1, 19), (26, 35), (30, 32), (10, 5), (10, 34), (5, 27), (29, 28), (12, 32), (12, 36), (27, 28), (3, 23), (28, 5), (0, 15), (23, 9), (18, 26), (21, 29), (9, 36), (28, 14), (21, 20), (7, 7), (6, 20), (25, 30), (8, 26), (31, 18), (14, 15), (20, 34), (12, 5), (29, 33), (31, 36), (29, 22), (22, 30), (24, 16), (24, 31), (23, 7), (24, 36), (17, 3), (9, 8), (14, 1), (16, 22), (13, 29), (28, 34), (21, 26), (27, 32), (2, 7), (2, 25), (26, 33), (16, 37), (19, 8), (31, 27), (2, 34), (6, 24), (7, 36), (1, 7), (9, 13), (13, 33), (8, 14), (7, 37), (18, 18), (26, 18), (33, 15), (30, 23), (4, 1), (19, 9), (24, 23), (2, 5), (3, 35), (26, 37), (20, 6), (12, 21), (25, 16), (5, 17), (30, 6), (19, 2), (10, 14), (28, 19), (4, 14), (2, 23), (14, 4), (29, 4), (13, 31), (31, 21), (6, 18), (15, 16), (1, 2), (25, 6), (10, 28), (10, 3), (9, 9), (33, 16), (32, 12), (10, 10), (23, 29), (17, 14), (28, 12), (19, 22), (0, 22), (18, 36), (23, 3), (11, 15), (23, 15), (11, 0), (8, 16), (5, 25), (6, 31), (26, 1), (23, 35), (22, 22), (2, 11), (23, 18), (1, 10), (1, 4), (14, 0), (2, 9), (32, 15), (11, 22), (26, 30), (25, 19), (13, 28), (17, 27), (12, 1), (1, 3), (0, 9), (19, 15), (25, 11), (22, 13), (25, 33), (12, 11), (29, 24), (14, 12), (29, 11), (23, 1), (33, 35), (10, 26), (16, 24), (17, 10), (5, 7), (18, 12), (17, 34), (4, 31), (8, 2), (4, 25), (18, 2), (33, 26), (0, 33), (32, 0), (11, 25), (24, 2), (6, 5), (30, 28), (13, 26), (24, 35), (22, 0), (2, 14), (33, 19), (16, 16), (5, 6), (19, 28), (14, 13), (12, 4), (5, 14), (3, 4), (0, 6), (28, 25), (16, 3), (19, 4), (13, 23), (13, 0), (20, 18), (3, 12), (32, 8), (19, 34), (4, 32), (6, 17), (22, 8), (30, 10), (14, 18), (17, 2), (21, 11), (14, 28), (7, 27), (18, 35), (6, 29), (31, 32), (25, 13), (28, 32), (31, 25), (8, 30), (21, 17), (23, 0), (4, 9), (1, 33), (29, 16), (30, 22), (28, 21), (10, 21), (12, 18), (5, 11), (8, 25), (3, 16), (5, 13), (20, 12), (10, 19), (10, 2), (13, 6), (17, 19), (2, 17), (4, 12), (23, 32), (27, 4), (15, 5), (29, 10), (20, 5), (10, 37), (25, 37), (0, 31), (23, 11), (23, 19), (20, 2), (17, 6), (24, 4), (17, 37), (6, 0), (14, 25), (15, 21), (6, 27), (5, 37), (9, 23), (27, 16), (8, 17), (9, 17), (22, 33), (17, 13), (0, 27), (19, 16), (12, 29), (19, 13), (3, 24), (22, 15), (22, 19), (33, 17), (29, 2), (11, 16), (5, 9), (2, 13), (29, 27), (26, 10), (30, 36), (8, 34), (16, 30), (7, 8), (16, 34), (15, 19), (32, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "349936", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 29), (35, 24), (26, 19), (26, 31), (23, 33), (18, 12), (3, 24), (36, 8), (10, 22), (12, 25), (2, 18), (3, 21), (17, 5), (10, 17), (7, 0), (10, 6), (2, 26), (2, 22), (15, 20), (12, 3), (37, 9), (15, 2), (33, 27), (6, 22), (27, 31), (27, 8), (26, 14), (23, 9), (12, 14), (6, 32), (19, 18), (22, 28), (0, 29), (19, 22), (15, 25), (17, 10), (2, 5), (37, 32), (8, 4), (16, 8), (18, 28), (6, 29), (18, 0), (18, 4), (25, 30), (0, 4), (2, 13), (26, 23), (26, 0), (23, 18), (3, 31), (24, 30), (31, 32), (9, 31), (9, 13), (25, 29), (28, 30), (17, 0), (34, 19), (17, 20), (33, 31), (17, 6), (21, 32), (29, 33), (37, 26), (38, 28), (26, 17), (11, 0), (2, 32), (4, 7), (32, 3), (21, 17), (3, 1), (27, 6), (4, 31), (34, 25), (34, 1), (10, 5), (7, 23), (22, 31), (8, 5), (0, 6), (9, 12), (14, 10), (18, 14), (15, 24), (0, 25), (21, 7), (31, 26), (6, 9), (34, 9), (27, 11), (13, 24), (17, 2), (18, 16), (7, 8), (29, 26), (7, 25), (26, 11), (30, 0), (34, 29), (35, 19), (35, 0), (30, 30), (6, 23), (21, 19), (3, 30), (8, 2), (20, 33), (25, 16), (22, 1), (37, 29), (7, 17), (32, 9), (36, 3), (37, 15), (4, 0), (11, 30), (26, 28), (28, 21), (7, 26), (36, 15), (22, 32), (18, 11), (28, 5), (11, 33), (0, 7), (23, 32), (6, 20), (2, 28), (3, 20), (20, 8), (20, 11), (9, 32), (7, 10), (3, 22), (26, 26), (11, 12), (26, 15), (14, 13), (27, 3), (18, 26), (31, 24), (17, 28), (29, 17), (19, 33), (35, 14), (24, 26), (19, 3), (1, 4), (32, 21), (35, 5), (31, 23), (12, 5), (9, 25), (3, 9), (8, 14), (7, 4), (15, 21), (18, 3), (32, 11), (32, 17), (33, 5), (8, 10), (34, 33), (6, 33), (24, 17), (5, 19), (35, 12), (1, 7), (11, 1), (5, 12), (26, 8), (2, 1), (6, 4), (38, 1), (29, 22), (1, 5), (19, 30), (34, 30), (28, 26), (18, 20), (30, 25), (37, 23), (34, 3), (17, 29), (12, 7), (10, 27), (7, 2), (13, 30), (27, 28), (15, 1), (17, 23), (24, 28), (8, 1), (17, 30), (5, 30), (14, 11), (34, 13), (13, 0), (15, 10), (28, 0), (0, 5), (38, 14), (19, 27), (1, 16), (0, 16), (20, 9), (23, 11), (28, 8), (38, 25), (30, 2), (37, 28), (12, 24), (28, 11), (22, 15), (22, 24), (3, 10), (28, 13), (11, 18), (10, 8), (23, 16), (3, 7), (1, 2), (15, 27), (22, 29), (25, 6), (36, 16), (7, 30), (28, 16), (0, 26), (27, 21), (4, 9), (2, 21), (10, 33), (18, 19), (23, 20), (11, 15), (38, 10), (24, 9), (24, 13), (34, 16), (0, 19), (28, 28), (20, 13), (38, 15), (12, 8), (21, 9), (17, 25), (38, 3), (34, 32), (27, 22), (9, 27), (1, 24), (18, 22), (11, 26), (7, 13), (38, 4), (8, 15), (14, 7), (13, 33), (10, 32), (1, 1), (29, 27), (32, 7), (21, 22), (10, 26), (20, 14), (16, 13), (38, 19), (13, 32), (11, 4), (11, 25), (3, 0), (30, 27), (38, 0), (0, 22), (9, 15), (31, 6), (30, 24), (1, 10), (18, 29), (24, 22), (1, 11), (25, 25), (10, 28), (33, 0), (21, 15), (36, 29), (10, 18), (2, 12), (30, 3), (31, 18), (11, 9), (9, 17), (28, 19), (5, 21), (16, 15), (11, 6), (25, 23), (6, 30), (30, 13), (24, 31), (1, 14), (8, 23), (20, 7), (10, 4), (13, 19), (3, 14), (16, 5), (4, 22), (11, 29), (31, 25), (13, 14), (27, 27), (5, 1), (2, 16), (12, 12), (28, 25), (9, 8), (8, 7), (25, 18), (32, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73728", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), 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, 4), (8, 8), (26, 4), (1, 27), (5, 28), (9, 14), (10, 32), (23, 4), (21, 9), (20, 36), (21, 4), (30, 22), (15, 24), (13, 20), (4, 21), (17, 29), (6, 12), (23, 10), (30, 27), (27, 2), (9, 20), (32, 11), (9, 10), (23, 19), (24, 27), (15, 0), (20, 18), (10, 14), (14, 18), (7, 33), (25, 30), (4, 17), (15, 10), (29, 7), (24, 19), (30, 23), (26, 24), (12, 15), (7, 21), (2, 28), (11, 6), (22, 8), (27, 8), (2, 4), (18, 9), (3, 24), (32, 17), (21, 3), (7, 27), (5, 13), (21, 34), (23, 1), (1, 11), (17, 16), (0, 8), (10, 26), (26, 27), (32, 3), (9, 3), (22, 12), (10, 8), (4, 35), (28, 26), (6, 5), (17, 11), (32, 7), (15, 4), (3, 32), (29, 29), (27, 11), (12, 27), (6, 16), (27, 18), (26, 12), (5, 10), (27, 4), (20, 15), (3, 16), (18, 0), (13, 33), (25, 2), (30, 9), (10, 1), (8, 35), (27, 6), (10, 17), (26, 23), (8, 29), (21, 2), (26, 14), (31, 3), (28, 32), (23, 25), (12, 23), (13, 22), (7, 0), (26, 32), (29, 3), (6, 18), (8, 2), (8, 28), (19, 22), (20, 35), (12, 12), (27, 1), (13, 3), (20, 24), (15, 13), (22, 9), (15, 5), (32, 14), (29, 18), (19, 0), (2, 20), (13, 28), (9, 0), (32, 25), (13, 17), (25, 26), (18, 29), (0, 30), (24, 24), (16, 25), (6, 15), (18, 36), (6, 25), (28, 8), (8, 6), (18, 2), (18, 1), (24, 29), (13, 30), (10, 24), (7, 36), (1, 3), (22, 10), (21, 13), (30, 12), (19, 18), (30, 33), (6, 7), (15, 34), (9, 28), (12, 4), (27, 13), (11, 29), (17, 3), (31, 26), (26, 20), (12, 14), (22, 36), (4, 1), (2, 6), (31, 31), (9, 18), (22, 19), (2, 16), (29, 22), (5, 25), (31, 22), (19, 36), (9, 7), (28, 21), (18, 30), (19, 13), (11, 34), (19, 7), (17, 24), (32, 16), (22, 25), (29, 26), (5, 26), (14, 9), (1, 13), (2, 15), (14, 26), (32, 27), (6, 33), (29, 1), (26, 5), (26, 0), (14, 24), (14, 11), (20, 22), (27, 17), (4, 29), (10, 31), (20, 10), (31, 24), (24, 2), (24, 33), (3, 1), (2, 12), (12, 5), (17, 4), (22, 33), (6, 23), (18, 7), (5, 8), (13, 6), (4, 33), (0, 13), (31, 12), (15, 20), (9, 29), (30, 31), (4, 14), (23, 6), (22, 1), (8, 10), (30, 5), (19, 23), (3, 27), (12, 17), (25, 13), (3, 17), (5, 23), (25, 29), (2, 29), (29, 21), (25, 14), (28, 10), (18, 35), (15, 17), (9, 8), (14, 30), (23, 13), (31, 34), (29, 15), (29, 12), (13, 24), (11, 21), (2, 22), (18, 4), (31, 32), (31, 9), (3, 25), (15, 29), (4, 32), (26, 35), (17, 15), (30, 6), (24, 17), (8, 19), (27, 33), (21, 20), (9, 12), (28, 20), (11, 1), (20, 21), (19, 30), (4, 19), (10, 35), (11, 22), (31, 5), (0, 28), (10, 34), (20, 9), (32, 1), (0, 20), (11, 12), (3, 28), (27, 10), (29, 6), (2, 3), (13, 32), (28, 17), (1, 29), (17, 20), (18, 20), (16, 15), (10, 9), (10, 30), (9, 24), (24, 35), (22, 17), (13, 12), (7, 13), (28, 23), (26, 28), (25, 22), (27, 12), (0, 26), (5, 7), (8, 25), (1, 23), (20, 2), (10, 33), (28, 18), (23, 18), (9, 23), (29, 25), (11, 24), (7, 30), (20, 0), (26, 10), (16, 30), (0, 25), (24, 13), (8, 13), (27, 21), (3, 0), (17, 2), (15, 27), (4, 0), (16, 28), (4, 36), (14, 15), (30, 8), (30, 36), (14, 32), (24, 3), (19, 20), (3, 9), (22, 22), (12, 26), (24, 32), (7, 16), (18, 26), (3, 30), (9, 32), (10, 3), (8, 26), (7, 9), (29, 11), (1, 21), (7, 31), (12, 28), (19, 2), (17, 6), (11, 16), (30, 3), (16, 6), (7, 25), (15, 7), (8, 34), (11, 25), (18, 24), (25, 27), (24, 10), (28, 14), (26, 36), (7, 14), (2, 14), (17, 36), (4, 3), (31, 28), (2, 17), (11, 31), (0, 7), (12, 0), (31, 16), (24, 9), (15, 33), (12, 21), (1, 24), (8, 24), (24, 31), (24, 16), (29, 19), (18, 22), (19, 14), (15, 35), (26, 11), (16, 1), (23, 24), (18, 23), (7, 2), (9, 19), (19, 10), (5, 29), (7, 18), (30, 17), (0, 15), (3, 18), (20, 27), (6, 13), (0, 9), (24, 21), (29, 30), (7, 35), (23, 32), (16, 23), (26, 25), (22, 21), (5, 27), (6, 36), (20, 31), (25, 12), (5, 31), (25, 25), (30, 4), (17, 12), (16, 17), (29, 10), (28, 2), (20, 23), (14, 10), (25, 6), (23, 21), (29, 9), (25, 36), (3, 19), (13, 15), (30, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "691200", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), 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), (29, 6), (4, 30), (6, 2), (1, 21), (8, 8), (24, 10), (13, 30), (24, 31), (26, 30), (26, 8), (28, 36), (12, 34), (22, 17), (23, 25), (23, 33), (12, 19), (13, 31), (17, 0), (14, 31), (8, 25), (24, 35), (15, 33), (9, 28), (28, 12), (29, 17), (2, 17), (22, 27), (8, 22), (11, 31), (13, 1), (13, 3), (22, 2), (5, 26), (12, 7), (1, 31), (12, 21), (29, 33), (7, 20), (29, 18), (23, 17), (26, 33), (6, 36), (20, 22), (20, 1), (0, 20), (26, 26), (13, 19), (27, 6), (10, 27), (8, 16), (27, 20), (5, 33), (22, 13), (3, 26), (22, 15), (14, 3), (27, 7), (17, 33), (4, 16), (28, 30), (16, 19), (0, 17), (28, 11), (20, 20), (29, 0), (13, 15), (4, 25), (22, 18), (6, 14), (12, 32), (16, 32), (22, 32), (11, 23), (19, 3), (16, 24), (4, 15), (19, 20), (13, 9), (14, 22), (18, 15), (23, 31), (1, 14), (22, 7), (21, 19), (13, 35), (12, 3), (25, 18), (12, 23), (29, 15), (9, 11), (25, 7), (8, 28), (17, 26), (2, 26), (21, 21), (8, 3), (14, 5), (20, 13), (23, 4), (4, 8), (23, 28), (9, 0), (22, 3), (7, 25), (3, 1), (23, 18), (18, 26), (10, 18), (3, 20), (29, 7), (2, 24), (4, 31), (6, 18), (2, 15), (21, 2), (16, 1), (17, 20), (3, 13), (26, 16), (29, 5), (22, 24), (18, 29), (19, 25), (3, 6), (8, 7), (22, 1), (10, 5), (23, 9), (0, 36), (9, 34), (9, 23), (5, 27), (0, 23), (10, 4), (21, 30), (25, 36), (17, 12), (20, 12), (19, 2), (14, 7), (9, 10), (4, 12), (24, 3), (0, 11), (2, 12), (27, 12), (16, 12), (11, 6), (29, 3), (3, 25), (23, 35), (6, 20), (12, 28), (29, 34), (12, 27), (14, 18), (5, 3), (23, 15), (13, 17), (2, 28), (9, 17), (5, 14), (10, 10), (12, 17), (0, 27), (23, 3), (7, 11), (22, 4), (5, 15), (14, 34), (12, 0), (18, 0), (25, 13), (26, 12), (15, 21), (28, 15), (2, 23), (0, 12), (5, 1), (27, 3), (19, 5), (6, 29), (21, 24), (19, 10), (29, 11), (20, 25), (29, 14), (4, 19), (16, 0), (25, 31), (15, 36), (18, 10), (20, 23), (18, 4), (0, 7), (26, 0), (4, 29), (9, 35), (0, 6), (7, 26), (19, 33), (15, 28), (9, 2), (27, 22), (13, 12), (27, 0), (19, 8), (15, 14), (7, 23), (3, 31), (26, 23), (28, 17), (26, 2), (6, 23), (18, 19), (4, 1), (8, 36), (22, 9), (10, 3), (28, 32), (20, 6), (18, 13), (23, 19), (26, 4), (12, 6), (18, 20), (18, 3), (20, 31), (15, 13), (10, 17), (9, 32), (1, 1), (6, 27), (16, 5), (19, 26), (23, 23), (12, 35), (23, 34), (10, 13), (12, 13), (24, 17), (7, 19), (25, 20), (2, 2), (20, 33), (21, 7), (22, 11), (1, 19), (26, 11), (23, 21), (16, 25), (13, 25), (17, 23), (16, 16), (25, 27), (21, 8), (18, 23), (24, 16), (24, 0), (20, 11), (11, 18), (6, 11), (3, 34), (26, 6), (23, 20), (18, 33), (9, 22), (25, 16), (10, 34), (10, 21), (26, 13), (11, 32), (18, 11), (28, 3), (10, 14), (4, 22), (3, 33), (28, 29), (27, 14), (4, 33), (26, 5), (0, 33), (6, 7), (4, 5), (13, 34), (24, 4), (23, 10), (17, 19), (7, 21), (9, 5), (5, 4), (6, 10), (14, 33), (15, 0), (14, 15), (24, 26), (8, 1), (1, 4), (0, 15), (13, 4), (13, 33), (8, 12), (2, 29), (8, 29), (9, 25), (16, 33), (2, 11), (21, 11), (4, 14), (19, 6), (26, 36), (10, 25), (3, 21), (23, 16), (17, 35), (19, 7), (22, 31), (7, 30), (8, 21), (9, 12), (19, 21), (17, 13), (4, 21), (8, 34), (13, 18), (22, 22), (15, 26), (18, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554232", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 4), (5, 18), (24, 9), (26, 27), (27, 16), (1, 16), (20, 27), (3, 25), (30, 5), (28, 29), (1, 29), (16, 24), (18, 16), (2, 6), (14, 20), (23, 4), (8, 8), (4, 8), (20, 9), (14, 5), (20, 21), (26, 28), (16, 20), (10, 3), (25, 21), (18, 5), (1, 19), (33, 5), (17, 12), (3, 7), (7, 7), (24, 5), (11, 11), (21, 18), (24, 15), (16, 23), (19, 17), (24, 14), (26, 18), (17, 2), (16, 17), (25, 0), (5, 4), (14, 29), (27, 15), (9, 20), (32, 26), (20, 15), (13, 1), (0, 2), (10, 15), (20, 22), (21, 2), (16, 29), (13, 21), (26, 21), (15, 7), (19, 27), (31, 17), (9, 6), (27, 22), (15, 17), (3, 2), (13, 17), (31, 2), (26, 9), (18, 17), (18, 28), (30, 9), (13, 16), (8, 28), (26, 14), (30, 28), (32, 1), (23, 13), (19, 29), (3, 13), (17, 7), (22, 28), (23, 3), (11, 26), (0, 1), (7, 27), (18, 6), (10, 24), (16, 16), (7, 2), (8, 25), (21, 7), (16, 18), (24, 26), (32, 14), (30, 24), (8, 18), (21, 14), (11, 1), (28, 1), (22, 19), (5, 17), (27, 6), (6, 28), (29, 17), (13, 10), (14, 2), (33, 3), (21, 4), (7, 19), (12, 25), (9, 7), (2, 0), (3, 21), (21, 22), (7, 3), (26, 25), (10, 27), (11, 13), (2, 2), (23, 8), (11, 7), (9, 18), (33, 21), (26, 15), (24, 27), (29, 27), (31, 8), (3, 23), (13, 8), (14, 16), (5, 19), (22, 24), (26, 8), (16, 6), (2, 22), (21, 1), (12, 22), (8, 9), (28, 6), (27, 20), (22, 9), (22, 11), (11, 10), (31, 11), (28, 19), (9, 10), (21, 17), (24, 12), (28, 26), (6, 23), (20, 14), (0, 16), (18, 1), (31, 26), (12, 10), (6, 11), (21, 29), (17, 21), (29, 5), (26, 29), (27, 18), (32, 6), (31, 5), (25, 25), (10, 20), (4, 10), (2, 11), (17, 3), (26, 26), (3, 6), (2, 16), (26, 7), (8, 19), (0, 20), (23, 7), (18, 18), (14, 15), (20, 24), (30, 20), (2, 19), (22, 15), (33, 26), (4, 13), (5, 25), (19, 28), (14, 1), (6, 24), (7, 9), (27, 2), (0, 6), (28, 0), (33, 8), (4, 3), (12, 14), (3, 12), (32, 18), (1, 15), (14, 12), (11, 23), (5, 10), (26, 3), (17, 6), (23, 9), (30, 23), (19, 5), (22, 12), (24, 0), (25, 8), (7, 26), (32, 24), (12, 15), (29, 8), (13, 22), (20, 16), (15, 26), (10, 26), (9, 21), (31, 9), (33, 28), (25, 15), (0, 10), (18, 20), (25, 11), (18, 12), (11, 4), (9, 12), (9, 19), (7, 5), (28, 21), (5, 1), (2, 21), (28, 14), (1, 12), (1, 20), (17, 4), (20, 0), (16, 12), (18, 27), (6, 2), (31, 19), (15, 6), (31, 6), (29, 10), (29, 4), (4, 26), (1, 27), (23, 22), (20, 20), (29, 22), (9, 27), (23, 26), (19, 21), (7, 24), (14, 23), (27, 27), (23, 25), (5, 7), (17, 22), (27, 8), (28, 17), (25, 6), (17, 24), (22, 7), (0, 14), (30, 21), (8, 12), (33, 2), (2, 9), (17, 5), (12, 8), (12, 24), (30, 1), (5, 23), (16, 19), (19, 3), (28, 4), (20, 11), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "171072", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 29), (29, 4), (1, 19), (12, 15), (6, 30), (13, 3), (1, 22), (18, 9), (4, 25), (30, 25), (29, 30), (34, 10), (12, 18), (8, 25), (13, 25), (6, 4), (7, 22), (24, 26), (3, 13), (21, 6), (17, 9), (4, 22), (35, 1), (7, 9), (29, 13), (12, 12), (32, 11), (6, 8), (20, 7), (17, 16), (6, 14), (11, 17), (36, 29), (35, 16), (11, 30), (3, 28), (4, 6), (12, 30), (32, 16), (4, 30), (24, 4), (29, 29), (11, 9), (36, 20), (27, 15), (24, 28), (33, 15), (33, 19), (4, 17), (3, 29), (1, 26), (35, 8), (3, 5), (16, 30), (17, 28), (11, 1), (22, 16), (20, 15), (2, 0), (23, 21), (1, 29), (29, 17), (18, 1), (29, 22), (18, 6), (0, 17), (16, 7), (27, 28), (12, 7), (0, 25), (25, 18), (23, 6), (27, 27), (20, 10), (0, 1), (14, 20), (5, 16), (32, 21), (0, 16), (4, 26), (7, 7), (33, 18), (25, 26), (9, 14), (3, 21), (4, 2), (28, 5), (0, 13), (0, 9), (5, 26), (22, 18), (25, 11), (32, 15), (25, 12), (25, 14), (35, 10), (22, 0), (4, 28), (10, 2), (29, 9), (33, 6), (30, 3), (33, 9), (0, 14), (25, 6), (27, 12), (32, 0), (27, 24), (31, 28), (19, 19), (23, 22), (3, 27), (26, 18), (28, 28), (23, 27), (35, 22), (2, 13), (7, 8), (26, 17), (25, 0), (11, 8), (25, 28), (14, 2), (8, 5), (16, 1), (28, 30), (31, 6), (0, 20), (25, 22), (2, 7), (23, 18), (0, 7), (35, 29), (16, 19), (34, 4), (23, 16), (9, 11), (17, 29), (9, 0), (24, 30), (32, 27), (8, 30), (34, 29), (3, 6), (25, 3), (29, 18), (16, 25), (4, 27), (14, 13), (22, 14), (3, 16), (18, 11), (15, 20), (10, 3), (12, 26), (3, 19), (2, 24), (15, 5), (14, 19), (33, 14), (10, 4), (25, 2), (34, 1), (29, 6), (19, 20), (21, 26), (29, 16), (12, 24), (5, 25), (24, 24), (35, 4), (17, 25), (26, 24), (15, 18), (29, 5), (4, 10), (13, 15), (25, 17), (31, 10), (15, 26), (11, 14), (23, 0), (18, 17), (3, 15), (14, 7), (0, 4), (23, 9), (9, 2), (19, 12), (33, 16), (31, 20), (27, 19), (16, 26), (27, 2), (33, 12), (25, 7), (8, 8), (13, 19), (14, 14), (8, 0), (0, 12), (21, 3), (2, 26), (6, 20), (11, 28), (24, 16), (36, 15), (28, 13), (26, 7), (12, 6), (20, 0), (12, 0), (22, 19), (27, 3), (26, 22), (24, 5), (28, 9), (13, 16), (5, 14), (36, 5), (1, 9), (5, 7), (33, 22), (17, 15), (0, 10), (9, 27), (29, 20), (36, 24), (35, 11), (6, 19), (3, 10), (36, 19), (18, 22), (26, 27), (30, 27), (8, 20), (34, 20), (30, 28), (1, 30), (14, 6), (8, 16), (14, 23), (31, 8), (1, 14), (5, 2), (29, 2), (28, 26), (6, 24), (13, 7), (6, 6), (8, 18), (8, 26), (30, 19), (15, 25), (33, 3), (16, 24), (22, 28), (1, 28), (33, 4), (23, 25), (30, 13), (2, 6), (9, 29), (29, 28), (32, 12), (0, 30), (21, 10), (31, 4), (27, 10), (17, 4), (10, 18), (8, 11), (31, 14), (26, 30), (15, 0), (11, 27), (34, 12), (0, 22), (25, 20), (22, 20), (18, 20), (5, 17), (31, 12), (15, 22), (2, 29), (27, 23), (28, 11), (7, 23), (17, 22), (2, 20), (12, 2), (5, 22), (10, 30), (2, 9), (36, 0), (4, 0), (15, 13), (19, 2), (1, 15), (26, 20), (29, 19), (9, 26), (9, 20), (4, 11), (8, 7), (25, 25), (18, 21), (36, 17), (32, 29), (23, 15), (33, 17), (2, 18), (26, 3), (9, 16), (0, 28), (20, 22), (3, 17), (34, 6), (26, 0), (25, 13), (5, 15), (16, 21), (30, 22), (3, 20), (10, 20), (13, 1), (17, 19), (16, 6), (33, 5), (18, 14), (35, 5), (29, 8), (24, 2), (24, 27), (30, 0), (27, 22), (35, 20), (21, 20), (20, 11), (4, 13), (27, 7), (15, 23), (13, 14), (36, 23), (18, 26), (14, 11), (12, 25), (19, 23), (22, 30), (25, 16), (19, 8), (21, 0), (23, 23), (6, 2), (36, 12), (31, 21), (32, 4), (34, 16), (18, 8), (20, 1), (9, 7), (27, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "507222", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 25), (1, 12), (28, 6), (8, 4), (14, 31), (0, 5), (29, 20), (5, 9), (24, 12), (29, 19), (21, 12), (22, 1), (7, 1), (8, 14), (34, 4), (19, 18), (21, 17), (0, 10), (26, 17), (27, 2), (9, 20), (20, 7), (22, 11), (4, 23), (32, 18), (19, 30), (30, 9), (24, 0), (11, 23), (3, 2), (28, 8), (32, 23), (16, 23), (0, 3), (21, 11), (24, 6), (28, 16), (23, 21), (31, 20), (7, 2), (3, 30), (5, 17), (30, 14), (22, 8), (4, 13), (2, 8), (19, 7), (2, 24), (15, 26), (7, 24), (18, 7), (27, 5), (20, 8), (10, 14), (27, 25), (27, 26), (15, 13), (30, 4), (4, 11), (24, 9), (6, 26), (16, 5), (11, 3), (28, 26), (34, 7), (12, 6), (11, 7), (16, 15), (9, 5), (16, 24), (22, 3), (1, 22), (25, 23), (8, 3), (25, 1), (31, 12), (12, 29), (11, 16), (7, 30), (21, 10), (7, 18), (13, 20), (1, 25), (6, 17), (28, 30), (31, 17), (5, 3), (25, 17), (5, 0), (4, 16), (23, 24), (2, 16), (22, 15), (33, 21), (26, 10), (28, 9), (29, 21), (18, 29), (17, 7), (23, 0), (1, 30), (0, 28), (34, 20), (8, 12), (10, 21), (9, 19), (3, 23), (30, 2), (29, 23), (34, 10), (9, 22), (24, 16), (12, 22), (26, 31), (16, 6), (22, 25), (18, 15), (32, 2), (1, 24), (19, 15), (12, 17), (3, 6), (31, 22), (2, 11), (2, 2), (18, 16), (23, 6), (15, 29), (6, 5), (13, 7), (3, 22), (25, 16), (1, 7), (16, 17), (34, 22), (20, 20), (26, 8), (18, 19), (31, 18), (9, 14), (31, 27), (8, 10), (30, 11), (3, 25), (23, 9), (30, 30), (25, 24), (31, 0), (21, 3), (17, 0), (14, 3), (27, 9), (17, 24), (31, 24), (13, 25), (19, 6), (12, 12), (0, 19), (19, 10), (9, 12), (30, 3), (6, 14), (25, 8), (14, 14), (6, 3), (6, 10), (31, 2), (30, 15), (7, 22), (2, 5), (31, 26), (17, 31), (16, 30), (7, 16), (8, 5), (19, 4), (16, 27), (5, 20), (33, 22), (0, 12), (19, 22), (22, 28), (33, 24), (27, 6), (31, 11), (3, 28), (11, 28), (20, 5), (13, 21), (8, 8), (12, 11), (25, 18), (7, 23), (9, 24), (0, 24), (32, 16), (23, 11), (22, 0), (26, 26), (16, 21), (1, 3), (4, 7), (6, 13), (26, 25), (1, 17), (28, 19), (1, 18), (13, 6), (25, 6), (9, 7), (9, 18), (8, 31), (0, 18), (28, 15), (25, 11), (8, 24), (18, 2), (32, 14), (20, 30), (1, 19), (34, 9), (3, 16), (27, 28), (11, 30), (17, 12), (13, 29), (4, 5), (24, 18), (34, 18), (19, 27), (17, 6), (8, 19), (2, 27), (10, 6), (34, 6), (33, 10), (1, 8), (21, 22), (13, 9), (6, 18), (9, 15), (28, 12), (6, 12), (31, 30), (19, 20), (10, 18), (18, 11), (2, 6), (19, 23), (1, 0), (3, 11), (1, 16), (2, 10), (15, 23), (5, 6), (33, 14), (24, 27), (6, 0), (24, 8), (20, 23), (24, 10), (15, 25), (12, 8), (21, 24), (9, 16), (16, 9), (14, 29), (23, 5), (33, 4), (20, 12), (18, 14), (5, 27), (26, 12), (21, 20), (31, 23), (16, 8), (16, 2), (21, 21), (27, 24), (20, 3), (27, 3), (18, 6), (4, 20), (10, 1), (6, 16), (9, 30), (19, 29), (28, 14), (22, 30), (8, 25), (26, 18), (12, 25), (24, 31), (34, 27), (30, 0), (0, 23), (25, 13), (5, 25), (16, 0), (13, 5), (6, 23), (8, 13), (10, 29), (29, 10), (25, 3), (34, 21), (8, 11), (17, 25), (23, 4), (28, 20), (21, 15), (8, 22), (23, 14), (9, 23), (5, 11), (1, 14), (0, 16), (33, 16), (23, 10), (23, 26), (1, 21), (11, 4), (7, 28), (21, 18), (21, 14), (29, 17), (21, 8), (22, 24), (7, 17), (25, 26), (25, 29), (1, 29), (18, 30), (24, 7), (9, 26), (27, 0), (31, 13), (33, 17), (25, 15), (19, 9), (11, 15), (6, 7), (24, 28), (20, 2), (27, 11), (29, 26), (23, 20), (3, 4), (28, 10), (12, 19), (30, 31), (34, 30), (1, 23), (22, 17), (4, 6), (28, 7), (8, 17), (33, 15), (10, 17), (17, 23), (25, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "741608", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), 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), (9, 29), (19, 23), (15, 3), (2, 1), (1, 22), (5, 13), (29, 2), (32, 7), (36, 6), (11, 29), (13, 26), (2, 16), (2, 4), (32, 5), (32, 21), (33, 0), (17, 10), (6, 24), (22, 30), (3, 6), (36, 20), (24, 25), (21, 10), (33, 34), (4, 20), (0, 28), (12, 18), (21, 17), (19, 13), (27, 2), (0, 19), (20, 33), (16, 22), (20, 23), (28, 17), (21, 24), (0, 32), (0, 12), (21, 25), (19, 35), (0, 18), (26, 35), (24, 6), (7, 15), (26, 17), (3, 23), (7, 0), (17, 21), (17, 25), (28, 22), (28, 23), (10, 11), (4, 16), (20, 31), (11, 21), (22, 13), (1, 19), (12, 11), (12, 16), (22, 28), (28, 19), (21, 11), (22, 25), (22, 18), (24, 34), (24, 32), (36, 33), (28, 12), (13, 18), (31, 20), (36, 7), (31, 19), (27, 5), (2, 6), (15, 17), (30, 28), (14, 1), (2, 30), (4, 15), (18, 13), (36, 25), (16, 2), (34, 14), (25, 10), (29, 0), (7, 21), (26, 34), (9, 23), (30, 31), (15, 32), (30, 26), (35, 28), (17, 24), (4, 12), (21, 21), (36, 34), (24, 18), (22, 23), (15, 14), (34, 9), (10, 16), (19, 30), (26, 1), (21, 7), (4, 19), (7, 19), (34, 4), (12, 26), (25, 0), (8, 29), (0, 17), (23, 0), (35, 26), (5, 34), (25, 23), (32, 35), (23, 25), (22, 12), (10, 14), (6, 14), (2, 35), (26, 0), (8, 27), (32, 4), (3, 11), (18, 22), (31, 23), (31, 18), (8, 34), (9, 10), (6, 17), (23, 10), (7, 9), (13, 16), (36, 9), (25, 28), (20, 16), (3, 8), (17, 26), (11, 24), (10, 23), (25, 32), (9, 19), (1, 23), (29, 17), (12, 9), (28, 20), (33, 20), (13, 30), (0, 25), (6, 34), (4, 21), (21, 33), (33, 9), (10, 32), (3, 4), (11, 1), (22, 5), (17, 4), (30, 2), (23, 28), (9, 0), (24, 26), (35, 22), (23, 2), (4, 24), (28, 14), (31, 4), (8, 24), (28, 24), (8, 6), (4, 1), (32, 13), (13, 34), (7, 13), (14, 26), (19, 4), (8, 31), (21, 19), (31, 30), (21, 20), (9, 33), (22, 24), (31, 27), (32, 25), (25, 13), (22, 34), (24, 1), (22, 0), (18, 0), (20, 6), (11, 28), (9, 22), (1, 15), (22, 33), (31, 2), (36, 18), (1, 6), (10, 3), (19, 34), (10, 17), (3, 25), (2, 10), (30, 15), (33, 35), (13, 15), (28, 21), (15, 6), (6, 11), (1, 3), (1, 27), (35, 13), (18, 8), (35, 1), (36, 11), (10, 21), (5, 6), (22, 32), (24, 24), (23, 30), (24, 7), (18, 30), (34, 21), (29, 5), (9, 15), (10, 30), (34, 15), (20, 1), (14, 35), (10, 29), (3, 5), (17, 5), (23, 18), (34, 30), (17, 8), (19, 19), (8, 7), (19, 9), (4, 13), (19, 21), (35, 33), (0, 13), (34, 32), (13, 28), (17, 22), (33, 6), (31, 11), (25, 7), (22, 20), (14, 30), (25, 1), (7, 6), (3, 24), (25, 3), (7, 16), (21, 3), (27, 32), (6, 32), (8, 9), (30, 0), (1, 1), (24, 33), (7, 1), (24, 2), (24, 15), (10, 25), (27, 11), (36, 10), (30, 18), (11, 23), (11, 16), (11, 9), (9, 20), (30, 9), (4, 18), (2, 11), (15, 21), (13, 10), (33, 8), (13, 7), (27, 14), (20, 20), (11, 32), (34, 28), (33, 4), (2, 18), (8, 15), (20, 19), (30, 29), (26, 2), (15, 34), (20, 4), (5, 28), (8, 35), (0, 16), (3, 30), (5, 8), (16, 23), (16, 3), (6, 3), (21, 12), (31, 1), (10, 26), (14, 32), (20, 30), (19, 17), (27, 4), (16, 6), (24, 8), (27, 10), (25, 18), (16, 25), (23, 1), (17, 12), (20, 15), (26, 31), (5, 22), (11, 27), (23, 19), (10, 24), (9, 18), (14, 33), (32, 0), (19, 11), (33, 31), (7, 4), (16, 7), (13, 19), (26, 6), (0, 21), (11, 6), (1, 8), (26, 30), (1, 9), (1, 10), (8, 26), (0, 34), (19, 14), (32, 10), (19, 1), (17, 1), (31, 6), (11, 20), (10, 4), (31, 15), (17, 27), (10, 2), (13, 8), (21, 35), (26, 5), (8, 11), (23, 4), (21, 22), (4, 23), (28, 29), (25, 33), (30, 25), (31, 21), (30, 17), (18, 4), (0, 3), (27, 23), (14, 24), (20, 34), (33, 16), (20, 13), (35, 0), (18, 15), (18, 11), (13, 2), (35, 25), (3, 27), (3, 28), (27, 18), (2, 28), (17, 2), (25, 16), (22, 7), (7, 10), (32, 11), (8, 14), (6, 25), (24, 0), (33, 15), (35, 8), (4, 5), (2, 13), (18, 9), (23, 12), (8, 1), (1, 21), (20, 35), (11, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "375516", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 34), (2, 18), (16, 10), (2, 20), (8, 12), (3, 21), (8, 1), (9, 26), (2, 5), (25, 22), (15, 24), (6, 33), (3, 25), (11, 14), (6, 15), (13, 25), (19, 19), (10, 10), (15, 32), (32, 17), (18, 14), (25, 21), (3, 23), (26, 25), (8, 14), (1, 25), (29, 3), (4, 27), (22, 31), (8, 25), (12, 17), (13, 6), (22, 24), (14, 3), (17, 12), (13, 19), (22, 13), (7, 13), (19, 10), (24, 19), (16, 0), (13, 33), (9, 12), (18, 24), (22, 12), (21, 11), (26, 23), (3, 1), (7, 27), (21, 28), (8, 21), (1, 27), (23, 9), (16, 7), (8, 24), (27, 3), (33, 19), (9, 25), (14, 8), (4, 11), (10, 14), (2, 22), (32, 8), (2, 13), (19, 32), (28, 25), (30, 1), (22, 21), (29, 33), (5, 21), (25, 30), (7, 24), (17, 10), (28, 24), (16, 2), (14, 10), (15, 16), (30, 34), (20, 0), (20, 1), (5, 0), (15, 20), (0, 1), (0, 9), (9, 30), (13, 26), (7, 2), (4, 10), (31, 20), (30, 20), (30, 26), (20, 28), (21, 2), (8, 0), (6, 12), (20, 33), (14, 23), (15, 10), (24, 31), (29, 14), (10, 26), (2, 8), (5, 32), (10, 12), (10, 28), (23, 28), (5, 24), (10, 0), (12, 30), (2, 9), (15, 14), (21, 12), (10, 9), (31, 34), (11, 0), (8, 15), (3, 11), (28, 17), (9, 14), (9, 27), (29, 24), (18, 17), (4, 3), (17, 2), (27, 19), (24, 32), (8, 31), (15, 9), (12, 5), (21, 18), (4, 12), (3, 17), (33, 22), (12, 4), (18, 20), (15, 29), (23, 3), (29, 27), (15, 19), (33, 28), (5, 10), (23, 21), (28, 27), (3, 0), (28, 26), (20, 23), (24, 14), (7, 18), (16, 23), (19, 3), (27, 7), (3, 31), (15, 21), (17, 29), (21, 25), (22, 25), (30, 32), (18, 4), (29, 16), (33, 0), (18, 29), (12, 22), (32, 3), (31, 9), (13, 1), (2, 23), (14, 12), (13, 16), (19, 1), (21, 26), (29, 10), (5, 15), (22, 33), (18, 28), (24, 6), (25, 9), (0, 13), (2, 12), (26, 7), (13, 23), (12, 14), (24, 1), (30, 8), (9, 23), (20, 15), (5, 30), (26, 5), (8, 33), (30, 19), (14, 19), (24, 33), (19, 15), (9, 10), (0, 3), (7, 26), (19, 17), (2, 14), (26, 13), (9, 15), (8, 29), (27, 17), (6, 4), (8, 19), (0, 10), (15, 0), (33, 7), (14, 32), (4, 16), (23, 23), (30, 23), (3, 20), (19, 27), (9, 17), (14, 26), (24, 9), (15, 8), (30, 31), (0, 20), (14, 13), (25, 16), (27, 11), (23, 25), (19, 8), (13, 20), (33, 33), (26, 1), (12, 13), (10, 22), (26, 31), (17, 30), (3, 5), (31, 24), (24, 22), (10, 2), (3, 4), (22, 18), (1, 29), (27, 6), (22, 15), (22, 11), (17, 33), (29, 1), (1, 11), (12, 26), (33, 9), (18, 25), (17, 13), (9, 34), (30, 24), (6, 1), (19, 29), (23, 31), (30, 7), (4, 14), (32, 0), (8, 10), (26, 32), (18, 21), (20, 16), (12, 24), (16, 18), (1, 9), (3, 28), (32, 16), (20, 22), (23, 34), (27, 4), (33, 32), (32, 13), (5, 27), (27, 5), (3, 8), (5, 23), (16, 34), (27, 16), (12, 21), (24, 21), (5, 8), (24, 15), (33, 4), (12, 31), (6, 7), (7, 3), (6, 34), (4, 1), (27, 12), (19, 14), (6, 6), (7, 14), (10, 20), (17, 16), (32, 14), (2, 31), (26, 14), (0, 22), (7, 16), (9, 21), (16, 33), (19, 33), (27, 8), (17, 21), (18, 9), (7, 19), (16, 32), (27, 18), (3, 3), (25, 31), (12, 27), (8, 18), (11, 2), (14, 29), (2, 33), (25, 24), (33, 27), (28, 16), (14, 28), (10, 21), (29, 9), (20, 12), (24, 17), (29, 21), (8, 26), (20, 5), (22, 16), (14, 33), (11, 13), (19, 2), (14, 9), (33, 10), (0, 5), (24, 8), (1, 4), (27, 20), (1, 7), (28, 22), (8, 23), (6, 25), (31, 16), (13, 0), (2, 3), (0, 34), (11, 7), (22, 32), (17, 17), (33, 30), (23, 7), (1, 2), (3, 13), (12, 12), (4, 34), (7, 30), (2, 17), (28, 20), (6, 21), (14, 18), (0, 6), (27, 31), (7, 10), (12, 23), (26, 4), (0, 16), (13, 31), (7, 15), (31, 5), (3, 10), (31, 3), (27, 15), (29, 2), (7, 28), (20, 14), (32, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "648000", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 8), (18, 21), (18, 16), (9, 11), (20, 25), (8, 28), (13, 15), (0, 29), (28, 29), (11, 7), (16, 27), (2, 20), (15, 19), (15, 7), (26, 16), (21, 8), (11, 25), (5, 4), (29, 15), (6, 3), (18, 29), (1, 8), (24, 3), (24, 2), (19, 19), (12, 21), (30, 27), (20, 1), (22, 29), (8, 14), (16, 23), (14, 29), (18, 17), (21, 34), (19, 2), (21, 20), (23, 2), (7, 26), (0, 22), (4, 20), (14, 26), (10, 3), (10, 31), (11, 2), (23, 32), (20, 30), (5, 8), (1, 10), (10, 26), (15, 4), (28, 13), (24, 18), (14, 0), (6, 18), (3, 13), (28, 15), (24, 6), (11, 13), (3, 7), (10, 12), (12, 34), (28, 11), (23, 23), (3, 1), (4, 27), (21, 22), (26, 22), (30, 19), (23, 26), (18, 25), (10, 1), (13, 31), (29, 6), (24, 32), (19, 25), (1, 9), (20, 28), (17, 35), (24, 1), (21, 19), (6, 9), (4, 14), (17, 9), (23, 21), (8, 17), (16, 3), (16, 13), (10, 29), (12, 19), (9, 22), (16, 16), (21, 16), (15, 31), (25, 35), (29, 21), (24, 10), (2, 29), (10, 33), (30, 17), (15, 27), (24, 5), (22, 7), (26, 11), (23, 24), (24, 19), (20, 24), (18, 12), (22, 1), (8, 30), (12, 33), (14, 33), (28, 14), (7, 29), (9, 18), (4, 26), (22, 32), (13, 21), (18, 18), (7, 28), (15, 22), (16, 25), (24, 17), (3, 21), (12, 6), (10, 14), (12, 29), (9, 7), (20, 31), (16, 22), (12, 23), (4, 19), (3, 35), (28, 18), (9, 25), (22, 21), (22, 27), (2, 9), (17, 22), (18, 5), (17, 14), (10, 18), (17, 12), (1, 27), (8, 23), (14, 5), (14, 16), (28, 9), (21, 17), (15, 26), (5, 7), (16, 26), (5, 32), (26, 10), (9, 23), (0, 26), (15, 9), (17, 25), (6, 30), (1, 25), (26, 13), (25, 14), (2, 15), (30, 9), (21, 7), (7, 20), (9, 16), (18, 28), (25, 6), (23, 13), (12, 14), (4, 9), (3, 18), (22, 17), (25, 1), (9, 31), (10, 7), (8, 18), (23, 11), (18, 7), (9, 24), (20, 6), (8, 9), (5, 9), (9, 26), (17, 34), (17, 32), (26, 33), (16, 6), (1, 24), (26, 19), (18, 10), (1, 16), (21, 28), (17, 2), (4, 34), (23, 31), (18, 20), (24, 21), (22, 31), (9, 32), (10, 27), (24, 26), (8, 1), (21, 1), (28, 6), (21, 0), (5, 6), (9, 8), (2, 23), (19, 3), (19, 31), (20, 20), (0, 30), (7, 10), (0, 5), (11, 6), (2, 1), (30, 30), (20, 11), (10, 16), (10, 24), (23, 12), (24, 12), (14, 21), (13, 22), (9, 30), (25, 10), (4, 4), (26, 8), (22, 24), (25, 5), (16, 5), (23, 34), (13, 32), (13, 13), (7, 5), (14, 8), (6, 5), (20, 4), (9, 29), (30, 13), (26, 18), (28, 30), (28, 4), (29, 32), (29, 28), (2, 21), (3, 30), (6, 25), (9, 0), (1, 34), (28, 17), (21, 4), (1, 23), (14, 23), (3, 29), (18, 13), (25, 0), (10, 8), (19, 21), (14, 30), (18, 32), (25, 17), (29, 30), (22, 6), (16, 15), (7, 15), (12, 7), (2, 14), (19, 22), (15, 17), (7, 35), (17, 17), (23, 20), (23, 1), (21, 14), (16, 34), (27, 6), (18, 8), (28, 21), (1, 11), (2, 0), (4, 7), (17, 29), (30, 28), (28, 19), (23, 3), (29, 13), (22, 34), (14, 31), (24, 35), (6, 0), (24, 20), (14, 22), (10, 34), (13, 2), (27, 4), (16, 4), (28, 31), (13, 33), (3, 4), (26, 14), (26, 26), (6, 26), (15, 23), (11, 29), (18, 22), (25, 26), (4, 31), (20, 9), (5, 26), (0, 35), (16, 17), (26, 34)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "228096", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 21), (18, 31), (22, 7), (20, 32), (20, 4), (11, 14), (3, 2), (6, 18), (13, 20), (7, 15), (28, 0), (7, 1), (28, 26), (8, 13), (23, 14), (18, 24), (5, 14), (8, 8), (3, 26), (18, 26), (15, 7), (4, 23), (14, 5), (17, 10), (7, 18), (4, 12), (8, 10), (12, 4), (4, 21), (7, 21), (23, 28), (0, 13), (16, 33), (18, 28), (15, 29), (24, 19), (13, 9), (18, 30), (5, 16), (26, 27), (7, 16), (21, 16), (20, 12), (10, 27), (7, 25), (6, 24), (17, 12), (13, 26), (8, 27), (11, 17), (1, 3), (28, 7), (13, 27), (10, 29), (4, 5), (28, 10), (24, 15), (17, 8), (19, 9), (13, 22), (23, 29), (4, 0), (9, 12), (15, 4), (14, 31), (12, 10), (15, 18), (1, 15), (6, 5), (23, 5), (21, 8), (14, 23), (28, 6), (22, 10), (1, 5), (12, 22), (25, 21), (12, 5), (5, 33), (3, 8), (14, 16), (7, 2), (10, 26), (19, 25), (9, 26), (10, 31), (23, 16), (29, 8), (22, 24), (6, 6), (15, 23), (28, 29), (4, 6), (30, 19), (11, 16), (24, 1), (24, 18), (28, 15), (0, 20), (9, 23), (3, 31), (29, 32), (11, 8), (9, 28), (2, 19), (0, 8), (6, 26), (24, 33), (18, 23), (17, 31), (12, 20), (2, 28), (2, 9), (0, 25), (29, 29), (30, 32), (5, 10), (7, 22), (14, 4), (26, 23), (0, 26), (1, 23), (24, 21), (30, 12), (13, 13), (16, 32), (24, 29), (7, 33), (24, 17), (8, 28), (23, 7), (18, 22), (3, 29), (15, 16), (5, 11), (21, 7), (15, 9), (21, 31), (27, 28), (1, 17), (4, 13), (11, 26), (15, 33), (20, 9), (16, 18), (4, 20), (16, 10), (18, 27), (30, 9), (11, 21), (30, 23), (20, 27), (17, 2), (4, 24), (5, 29), (24, 16), (18, 4), (22, 6), (17, 1), (0, 12), (14, 14), (21, 20), (27, 32), (8, 14), (6, 19), (15, 14), (26, 6), (9, 1), (12, 17), (5, 30), (3, 6), (12, 27), (19, 30), (20, 14), (28, 14), (18, 32), (15, 10), (4, 19), (6, 8), (29, 30), (15, 15), (29, 24), (25, 33), (18, 5), (20, 18), (16, 26), (23, 22), (28, 1), (5, 8), (14, 28), (2, 33), (21, 29), (16, 23), (6, 0), (22, 21), (4, 10), (22, 4), (20, 11), (7, 10), (29, 13), (5, 26), (5, 22), (8, 22), (20, 15), (2, 8), (5, 32), (1, 25), (17, 5), (11, 28), (27, 22), (25, 31), (1, 0), (26, 11), (0, 9), (17, 3), (15, 11), (18, 7), (12, 0), (20, 29), (27, 27), (16, 16), (24, 24), (5, 18), (21, 6), (17, 24), (4, 7), (24, 5), (25, 32), (9, 15), (9, 31), (10, 24), (29, 31), (22, 17), (25, 6), (24, 26), (13, 6), (17, 30), (4, 17), (9, 22), (5, 4), (11, 9), (16, 27), (0, 7), (10, 32), (28, 5), (2, 21), (20, 21), (28, 20), (14, 33), (7, 28), (9, 0), (15, 6), (17, 28), (12, 8), (12, 9), (30, 2), (11, 33), (12, 16), (10, 22), (6, 17), (19, 23), (0, 21), (20, 31), (30, 22), (4, 29), (27, 13), (11, 31), (28, 3), (21, 9), (3, 33), (25, 22), (16, 1), (9, 18), (20, 2), (18, 6), (9, 10), (21, 23), (1, 8), (17, 26), (30, 13), (27, 31), (28, 13), (19, 33), (21, 3), (14, 15), (2, 24), (0, 11), (25, 5), (26, 1), (26, 21), (2, 4), (1, 28), (21, 25), (18, 29), (18, 9), (23, 11), (30, 18), (3, 24), (23, 9), (30, 15), (13, 31), (15, 26), (22, 26), (18, 16), (30, 4), (14, 13), (18, 17), (30, 11), (29, 22), (12, 28), (3, 32), (10, 3), (6, 9), (22, 28), (7, 27), (27, 26), (4, 30), (5, 19), (20, 24), (6, 2), (28, 8), (22, 0), (27, 7), (28, 21), (6, 1), (27, 1), (13, 8), (25, 1), (9, 13), (21, 5), (1, 12), (5, 0), (21, 0), (26, 9), (29, 9), (6, 15), (21, 19), (9, 25), (6, 27), (5, 20), (22, 18), (21, 11), (11, 25), (30, 0), (15, 27), (6, 21), (10, 9), (3, 5), (3, 3), (27, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "700800", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), 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), (30, 5), (28, 7), (27, 20), (7, 29), (14, 17), (21, 17), (27, 19), (21, 23), (15, 14), (0, 24), (30, 14), (17, 21), (16, 22), (2, 2), (16, 13), (4, 21), (26, 23), (7, 20), (24, 4), (13, 6), (4, 15), (4, 27), (27, 3), (5, 4), (24, 12), (25, 17), (0, 7), (27, 27), (12, 30), (9, 6), (9, 1), (25, 7), (29, 3), (22, 18), (3, 28), (11, 24), (12, 25), (22, 1), (16, 29), (28, 1), (6, 18), (1, 29), (11, 26), (4, 17), (24, 2), (8, 22), (13, 11), (26, 27), (19, 1), (26, 22), (19, 18), (23, 16), (30, 8), (23, 7), (9, 18), (7, 5), (27, 22), (30, 21), (13, 25), (12, 24), (6, 16), (2, 29), (1, 27), (4, 3), (1, 7), (1, 14), (3, 3), (5, 28), (30, 17), (10, 7), (3, 9), (9, 23), (5, 27), (6, 21), (3, 16), (28, 13), (12, 20), (9, 8), (13, 21), (28, 4), (20, 9), (20, 11), (5, 30), (11, 1), (16, 21), (0, 28), (25, 18), (18, 13), (13, 24), (10, 25), (3, 18), (9, 19), (22, 13), (15, 27), (0, 25), (16, 10), (24, 16), (29, 25), (22, 9), (6, 22), (23, 22), (29, 24), (15, 19), (13, 30), (2, 9), (29, 8), (8, 6), (25, 26), (27, 17), (8, 29), (19, 8), (9, 17), (6, 25), (21, 7), (14, 0), (21, 29), (23, 28), (15, 10), (23, 26), (10, 10), (24, 22), (17, 1), (16, 3), (21, 8), (19, 3), (18, 5), (28, 28), (27, 5), (20, 23), (23, 10), (28, 12), (0, 10), (29, 21), (25, 3), (2, 13), (27, 7), (7, 11), (22, 24), (24, 3), (22, 17), (22, 28), (17, 15), (5, 2), (4, 7), (13, 10), (17, 18), (24, 29), (30, 1), (26, 21), (30, 0), (23, 4), (5, 12), (20, 10), (25, 30), (0, 13), (17, 12), (29, 4), (11, 30), (0, 22), (18, 15), (4, 16), (28, 25), (25, 22), (18, 29), (13, 17), (12, 3), (20, 24), (10, 29), (15, 20), (20, 25), (25, 14), (11, 22), (29, 5), (22, 8), (26, 9), (9, 26), (1, 2), (14, 30), (11, 19), (28, 30), (6, 5), (23, 23), (26, 7), (16, 12), (17, 8), (30, 26), (23, 13), (30, 28), (7, 28), (12, 13), (9, 15), (10, 14), (21, 4), (1, 4), (4, 12), (21, 26), (4, 18), (7, 14), (15, 7), (8, 10), (6, 1), (5, 17), (19, 19), (27, 23), (8, 21), (30, 25), (10, 23), (7, 22), (14, 16), (0, 3), (24, 5), (15, 29), (30, 29), (19, 23), (17, 3), (25, 6), (7, 24), (30, 3), (11, 9), (8, 13), (30, 9), (23, 6), (24, 18), (24, 15), (2, 7), (15, 1), (9, 12), (18, 26), (24, 21), (4, 5), (19, 24), (15, 12), (8, 19), (1, 9), (22, 5), (28, 8), (5, 13), (22, 12), (8, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "510720", "dataset": "MATH"}
{"messages": [{"content": "In a 32x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 7), (12, 33), (13, 32), (21, 32), (31, 8), (23, 6), (28, 4), (30, 20), (7, 19), (8, 21), (16, 5), (18, 19), (7, 16), (17, 37), (28, 3), (26, 23), (25, 11), (1, 16), (13, 13), (31, 19), (22, 7), (10, 20), (23, 21), (26, 13), (16, 22), (22, 17), (21, 13), (4, 37), (1, 14), (13, 17), (22, 8), (22, 25), (21, 4), (8, 23), (3, 29), (29, 5), (0, 14), (5, 2), (6, 32), (9, 31), (21, 21), (10, 18), (15, 10), (8, 5), (3, 14), (1, 22), (0, 30), (3, 9), (9, 32), (8, 31), (19, 19), (10, 17), (2, 32), (15, 33), (19, 31), (2, 6), (12, 30), (6, 29), (14, 19), (15, 28), (29, 8), (0, 1), (10, 6), (26, 7), (5, 31), (29, 23), (0, 26), (25, 16), (17, 1), (23, 8), (25, 10), (31, 7), (30, 3), (0, 4), (31, 27), (11, 21), (24, 32), (22, 6), (4, 36), (25, 8), (9, 23), (1, 33), (30, 17), (29, 33), (25, 20), (31, 35), (23, 23), (0, 24), (14, 35), (24, 21), (17, 13), (23, 32), (17, 28), (27, 34), (1, 8), (10, 29), (29, 27), (7, 8), (27, 14), (0, 7), (30, 22), (14, 12), (11, 29), (23, 5), (11, 9), (10, 16), (6, 8), (31, 11), (15, 4), (14, 14), (17, 38), (6, 2), (31, 14), (22, 29), (27, 8), (17, 22), (18, 28), (11, 36), (14, 11), (12, 36), (30, 5), (22, 14), (5, 36), (5, 9), (0, 23), (11, 35), (14, 16), (27, 33), (15, 26), (4, 17), (30, 7), (7, 18), (26, 12), (26, 11), (31, 13), (4, 27), (0, 6), (28, 31), (10, 10), (4, 5), (25, 37), (3, 15), (6, 15), (5, 15), (17, 17), (8, 25), (2, 14), (25, 26), (19, 5), (10, 12), (24, 12), (11, 11), (24, 3), (1, 32), (3, 24), (6, 11), (21, 0), (26, 22), (27, 19), (7, 15), (20, 32), (22, 18), (6, 36), (3, 23), (21, 15), (4, 28), (31, 21), (21, 16), (7, 12), (10, 31), (5, 13), (8, 4), (21, 36), (21, 22), (18, 38), (15, 15), (4, 22), (2, 11), (13, 11), (14, 37), (27, 36), (7, 33), (0, 34), (14, 30), (13, 27), (24, 0), (8, 37), (26, 15), (4, 11), (9, 20), (25, 29), (14, 31), (6, 4), (14, 9), (1, 9), (6, 33), (31, 15), (27, 12), (10, 1), (25, 14), (16, 29), (0, 35), (27, 17), (7, 24), (17, 16), (19, 34), (18, 7), (22, 38), (25, 5), (11, 25), (25, 36), (15, 16), (17, 24), (4, 38), (28, 35), (16, 10), (2, 25), (9, 8), (25, 32), (19, 11), (14, 34), (16, 32), (28, 26), (14, 8), (0, 9), (20, 13), (1, 5), (29, 25), (28, 11), (18, 24), (24, 35), (26, 28), (17, 9), (23, 9), (25, 28), (18, 2), (29, 28), (14, 28), (3, 11), (18, 13), (2, 18), (19, 20), (7, 34), (29, 0), (30, 0), (23, 35), (21, 20), (5, 33), (27, 1), (13, 37), (20, 0), (5, 19), (0, 13), (12, 21), (21, 28), (13, 26), (19, 26), (29, 13), (21, 19), (2, 4), (10, 9), (19, 12), (5, 34), (21, 7), (18, 36), (22, 19), (7, 10), (8, 14), (9, 7), (3, 32), (13, 5), (23, 27), (27, 26), (17, 34), (8, 0), (29, 1), (2, 0), (28, 33), (10, 2), (5, 17), (0, 16), (12, 38), (24, 31), (24, 19), (3, 17), (24, 9), (22, 21), (0, 38), (27, 0), (17, 23), (4, 21), (7, 27), (12, 35), (13, 6), (24, 2), (12, 7), (27, 37), (19, 22), (31, 25), (28, 16), (2, 38), (15, 1), (2, 10), (3, 25), (27, 7), (22, 3), (31, 26), (21, 26), (17, 6), (22, 31), (23, 19), (30, 8), (10, 11), (9, 38), (19, 25), (21, 38), (4, 18), (6, 16), (13, 20), (1, 35), (26, 6), (16, 13), (7, 9), (12, 15), (19, 14), (15, 37), (5, 11), (1, 4), (16, 21), (14, 20), (10, 8), (29, 9), (18, 31), (9, 21), (17, 32), (5, 5), (25, 21), (4, 24), (18, 30), (6, 26), (20, 35), (28, 38), (18, 0), (16, 31), (18, 35), (5, 38), (16, 2), (8, 12), (16, 24), (27, 24), (1, 24), (22, 32), (19, 35), (21, 8), (4, 34), (16, 7), (2, 13), (1, 25), (24, 28), (3, 13), (31, 9), (6, 38), (19, 10), (7, 23), (7, 22), (3, 1), (5, 1), (5, 20), (20, 4), (29, 31), (26, 21), (1, 15), (17, 20), (2, 17), (24, 4), (29, 16), (15, 12), (27, 16), (10, 38), (3, 38), (12, 27), (29, 19), (10, 28), (30, 6), (24, 34), (31, 16), (11, 19), (15, 5), (24, 22), (0, 17), (11, 33), (15, 24), (31, 5), (26, 1), (27, 9), (31, 37), (8, 29), (23, 29), (26, 17), (20, 37), (12, 34), (11, 34), (20, 16), (14, 38), (20, 17), (10, 22), (25, 4), (31, 1), (31, 28), (2, 29), (12, 13), (6, 20), (4, 31), (21, 18), (25, 7), (25, 2), (15, 30), (19, 23), (12, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758241", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 24), (27, 11), (22, 7), (32, 7), (9, 20), (23, 19), (12, 26), (19, 16), (7, 3), (11, 30), (6, 23), (6, 17), (17, 11), (13, 4), (10, 30), (26, 6), (1, 24), (1, 23), (29, 7), (13, 24), (0, 28), (10, 14), (27, 16), (14, 21), (27, 13), (18, 2), (0, 29), (32, 9), (12, 18), (26, 18), (34, 5), (16, 3), (12, 28), (25, 27), (22, 27), (32, 26), (4, 21), (2, 17), (22, 17), (27, 5), (31, 23), (25, 20), (6, 16), (29, 16), (17, 14), (2, 9), (24, 0), (19, 17), (9, 1), (14, 4), (3, 28), (0, 31), (15, 24), (5, 11), (12, 20), (11, 2), (6, 8), (13, 14), (23, 4), (8, 31), (16, 12), (3, 16), (1, 20), (27, 10), (16, 21), (33, 26), (20, 15), (30, 20), (15, 29), (13, 25), (26, 13), (11, 20), (24, 3), (29, 22), (31, 16), (26, 1), (28, 18), (24, 8), (1, 6), (2, 25), (10, 16), (22, 14), (10, 4), (34, 8), (9, 0), (12, 1), (22, 6), (5, 4), (11, 11), (4, 20), (14, 10), (5, 18), (8, 22), (34, 26), (12, 4), (11, 12), (29, 10), (29, 23), (1, 2), (16, 24), (17, 29), (11, 22), (4, 22), (26, 17), (7, 16), (13, 28), (14, 16), (25, 6), (23, 14), (3, 30), (9, 16), (33, 24), (12, 24), (11, 21), (2, 27), (8, 11), (10, 1), (15, 15), (27, 1), (9, 4), (30, 8), (27, 25), (15, 1), (25, 25), (3, 21), (11, 1), (12, 31), (16, 20), (25, 15), (31, 21), (16, 30), (22, 16), (0, 18), (34, 18), (25, 23), (30, 3), (9, 15), (18, 22), (28, 11), (10, 20), (18, 13), (14, 27), (7, 21), (8, 16), (8, 9), (19, 29), (11, 19), (30, 31), (32, 28), (14, 3), (17, 22), (6, 7), (24, 21), (24, 2), (33, 21), (8, 3), (28, 9), (4, 4), (7, 7), (13, 29), (10, 11), (15, 23), (16, 19), (32, 16), (30, 29), (20, 19), (11, 31), (32, 12), (6, 30), (25, 7), (24, 13), (10, 17), (12, 11), (34, 19), (10, 21), (33, 12), (19, 2), (27, 22), (22, 29), (22, 24), (19, 3), (33, 22), (10, 27), (5, 23), (27, 9), (17, 18), (25, 12), (2, 16), (18, 25), (12, 2), (28, 13), (32, 29), (13, 17), (25, 21), (13, 8), (2, 1), (12, 23), (12, 6), (8, 28), (31, 7), (9, 22), (8, 21), (15, 18), (0, 14), (29, 29), (15, 7), (7, 22), (11, 6), (1, 22), (2, 21), (29, 12), (15, 5), (23, 3), (14, 20), (28, 16), (4, 26), (26, 31), (23, 23), (29, 19), (31, 24), (4, 31), (8, 23), (15, 26), (3, 1), (20, 13), (34, 2), (32, 24), (17, 9), (4, 17), (0, 13), (6, 19), (2, 12), (9, 10), (18, 29), (20, 2), (11, 17), (4, 11), (24, 1), (11, 14), (1, 14), (18, 26), (32, 31), (32, 4), (16, 14), (26, 28), (32, 30), (30, 25), (23, 21), (33, 6), (0, 26), (10, 24), (7, 11), (20, 17), (26, 3), (15, 13), (29, 20), (16, 25), (11, 24), (4, 15), (8, 18), (18, 15), (4, 28), (13, 5), (27, 29), (25, 4), (26, 8), (23, 25), (34, 12), (2, 31), (9, 13), (15, 19), (2, 6), (18, 17), (11, 26), (26, 12), (2, 30), (12, 16), (2, 28), (30, 11), (31, 17), (11, 8), (18, 19), (24, 6), (2, 22), (4, 29), (26, 16), (17, 8), (13, 30), (12, 19), (33, 31), (34, 7), (3, 24), (28, 28), (17, 21), (8, 7), (19, 0), (26, 7), (6, 15), (2, 11), (30, 30), (16, 5), (16, 13), (34, 9), (28, 26), (30, 4), (27, 8), (12, 25), (33, 25), (0, 16), (23, 26), (17, 30), (28, 6), (14, 17), (19, 9), (7, 18), (29, 26), (7, 13), (0, 25), (2, 14), (29, 24), (23, 28), (15, 0), (22, 31), (3, 15), (32, 15), (5, 10), (17, 7), (11, 4), (34, 1), (10, 18), (26, 22), (13, 15), (8, 2), (34, 6), (7, 20), (8, 25), (8, 13), (16, 9), (24, 15), (14, 30), (13, 7), (6, 31), (18, 14), (8, 30), (18, 28), (25, 31), (34, 13), (31, 19), (3, 8), (28, 22), (16, 29), (16, 2), (20, 6), (27, 28), (18, 18), (13, 10), (21, 4), (3, 9), (26, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "572000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 32), (12, 8), (24, 9), (15, 13), (10, 9), (16, 29), (10, 15), (6, 13), (22, 16), (30, 3), (13, 18), (25, 17), (13, 6), (32, 17), (24, 17), (17, 13), (5, 8), (29, 20), (28, 11), (7, 30), (10, 0), (22, 8), (11, 5), (2, 34), (7, 33), (10, 1), (31, 12), (12, 28), (8, 28), (15, 4), (24, 20), (31, 24), (15, 21), (5, 4), (6, 0), (32, 0), (30, 10), (29, 7), (23, 31), (22, 12), (24, 22), (15, 10), (28, 26), (21, 33), (13, 30), (15, 25), (7, 7), (2, 31), (24, 16), (7, 19), (24, 15), (27, 15), (13, 14), (26, 26), (16, 16), (21, 16), (17, 9), (29, 16), (12, 14), (5, 21), (24, 19), (15, 14), (8, 12), (22, 23), (4, 16), (29, 2), (19, 14), (30, 12), (31, 27), (0, 17), (22, 20), (28, 28), (2, 11), (26, 6), (27, 6), (12, 6), (16, 2), (11, 33), (1, 13), (5, 23), (19, 31), (15, 2), (24, 26), (13, 28), (9, 0), (24, 35), (9, 16), (0, 12), (16, 13), (29, 32), (30, 27), (14, 32), (24, 34), (12, 29), (10, 32), (16, 4), (15, 35), (12, 21), (29, 35), (7, 2), (6, 19), (22, 9), (1, 22), (21, 15), (20, 30), (23, 32), (18, 30), (10, 27), (18, 12), (4, 2), (16, 19), (14, 6), (15, 31), (24, 23), (5, 3), (30, 25), (33, 30), (16, 15), (0, 10), (3, 19), (0, 25), (20, 21), (25, 30), (0, 15), (23, 28), (5, 5), (14, 30), (28, 0), (1, 24), (30, 24), (23, 7), (31, 15), (31, 19), (7, 17), (8, 17), (7, 31), (26, 29), (29, 8), (21, 24), (27, 26), (1, 16), (14, 26), (10, 7), (7, 21), (12, 7), (12, 12), (3, 34), (20, 4), (12, 30), (20, 18), (5, 1), (29, 1), (20, 12), (11, 4), (21, 6), (23, 13), (14, 24), (27, 23), (24, 2), (0, 1), (18, 14), (19, 9), (4, 34), (19, 17), (0, 4), (4, 7), (2, 33), (27, 12), (10, 34), (6, 32), (26, 8), (6, 20), (3, 0), (4, 33), (22, 29), (24, 28), (27, 29), (8, 20), (29, 21), (22, 31), (30, 28), (10, 3), (13, 16), (27, 32), (17, 1), (5, 9), (24, 24), (20, 29), (25, 15), (30, 1), (22, 14), (15, 23), (21, 23), (2, 30), (1, 14), (18, 35), (3, 24), (27, 24), (19, 10), (18, 5), (15, 12), (31, 25), (16, 0), (4, 4), (19, 12), (3, 12), (19, 1), (13, 32), (29, 22), (20, 26), (25, 16), (25, 9), (9, 5), (6, 8), (14, 17), (20, 19), (33, 13), (3, 20), (7, 29), (17, 8), (11, 19), (5, 6), (4, 10), (18, 25), (22, 30), (7, 6), (20, 14), (33, 20), (8, 11), (26, 1), (21, 18), (28, 18), (29, 29), (11, 28), (27, 11), (0, 11), (33, 6), (3, 26), (19, 35), (20, 7), (14, 2), (0, 31), (31, 9), (31, 8), (15, 17), (33, 28), (4, 15), (33, 9), (28, 2), (14, 16), (0, 23), (5, 12), (30, 9), (28, 8), (12, 16), (4, 5), (4, 14), (18, 19), (22, 6), (33, 31), (16, 25), (21, 2), (14, 7), (21, 8), (6, 15), (19, 32), (6, 17), (6, 29), (18, 18), (26, 30), (7, 9), (25, 20), (23, 12), (6, 27), (32, 32), (17, 14), (20, 33), (22, 3), (28, 14), (30, 14), (3, 13), (26, 21), (13, 4), (11, 8), (16, 1), (24, 10), (10, 31), (2, 27), (5, 17), (8, 7), (15, 15), (19, 18), (4, 26), (8, 26), (26, 14), (0, 35), (30, 2), (33, 21), (29, 31), (2, 20), (32, 28), (16, 33), (7, 0), (4, 27), (32, 10), (8, 35), (30, 21), (11, 7), (29, 5), (15, 5), (31, 22), (33, 27), (33, 7), (17, 27), (8, 14), (12, 0), (5, 7), (12, 15), (4, 24), (10, 24), (24, 32), (24, 27), (23, 35), (7, 10), (18, 1), (14, 31), (11, 14), (12, 22), (30, 23), (29, 18), (7, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "267300", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), 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, 17), (7, 26), (3, 16), (15, 11), (22, 23), (0, 2), (8, 29), (24, 16), (11, 22), (19, 13), (7, 12), (23, 28), (8, 6), (28, 25), (24, 27), (29, 4), (16, 24), (30, 25), (1, 6), (13, 25), (0, 15), (2, 24), (4, 14), (1, 17), (3, 14), (21, 9), (28, 4), (19, 17), (26, 14), (13, 14), (0, 8), (23, 27), (29, 8), (4, 28), (2, 10), (28, 17), (22, 7), (18, 10), (5, 13), (5, 29), (33, 5), (9, 26), (0, 7), (6, 10), (19, 20), (6, 18), (5, 27), (26, 28), (31, 25), (28, 28), (14, 22), (19, 0), (4, 2), (33, 23), (4, 7), (17, 28), (31, 21), (31, 23), (6, 7), (31, 18), (22, 20), (23, 15), (30, 22), (5, 3), (5, 1), (5, 20), (27, 5), (21, 22), (8, 3), (14, 26), (3, 15), (21, 25), (13, 26), (14, 12), (12, 5), (9, 5), (4, 15), (0, 3), (20, 8), (14, 13), (32, 5), (21, 3), (13, 27), (33, 27), (19, 1), (9, 20), (16, 28), (21, 11), (17, 17), (9, 27), (19, 16), (22, 5), (3, 6), (32, 17), (18, 1), (18, 28), (3, 7), (12, 21), (27, 20), (15, 14), (21, 14), (30, 3), (3, 10), (0, 26), (19, 24), (17, 19), (5, 18), (32, 19), (27, 26), (4, 27), (31, 15), (31, 3), (33, 4), (1, 29), (1, 13), (16, 29), (18, 5), (7, 8), (14, 20), (26, 9), (22, 22), (29, 29), (17, 3), (21, 15), (12, 11), (2, 28), (27, 1), (6, 12), (31, 24), (20, 17), (1, 9), (12, 27), (11, 13), (13, 3), (33, 25), (33, 3), (23, 5), (14, 17), (31, 19), (18, 16), (5, 4), (12, 7), (20, 6), (29, 16), (27, 21), (9, 8), (10, 10), (12, 14), (1, 8), (29, 13), (10, 8), (5, 28), (25, 9), (25, 3), (13, 15), (30, 7), (30, 26), (28, 9), (31, 10), (12, 19), (18, 23), (22, 1), (18, 29), (12, 29), (6, 0), (31, 4), (32, 9), (7, 25), (28, 21), (1, 15), (4, 18), (6, 28), (26, 27), (15, 7), (11, 16), (8, 18), (5, 15), (3, 19), (12, 2), (20, 4), (32, 14), (10, 14), (22, 4), (17, 14), (33, 26), (8, 17), (4, 26), (20, 24), (20, 5), (31, 2), (27, 16), (3, 5), (26, 23), (29, 6), (23, 2), (16, 1), (19, 19), (4, 29), (17, 15), (6, 5), (13, 20), (11, 3), (11, 8), (1, 11), (28, 24), (10, 22), (33, 16), (24, 7), (22, 26), (13, 13), (17, 4), (20, 11), (8, 16), (19, 12), (19, 25), (23, 20), (14, 10), (31, 12), (27, 11), (21, 5), (10, 20), (32, 15), (10, 3), (33, 15), (18, 27), (9, 19), (19, 14), (20, 12), (15, 3), (13, 16), (2, 17), (16, 20), (30, 15), (8, 0), (5, 26), (30, 29), (8, 1), (8, 2), (16, 25), (18, 18), (28, 20), (33, 22), (9, 23), (13, 21), (23, 4), (26, 8), (13, 7), (18, 0), (27, 15), (11, 4), (32, 2), (15, 4), (32, 28), (7, 16), (10, 11), (30, 1), (1, 20), (21, 2), (1, 28), (24, 22), (7, 0), (19, 10), (33, 21), (8, 19), (22, 14), (24, 28), (15, 22), (21, 26), (7, 19), (25, 11), (17, 26), (3, 13), (18, 7), (21, 20), (17, 13), (11, 25), (16, 0), (24, 12), (1, 16), (26, 20), (17, 18), (11, 24), (16, 10), (16, 26), (12, 10), (32, 1), (7, 23), (1, 3), (26, 18), (33, 10), (13, 28), (3, 27), (15, 29), (10, 12), (17, 29), (28, 16), (22, 19), (4, 10), (13, 29), (3, 3), (23, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "998640", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 10), (11, 15), (17, 19), (32, 18), (31, 19), (19, 14), (27, 4), (38, 22), (25, 23), (25, 25), (12, 22), (14, 28), (13, 21), (16, 16), (4, 15), (22, 17), (0, 5), (13, 9), (35, 11), (23, 28), (2, 6), (34, 29), (19, 3), (12, 23), (34, 15), (29, 13), (17, 15), (23, 12), (21, 8), (29, 11), (14, 15), (34, 10), (5, 5), (8, 10), (22, 2), (32, 11), (3, 28), (6, 21), (32, 29), (36, 4), (9, 24), (2, 26), (31, 18), (30, 22), (38, 11), (15, 25), (28, 5), (8, 27), (34, 14), (2, 14), (3, 5), (11, 10), (31, 17), (35, 24), (33, 18), (0, 17), (4, 24), (35, 4), (1, 4), (33, 15), (24, 6), (20, 23), (9, 27), (20, 17), (34, 13), (36, 16), (5, 17), (13, 4), (16, 12), (7, 19), (7, 24), (21, 22), (6, 9), (27, 25), (12, 18), (13, 15), (19, 15), (9, 29), (10, 0), (23, 29), (4, 3), (3, 2), (25, 28), (22, 14), (38, 13), (31, 14), (11, 24), (31, 23), (11, 13), (18, 4), (2, 0), (38, 20), (3, 29), (10, 27), (30, 4), (30, 17), (30, 18), (36, 0), (32, 15), (14, 5), (30, 21), (27, 24), (16, 3), (37, 19), (27, 5), (10, 10), (10, 11), (27, 16), (34, 7), (21, 5), (29, 1), (19, 20), (7, 20), (28, 8), (12, 25), (26, 18), (10, 9), (25, 3), (30, 26), (15, 23), (7, 5), (17, 0), (7, 1), (21, 11), (34, 18), (12, 1), (14, 21), (7, 10), (22, 3), (25, 20), (25, 9), (7, 26), (30, 0), (23, 5), (36, 3), (26, 17), (26, 20), (38, 9), (20, 10), (26, 12), (34, 25), (38, 19), (25, 18), (19, 5), (5, 10), (33, 14), (2, 7), (31, 26), (7, 2), (36, 23), (24, 19), (12, 29), (22, 11), (7, 22), (33, 17), (35, 0), (36, 11), (29, 23), (14, 13), (34, 12), (8, 18), (35, 3), (10, 1), (20, 27), (25, 2), (26, 26), (30, 7), (8, 22), (33, 1), (6, 0), (6, 17), (32, 23), (10, 14), (16, 20), (29, 24), (31, 3), (31, 5), (36, 5), (19, 1), (16, 10), (18, 23), (19, 17), (11, 11), (1, 27), (27, 23), (38, 24), (2, 10), (17, 20), (30, 24), (8, 17), (2, 29), (37, 13), (15, 2), (13, 8), (26, 8), (6, 23), (18, 3), (16, 13), (36, 18), (4, 21), (21, 3), (24, 10), (27, 20), (17, 5), (23, 15), (7, 13), (25, 6), (17, 6), (4, 23), (38, 28), (2, 11), (17, 13), (0, 18), (12, 26), (23, 8), (7, 8), (24, 14), (37, 0), (15, 7), (29, 17), (0, 23), (27, 19), (14, 1), (21, 23), (21, 6), (30, 14), (10, 25), (24, 12), (10, 12), (1, 15), (22, 28), (14, 8), (20, 5), (23, 16), (31, 2), (3, 18), (15, 22), (22, 20), (29, 15), (21, 12), (4, 13), (38, 12), (36, 14), (23, 21), (37, 21), (9, 26), (11, 27), (7, 14), (26, 25), (18, 25), (3, 20), (20, 2), (29, 21), (36, 10), (11, 29), (30, 28), (32, 22), (24, 15), (33, 4), (36, 9), (26, 4), (0, 26), (26, 29), (8, 16), (18, 7), (4, 11), (1, 20), (22, 27), (25, 17), (3, 13), (20, 9), (4, 12), (18, 1), (12, 27), (1, 14), (22, 23), (7, 27), (1, 22), (32, 10), (24, 18), (10, 8), (25, 4), (26, 13), (0, 21), (29, 28), (27, 28), (13, 0), (9, 17), (2, 8), (33, 2), (20, 26), (22, 21), (32, 0), (4, 28), (18, 15), (29, 2), (12, 16), (23, 2), (34, 0), (14, 11), (28, 29), (7, 15), (15, 16), (1, 21), (33, 28), (22, 6), (22, 7), (38, 18), (37, 17), (11, 12), (5, 23), (10, 15), (10, 4), (12, 21), (28, 0), (32, 26), (23, 24), (11, 0), (3, 15), (35, 14), (14, 4), (16, 23), (29, 9), (5, 13), (18, 29), (23, 27), (29, 7), (5, 8), (24, 28), (14, 26), (2, 2), (27, 1), (5, 6), (34, 26), (11, 26), (3, 21), (0, 16), (33, 27), (26, 16), (7, 3), (22, 0), (10, 28), (21, 2), (2, 17), (20, 21), (0, 1), (13, 11), (29, 8), (22, 24), (13, 5), (6, 2), (22, 9), (21, 9), (5, 20), (30, 13), (32, 28), (13, 29), (19, 2), (0, 4), (16, 1), (11, 4), (15, 18), (11, 5), (20, 4), (31, 0), (10, 23), (16, 0), (24, 17), (13, 12), (14, 17), (8, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705600", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 1), (31, 25), (17, 29), (2, 29), (27, 19), (29, 6), (10, 34), (19, 21), (18, 21), (9, 0), (30, 28), (13, 1), (15, 23), (27, 33), (2, 33), (15, 30), (0, 11), (30, 20), (17, 9), (14, 9), (21, 10), (16, 13), (0, 18), (4, 11), (22, 1), (31, 28), (17, 18), (25, 32), (16, 15), (12, 26), (14, 13), (7, 29), (18, 4), (11, 31), (20, 26), (11, 29), (1, 9), (28, 6), (23, 18), (26, 14), (0, 31), (12, 5), (25, 22), (5, 34), (8, 25), (31, 16), (14, 28), (17, 3), (20, 20), (29, 28), (6, 6), (0, 17), (32, 6), (13, 15), (22, 33), (1, 26), (9, 3), (7, 32), (16, 8), (2, 0), (15, 31), (3, 17), (19, 20), (22, 21), (13, 25), (4, 1), (21, 12), (0, 32), (26, 20), (28, 30), (7, 3), (18, 31), (25, 1), (20, 28), (25, 21), (5, 9), (6, 9), (3, 28), (13, 11), (10, 21), (30, 17), (2, 19), (18, 30), (6, 24), (14, 1), (16, 17), (16, 23), (6, 25), (19, 30), (32, 16), (18, 0), (3, 12), (21, 28), (23, 24), (4, 28), (27, 9), (16, 11), (24, 16), (5, 17), (3, 7), (31, 26), (17, 10), (24, 23), (22, 32), (27, 26), (28, 11), (22, 27), (1, 21), (25, 10), (6, 27), (5, 32), (29, 32), (6, 30), (16, 26), (5, 29), (12, 19), (10, 22), (7, 10), (13, 3), (24, 10), (14, 29), (29, 4), (12, 8), (23, 31), (14, 18), (30, 1), (15, 32), (8, 6), (8, 24), (15, 9), (0, 16), (32, 8), (30, 4), (26, 6), (13, 28), (13, 26), (21, 31), (21, 18), (27, 31), (15, 22), (28, 7), (32, 24), (22, 30), (29, 5), (27, 5), (5, 6), (32, 11), (8, 31), (1, 7), (20, 9), (22, 31), (21, 29), (10, 18), (16, 9), (18, 17), (7, 16), (33, 6), (14, 30), (20, 3), (31, 7), (17, 5), (1, 18), (1, 28), (33, 15), (31, 5), (26, 7), (6, 33), (19, 27), (30, 27), (28, 13), (16, 16), (13, 6), (32, 31), (24, 21), (28, 23), (2, 21), (32, 26), (23, 30), (17, 20), (25, 17), (19, 1), (29, 33), (25, 4), (23, 4), (26, 25), (5, 1), (11, 5), (4, 17), (31, 33), (20, 32), (28, 9), (28, 0), (32, 2), (8, 5), (5, 13), (17, 30), (32, 12), (11, 24), (7, 14), (29, 10), (20, 22), (22, 6), (16, 20), (9, 23), (23, 33), (21, 13), (31, 3), (5, 5), (9, 15), (30, 2), (1, 14), (6, 26), (26, 5), (8, 0), (26, 11), (30, 31), (22, 14), (22, 12), (16, 22), (31, 15), (18, 26), (23, 32), (8, 3), (24, 30), (9, 12), (33, 25), (24, 29), (31, 31), (17, 1), (22, 22), (13, 7), (1, 2), (1, 22), (1, 25), (0, 1), (17, 17), (2, 11), (19, 7), (0, 4), (32, 21), (31, 0), (14, 7), (8, 29), (17, 12), (9, 14), (19, 16), (8, 21), (19, 33), (24, 25), (30, 32), (10, 29), (30, 9), (33, 31), (30, 26), (29, 30), (12, 13), (3, 21), (33, 0), (0, 5), (3, 26), (13, 12), (13, 31), (21, 24), (7, 7), (29, 1), (12, 0), (18, 27), (8, 15), (14, 31), (11, 13), (7, 33), (20, 27), (9, 24), (25, 30), (9, 19), (6, 17), (4, 2), (24, 7), (1, 20), (31, 21), (3, 32), (1, 13), (27, 24), (20, 8), (3, 20), (7, 27), (24, 2), (25, 15), (18, 24), (14, 15), (23, 22), (6, 28), (19, 19), (20, 12), (24, 9), (4, 22), (25, 25), (8, 30), (13, 18), (9, 18), (18, 11), (18, 28), (16, 24), (0, 33), (32, 5), (23, 7), (6, 13), (4, 13), (1, 8), (0, 12), (19, 25), (15, 19), (2, 10), (8, 34), (26, 3), (26, 33), (26, 16), (13, 33), (20, 24), (21, 14), (25, 19), (0, 19), (32, 27), (15, 3), (3, 14), (30, 19), (24, 4), (10, 14), (22, 3), (10, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "559584", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 11), (29, 2), (10, 7), (26, 9), (8, 19), (12, 26), (36, 5), (5, 3), (37, 6), (16, 30), (27, 15), (6, 25), (33, 32), (20, 0), (19, 26), (31, 15), (33, 4), (37, 12), (4, 14), (11, 7), (11, 22), (20, 3), (7, 28), (3, 13), (27, 21), (16, 7), (21, 19), (35, 12), (19, 29), (14, 7), (3, 24), (31, 22), (34, 16), (23, 3), (38, 1), (33, 25), (20, 23), (27, 24), (20, 17), (37, 24), (29, 34), (30, 21), (22, 17), (6, 11), (3, 25), (14, 32), (8, 6), (19, 17), (14, 18), (38, 10), (35, 7), (3, 2), (1, 10), (13, 30), (25, 10), (3, 19), (35, 9), (15, 7), (9, 6), (1, 27), (11, 27), (16, 22), (38, 23), (15, 6), (31, 31), (34, 22), (15, 30), (35, 4), (33, 16), (36, 10), (12, 3), (27, 22), (12, 33), (7, 21), (24, 29), (22, 28), (18, 14), (37, 34), (0, 20), (31, 7), (3, 22), (3, 10), (14, 9), (25, 18), (9, 30), (14, 2), (18, 20), (38, 15), (24, 14), (19, 6), (8, 5), (25, 22), (12, 17), (24, 25), (5, 23), (6, 29), (18, 13), (7, 34), (32, 2), (28, 9), (12, 28), (21, 3), (37, 23), (1, 2), (32, 32), (29, 23), (16, 13), (25, 1), (1, 13), (10, 2), (20, 22), (2, 34), (30, 17), (1, 30), (2, 10), (20, 20), (15, 0), (36, 1), (32, 19), (4, 26), (3, 28), (25, 21), (17, 10), (25, 27), (35, 14), (8, 22), (32, 15), (11, 10), (36, 27), (17, 18), (11, 16), (23, 11), (18, 28), (23, 28), (26, 19), (31, 34), (20, 25), (35, 31), (20, 32), (5, 5), (10, 27), (36, 30), (14, 10), (18, 1), (28, 25), (32, 1), (14, 26), (20, 6), (11, 2), (8, 30), (21, 28), (17, 6), (7, 23), (35, 0), (6, 2), (18, 17), (18, 8), (8, 26), (22, 31), (14, 1), (26, 17), (14, 8), (23, 20), (24, 16), (22, 6), (37, 26), (32, 13), (23, 31), (7, 25), (5, 27), (13, 26), (27, 31), (13, 29), (9, 33), (37, 11), (13, 17), (37, 9), (2, 22), (36, 23), (11, 34), (36, 34), (36, 17), (26, 21), (0, 3), (10, 21), (19, 4), (9, 16), (4, 19), (34, 2), (36, 4), (28, 7), (35, 11), (9, 22), (22, 34), (29, 13), (11, 19), (11, 28), (29, 32), (8, 18), (37, 10), (16, 6), (15, 5), (25, 7), (21, 0), (2, 28), (13, 9), (7, 31), (18, 32), (18, 9), (6, 28), (4, 24), (38, 29), (17, 8), (22, 22), (31, 19), (10, 9), (32, 10), (12, 18), (12, 12), (33, 27), (25, 0), (9, 28), (16, 0), (30, 1), (20, 29), (19, 31), (29, 12), (15, 33), (5, 0), (37, 32), (33, 0), (27, 29), (14, 6), (7, 18), (5, 32), (32, 18), (27, 18), (37, 0), (13, 2), (1, 26), (17, 32), (4, 22), (31, 3), (2, 1), (15, 15), (21, 13), (34, 3), (0, 33), (23, 33), (15, 8), (18, 2), (33, 1), (24, 7), (30, 22), (7, 19), (18, 22), (5, 17), (21, 1), (17, 21), (13, 7), (9, 9), (11, 29), (22, 10), (18, 10), (22, 3), (28, 6), (19, 19), (1, 15), (35, 5), (30, 9), (24, 19), (5, 7), (24, 11), (15, 31), (6, 7), (20, 8), (1, 21), (10, 31), (32, 11), (8, 14), (2, 12), (10, 12), (8, 24), (6, 22), (5, 29), (14, 20), (38, 22), (23, 26), (16, 12), (9, 13), (35, 20), (7, 7), (34, 14), (33, 12), (16, 26), (20, 15), (9, 29), (17, 23), (22, 1), (13, 0), (15, 13), (20, 31), (0, 4), (16, 28), (2, 26), (15, 26), (11, 0), (35, 8), (29, 24), (27, 14), (36, 26), (25, 13), (19, 33), (10, 17), (32, 21), (38, 31), (6, 20), (32, 4), (9, 10), (8, 8), (5, 16), (25, 25), (3, 31), (13, 6), (24, 12), (32, 23), (30, 27), (33, 18), (2, 17), (15, 11), (20, 19), (11, 26), (10, 4), (17, 30), (11, 15), (28, 10), (17, 22), (35, 32), (3, 15), (21, 33), (32, 31), (8, 9), (36, 24), (18, 25), (11, 12), (32, 8), (17, 12), (26, 15), (8, 17), (4, 5), (31, 0), (26, 16), (33, 7), (20, 24), (8, 15), (21, 31), (5, 34), (16, 19), (33, 22), (18, 27), (37, 25), (12, 34), (38, 32), (19, 3), (24, 28), (10, 25), (8, 2), (34, 18), (29, 31), (35, 15), (0, 31), (21, 14), (11, 3), (24, 0), (22, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97200", "dataset": "MATH"}
{"messages": [{"content": "In a 38x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (16, 23), (30, 19), (24, 6), (36, 17), (14, 9), (14, 4), (5, 0), (1, 0), (7, 9), (21, 2), (4, 22), (33, 17), (10, 29), (12, 10), (30, 2), (8, 16), (20, 25), (5, 27), (25, 19), (19, 18), (0, 29), (29, 31), (22, 3), (30, 12), (25, 15), (19, 25), (36, 25), (14, 1), (2, 28), (15, 10), (9, 12), (17, 20), (33, 27), (11, 9), (8, 4), (23, 9), (15, 7), (10, 13), (24, 28), (15, 1), (12, 25), (7, 19), (0, 23), (34, 12), (14, 5), (6, 0), (22, 10), (33, 8), (1, 7), (35, 8), (20, 0), (17, 12), (35, 25), (26, 9), (19, 1), (2, 15), (16, 8), (27, 30), (21, 23), (12, 20), (23, 7), (0, 10), (5, 1), (32, 23), (12, 3), (29, 29), (9, 29), (30, 15), (23, 18), (0, 8), (9, 23), (21, 20), (27, 4), (11, 7), (25, 21), (6, 20), (3, 3), (7, 27), (19, 27), (16, 15), (17, 19), (4, 2), (28, 19), (16, 21), (15, 2), (2, 21), (31, 20), (16, 30), (6, 4), (18, 29), (33, 30), (13, 29), (26, 0), (20, 20), (32, 22), (18, 26), (23, 1), (12, 30), (25, 27), (10, 21), (31, 12), (32, 30), (29, 13), (35, 2), (28, 24), (2, 9), (34, 19), (8, 31), (10, 19), (3, 10), (7, 13), (23, 30), (3, 22), (18, 4), (18, 24), (37, 15), (34, 26), (0, 9), (16, 19), (27, 28), (30, 7), (37, 11), (34, 31), (19, 14), (15, 21), (5, 3), (3, 16), (16, 16), (21, 27), (7, 30), (32, 3), (29, 7), (30, 20), (33, 7), (1, 15), (4, 14), (6, 31), (16, 3), (12, 12), (19, 6), (27, 9), (34, 22), (32, 24), (13, 4), (34, 5), (0, 5), (10, 18), (11, 21), (17, 1), (32, 7), (29, 17), (20, 14), (18, 22), (4, 11), (15, 11), (12, 2), (28, 7), (6, 2), (2, 1), (32, 27), (14, 14), (3, 14), (22, 20), (2, 14), (15, 27), (16, 9), (13, 7), (9, 28), (10, 17), (29, 26), (36, 29), (17, 23), (8, 1), (37, 1), (6, 10), (21, 28), (8, 15), (14, 31), (20, 21), (35, 22), (7, 20), (21, 24), (1, 27), (5, 15), (26, 15), (23, 6), (5, 6), (14, 23), (8, 28), (32, 8), (6, 29), (2, 8), (36, 13), (35, 27), (15, 20), (29, 30), (7, 4), (18, 0), (23, 24), (17, 21), (11, 24), (36, 31), (32, 12), (37, 4), (10, 20), (17, 26), (16, 14), (4, 23), (22, 30), (18, 13), (6, 23), (29, 4), (33, 3), (28, 0), (22, 14), (24, 10), (22, 8), (28, 29), (33, 15), (20, 27), (31, 10), (26, 7), (14, 21), (4, 10), (16, 27), (18, 7), (30, 14), (10, 3), (23, 15), (20, 4), (30, 29), (26, 23), (4, 26), (30, 9), (35, 17), (16, 18), (5, 20), (33, 12), (23, 27), (0, 13), (12, 7), (11, 10), (18, 10), (13, 8), (10, 10), (13, 21), (2, 19), (32, 25), (22, 13), (27, 13), (23, 4), (35, 13), (23, 26), (0, 14), (25, 11), (5, 4), (11, 18), (7, 17), (1, 16), (8, 7), (23, 11), (23, 8), (36, 24), (10, 22), (1, 14), (25, 1), (20, 29), (17, 6), (0, 3), (27, 17), (16, 12), (3, 27), (6, 26), (7, 6), (19, 17), (15, 0), (16, 22), (25, 2), (27, 19), (24, 29), (5, 25), (23, 12), (11, 11), (24, 19), (20, 31), (33, 10), (12, 22), (14, 3), (37, 20), (5, 13), (19, 29), (23, 14), (13, 3), (21, 7), (25, 14), (34, 18), (36, 20), (16, 6), (4, 8), (16, 31), (11, 27), (35, 6), (37, 23), (33, 13), (25, 3), (8, 29), (1, 10), (5, 30), (29, 3), (7, 26), (16, 26), (8, 6), (9, 1), (0, 4), (28, 13), (35, 5), (20, 12), (15, 6), (31, 24), (23, 5), (34, 29), (16, 25), (26, 24), (36, 6), (18, 5), (25, 10), (18, 2), (35, 31), (32, 2), (20, 5), (15, 28), (30, 10), (26, 16), (34, 8), (37, 9), (15, 16), (34, 1), (11, 31), (16, 1), (7, 11), (3, 23), (33, 24), (26, 20), (36, 0), (30, 22), (13, 22), (19, 21), (20, 7), (33, 25), (30, 23), (9, 18), (22, 2), (2, 22), (23, 13), (6, 7), (22, 25), (5, 2), (8, 10), (3, 6), (4, 7), (37, 14), (22, 12), (2, 25), (12, 6), (18, 14), (22, 17), (5, 31), (31, 30), (5, 14), (28, 9), (5, 29), (15, 25), (34, 4), (34, 24), (12, 19), (3, 30), (24, 7), (37, 2), (4, 24), (1, 30), (25, 31), (6, 11), (2, 16), (10, 5), (29, 14), (29, 21), (20, 9), (24, 2), (7, 12), (27, 29), (1, 31), (18, 27), (28, 17), (6, 30), (15, 12), (36, 30), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "783360", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (28, 29), (24, 13), (12, 8), (16, 25), (17, 27), (26, 7), (1, 4), (1, 5), (6, 15), (4, 26), (28, 13), (18, 14), (30, 21), (23, 28), (0, 28), (13, 9), (5, 24), (22, 12), (6, 20), (21, 17), (15, 16), (10, 19), (4, 15), (23, 14), (8, 17), (6, 25), (29, 3), (23, 4), (25, 29), (18, 10), (1, 6), (11, 25), (3, 31), (5, 3), (29, 7), (7, 5), (22, 11), (23, 0), (2, 21), (30, 14), (28, 25), (19, 20), (3, 12), (11, 23), (7, 23), (25, 11), (16, 1), (5, 19), (26, 6), (8, 18), (15, 25), (6, 14), (21, 4), (6, 16), (2, 27), (28, 0), (30, 17), (26, 5), (14, 7), (4, 7), (0, 21), (7, 22), (19, 3), (4, 20), (13, 11), (25, 17), (7, 26), (2, 13), (13, 18), (14, 4), (0, 20), (13, 7), (3, 29), (18, 21), (12, 18), (25, 7), (30, 23), (27, 28), (16, 12), (20, 11), (0, 9), (26, 9), (9, 10), (10, 22), (7, 15), (25, 21), (25, 28), (9, 30), (29, 15), (19, 27), (27, 24), (3, 18), (8, 0), (7, 11), (13, 14), (13, 26), (13, 8), (13, 23), (2, 25), (26, 8), (13, 30), (18, 18), (29, 23), (14, 6), (4, 22), (20, 13), (11, 5), (27, 8), (30, 19), (8, 15), (16, 2), (5, 25), (1, 2), (24, 22), (21, 8), (21, 31), (17, 9), (0, 12), (21, 9), (22, 30), (22, 2), (26, 17), (10, 28), (2, 2), (13, 4), (6, 10), (19, 19), (27, 1), (22, 23), (5, 30), (9, 29), (3, 8), (14, 26), (24, 2), (3, 20), (19, 28), (29, 30), (13, 17), (2, 15), (23, 16), (6, 28), (10, 23), (11, 28), (8, 12), (20, 19), (19, 22), (24, 30), (15, 17), (13, 29), (28, 2), (12, 11), (27, 7), (21, 5), (3, 27), (26, 19), (15, 7), (4, 2), (3, 1), (25, 6), (24, 5), (23, 12), (25, 15), (1, 26), (27, 0), (16, 0), (10, 20), (26, 10), (8, 29), (29, 24), (7, 21), (27, 22), (26, 25), (12, 10), (4, 18), (19, 13), (0, 22), (26, 20), (30, 12), (8, 14), (21, 28), (0, 16), (17, 12), (9, 5), (21, 22), (27, 21), (27, 20), (12, 6), (15, 21), (2, 26), (2, 17), (26, 18), (28, 17), (8, 24), (10, 2), (27, 17), (9, 21), (4, 6), (8, 7), (21, 19), (12, 19), (20, 17), (26, 28), (0, 26), (30, 29), (23, 25), (3, 25), (2, 6), (1, 13), (10, 13), (13, 0), (23, 5), (4, 25), (17, 29), (25, 0), (6, 30), (4, 10), (20, 27), (2, 29), (0, 2), (24, 11), (6, 17), (5, 10), (3, 6), (10, 11), (14, 17), (17, 21), (16, 3), (30, 22), (19, 8), (9, 11), (9, 7), (20, 26), (19, 2), (10, 6), (9, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400770", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (9, 28), (27, 17), (20, 15), (8, 13), (23, 24), (20, 26), (5, 15), (26, 7), (30, 26), (1, 27), (24, 10), (1, 6), (27, 6), (8, 24), (22, 19), (3, 29), (2, 3), (21, 12), (24, 0), (22, 14), (22, 27), (23, 22), (0, 28), (29, 26), (2, 20), (1, 28), (9, 5), (4, 27), (20, 6), (0, 6), (19, 27), (26, 17), (24, 7), (0, 24), (12, 14), (10, 21), (5, 11), (3, 24), (16, 13), (4, 0), (19, 6), (19, 26), (21, 10), (8, 21), (4, 8), (14, 2), (4, 12), (31, 13), (18, 3), (0, 4), (0, 23), (27, 4), (2, 2), (20, 11), (2, 19), (28, 7), (10, 25), (3, 15), (31, 23), (19, 12), (9, 17), (14, 4), (15, 22), (5, 24), (8, 26), (31, 11), (20, 1), (23, 19), (4, 1), (7, 2), (18, 8), (18, 24), (3, 17), (16, 2), (28, 4), (1, 25), (2, 1), (3, 13), (17, 24), (8, 15), (26, 22), (8, 17), (16, 6), (9, 20), (7, 11), (22, 7), (28, 22), (21, 11), (3, 18), (18, 2), (24, 21), (17, 16), (28, 15), (8, 5), (1, 7), (25, 5), (18, 6), (7, 21), (3, 26), (24, 3), (5, 4), (25, 28), (1, 26), (20, 14), (17, 10), (22, 20), (2, 23), (27, 5), (4, 18), (24, 14), (1, 8), (17, 23), (31, 0), (4, 14), (11, 27), (18, 4), (21, 26), (5, 1), (17, 15), (30, 0), (12, 12), (13, 26), (17, 19), (6, 21), (7, 13), (0, 19), (23, 18), (30, 5), (16, 4), (27, 27), (4, 7), (11, 5), (30, 1), (5, 2), (19, 18), (7, 22), (13, 14), (25, 3), (0, 29), (25, 20), (31, 14), (3, 0), (14, 1), (8, 2), (1, 9), (7, 6), (21, 6), (16, 23), (19, 29), (10, 28), (2, 14), (31, 3), (0, 5), (25, 4), (6, 3), (27, 26), (7, 0), (5, 9), (14, 16), (31, 28), (4, 25), (14, 8), (26, 1), (6, 12), (22, 28), (25, 12), (25, 18), (17, 8), (13, 28), (3, 25), (9, 6), (11, 16), (9, 0), (12, 22), (14, 23), (18, 18), (7, 14), (8, 29), (15, 4), (16, 15), (0, 8), (15, 0), (20, 23), (4, 17), (24, 5), (30, 16), (15, 3), (18, 19), (26, 5), (12, 27), (28, 23), (29, 23), (31, 2), (4, 9), (7, 19), (21, 27), (5, 25), (2, 22), (5, 16), (25, 2), (20, 9), (30, 25), (8, 28), (9, 22), (20, 10), (1, 21), (25, 17), (7, 29), (17, 25), (1, 0), (19, 16), (6, 18), (5, 28), (28, 5), (14, 17), (30, 6), (23, 5), (8, 18), (1, 29), (16, 27), (23, 6), (16, 24), (22, 3), (19, 0), (21, 24), (22, 5), (15, 16), (15, 25), (25, 24), (26, 3), (11, 12), (29, 24), (30, 27), (18, 29), (1, 10), (11, 21), (7, 28), (15, 9), (17, 5), (11, 24), (22, 17), (22, 23), (26, 16), (10, 15), (13, 17), (27, 28), (13, 3), (13, 20), (24, 20), (9, 9), (11, 25), (5, 13), (28, 12), (5, 12), (2, 25), (14, 21), (22, 8), (30, 17), (5, 5), (27, 10), (20, 20), (1, 13), (26, 8), (14, 11), (29, 12), (31, 7), (16, 29), (26, 9), (16, 9), (0, 13), (8, 19), (10, 11), (27, 1), (21, 8), (16, 0), (21, 7), (21, 17), (18, 15), (2, 26), (18, 7), (10, 29), (0, 10), (8, 10), (20, 4), (28, 28), (23, 8), (6, 28), (31, 12), (18, 28), (25, 8), (1, 23), (7, 1), (31, 26), (14, 22), (8, 9), (24, 23), (14, 28), (9, 12), (27, 7), (1, 1), (25, 7), (1, 18), (19, 14), (19, 3), (4, 24), (11, 9), (23, 21), (20, 0), (14, 29), (6, 16), (13, 12), (5, 19), (31, 19), (24, 6), (6, 1), (6, 15), (4, 23), (14, 12), (24, 2), (10, 0), (3, 22), (16, 18), (22, 1), (30, 15), (0, 22), (16, 25), (10, 26), (12, 11), (24, 11), (5, 20), (14, 3), (30, 13), (10, 18), (3, 12), (10, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622080", "dataset": "MATH"}
{"messages": [{"content": "In a 37x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 29), 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), (5, 0), (5, 5), (12, 21), (12, 14), (12, 11), (13, 25), (22, 19), (7, 10), (15, 3), (16, 29), (25, 21), (23, 6), (30, 6), (21, 18), (28, 27), (5, 9), (33, 4), (17, 26), (31, 5), (13, 20), (35, 14), (25, 16), (10, 10), (31, 21), (28, 0), (13, 27), (10, 7), (14, 19), (36, 22), (4, 4), (6, 25), (27, 9), (4, 16), (15, 22), (33, 24), (6, 9), (14, 17), (17, 5), (5, 17), (23, 3), (3, 7), (20, 28), (16, 22), (27, 21), (20, 8), (6, 26), (13, 7), (30, 28), (2, 15), (19, 29), (4, 17), (27, 18), (34, 16), (9, 13), (23, 23), (34, 17), (24, 13), (10, 27), (5, 7), (6, 7), (35, 3), (7, 28), (10, 15), (28, 9), (27, 8), (33, 8), (12, 2), (19, 9), (30, 24), (27, 6), (36, 1), (29, 25), (17, 0), (8, 26), (25, 19), (17, 17), (2, 16), (7, 0), (31, 13), (32, 18), (13, 6), (30, 29), (1, 3), (13, 0), (18, 21), (33, 29), (22, 7), (4, 0), (24, 18), (11, 11), (13, 5), (32, 27), (7, 11), (4, 1), (18, 3), (13, 14), (6, 29), (34, 14), (21, 5), (28, 12), (31, 22), (35, 5), (4, 14), (24, 8), (25, 10), (26, 4), (7, 4), (35, 13), (27, 27), (18, 9), (5, 4), (33, 27), (26, 17), (2, 24), (25, 27), (8, 28), (27, 5), (13, 10), (24, 2), (8, 16), (4, 10), (14, 3), (8, 12), (25, 13), (13, 18), (11, 29), (1, 4), (5, 14), (6, 22), (14, 11), (29, 16), (24, 23), (16, 26), (28, 23), (20, 29), (18, 14), (6, 0), (21, 26), (35, 9), (15, 26), (21, 19), (5, 21), (2, 8), (36, 5), (24, 14), (31, 8), (36, 19), (0, 27), (13, 26), (0, 13), (4, 19), (5, 23), (28, 8), (1, 22), (29, 8), (21, 22), (12, 24), (6, 20), (12, 22), (0, 8), (3, 23), (5, 1), (27, 17), (11, 16), (15, 27), (24, 26), (26, 14), (9, 25), (22, 29), (2, 13), (0, 7), (22, 18), (36, 7), (24, 25), (15, 18), (18, 7), (14, 0), (7, 23), (18, 19), (17, 16), (23, 16), (33, 15), (9, 9), (31, 28), (3, 2), (32, 15), (7, 27), (24, 4), (8, 24), (20, 1), (31, 3), (17, 15), (10, 16), (33, 10), (27, 23), (32, 23), (25, 14), (35, 15), (28, 17), (27, 29), (18, 0), (7, 16), (23, 15), (30, 20), (4, 15), (5, 8), (10, 1), (2, 25), (18, 26), (34, 26), (22, 28), (0, 12), (28, 1), (7, 6), (22, 5), (24, 20), (4, 29), (2, 18), (13, 11), (16, 4), (36, 17), (31, 15), (15, 16), (28, 29), (12, 29), (25, 26), (25, 2), (11, 10), (18, 25), (32, 2), (18, 22), (1, 19), (7, 22), (6, 18), (10, 3), (12, 13), (15, 29), (13, 17), (14, 28), (23, 2), (25, 15), (34, 5), (7, 19), (22, 1), (19, 6), (4, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886080", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), 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), (7, 26), (27, 27), (3, 31), (7, 15), (14, 5), (32, 29), (11, 25), (23, 17), (27, 7), (35, 28), (26, 4), (10, 21), (10, 25), (26, 33), (9, 28), (8, 17), (33, 12), (31, 6), (29, 6), (25, 18), (12, 3), (25, 33), (33, 29), (6, 16), (18, 21), (18, 32), (31, 28), (1, 27), (29, 3), (2, 13), (2, 31), (18, 34), (0, 14), (2, 26), (33, 0), (31, 4), (14, 29), (34, 23), (6, 8), (33, 5), (4, 6), (18, 20), (23, 8), (9, 27), (13, 6), (6, 13), (25, 28), (10, 16), (23, 5), (25, 25), (32, 7), (16, 31), (1, 22), (32, 21), (2, 9), (20, 25), (27, 32), (23, 3), (9, 7), (23, 21), (9, 34), (25, 14), (21, 34), (33, 10), (3, 28), (19, 18), (22, 3), (31, 12), (4, 16), (7, 18), (5, 21), (30, 32), (20, 23), (27, 28), (19, 8), (22, 19), (4, 18), (13, 11), (33, 1), (4, 8), (25, 3), (32, 15), (33, 2), (29, 10), (17, 12), (8, 33), (5, 32), (16, 12), (4, 14), (20, 32), (32, 31), (17, 14), (15, 16), (6, 31), (32, 6), (10, 15), (12, 11), (26, 32), (1, 8), (18, 14), (0, 10), (12, 31), (25, 12), (34, 13), (17, 7), (25, 11), (35, 6), (19, 30), (9, 29), (22, 8), (30, 23), (27, 10), (18, 18), (29, 33), (3, 12), (33, 17), (6, 3), (33, 3), (6, 14), (24, 17), (1, 12), (3, 32), (17, 17), (22, 23), (24, 11), (9, 2), (31, 33), (1, 11), (21, 3), (29, 2), (9, 13), (8, 21), (31, 24), (31, 22), (27, 20), (35, 18), (25, 20), (34, 28), (27, 1), (4, 1), (16, 5), (12, 14), (5, 2), (5, 13), (9, 22), (20, 2), (34, 11), (6, 0), (11, 31), (4, 27), (13, 14), (1, 33), (24, 16), (34, 8), (15, 23), (9, 6), (7, 25), (31, 23), (34, 21), (12, 28), (32, 32), (21, 26), (35, 14), (0, 24), (35, 11), (10, 6), (22, 30), (30, 16), (10, 2), (21, 23), (6, 2), (22, 22), (27, 14), (6, 26), (24, 23), (30, 24), (9, 0), (23, 31), (32, 23), (26, 27), (16, 11), (24, 7), (31, 32), (12, 4), (21, 21), (20, 15), (17, 5), (18, 5), (17, 33), (6, 11), (24, 21), (9, 4), (25, 13), (20, 26), (7, 7), (21, 11), (3, 10), (0, 8), (5, 14), (24, 13), (2, 12), (1, 17), (27, 9), (29, 17), (8, 0), (25, 26), (21, 10), (32, 3), (30, 5), (0, 21), (22, 14), (12, 21), (5, 17), (32, 18), (13, 15), (34, 7), (3, 24), (11, 0), (20, 10), (20, 31), (16, 30), (23, 6), (20, 30), (31, 15), (0, 17), (29, 34), (29, 16), (29, 26), (14, 28), (8, 27), (10, 12), (34, 25), (24, 24), (18, 28), (12, 27), (28, 33), (21, 27), (24, 5), (0, 13), (4, 10), (32, 11), (23, 16), (11, 2), (24, 3), (17, 11), (19, 21), (20, 9), (26, 18), (26, 0), (14, 4), (2, 15), (4, 13), (30, 33), (2, 24), (12, 24), (30, 28), (9, 10), (31, 34), (19, 9), (7, 23), (12, 20), (22, 16), (32, 28), (15, 32), (3, 19), (24, 8), (22, 28), (6, 7), (30, 27), (34, 18), (30, 2), (26, 7), (19, 28), (35, 25), (0, 31), (34, 30), (32, 17), (5, 0), (17, 29), (10, 14), (15, 8), (30, 0), (8, 6), (4, 24), (21, 17), (26, 6), (24, 30), (1, 29), (10, 13), (17, 16), (10, 7), (27, 4), (6, 33), (7, 3), (23, 2), (4, 25), (13, 3), (29, 22), (13, 13), (7, 4), (1, 16), (6, 17), (14, 31), (18, 19), (34, 26), (12, 8), (9, 17), (14, 23), (29, 11), (9, 25), (3, 23), (23, 19), (15, 14), (30, 13), (13, 16), (14, 9), (3, 9), (24, 14), (28, 28), (10, 28), (28, 3), (3, 20), (2, 16), (5, 27), (26, 20), (15, 13), (21, 32), (21, 4), (32, 25), (20, 19), (19, 12), (22, 0), (16, 17), (19, 14), (24, 26), (11, 5), (4, 0), (26, 25), (25, 4), (15, 2), (2, 33), (33, 4), (17, 27), (4, 22), (18, 29), (18, 23), (6, 5), (7, 27), (26, 15), (25, 16), (35, 26), (5, 12), (19, 13), (21, 16), (8, 31), (0, 22), (24, 0), (28, 6), (3, 34), (30, 3), (4, 30), (4, 17), (35, 12), (16, 4), (8, 26), (14, 21), (35, 0), (0, 34), (34, 10), (7, 8), (11, 27), (32, 9), (15, 22), (18, 24), (24, 33), (11, 22), (10, 31), (9, 23), (30, 1), (8, 22), (14, 33), (17, 32), (8, 9), (32, 2), (12, 15), (14, 17), (12, 2), (25, 32), (0, 16), (0, 2), (13, 0), (23, 32), (23, 9), (21, 24), (4, 31), (21, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202500", "dataset": "MATH"}
{"messages": [{"content": "In a 33x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 24), (4, 30), (8, 14), (1, 20), (7, 32), (7, 21), (15, 27), (9, 32), (14, 16), (30, 33), (10, 0), (17, 9), (20, 12), (13, 30), (8, 33), (8, 21), (16, 1), (17, 18), (22, 13), (22, 7), (31, 17), (10, 7), (6, 28), (10, 3), (10, 18), (14, 0), (0, 18), (23, 20), (16, 27), (21, 22), (25, 4), (5, 19), (14, 21), (16, 18), (21, 27), (30, 28), (4, 7), (16, 5), (28, 1), (28, 7), (3, 33), (17, 7), (17, 19), (10, 14), (23, 5), (11, 26), (8, 6), (21, 34), (7, 7), (28, 20), (11, 11), (17, 12), (8, 10), (8, 29), (26, 17), (24, 22), (20, 28), (3, 12), (16, 26), (28, 15), (4, 9), (29, 29), (17, 21), (20, 17), (14, 7), (3, 10), (16, 32), (0, 16), (23, 13), (10, 16), (28, 0), (16, 9), (22, 24), (11, 2), (4, 26), (24, 9), (11, 25), (32, 1), (10, 13), (16, 20), (27, 20), (22, 6), (18, 18), (15, 6), (18, 17), (30, 2), (1, 11), (21, 29), (0, 29), (5, 4), (23, 11), (30, 32), (18, 26), (3, 34), (23, 1), (15, 3), (13, 5), (5, 11), (1, 24), (10, 15), (15, 19), (32, 15), (30, 9), (30, 6), (28, 4), (16, 3), (15, 16), (19, 17), (26, 12), (30, 0), (10, 30), (20, 25), (18, 30), (15, 10), (18, 19), (28, 27), (0, 6), (23, 24), (10, 29), (3, 26), (10, 25), (3, 29), (22, 31), (12, 25), (8, 4), (14, 12), (1, 32), (7, 18), (13, 9), (12, 24), (18, 3), (4, 4), (4, 12), (5, 0), (12, 16), (0, 25), (1, 1), (7, 10), (23, 0), (27, 15), (4, 20), (29, 13), (1, 23), (27, 4), (29, 24), (5, 14), (18, 21), (15, 1), (4, 6), (19, 29), (29, 6), (4, 0), (0, 7), (13, 34), (32, 18), (28, 28), (7, 6), (21, 9), (27, 23), (2, 1), (29, 12), (8, 17), (30, 1), (24, 15), (18, 28), (22, 11), (12, 7), (15, 33), (16, 24), (9, 7), (2, 23), (5, 32), (2, 13), (27, 5), (14, 27), (19, 25), (11, 19), (27, 32), (25, 0), (3, 24), (28, 3), (26, 7), (3, 5), (9, 24), (18, 33), (29, 15), (15, 4), (18, 6), (15, 25), (27, 8), (27, 19), (6, 10), (29, 2), (24, 17), (6, 25), (6, 32), (11, 30), (10, 17), (0, 13), (30, 5), (15, 32), (2, 5), (25, 5), (11, 20), (7, 22), (19, 15), (1, 16), (28, 13), (29, 14), (10, 21), (27, 9), (1, 7), (19, 34), (7, 2), (6, 1), (17, 34), (16, 19), (10, 23), (11, 6), (0, 34), (32, 14), (13, 18), (31, 30), (15, 11), (7, 31), (4, 32), (4, 2), (3, 1), (27, 33), (16, 28), (23, 15), (32, 22), (6, 26), (29, 9), (8, 12), (15, 34), (11, 32), (30, 21), (12, 5), (30, 3), (2, 22), (3, 28), (8, 3), (15, 28), (29, 16), (2, 31), (25, 34), (2, 15), (28, 16), (11, 34), (2, 24), (16, 4), (19, 32), (20, 1), (15, 12), (2, 17), (19, 21), (28, 19), (27, 18), (8, 19), (18, 12), (17, 22), (2, 10), (15, 26), (25, 12), (9, 22), (20, 11), (25, 3), (2, 6), (26, 13), (17, 0), (5, 31), (14, 23), (28, 26), (24, 1), (14, 3), (5, 15), (9, 33), (14, 22), (10, 32), (1, 13), (20, 30), (3, 15), (6, 19), (9, 5), (11, 23), (20, 14), (32, 2), (16, 16), (1, 27), (29, 0), (11, 22), (6, 20), (16, 7), (24, 16), (21, 17), (6, 22), (7, 3), (4, 16), (2, 2), (32, 8), (32, 12), (20, 19), (30, 12), (17, 1), (32, 29), (21, 0), (31, 0), (12, 2), (25, 8), (26, 32), (26, 16), (32, 30), (28, 21), (31, 2), (9, 20), (27, 31), (26, 4), (24, 0), (16, 12), (10, 5), (22, 27), (8, 30), (24, 19), (22, 3), (28, 11), (32, 33), (10, 33), (20, 16), (8, 5), (29, 20), (14, 29), (23, 9), (14, 18), (26, 0), (14, 30), (7, 4), (14, 4), (0, 21), (5, 25), (3, 2), (9, 13), (18, 29), (27, 26), (12, 4), (10, 8), (10, 1), (5, 33), (21, 7), (11, 33), (27, 28), (26, 28), (16, 2), (23, 10), (3, 32), (8, 13), (9, 28), (19, 30), (0, 8), (4, 27), (25, 19), (6, 9), (25, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "386208", "dataset": "MATH"}
{"messages": [{"content": "In a 36x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 37), 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), (31, 22), (18, 35), (30, 15), (26, 10), (17, 26), (8, 1), (16, 3), (6, 8), (9, 12), (18, 12), (21, 37), (22, 12), (1, 10), (16, 1), (30, 19), (19, 7), (32, 29), (0, 20), (6, 26), (24, 20), (3, 14), (19, 9), (22, 24), (9, 27), (16, 13), (26, 9), (7, 1), (27, 28), (25, 28), (12, 1), (12, 19), (9, 32), (29, 2), (0, 36), (34, 18), (17, 25), (3, 24), (27, 30), (5, 9), (16, 9), (13, 32), (34, 21), (21, 36), (30, 9), (24, 29), (2, 11), (29, 29), (34, 23), (31, 12), (14, 23), (27, 18), (34, 6), (11, 15), (17, 13), (23, 3), (17, 11), (9, 29), (4, 8), (16, 12), (23, 36), (11, 7), (10, 4), (6, 21), (19, 1), (15, 37), (34, 31), (30, 4), (16, 31), (10, 19), (11, 23), (27, 35), (2, 33), (21, 11), (19, 27), (9, 0), (8, 9), (8, 8), (29, 26), (13, 29), (0, 35), (27, 0), (19, 37), (15, 36), (34, 5), (13, 12), (14, 9), (19, 20), (25, 20), (28, 14), (30, 33), (1, 5), (1, 17), (26, 29), (6, 34), (30, 20), (2, 2), (25, 21), (22, 26), (10, 12), (3, 35), (21, 10), (6, 16), (23, 15), (9, 22), (31, 1), (9, 17), (13, 23), (35, 23), (35, 35), (3, 28), (22, 35), (25, 34), (30, 30), (26, 1), (35, 32), (27, 9), (27, 17), (18, 36), (4, 31), (17, 4), (25, 35), (28, 34), (23, 4), (29, 8), (34, 15), (6, 13), (28, 2), (18, 31), (0, 27), (2, 0), (34, 0), (0, 17), (11, 22), (19, 30), (13, 30), (15, 18), (3, 32), (10, 3), (0, 11), (34, 30), (28, 37), (1, 30), (22, 23), (7, 2), (20, 15), (0, 5), (34, 27), (23, 35), (4, 11), (28, 33), (1, 14), (25, 9), (0, 30), (9, 26), (6, 0), (5, 13), (33, 30), (18, 30), (4, 32), (7, 37), (17, 32), (33, 1), (13, 27), (16, 18), (23, 14), (16, 33), (21, 13), (30, 6), (9, 23), (4, 30), (29, 7), (14, 31), (5, 32), (6, 3), (15, 15), (32, 34), (9, 15), (31, 7), (15, 25), (14, 14), (12, 11), (30, 8), (2, 37), (27, 29), (29, 1), (1, 23), (5, 4), (11, 33), (33, 31), (33, 5), (33, 9), (19, 3), (14, 15), (0, 14), (31, 15), (24, 0), (2, 23), (27, 2), (6, 17), (15, 17), (35, 26), (22, 17), (33, 14), (14, 27), (17, 17), (6, 29), (7, 31), (26, 26), (17, 8), (25, 15), (14, 30), (23, 25), (18, 3), (26, 8), (13, 16), (21, 23), (11, 36), (33, 12), (3, 6), (12, 29), (1, 20), (25, 26), (7, 12), (5, 22), (32, 20), (9, 3), (35, 13), (18, 22), (5, 0), (27, 24), (34, 35), (8, 2), (21, 17), (19, 32), (6, 4), (5, 19), (20, 7), (13, 8), (17, 14), (12, 30), (23, 11), (18, 23), (25, 7), (12, 34), (12, 33), (30, 23), (25, 2), (1, 21), (7, 36), (20, 31), (5, 17), (6, 27), (20, 28), (19, 21), (26, 22), (35, 34), (25, 18), (33, 15), (2, 26), (15, 0), (23, 8), (21, 4), (24, 11), (7, 15), (4, 33), (10, 32), (30, 37), (6, 11), (2, 28), (16, 7), (35, 18), (3, 23), (16, 37), (3, 20), (8, 16), (19, 22), (3, 30), (22, 25), (21, 2), (10, 31), (28, 35), (18, 13), (34, 11), (18, 10), (3, 10), (0, 2), (3, 3), (35, 4), (9, 37), (33, 11), (19, 12), (13, 22), (18, 2), (4, 6), (3, 12), (27, 16), (35, 36), (26, 19), (12, 18), (35, 3), (24, 9), (4, 27), (28, 16), (32, 3), (20, 17), (8, 18), (13, 11), (8, 5), (2, 34), (31, 29), (12, 23), (21, 6), (7, 22), (28, 19), (34, 13), (29, 22), (28, 24), (23, 37), (15, 24), (5, 12), (23, 30), (15, 19), (18, 7), (19, 4), (24, 1), (1, 9), (20, 34), (20, 33), (24, 15), (11, 3), (3, 19), (35, 20), (23, 29), (4, 23), (10, 34), (33, 32), (32, 35), (24, 8), (32, 7), (26, 13), (27, 33), (21, 26), (26, 31), (25, 33), (2, 32), (17, 28), (29, 14), (10, 13), (3, 17), (0, 8), (1, 0), (5, 14), (12, 31), (26, 37), (7, 20), (35, 30), (26, 20), (33, 26), (4, 26), (31, 37), (20, 20), (26, 36), (28, 6), (22, 2), (8, 29), (29, 9), (29, 18), (30, 26), (10, 29), (25, 31), (21, 28), (28, 28), (25, 37), (9, 2), (20, 13), (15, 9), (1, 24), (6, 5), (6, 7), (22, 27), (6, 19), (31, 32), (8, 23), (29, 4), (14, 4), (24, 6), (10, 0), (11, 27), (4, 21), (9, 9), (1, 13), (30, 14), (34, 34), (22, 31), (1, 15), (12, 27), (26, 25), (23, 18), (8, 37), (34, 14), (18, 29), (12, 26), (8, 11), (28, 7), (22, 8), (30, 5), (4, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "324648", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), 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), (13, 18), (15, 23), (27, 5), (25, 29), (1, 2), (30, 9), (3, 26), (30, 10), (23, 22), (34, 15), (27, 13), (1, 25), (38, 2), (23, 16), (17, 1), (20, 26), (38, 21), (6, 11), (35, 6), (29, 16), (9, 2), (34, 1), (9, 26), (0, 4), (1, 22), (9, 1), (3, 29), (8, 26), (35, 12), (26, 27), (21, 26), (17, 11), (29, 32), (38, 3), (32, 33), (37, 7), (10, 11), (30, 25), (4, 21), (20, 15), (29, 28), (35, 28), (5, 22), (11, 25), (35, 3), (33, 9), (11, 34), (26, 1), (17, 14), (35, 24), (19, 26), (17, 6), (5, 12), (11, 3), (13, 17), (20, 19), (21, 12), (15, 10), (2, 26), (30, 5), (5, 19), (5, 21), (15, 2), (38, 32), (14, 19), (17, 34), (4, 10), (35, 9), (38, 28), (9, 6), (23, 0), (32, 15), (25, 24), (7, 17), (23, 25), (22, 9), (24, 26), (0, 28), (34, 32), (16, 4), (16, 5), (7, 7), (8, 7), (9, 33), (28, 23), (2, 28), (31, 13), (12, 16), (2, 14), (37, 26), (25, 13), (25, 30), (27, 20), (9, 15), (5, 7), (28, 10), (4, 23), (24, 24), (25, 33), (5, 4), (14, 2), (14, 25), (4, 22), (7, 3), (5, 17), (3, 14), (34, 19), (16, 3), (23, 29), (7, 24), (20, 30), (21, 1), (20, 16), (17, 7), (14, 20), (16, 7), (4, 20), (5, 3), (29, 20), (22, 14), (0, 29), (30, 16), (27, 17), (32, 5), (11, 6), (37, 16), (18, 4), (21, 21), (19, 19), (22, 5), (26, 13), (15, 28), (26, 28), (6, 26), (5, 24), (20, 14), (10, 16), (37, 17), (0, 24), (0, 33), (24, 21), (32, 7), (11, 24), (20, 29), (24, 17), (22, 0), (15, 9), (27, 29), (33, 16), (36, 4), (22, 19), (22, 22), (35, 10), (34, 24), (18, 11), (14, 6), (10, 1), (20, 8), (23, 24), (18, 32), (14, 12), (13, 30), (7, 30), (13, 21), (5, 26), (24, 18), (28, 12), (7, 18), (38, 31), (33, 3), (7, 34), (37, 10), (12, 10), (22, 33), (36, 21), (26, 15), (13, 7), (16, 34), (34, 28), (7, 5), (10, 33), (3, 19), (19, 5), (10, 9), (30, 18), (25, 2), (34, 4), (32, 10), (30, 21), (10, 20), (23, 34), (25, 19), (33, 1), (20, 17), (12, 29), (21, 16), (27, 27), (4, 29), (19, 8), (24, 1), (14, 27), (36, 8), (4, 2), (16, 18), (38, 9), (5, 33), (32, 18), (16, 23), (26, 6), (10, 32), (4, 11), (5, 18), (22, 13), (0, 15), (8, 10), (21, 33), (27, 0), (12, 34), (10, 24), (22, 21), (17, 2), (0, 11), (38, 33), (0, 32), (18, 25), (21, 17), (35, 22), (9, 32), (36, 18), (31, 2), (17, 30), (10, 29), (34, 20), (37, 30), (30, 20), (20, 23), (33, 8), (24, 30), (3, 25), (28, 33), (31, 9), (36, 13), (25, 8), (35, 29), (0, 13), (12, 12), (7, 23), (22, 30), (38, 1), (25, 28), (17, 21), (12, 3), (8, 23), (27, 15), (19, 1), (4, 25), (35, 32), (24, 13), (5, 25), (31, 32), (0, 27), (34, 30), (7, 4), (3, 12), (37, 29), (6, 12), (15, 20), (37, 13), (9, 16), (9, 14), (24, 16), (17, 3), (10, 30), (24, 14), (33, 24), (27, 19), (30, 1), (7, 33), (31, 27), (30, 17), (2, 2), (3, 33), (14, 24), (36, 2), (31, 29), (16, 13), (21, 18), (24, 11), (21, 8), (22, 12), (31, 19), (22, 27), (12, 27), (0, 30), (2, 6), (29, 12), (6, 34), (19, 25), (36, 20), (11, 18), (11, 19), (18, 7), (19, 10), (6, 17), (23, 19), (34, 10), (14, 9), (25, 1), (38, 8), (33, 23), (37, 2), (38, 24), (7, 11), (18, 3), (33, 11), (10, 25), (9, 24), (4, 34), (27, 30), (21, 0), (25, 25), (8, 11), (8, 20), (25, 21), (1, 11), (21, 25), (30, 8), (12, 4), (3, 15), (7, 29), (17, 4), (38, 6), (24, 25), (24, 4), (29, 1), (30, 23), (38, 7), (25, 11), (9, 12), (35, 34), (8, 2), (36, 17), (15, 18), (37, 4), (36, 9), (27, 14), (1, 17), (26, 34), (24, 29), (6, 19), (11, 29), (18, 28), (11, 17), (26, 29), (4, 1), (13, 22), (33, 2), (12, 15), (25, 26), (22, 25), (11, 11), (31, 18), (36, 22), (27, 21), (19, 32), (23, 27), (22, 29), (32, 19), (20, 4), (30, 32), (12, 24), (30, 15), (27, 33), (34, 29), (37, 32), (9, 17), (15, 19), (6, 15), (11, 13), (7, 8), (1, 8), (33, 13), (31, 24), (3, 7), (34, 27), (3, 34), (28, 20), (34, 25), (36, 7), (34, 18), (31, 26), (21, 28), (9, 7), (28, 6), (27, 1), (16, 22), (29, 14), (29, 15), (21, 2), (0, 21), (36, 11), (33, 33), (4, 13), (19, 2), (25, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "408424", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 20), (7, 25), (5, 32), (9, 30), (12, 14), (22, 16), (28, 28), (16, 32), (1, 16), (19, 14), (17, 26), (25, 16), (24, 2), (18, 24), (19, 1), (27, 26), (2, 11), (10, 30), (22, 9), (8, 10), (17, 7), (25, 10), (15, 2), (4, 30), (23, 18), (21, 14), (16, 5), (22, 31), (24, 19), (14, 21), (0, 7), (5, 25), (8, 28), (4, 21), (24, 14), (3, 9), (8, 8), (26, 1), (26, 30), (7, 28), (7, 17), (12, 32), (27, 24), (18, 10), (5, 3), (18, 5), (18, 26), (17, 10), (25, 30), (0, 16), (20, 3), (20, 4), (13, 29), (29, 9), (23, 17), (9, 29), (12, 9), (20, 23), (8, 27), (3, 29), (19, 21), (26, 21), (13, 23), (25, 11), (19, 4), (21, 23), (1, 26), (29, 7), (26, 24), (10, 2), (23, 24), (11, 17), (2, 10), (28, 6), (22, 3), (0, 22), (26, 31), (15, 16), (8, 24), (7, 20), (8, 32), (1, 19), (7, 31), (20, 25), (29, 19), (9, 8), (8, 20), (24, 31), (5, 9), (24, 32), (0, 27), (27, 31), (23, 7), (24, 4), (20, 15), (14, 29), (7, 21), (12, 19), (10, 1), (19, 5), (3, 3), (14, 5), (10, 24), (29, 16), (10, 6), (14, 28), (13, 20), (1, 24), (17, 32), (15, 12), (8, 30), (22, 7), (20, 0), (13, 17), (11, 8), (4, 18), (3, 10), (24, 17), (28, 5), (10, 20), (15, 10), (15, 28), (29, 12), (6, 30), (29, 15), (22, 11), (4, 4), (8, 22), (16, 23), (9, 13), (12, 23), (3, 16), (6, 5), (23, 5), (28, 9), (14, 2), (3, 19), (13, 32), (12, 13), (21, 31), (28, 30), (18, 6), (24, 7), (0, 10), (29, 10), (0, 2), (5, 1), (27, 11), (6, 21), (2, 7), (15, 11), (20, 14), (29, 11), (7, 29), (19, 8), (20, 27), (0, 6), (24, 25), (7, 16), (5, 31), (21, 2), (22, 25), (16, 28), (21, 19), (4, 10), (16, 18), (24, 24), (6, 24), (29, 21), (12, 2), (19, 2), (6, 9), (27, 3), (7, 4), (16, 12), (0, 17), (2, 6), (25, 8), (22, 26), (22, 23), (25, 13), (11, 1), (25, 27), (15, 23), (6, 13), (1, 1), (15, 29), (22, 24), (4, 19), (3, 21), (6, 1), (27, 27), (12, 26), (11, 11), (9, 26), (29, 26), (3, 24), (11, 12), (2, 20), (2, 12), (6, 2), (14, 9), (11, 18), (3, 28), (14, 4), (25, 29), (24, 23), (18, 7), (8, 3), (13, 5), (0, 4), (13, 24), (1, 23), (3, 11), (21, 11), (17, 3), (24, 26), (11, 29), (24, 0), (17, 5), (15, 14), (1, 11), (18, 3), (12, 28), (3, 31), (20, 21), (3, 6), (27, 9), (19, 18), (3, 23), (21, 3), (17, 0), (27, 4), (1, 3), (26, 27), (3, 18), (19, 20), (10, 0), (28, 32), (19, 22), (4, 3), (9, 6), (0, 14), (5, 27), (11, 3), (28, 13), (24, 1), (3, 26), (13, 22), (25, 5), (14, 24), (15, 8), (7, 15), (7, 8), (15, 26), (29, 24), (8, 16), (12, 12), (2, 4), (19, 25), (7, 9), (7, 5), (9, 10), (18, 0), (14, 30), (20, 16), (21, 13), (11, 24), (21, 18), (18, 25), (9, 14), (14, 13), (18, 8), (10, 25), (22, 22), (21, 5), (11, 13), (23, 21), (28, 3), (9, 31), (26, 25), (4, 12), (26, 3), (8, 23), (25, 20), (9, 22), (28, 12), (28, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "895056", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (2, 22), (23, 21), (28, 25), (0, 13), (12, 8), (17, 8), (21, 30), (20, 15), (25, 33), (30, 19), (1, 20), (35, 8), (3, 29), (0, 16), (3, 2), (0, 9), (20, 35), (7, 3), (3, 10), (13, 17), (34, 13), (20, 10), (18, 14), (31, 26), (5, 12), (16, 7), (18, 7), (22, 1), (10, 16), (11, 5), (14, 16), (17, 17), (23, 9), (16, 31), (3, 25), (19, 34), (16, 5), (20, 11), (36, 20), (14, 19), (34, 36), (23, 27), (35, 6), (20, 33), (13, 14), (10, 29), (4, 21), (28, 3), (29, 29), (21, 7), (8, 20), (12, 0), (7, 35), (11, 36), (10, 12), (13, 8), (14, 26), (8, 19), (24, 7), (12, 36), (7, 13), (4, 28), (28, 0), (21, 26), (37, 9), (35, 9), (23, 29), (29, 34), (6, 31), (27, 14), (5, 10), (13, 18), (28, 13), (10, 3), (28, 4), (15, 10), (37, 21), (0, 12), (7, 34), (6, 18), (8, 28), (13, 10), (3, 12), (20, 31), (25, 5), (15, 11), (5, 1), (0, 19), (36, 34), (8, 22), (13, 29), (33, 20), (37, 14), (23, 17), (22, 6), (6, 7), (7, 24), (9, 14), (36, 27), (6, 17), (22, 35), (19, 10), (31, 30), (30, 12), (28, 14), (12, 7), (31, 7), (11, 15), (32, 12), (26, 6), (24, 21), (32, 29), (29, 2), (24, 0), (36, 31), (3, 5), (31, 24), (13, 19), (6, 2), (26, 5), (30, 24), (34, 30), (16, 30), (6, 27), (26, 31), (25, 10), (6, 30), (4, 24), (6, 25), (14, 27), (24, 1), (5, 31), (27, 29), (25, 24), (22, 2), (37, 17), (33, 17), (4, 20), (34, 9), (16, 12), (2, 27), (1, 25), (7, 22), (30, 32), (18, 4), (1, 35), (19, 23), (22, 19), (6, 0), (37, 8), (28, 33), (14, 25), (15, 9), (26, 16), (22, 16), (34, 29), (34, 15), (13, 16), (18, 30), (36, 18), (4, 26), (9, 9), (36, 32), (19, 17), (22, 14), (20, 18), (20, 22), (11, 35), (9, 10), (19, 4), (24, 4), (32, 4), (37, 30), (35, 22), (12, 23), (17, 13), (8, 3), (13, 25), (1, 23), (36, 1), (13, 21), (32, 27), (28, 29), (31, 12), (14, 2), (30, 7), (22, 21), (0, 6), (7, 4), (30, 16), (15, 6), (13, 6), (25, 16), (24, 5), (17, 2), (15, 21), (3, 28), (21, 3), (29, 32), (24, 17), (10, 27), (0, 10), (23, 2), (28, 19), (9, 5), (15, 13), (14, 28), (22, 33), (36, 28), (29, 23), (34, 23), (21, 28), (29, 31), (20, 30), (33, 10), (27, 27), (31, 5), (12, 18), (32, 28), (2, 2), (34, 2), (24, 33), (37, 23), (18, 36), (2, 24), (22, 26), (9, 33), (33, 5), (34, 6), (12, 11), (30, 8), (19, 8), (33, 7), (22, 11), (15, 12), (32, 34), (26, 3), (0, 15), (0, 30), (26, 11), (19, 27), (29, 6), (29, 27), (36, 10), (18, 0), (35, 13), (26, 32), (11, 32), (17, 9), (37, 26), (30, 31), (4, 27), (36, 3), (15, 36), (15, 5), (2, 19), (34, 8), (0, 7), (24, 35), (9, 35), (6, 33), (29, 9), (30, 5), (17, 23), (6, 36), (1, 9), (22, 22), (30, 9), (29, 24), (15, 4), (5, 5), (20, 2), (10, 11), (12, 31), (20, 26), (13, 23), (12, 10), (17, 30), (19, 32), (36, 17), (5, 20), (3, 24), (37, 33), (30, 25), (0, 3), (7, 33), (23, 22), (28, 8), (5, 15), (24, 6), (29, 26), (28, 20), (5, 17), (29, 3), (26, 25), (10, 18), (1, 8), (14, 0), (31, 13), (11, 26), (20, 5), (2, 15), (33, 36), (19, 28), (30, 17), (10, 13), (14, 11), (11, 16), (5, 30), (9, 13), (9, 24), (20, 23), (33, 19), (7, 18), (30, 30), (23, 12), (3, 9), (12, 29), (9, 17), (1, 12), (7, 23), (25, 3), (21, 13), (21, 16), (3, 21), (35, 14), (35, 3), (27, 5), (5, 27), (16, 18), (23, 7), (21, 19), (32, 3), (8, 10), (26, 22), (36, 8), (13, 9), (18, 28), (12, 22), (32, 5), (4, 19), (17, 0), (4, 35), (11, 7), (36, 4), (32, 13), (27, 35), (21, 23), (10, 17), (9, 0), (27, 23), (25, 18), (0, 32), (1, 17), (27, 3), (1, 4), (1, 33), (4, 11), (35, 19), (35, 11), (27, 10), (25, 25), (6, 11), (2, 35), (27, 21), (12, 1), (21, 35), (16, 3), (12, 16), (6, 14), (9, 16), (13, 0), (22, 4), (24, 29), (11, 13), (14, 12), (35, 32), (26, 35), (10, 31), (24, 34), (32, 1), (35, 1), (21, 20), (33, 30), (2, 18), (10, 2), (13, 3), (21, 10), (6, 34), (8, 15), (15, 15), (31, 29), (25, 2), (37, 32), (30, 1), (27, 4), (4, 23), (16, 34), (14, 3), (7, 6), (20, 32), (3, 36), (0, 25), (21, 9), (36, 36), (5, 13), (10, 35), (33, 22), (0, 26), (12, 19), (23, 8), (14, 34), (16, 36), (30, 6), (12, 20), (17, 20), (17, 18), (35, 25), (22, 31), (37, 0), (2, 1), (23, 10), (4, 12), (31, 8), (2, 32), (10, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "914058", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), 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), (26, 33), (25, 7), (23, 14), (0, 12), (10, 30), (7, 4), (16, 24), (0, 25), (32, 30), (5, 12), (28, 0), (17, 26), (23, 1), (24, 34), (11, 1), (24, 21), (0, 9), (11, 18), (4, 13), (19, 9), (20, 30), (16, 17), (18, 5), (16, 20), (28, 3), (9, 27), (28, 12), (32, 29), (19, 24), (4, 7), (12, 9), (32, 9), (0, 11), (2, 0), (12, 28), (17, 11), (29, 0), (2, 28), (12, 14), (19, 6), (21, 26), (0, 21), (26, 31), (2, 21), (23, 18), (24, 29), (19, 14), (7, 22), (17, 35), (8, 9), (24, 27), (10, 26), (27, 4), (2, 11), (8, 17), (23, 35), (30, 10), (15, 4), (12, 8), (11, 32), (18, 22), (28, 29), (11, 29), (8, 12), (6, 8), (9, 3), (24, 33), (27, 21), (16, 30), (29, 33), (7, 30), (6, 7), (13, 10), (22, 33), (3, 2), (24, 15), (7, 14), (0, 26), (13, 26), (8, 7), (11, 7), (26, 2), (2, 25), (31, 12), (21, 31), (3, 31), (25, 19), (9, 15), (5, 22), (16, 31), (29, 35), (12, 0), (16, 10), (26, 21), (29, 12), (32, 11), (13, 34), (25, 31), (8, 34), (17, 29), (21, 19), (5, 35), (21, 14), (24, 3), (28, 24), (6, 25), (6, 23), (24, 9), (21, 33), (29, 28), (16, 11), (17, 12), (0, 13), (17, 4), (29, 34), (32, 8), (24, 10), (17, 32), (18, 34), (11, 35), (16, 34), (5, 23), (10, 21), (1, 15), (16, 3), (27, 11), (13, 6), (24, 1), (17, 6), (27, 35), (25, 22), (28, 31), (12, 24), (27, 34), (22, 14), (1, 17), (30, 31), (2, 5), (22, 17), (13, 20), (18, 25), (31, 18), (23, 13), (28, 27), (30, 8), (7, 32), (11, 2), (2, 26), (3, 4), (22, 23), (31, 6), (9, 14), (32, 25), (26, 4), (8, 32), (1, 30), (13, 7), (21, 13), (27, 29), (8, 28), (4, 17), (10, 33), (24, 14), (1, 3), (25, 34), (24, 31), (20, 10), (14, 35), (6, 28), (11, 33), (30, 17), (23, 2), (18, 30), (3, 33), (25, 20), (23, 10), (10, 0), (6, 18), (9, 30), (17, 27), (6, 1), (21, 9), (25, 1), (1, 20), (18, 9), (0, 33), (18, 35), (5, 2), (20, 9), (22, 32), (18, 29), (24, 5), (2, 16), (18, 3), (26, 20), (31, 4), (15, 35), (18, 16), (14, 27), (0, 7), (31, 3), (23, 31), (23, 19), (14, 9), (6, 15), (9, 33), (20, 33), (3, 25), (30, 0), (10, 32), (27, 25), (18, 8), (17, 3), (21, 32), (19, 19), (12, 4), (0, 8), (5, 7), (21, 24), (20, 18), (25, 29), (12, 29), (4, 27), (27, 19), (12, 5), (30, 18), (13, 29), (17, 24), (19, 5), (20, 31), (13, 15), (0, 6), (18, 7), (10, 1), (32, 10), (12, 35), (11, 15), (30, 25), (5, 3), (21, 10), (27, 2), (11, 11), (21, 5), (11, 20), (16, 26), (31, 16), (8, 26), (14, 0), (20, 6), (6, 34), (12, 34), (3, 19), (18, 31), (2, 19), (14, 3), (27, 12), (10, 23), (14, 15), (17, 0), (5, 26), (13, 19), (19, 16), (17, 9), (7, 8), (19, 33), (8, 8), (32, 21), (17, 15), (15, 29), (15, 5), (22, 30), (27, 15), (2, 2), (30, 35), (22, 25), (4, 10), (14, 7), (24, 7), (1, 28), (19, 11), (1, 24), (32, 0), (29, 4), (11, 23), (8, 19), (4, 24), (15, 20), (7, 23), (5, 33), (17, 28), (18, 11), (15, 14), (3, 29), (8, 16), (1, 27), (30, 24), (31, 8), (29, 10), (3, 10), (9, 4), (32, 22), (26, 7), (30, 15), (14, 30), (25, 23), (0, 5), (23, 32), (30, 20), (21, 27), (13, 23), (30, 21), (6, 3), (16, 28), (7, 33), (9, 29), (3, 0), (14, 29), (32, 27), (6, 32), (26, 3), (28, 11), (22, 12), (22, 10), (27, 28), (21, 25), (7, 9), (23, 33), (13, 1), (6, 16), (16, 32), (31, 14), (31, 9), (18, 20), (14, 13), (11, 14), (14, 19), (17, 20), (30, 3), (20, 8), (16, 29), (29, 19), (1, 11), (11, 24), (9, 31), (29, 29), (13, 8), (8, 0), (29, 5), (15, 2), (27, 5), (21, 20), (30, 5), (7, 21), (24, 28), (18, 17), (8, 33), (4, 33), (8, 24), (15, 0), (5, 5), (24, 26), (7, 13), (21, 3), (31, 15), (9, 17), (18, 14), (9, 28), (31, 21), (3, 3), (14, 25), (27, 17), (30, 30), (26, 32), (29, 23), (26, 35), (20, 20), (32, 12), (17, 5), (26, 12), (9, 26), (6, 2), (5, 10), (2, 24), (18, 6), (2, 3), (27, 14), (0, 20), (32, 7), (3, 17), (22, 29), (9, 25), (13, 2), (28, 23), (20, 28), (4, 22), (25, 30), (6, 13), (10, 18), (22, 3), (21, 29), (26, 10), (26, 24), (3, 5), (9, 19), (11, 28), (25, 2), (8, 14), (9, 5), (16, 5), (7, 12), (26, 30), (17, 2), (6, 20), (20, 2), (13, 32), (7, 2), (10, 6), (31, 17), (22, 6), (0, 23), (2, 18), (10, 3), (30, 19), (1, 13), (1, 10), (2, 27), (9, 0), (1, 22), (14, 5), (29, 27), (12, 7), (5, 30), (14, 2), (14, 21), (24, 2), (26, 0), (19, 17), (15, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "624960", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 7), (26, 24), (29, 7), (5, 2), (12, 17), (4, 12), (10, 8), (10, 32), (20, 0), (25, 8), (15, 26), (31, 18), (16, 31), (17, 5), (26, 23), (20, 26), (17, 15), (31, 0), (2, 0), (5, 1), (11, 12), (26, 12), (6, 27), (5, 4), (18, 17), (15, 18), (20, 32), (7, 17), (18, 24), (20, 16), (25, 3), (26, 31), (16, 28), (26, 9), (4, 16), (24, 10), (5, 17), (4, 17), (15, 12), (8, 8), (22, 7), (2, 23), (3, 20), (25, 13), (30, 19), (7, 7), (27, 25), (20, 19), (16, 16), (12, 11), (26, 25), (27, 4), (29, 22), (25, 21), (24, 33), (12, 15), (7, 27), (2, 22), (25, 0), (0, 24), (30, 30), (8, 14), (17, 23), (23, 7), (3, 21), (27, 13), (8, 31), (4, 33), (23, 24), (23, 17), (20, 5), (28, 33), (16, 17), (19, 18), (6, 2), (5, 18), (29, 4), (18, 1), (7, 15), (8, 18), (9, 14), (12, 19), (11, 7), (26, 29), (15, 22), (22, 17), (6, 16), (17, 24), (23, 32), (24, 4), (8, 25), (0, 23), (23, 9), (17, 32), (2, 25), (19, 4), (0, 22), (18, 12), (1, 33), (17, 0), (23, 21), (10, 22), (27, 33), (19, 28), (0, 2), (7, 4), (20, 30), (9, 8), (8, 11), (27, 2), (24, 5), (29, 10), (1, 29), (23, 14), (27, 15), (24, 23), (21, 30), (9, 33), (14, 18), (1, 5), (2, 31), (21, 27), (15, 6), (14, 31), (14, 15), (12, 6), (31, 5), (19, 22), (4, 15), (18, 26), (29, 17), (18, 11), (19, 9), (21, 7), (28, 13), (29, 1), (10, 30), (8, 29), (22, 18), (27, 0), (3, 30), (10, 14), (6, 15), (13, 12), (30, 14), (25, 7), (11, 21), (5, 24), (21, 0), (28, 22), (28, 16), (28, 20), (18, 4), (19, 6), (30, 25), (3, 10), (10, 27), (10, 2), (12, 31), (13, 13), (21, 11), (8, 9), (2, 29), (24, 17), (14, 14), (0, 9), (1, 4), (9, 2), (2, 16), (23, 15), (3, 7), (16, 18), (31, 14), (15, 4), (23, 23), (9, 4), (17, 26), (8, 1), (6, 23), (1, 25), (7, 13), (10, 31), (0, 1), (11, 3), (19, 5), (28, 12), (0, 19), (23, 27), (2, 1), (6, 7), (1, 19), (21, 17), (20, 14), (24, 7), (25, 23), (20, 15), (27, 5), (31, 15), (23, 29), (9, 1), (9, 21), (26, 33), (15, 2), (1, 32), (6, 19), (8, 28), (5, 14), (3, 33), (22, 26), (11, 2), (20, 12), (12, 13), (23, 16), (18, 31), (24, 21), (10, 29), (19, 25), (1, 16), (20, 23), (13, 20), (22, 8), (28, 11), (10, 12), (21, 24), (3, 31), (11, 31), (27, 21), (23, 22), (7, 19), (2, 14), (29, 3), (0, 17), (16, 1), (29, 9), (10, 10), (5, 20), (22, 13), (19, 33), (0, 14), (15, 24), (16, 21), (10, 16), (15, 16), (31, 4), (28, 19), (31, 24), (21, 6), (24, 14), (31, 23), (0, 4), (9, 15), (14, 9), (22, 6), (27, 3), (24, 26), (13, 4), (19, 29), (18, 32), (0, 27), (25, 9), (17, 12), (23, 10), (3, 2), (29, 15), (14, 10), (18, 27), (6, 32), (7, 8), (14, 26), (21, 33), (5, 10), (27, 7), (4, 5), (26, 5), (26, 27), (27, 14), (20, 18), (9, 28), (6, 22), (16, 20), (1, 28), (14, 33), (28, 28), (22, 24), (25, 22), (28, 17), (18, 25), (18, 33), (19, 21), (12, 22), (2, 33), (3, 13), (27, 11), (14, 17), (17, 21), (24, 15), (3, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "801000", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), 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), (19, 23), (17, 20), (12, 15), (8, 8), (8, 2), (21, 10), (16, 32), (23, 9), (20, 4), (22, 34), (2, 17), (14, 19), (4, 19), (25, 6), (1, 29), (8, 13), (13, 3), (0, 17), (23, 22), (1, 31), (14, 23), (3, 20), (25, 32), (32, 20), (7, 15), (1, 11), (9, 23), (26, 9), (26, 4), (32, 18), (0, 22), (9, 33), (3, 7), (11, 26), (28, 11), (10, 18), (18, 37), (6, 35), (19, 18), (3, 15), (6, 5), (33, 20), (23, 15), (29, 34), (6, 17), (20, 31), (25, 5), (33, 17), (11, 11), (8, 31), (31, 17), (14, 12), (15, 13), (17, 9), (16, 13), (22, 26), (26, 10), (29, 7), (26, 33), (15, 33), (19, 12), (13, 15), (13, 16), (29, 37), (32, 26), (21, 4), (2, 29), (17, 32), (18, 28), (13, 25), (10, 15), (24, 31), (2, 18), (11, 19), (25, 19), (29, 1), (8, 28), (28, 15), (18, 35), (27, 31), (8, 11), (0, 13), (16, 34), (1, 20), (20, 28), (33, 12), (31, 32), (2, 26), (21, 30), (29, 8), (30, 1), (21, 15), (26, 31), (12, 3), (22, 15), (14, 16), (20, 8), (26, 15), (13, 31), (14, 30), (33, 9), (19, 28), (9, 26), (33, 3), (12, 11), (24, 33), (2, 13), (32, 13), (20, 35), (2, 16), (4, 12), (20, 13), (6, 7), (7, 35), (18, 0), (7, 24), (27, 28), (27, 10), (20, 1), (6, 37), (8, 12), (26, 12), (4, 5), (25, 25), (27, 4), (6, 1), (31, 21), (16, 12), (7, 27), (0, 20), (13, 8), (22, 31), (9, 9), (12, 37), (17, 16), (13, 24), (19, 21), (29, 26), (20, 12), (20, 10), (33, 11), (20, 32), (31, 8), (9, 32), (19, 8), (18, 17), (22, 30), (24, 4), (32, 31), (23, 2), (0, 30), (9, 30), (33, 30), (4, 37), (30, 35), (12, 34), (7, 34), (19, 0), (27, 18), (30, 3), (12, 0), (6, 11), (1, 15), (25, 36), (27, 23), (30, 11), (22, 12), (10, 9), (0, 36), (1, 4), (17, 35), (7, 11), (8, 25), (27, 35), (10, 0), (1, 8), (23, 13), (3, 30), (0, 26), (0, 23), (24, 25), (16, 26), (6, 26), (15, 10), (14, 33), (33, 10), (32, 28), (30, 31), (11, 13), (11, 23), (32, 16), (33, 36), (4, 34), (11, 34), (30, 16), (7, 1), (26, 28), (26, 27), (23, 24), (18, 8), (23, 20), (18, 11), (14, 22), (16, 18), (9, 18), (32, 1), (15, 37), (22, 6), (30, 37), (33, 29), (27, 37), (5, 2), (24, 34), (6, 20), (12, 10), (19, 13), (11, 5), (5, 21), (10, 1), (17, 24), (26, 17), (3, 6), (24, 19), (4, 22), (22, 37), (22, 32), (0, 8), (8, 23), (2, 15), (20, 17), (14, 21), (22, 2), (27, 29), (21, 6), (8, 35), (13, 2), (19, 2), (27, 15), (24, 32), (8, 10), (13, 32), (17, 11), (14, 20), (11, 1), (4, 16), (23, 29), (2, 21), (4, 31), (3, 8), (5, 9), (25, 15), (2, 32), (0, 24), (10, 4), (5, 37), (27, 2), (6, 24), (29, 29), (16, 30), (19, 9), (32, 33), (22, 1), (15, 35), (15, 8), (6, 9), (21, 35), (30, 7), (17, 19), (10, 7), (12, 27), (18, 31), (12, 13), (5, 19), (15, 3), (33, 15), (13, 17), (8, 6), (1, 3), (3, 31), (5, 28), (27, 13), (9, 0), (11, 29), (6, 8), (20, 16), (11, 14), (9, 15), (25, 0), (6, 25), (27, 30), (15, 24), (33, 31), (9, 4), (9, 28), (19, 31), (24, 13), (22, 24), (16, 1), (4, 14), (11, 7), (19, 4), (20, 2), (14, 2), (23, 11), (16, 24), (0, 6), (22, 5), (17, 15), (18, 36), (7, 23), (23, 27), (24, 14), (22, 0), (7, 19), (5, 17), (10, 37), (5, 32), (21, 24), (27, 32), (2, 37), (23, 30), (6, 6), (25, 28), (27, 25), (8, 16), (22, 14), (3, 37), (2, 6), (30, 19), (8, 33), (2, 5), (30, 2), (4, 18), (19, 5), (23, 4), (15, 26), (7, 8), (19, 29), (5, 36), (32, 0), (32, 22), (6, 23), (20, 7), (6, 4), (25, 10), (3, 21), (6, 30), (21, 32), (16, 2), (7, 4), (1, 13), (32, 21), (11, 6), (15, 0), (18, 3), (22, 7), (3, 4), (32, 6), (28, 33), (6, 3), (19, 26), (33, 4), (33, 24), (4, 26), (11, 16), (12, 12), (32, 36)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "451872", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (8, 0), (14, 32), (3, 10), (27, 32), (10, 18), (7, 17), (28, 5), (16, 16), (32, 3), (30, 26), (9, 26), (28, 24), (28, 32), (8, 18), (22, 28), (29, 6), (14, 11), (10, 10), (2, 16), (9, 32), (12, 22), (20, 22), (1, 20), (27, 4), (18, 1), (33, 14), (26, 27), (31, 15), (15, 11), (32, 16), (12, 8), (0, 2), (21, 21), (17, 5), (7, 32), (13, 29), (1, 17), (7, 12), (10, 27), (16, 13), (31, 14), (13, 1), (18, 15), (32, 1), (3, 2), (5, 30), (30, 2), (16, 17), (33, 28), (28, 23), (6, 3), (15, 7), (4, 6), (10, 31), (6, 30), (20, 27), (17, 7), (15, 25), (9, 27), (14, 23), (22, 13), (15, 22), (26, 14), (28, 22), (0, 8), (19, 25), (30, 30), (15, 17), (8, 13), (6, 9), (20, 9), (3, 29), (21, 2), (29, 30), (27, 28), (19, 29), (2, 32), (33, 29), (33, 17), (16, 6), (7, 23), (29, 10), (3, 20), (29, 18), (7, 3), (8, 27), (9, 3), (30, 5), (18, 24), (11, 10), (28, 30), (14, 3), (8, 29), (32, 7), (13, 0), (6, 16), (27, 16), (25, 17), (30, 13), (13, 4), (20, 24), (2, 6), (1, 4), (19, 4), (23, 17), (7, 1), (12, 14), (25, 7), (9, 7), (18, 12), (11, 18), (25, 3), (11, 12), (20, 6), (16, 27), (30, 14), (22, 18), (0, 27), (24, 15), (31, 3), (18, 17), (0, 10), (20, 4), (32, 0), (3, 13), (13, 9), (21, 19), (13, 31), (31, 10), (11, 21), (31, 21), (8, 11), (13, 17), (12, 24), (31, 32), (1, 22), (3, 28), (31, 19), (8, 4), (33, 20), (11, 34), (20, 23), (29, 14), (9, 16), (11, 22), (15, 34), (19, 33), (7, 24), (2, 5), (26, 3), (13, 26), (4, 22), (13, 22), (0, 35), (23, 15), (10, 4), (27, 35), (20, 29), (26, 2), (24, 11), (21, 1), (3, 22), (20, 26), (13, 30), (2, 19), (28, 0), (19, 0), (21, 18), (25, 26), (21, 20), (0, 23), (15, 30), (33, 3), (29, 31), (0, 6), (25, 31), (3, 17), (25, 13), (1, 1), (33, 8), (33, 9), (29, 7), (13, 3), (22, 12), (26, 26), (10, 25), (3, 12), (32, 11), (27, 17), (7, 34), (20, 8), (18, 0), (18, 5), (14, 20), (31, 30), (4, 27), (14, 29), (14, 21), (26, 20), (27, 31), (19, 35), (31, 22), (14, 5), (30, 16), (24, 10), (6, 24), (27, 9), (6, 29), (23, 27), (19, 28), (14, 17), (23, 16), (17, 9), (3, 32), (4, 24), (9, 33), (12, 25), (31, 28), (23, 33), (6, 15), (12, 13), (31, 27), (27, 11), (16, 28), (6, 33), (7, 6), (5, 18), (24, 9), (31, 12), (32, 12), (33, 23), (28, 15), (1, 31), (17, 11), (10, 20), (6, 14), (20, 11), (4, 26), (10, 2), (15, 29), (22, 31), (6, 10), (6, 1), (12, 30), (27, 14), (10, 1), (23, 11), (26, 35), (5, 5), (15, 6), (17, 31), (8, 15), (11, 4), (29, 26), (19, 27), (15, 3), (5, 24), (27, 33), (28, 26), (31, 8), (23, 10), (0, 9), (4, 30), (19, 30), (11, 2), (32, 2), (9, 18), (24, 7), (9, 6), (14, 4), (8, 5), (8, 32), (0, 17), (19, 24), (2, 27), (1, 23), (0, 25), (30, 31), (16, 11), (7, 13), (33, 30), (17, 20), (0, 29), (8, 23), (5, 29), (21, 23), (11, 31), (25, 14), (20, 5), (17, 8), (5, 3), (14, 0), (5, 15), (1, 13), (21, 7), (28, 2), (1, 7), (1, 6), (25, 16), (15, 18), (20, 30), (5, 1), (16, 14), (27, 29), (5, 8), (18, 27), (30, 0), (8, 3), (0, 32), (25, 2), (31, 34), (10, 34), (5, 31), (4, 29), (5, 2), (10, 32), (0, 13), (21, 3), (30, 23), (19, 7), (10, 22), (23, 13), (11, 25), (21, 26), (26, 13), (13, 18), (26, 30), (23, 6), (23, 31), (16, 23), (23, 23), (1, 29), (5, 7), (33, 7), (7, 20), (10, 19), (32, 6), (8, 12), (31, 1), (5, 19), (15, 12), (33, 32), (16, 5), (29, 20), (2, 11), (5, 26), (18, 29), (14, 33), (15, 24), (15, 28), (1, 33), (33, 19), (23, 28), (30, 7), (13, 15), (5, 21), (29, 2), (10, 26), (24, 4), (17, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46368", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 26), (28, 10), (2, 24), (22, 17), (7, 0), (13, 36), (35, 0), (14, 27), (10, 27), (5, 6), (37, 8), (18, 35), (3, 37), (24, 29), (19, 33), (16, 37), (1, 37), (0, 29), (0, 16), (21, 20), (10, 2), (6, 16), (25, 17), (5, 35), (1, 9), (0, 27), (4, 34), (15, 16), (21, 23), (19, 1), (4, 10), (8, 31), (16, 11), (26, 4), (35, 8), (24, 6), (17, 8), (22, 4), (10, 1), (8, 28), (0, 34), (3, 25), (24, 3), (33, 14), (31, 27), (25, 24), (21, 25), (9, 3), (3, 35), (29, 35), (12, 33), (28, 5), (10, 19), (27, 1), (25, 37), (6, 23), (27, 37), (10, 15), (36, 0), (11, 22), (27, 15), (11, 21), (2, 15), (33, 22), (14, 28), (30, 9), (1, 16), (19, 27), (27, 8), (2, 12), (11, 1), (25, 12), (7, 8), (31, 30), (36, 18), (10, 26), (22, 23), (20, 32), (12, 19), 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17), (31, 3), (6, 22), (21, 3), (35, 16), (20, 29), (17, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362880", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), 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), (27, 27), (11, 30), (9, 11), (9, 3), (7, 7), (22, 28), (6, 8), (16, 3), (23, 21), (3, 13), (14, 9), (23, 15), (13, 32), (22, 11), (2, 4), (29, 20), (10, 18), (24, 23), (3, 9), (3, 31), (25, 1), (22, 33), (4, 31), (29, 0), (4, 13), (19, 16), (23, 24), (7, 21), (27, 15), (6, 23), (7, 11), (8, 19), (27, 1), (10, 19), (9, 21), (1, 32), (1, 24), (28, 26), (17, 27), (8, 13), (17, 26), (15, 3), (11, 17), (16, 4), (23, 31), (24, 34), (16, 33), (25, 31), (20, 27), (8, 18), (14, 25), (0, 19), (16, 11), (26, 26), (23, 8), (14, 1), (3, 32), (11, 29), (7, 10), (15, 24), (2, 18), (0, 22), (6, 2), (6, 16), (6, 25), (15, 8), (25, 13), (2, 32), (13, 10), (16, 21), (8, 5), (10, 32), (13, 22), (16, 18), (3, 19), (20, 4), (12, 1), (24, 21), (13, 19), (29, 10), (14, 3), (20, 23), (22, 19), (23, 12), (16, 5), (23, 0), (23, 34), (21, 13), (21, 22), (3, 11), (21, 3), (7, 0), (11, 34), (15, 9), (12, 6), (18, 23), (3, 15), (18, 3), (19, 9), (13, 14), (19, 18), (21, 4), (17, 28), (28, 23), (6, 10), (0, 24), (7, 13), (10, 15), (26, 11), (25, 8), (14, 2), (28, 28), (21, 6), (1, 30), (26, 9), (18, 5), (22, 7), (29, 33), (23, 7), (3, 12), (19, 8), (7, 9), (3, 20), (29, 7), (2, 23), (7, 26), (29, 15), (15, 32), (1, 17), (20, 31), (29, 25), (29, 29), (10, 16), (2, 25), (3, 27), (1, 2), (20, 16), (9, 14), (11, 5), (11, 2), (1, 15), (23, 11), (6, 27), (11, 12), (14, 11), (26, 29), (19, 27), (5, 22), (11, 23), (10, 17), (11, 0), (27, 18), (28, 30), (3, 10), (14, 28), (18, 0), (8, 34), (15, 29), (15, 5), (25, 7), (24, 6), (1, 28), (19, 24), (20, 34), (2, 3), (10, 20), (28, 24), (25, 16), (5, 33), (8, 4), (20, 17), (17, 5), (21, 34), (9, 24), (19, 25), (24, 0), (17, 18), (11, 18), (21, 33), (9, 20), (9, 25), (9, 27), (3, 25), (28, 0), (4, 16), (9, 19), (23, 10), (4, 4), (2, 7), (20, 14), (28, 15), (22, 27), (0, 13), (25, 21), (13, 25), (11, 3), (25, 34), (27, 16), (6, 32), (2, 2), (12, 18), (28, 21), (15, 31), (9, 9), (15, 21), (21, 8), (25, 14), (12, 19), (9, 34), (20, 32), (21, 20), (28, 27), (17, 31), (16, 16), (13, 0), (22, 2), (14, 33), (28, 1), (5, 7), (6, 19), (6, 14), (13, 31), (28, 11), (24, 5), (10, 34), (8, 27), (14, 4), (4, 0), (11, 21), (13, 1), (1, 1), (6, 17), (9, 13), (3, 21), (11, 31), (17, 15), (4, 10), (24, 15), (7, 27), (10, 11), (16, 29), (28, 31), (7, 2), (15, 18), (24, 28), (19, 11), (8, 3), (15, 34), (11, 32), (15, 1), (27, 13), (15, 30), (28, 14), (1, 3), (9, 26), (9, 33), (4, 14), (25, 17), (10, 12), (17, 9), (22, 26), (7, 6), (11, 8), (21, 18), (20, 29), (15, 33), (17, 2), (26, 30), (17, 24), (21, 19), (5, 34), (16, 34), (16, 17), (8, 6), (17, 30), (26, 21), (14, 30), (1, 6), (6, 15), (12, 29), (11, 14), (16, 14), (25, 26), (27, 24), (18, 12), (23, 4), (14, 5), (10, 13), (0, 7), (12, 0), (15, 6), (4, 30), (25, 0), (10, 30), (18, 10), (5, 25), (24, 26), (14, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "618444", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), 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), (4, 37), (5, 4), (36, 34), (31, 28), (0, 8), (13, 5), (5, 30), (20, 17), (34, 18), (31, 4), (25, 36), (26, 29), (3, 1), (28, 8), (13, 28), (18, 1), (32, 4), (2, 20), (9, 15), (20, 19), (16, 20), (16, 24), (14, 38), (33, 36), (15, 18), (23, 12), (24, 8), (26, 11), (31, 8), (25, 33), (0, 10), (22, 37), (0, 12), (29, 35), (25, 20), (8, 36), (21, 30), (10, 2), (2, 32), (27, 38), (31, 38), (37, 9), (31, 34), (8, 22), (5, 23), (14, 33), (20, 4), (7, 1), (15, 34), (18, 8), (11, 7), (19, 20), (34, 12), (3, 13), (25, 17), (9, 11), (23, 30), (6, 22), (34, 37), (23, 37), (26, 7), (18, 37), (5, 36), (5, 2), (32, 6), (28, 33), (8, 32), (12, 27), (28, 11), (27, 34), (23, 3), (16, 12), (3, 3), (9, 38), (21, 37), (2, 14), (37, 2), (14, 16), (35, 4), (7, 38), (21, 13), (32, 18), (8, 4), (22, 32), (33, 15), (37, 16), (5, 38), (15, 2), (12, 36), (13, 1), (21, 20), (36, 38), (21, 17), (28, 31), (29, 15), (26, 8), (6, 30), (29, 3), (8, 27), (32, 12), (35, 7), (2, 17), (34, 16), (30, 2), (1, 8), (12, 9), (11, 5), (27, 8), (18, 9), (2, 27), (8, 25), (33, 31), (32, 25), (13, 26), (20, 36), (11, 29), (13, 19), (15, 36), (19, 13), (6, 15), (9, 31), (21, 27), (17, 8), (7, 31), (19, 2), (10, 29), (1, 32), (22, 22), (1, 4), (0, 24), (35, 11), (13, 27), (26, 32), (1, 31), (20, 30), (26, 18), (28, 6), (24, 24), (6, 5), (2, 8), (13, 17), (28, 4), (0, 18), (8, 29), (2, 31), (10, 10), (31, 23), (36, 15), (21, 28), (34, 23), (35, 37), (35, 20), (4, 38), (13, 4), (14, 24), (30, 12), (33, 0), (13, 7), (5, 35), (2, 16), (5, 1), (14, 11), (24, 17), (2, 38), (24, 31), (12, 5), (7, 13), (37, 33), (34, 26), (13, 21), (12, 10), (23, 15), (37, 22), (25, 2), (12, 1), (24, 19), (10, 11), (23, 13), (20, 7), (3, 25), (0, 16), (32, 26), (1, 20), (20, 25), (34, 29), (12, 11), (22, 38), (27, 4), (3, 8), (27, 26), (31, 2), (28, 12), (29, 17), (26, 13), (33, 12), (30, 22), (37, 30), (36, 25), (34, 20), (36, 1), (12, 21), (24, 26), (0, 26), (24, 29), (0, 7), (19, 9), (28, 9), (3, 35), (36, 30), (23, 21), (0, 17), (13, 14), (15, 26), (11, 2), (5, 24), (9, 20), (10, 20), (8, 13), (6, 13), (8, 10), (29, 20), (25, 24), (33, 38), (27, 6), (12, 6), (32, 2), (20, 35), (16, 10), (13, 34), (14, 5), (35, 34), (37, 24), (28, 32), (28, 13), (37, 13), (37, 4), (18, 14), (34, 8), (32, 5), (0, 15), (35, 0), (5, 9), (24, 10), (34, 7), (29, 24), (35, 10), (7, 17), (22, 17), (16, 34), (12, 33), (37, 36), (29, 22), (27, 15), (25, 29), (37, 8), (27, 5), (34, 13), (26, 23), (17, 11), (35, 12), (8, 24), (16, 27), (23, 11), (32, 20), (26, 17), (16, 33), (5, 22), (36, 5), (11, 38), (27, 12), (12, 37), (9, 28), (33, 10), (21, 15), (10, 24), (2, 23), (37, 18), (19, 10), (9, 17), (36, 17), (33, 23), (19, 21), (10, 7), (24, 1), (32, 13), (15, 35), (27, 10), (29, 27), (16, 1), (20, 15), (6, 21), (13, 6), (20, 2), (37, 5), (10, 25), (11, 23), (0, 22), (31, 31), (8, 17), (23, 2), (1, 26), (20, 8), (27, 20), (26, 19), (12, 0), (25, 38), (2, 5), (21, 38), (5, 29), (1, 6), (14, 12), (17, 1), (36, 11), (17, 5), (26, 5), (8, 26), (17, 12), (33, 5), (21, 0), (15, 25), (26, 3), (7, 37), (8, 28), (25, 5), (29, 23), (19, 37), (0, 37), (16, 26), (25, 3), (30, 31), (6, 3), (1, 16), (19, 30), (16, 4), (17, 24), (14, 36), (8, 9), (11, 31), (21, 22), (23, 17), (21, 32), (35, 1), (15, 3), (4, 13), (30, 0), (14, 13), (16, 15), (34, 31), (27, 18), (22, 36), (6, 26), (8, 7), (7, 19), (5, 12), (21, 24), (18, 32), (17, 30), (2, 10), (14, 29), (36, 26), (15, 6), (24, 35), (16, 13), (20, 6), (22, 5), (0, 36), (26, 31), (19, 7), (24, 16), (26, 10), (15, 38), (24, 9), (22, 25), (34, 34), (7, 36), (4, 36), (11, 30), (2, 29), (1, 3), (1, 29), (25, 15), (2, 13), (17, 26), (1, 11), (32, 16), (25, 32), (15, 0), (19, 25), (32, 33), (8, 11), (6, 24), (36, 22), (2, 21), (36, 13), (32, 21), (16, 19), (12, 13), (13, 31), (0, 27), (27, 3), (33, 7), (10, 27), (19, 15), (8, 23), (21, 34), (0, 6), (30, 17), (16, 37), (27, 30), (28, 16), (8, 19), (18, 17), (2, 19), (33, 37), (33, 33), (21, 1), (23, 24), (0, 23), (34, 33), (36, 7), (8, 34), (5, 32), (9, 26), (31, 33), (28, 2), (1, 23), (29, 16), (35, 13), (3, 28), (10, 35), (36, 19), (20, 31), (7, 6), (34, 32), (19, 29), (29, 18), (27, 33), (34, 4), (4, 2), (16, 29), (33, 6), (15, 20), (4, 16), (24, 20), (35, 28), (9, 33), (8, 31), (32, 29), (6, 1), (4, 32), (33, 11), (20, 20), (19, 34), (31, 17), (29, 0), (16, 28), (15, 27), (24, 13), (12, 24), (11, 34), (33, 1), (19, 1), (27, 29), (17, 23), (13, 37), (14, 4), (12, 20), (23, 25), (30, 30), (20, 16), (17, 18), (1, 18), (5, 13), (15, 24), (10, 26), (33, 8), (14, 31), (23, 28), (11, 28), (7, 8), (9, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6696", "dataset": "MATH"}
{"messages": [{"content": "In a 31x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 6), (4, 26), (15, 22), (3, 20), (23, 12), (17, 4), (7, 28), (6, 17), (0, 8), (29, 19), (11, 0), (12, 14), (20, 2), (22, 17), (15, 13), (5, 5), (27, 20), (20, 8), (4, 18), (7, 1), (0, 24), (27, 10), (12, 1), (10, 11), (28, 6), (8, 26), (11, 4), (15, 6), (17, 29), (28, 0), (13, 2), (8, 28), (2, 2), (9, 26), (0, 28), (0, 18), (1, 5), (28, 3), (16, 19), (17, 18), (22, 29), (17, 30), (19, 26), (2, 10), (16, 7), (7, 20), (29, 21), (30, 14), (29, 25), (25, 10), (19, 27), (19, 0), (17, 28), (30, 6), (4, 15), (24, 25), (2, 6), (25, 12), (7, 11), (18, 17), (5, 27), (21, 27), (3, 15), (10, 23), (8, 15), (3, 14), (22, 24), (25, 4), (7, 3), (12, 6), (4, 25), (6, 20), (6, 14), (27, 16), (24, 7), (6, 1), (5, 29), (30, 19), (4, 14), (13, 29), (18, 30), (28, 10), (16, 5), (30, 4), (5, 23), (0, 30), (12, 22), (22, 27), (8, 27), (22, 2), (19, 4), (6, 7), (9, 24), (14, 22), (17, 27), (24, 23), (13, 28), (20, 3), (26, 5), (3, 1), (23, 3), (0, 15), (9, 5), (18, 18), (6, 19), (3, 7), (0, 14), (17, 3), (1, 7), (5, 7), (15, 10), (8, 24), (12, 28), (1, 27), (17, 21), (23, 6), (21, 10), (27, 28), (24, 3), (14, 3), (25, 16), (0, 27), (8, 12), (2, 28), (18, 16), (11, 3), (5, 17), (22, 4), (11, 8), (6, 8), (15, 18), (9, 13), (25, 13), (28, 16), (20, 25), (14, 16), (17, 15), (30, 25), (22, 13), (1, 0), (6, 0), (12, 21), (16, 23), (3, 3), (21, 18), (16, 2), (30, 26), (4, 12), (25, 6), (13, 16), (6, 10), (8, 9), (28, 8), (2, 30), (11, 6), (20, 28), (0, 26), (27, 13), (28, 7), (10, 6), (13, 6), (30, 2), (14, 15), (25, 23), (24, 0), (10, 14), (27, 1), (17, 6), (23, 17), (13, 1), (27, 27), (19, 2), (0, 25), (13, 30), (20, 19), (13, 18), (5, 18), (29, 17), (21, 20), (29, 11), (18, 26), (2, 5), (7, 25), (19, 18), (18, 25), (19, 15), (15, 1), (16, 25), (11, 25), (10, 4), (17, 8), (16, 3), (6, 30), (20, 23), (1, 13), (25, 17), (26, 12), (7, 8), (2, 7), (27, 24), (24, 30), (11, 1), (12, 3), (2, 3), (21, 30), (2, 26), (26, 27), (29, 12), (12, 25), (16, 12), (25, 21), (15, 7), (18, 24), (1, 9), (10, 16), (26, 16), (15, 21), (3, 28), (16, 18), (29, 20), (28, 20), (0, 22), (13, 22), (11, 22), (24, 27), (21, 21), (1, 20), (14, 17), (7, 30), (26, 20), (16, 21), (24, 5), (16, 26), (13, 25), (25, 19), (22, 19), (6, 21), (0, 6), (22, 12), (9, 19), (4, 24), (19, 6), (22, 1), (22, 16), (17, 22), (6, 16), (24, 24), (14, 4), (14, 26), (12, 17), (28, 29), (23, 26), (9, 23), (28, 18), (4, 5), (6, 6), (20, 7), (5, 6), (28, 2), (15, 14), (16, 15), (8, 5), (15, 29), (9, 7), (10, 20), (23, 29), (6, 22), (19, 28), (22, 22), (22, 26), (16, 9), (23, 24), (3, 11), (19, 29), (23, 28), (3, 25), (7, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604032", "dataset": "MATH"}
{"messages": [{"content": "In a 35x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 32), (10, 8), (18, 5), (29, 19), (4, 7), (4, 19), (28, 26), (0, 22), (33, 19), (21, 27), (23, 3), (7, 23), (27, 11), (1, 14), (1, 12), (31, 5), (31, 10), (17, 4), (31, 24), (12, 19), (26, 27), (12, 28), (15, 23), (8, 20), (21, 13), (17, 9), (19, 21), (16, 16), (6, 12), (33, 17), (0, 4), (32, 27), (30, 31), (1, 30), (29, 0), (6, 10), (4, 23), (5, 30), (11, 32), (25, 31), (2, 6), (11, 23), (25, 6), (16, 3), (19, 28), (18, 27), (3, 3), (5, 5), (11, 17), (18, 33), (6, 24), (30, 26), (6, 23), (8, 12), (15, 32), (23, 32), (26, 22), (7, 24), (1, 20), (28, 0), (18, 14), (7, 2), (17, 18), (8, 13), (17, 30), (25, 13), (26, 28), (4, 14), (28, 11), (7, 14), (13, 4), (12, 21), (20, 22), (14, 0), (18, 8), (14, 2), (21, 14), (24, 18), (15, 21), (31, 28), (20, 17), (32, 29), (5, 2), (33, 21), (10, 10), (20, 5), (16, 23), (33, 0), (9, 25), (17, 11), (1, 21), (4, 0), (23, 7), (15, 19), (27, 23), (27, 9), (33, 28), (9, 4), (27, 18), (33, 6), (24, 9), (1, 15), (7, 12), (26, 25), (21, 30), (30, 13), (10, 33), (20, 13), (13, 12), (25, 4), (20, 2), (13, 21), (29, 12), (15, 26), (31, 11), (4, 11), (22, 11), (1, 0), (34, 12), (29, 14), (27, 28), (0, 3), (25, 17), (20, 8), (11, 7), (32, 18), (23, 20), (24, 22), (12, 27), (25, 3), (8, 11), (33, 30), (3, 6), (22, 0), (29, 1), (29, 25), (28, 7), (33, 27), (8, 15), (9, 18), (5, 12), (27, 8), (5, 4), (32, 20), (23, 17), (2, 16), (1, 31), (28, 14), (0, 29), (5, 3), (18, 21), (25, 14), (24, 19), (22, 26), (34, 24), (27, 30), (14, 7), (33, 33), (22, 10), (12, 23), (28, 17), (25, 9), (20, 32), (2, 32), (7, 32), (10, 15), (12, 24), (2, 17), (9, 30), (16, 31), (34, 31), (34, 2), (8, 31), (10, 11), (26, 18), (0, 28), (34, 18), (21, 17), (25, 8), (20, 9), (17, 12), (34, 8), (16, 0), (11, 19), (27, 4), (6, 21), (0, 5), (27, 32), (17, 13), (8, 5), (5, 8), (3, 1), (13, 8), (9, 14), (18, 24), (17, 3), (22, 2), (18, 18), (33, 11), (6, 1), (18, 23), (16, 17), (12, 31), (25, 0), (24, 6), (16, 22), (19, 27), (0, 33), (28, 12), (33, 10), (1, 9), (6, 28), (8, 19), (24, 7), (23, 15), (33, 24), (33, 25), (24, 21), (34, 9), (13, 0), (29, 21), (23, 29), (13, 9), (9, 22), (20, 4), (13, 23), (23, 6), (21, 6), (32, 15), (7, 28), (20, 14), (13, 25), (17, 25), (3, 24), (13, 17), (16, 11), (1, 27), (22, 21), (15, 31), (24, 15), (4, 3), (17, 24), (24, 3), (10, 30), (31, 0), (22, 18), (2, 2), (30, 6), (28, 5), (22, 15), (32, 32), (33, 29), (10, 12), (23, 11), (12, 33), (20, 24), (27, 29), (9, 12), (5, 17), (3, 21), (29, 2), (10, 1), (6, 16), (13, 7), (34, 10), (3, 25), (6, 33), (32, 23), (15, 18), (15, 13), (22, 5), (3, 0), (0, 10), (17, 20), (23, 16), (0, 14), (10, 6), (30, 22), (11, 25), (7, 0), (7, 8), (5, 16), (6, 13), (9, 6), (2, 15), (1, 25), (30, 19), (27, 19), (8, 4), (30, 29), (11, 24), (7, 9), (13, 14), (8, 17), (4, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "483840", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (13, 30), (26, 23), (23, 9), (29, 18), (21, 9), (22, 24), (18, 20), (0, 15), (8, 15), (34, 19), (3, 1), (22, 21), (6, 19), (3, 23), (19, 2), (3, 20), (35, 9), (33, 1), (35, 22), (30, 29), (7, 6), (26, 26), (4, 5), (28, 14), (16, 10), (35, 5), (3, 4), (24, 20), (29, 10), (24, 27), (18, 7), (34, 21), (14, 25), (9, 23), (1, 28), (5, 31), (32, 26), (11, 12), (5, 13), (17, 3), (27, 8), (30, 23), (25, 31), (31, 7), (28, 25), (17, 25), (4, 20), (3, 2), (20, 8), (14, 9), (17, 4), (11, 31), (19, 22), (15, 28), (35, 4), (29, 25), (15, 31), (9, 29), (26, 7), (35, 23), (7, 14), (28, 6), (20, 0), (4, 12), (13, 28), (28, 12), (33, 27), (10, 29), (23, 11), (25, 19), (14, 13), (15, 17), (5, 30), (1, 9), (28, 0), (28, 27), (14, 28), (5, 10), (16, 16), (22, 29), (13, 31), (10, 14), (18, 25), (31, 20), (2, 30), (14, 12), (0, 9), (16, 31), (11, 1), (15, 4), (7, 2), (8, 5), (12, 29), (25, 3), (7, 3), (28, 2), (24, 13), (19, 26), (25, 6), (31, 21), (8, 17), (7, 29), (13, 1), (28, 3), (20, 6), (8, 9), (1, 7), (25, 27), (19, 13), (31, 31), (30, 28), (7, 31), (0, 6), (11, 26), (17, 23), (10, 7), (18, 31), (12, 11), (12, 9), (2, 6), (5, 17), (25, 0), (7, 11), (6, 9), (30, 15), (26, 0), (16, 27), (19, 20), (33, 7), (0, 3), (19, 30), (9, 21), (13, 3), (13, 8), (8, 2), (13, 10), (19, 6), (10, 17), (6, 22), (16, 22), (15, 10), (20, 2), (16, 13), (28, 30), (4, 24), (11, 8), (7, 20), (10, 25), (34, 22), (1, 24), (17, 8), (14, 7), (1, 19), (25, 28), (15, 0), (31, 24), (25, 15), (4, 11), (6, 7), (16, 2), (27, 3), (29, 8), (15, 30), (33, 28), (8, 22), (14, 15), (10, 19), (22, 19), (22, 4), (29, 3), (18, 6), (8, 21), (20, 30), (0, 1), (19, 24), (27, 23), (10, 18), (17, 9), (31, 12), (6, 29), (19, 5), (19, 21), (6, 20), (14, 22), (22, 3), (16, 23), (15, 1), (22, 6), (32, 16), (23, 15), (17, 14), (34, 10), (12, 12), (35, 2), (4, 23), (28, 8), (2, 19), (6, 11), (5, 28), (0, 18), (30, 16), (14, 24), (2, 15), (12, 14), (31, 30), (11, 10), (20, 23), (21, 13), (29, 27), (10, 31), (28, 18), (34, 3), (24, 22), (27, 6), (1, 31), (15, 6), (25, 10), (34, 1), (21, 23), (1, 8), (22, 20), (5, 11), (16, 12), (13, 16), (28, 4), (12, 17), (21, 20), (3, 9), (23, 21), (15, 25), (34, 31), (32, 23), (23, 13), (29, 13), (22, 11), (1, 23), (23, 23), (26, 15), (25, 14), (14, 29), (35, 11), (8, 20), (1, 5), (2, 3), (24, 7), (26, 3), (21, 26), (14, 0), (0, 29), (28, 5), (20, 18), (26, 25), (33, 10), (28, 23), (9, 19), (17, 24), (0, 21), (13, 9), (22, 18), (1, 18), (2, 20), (25, 29), (26, 14), (30, 19), (20, 22), (34, 9), (21, 7), (28, 28), (9, 18), (3, 26), (17, 30), (12, 23), (24, 17), (2, 0), (31, 14), (3, 11), (34, 30), (29, 5), (16, 14), (3, 15), (23, 4), (28, 17), (16, 19), (11, 29), (10, 8), (30, 3), (5, 12), (13, 12), (21, 3), (18, 11), (20, 15), (33, 12), (33, 4), (15, 24), (27, 15), (6, 16), (32, 9), (2, 16), (2, 24), (24, 31), (14, 27), (19, 3), (16, 24), (34, 26), (26, 13), (22, 31), (32, 7), (24, 25), (17, 29), (27, 22), (17, 20), (10, 22), (25, 20), (22, 2), (32, 31), (16, 9), (6, 31), (7, 17), (30, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960660", "dataset": "MATH"}
{"messages": [{"content": "In a 38x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 36), 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), (31, 32), (34, 35), (27, 3), (18, 4), (13, 21), (37, 21), (20, 7), (0, 11), (6, 24), (10, 29), (20, 14), (1, 23), (21, 24), (23, 4), (9, 6), (13, 9), (15, 19), (13, 33), (3, 8), (35, 20), (4, 2), (27, 19), (7, 8), (37, 25), (29, 21), (15, 27), (12, 14), (3, 17), (36, 10), (31, 6), (1, 16), (16, 16), (17, 0), (4, 8), (36, 23), (32, 28), (17, 24), (5, 11), (32, 16), (20, 5), (35, 18), (16, 3), (6, 31), (32, 2), (20, 0), (7, 14), (37, 23), (15, 3), (18, 27), (10, 27), (21, 18), (2, 32), (0, 23), (22, 2), (28, 36), (12, 26), (30, 5), (12, 2), (3, 36), (5, 8), (6, 20), (33, 27), (0, 31), (32, 15), (6, 33), (32, 23), (28, 30), (27, 21), (2, 27), (22, 14), (9, 7), (29, 30), (8, 13), (15, 26), (17, 15), (5, 17), (15, 29), (19, 16), (3, 25), (21, 4), (32, 6), (13, 25), (28, 13), (36, 29), (8, 21), (28, 6), (25, 24), (7, 22), (22, 20), (4, 34), (30, 20), (25, 22), (13, 24), (6, 28), (33, 12), (35, 33), (18, 0), (13, 26), (13, 22), (17, 4), (9, 4), (24, 3), (32, 26), (25, 6), (27, 22), (4, 20), (34, 27), (11, 25), (34, 33), (32, 9), (1, 15), (23, 17), (16, 20), (16, 7), (34, 19), (11, 10), (30, 4), (16, 2), (0, 30), (3, 7), (33, 13), (34, 21), (10, 0), (17, 1), (12, 13), (23, 2), (34, 30), (5, 2), (31, 15), (24, 21), (18, 10), (29, 20), (7, 36), (7, 16), (7, 19), (25, 27), (11, 23), (17, 7), (10, 31), (28, 2), (7, 31), (6, 2), (21, 31), (4, 13), (37, 15), (25, 4), (16, 14), (13, 31), (24, 6), (24, 14), (17, 27), (24, 18), (12, 24), (20, 34), (35, 17), (16, 26), (23, 30), (0, 32), (14, 33), (32, 33), (7, 9), (35, 28), (37, 5), (19, 4), (18, 9), (2, 12), (17, 5), (22, 27), (34, 16), (33, 6), (12, 33), (29, 3), (8, 11), (32, 12), (27, 13), (37, 22), (23, 31), (17, 17), (16, 19), (36, 22), (17, 19), (5, 1), (23, 10), (37, 1), (4, 12), (30, 34), (9, 11), (8, 32), (0, 2), (33, 9), (34, 5), (3, 18), (18, 35), (28, 27), (26, 7), (30, 11), (0, 20), (35, 31), (4, 7), (16, 23), (32, 27), (0, 28), (36, 16), (20, 19), (23, 15), (2, 29), (2, 21), (27, 34), (9, 16), (12, 34), (4, 16), (32, 29), (2, 20), (25, 7), (27, 24), (8, 4), (11, 26), (30, 15), (10, 33), (19, 36), (16, 25), (20, 4), (10, 12), (8, 27), (19, 11), (26, 9), (32, 32), (30, 29), (0, 26), (10, 1), (8, 18), (24, 12), (4, 17), (19, 17), (32, 0), (29, 27), (9, 3), (12, 8), (24, 25), (26, 2), (30, 31), (19, 9), (21, 3), (25, 35), (6, 15), (15, 17), (21, 26), (16, 35), (27, 14), (19, 19), (24, 4), (4, 11), (17, 2), (2, 0), (17, 32), (1, 10), (19, 6), (37, 9), (18, 33), (37, 30), (14, 34), (8, 20), (36, 35), (16, 5), (9, 12), (24, 22), (6, 19), (33, 1), (7, 25), (26, 17), (13, 32), (3, 6), (2, 2), (32, 30), (31, 13), (21, 8), (9, 27), (23, 18), (15, 22), (16, 6), (22, 4), (34, 1), (5, 20), (15, 25), (30, 24), (0, 12), (28, 29), (29, 31), (24, 29), (29, 28), (11, 32), (26, 27), (6, 9), (27, 27), (6, 12), (5, 4), (31, 18), (24, 0), (27, 25), (23, 35), (35, 22), (0, 27), (32, 4), (12, 17), (12, 31), (28, 7), (5, 35), (26, 3), (22, 30), (22, 21), (8, 9), (6, 0), (22, 12), (26, 6), (7, 24), (6, 35), (34, 11), (16, 10), (13, 36), (8, 0), (22, 15), (15, 28), (5, 31), (36, 26), (14, 13), (16, 31), (7, 13), (28, 25), (25, 15), (25, 3), (20, 10), (31, 4), (1, 17), (2, 15), (19, 30), (6, 1), (0, 24), (22, 7), (20, 23), (22, 11), (28, 26), (37, 7), (31, 28), (12, 15), (37, 10), (34, 36), (11, 20), (37, 31), (32, 35), (29, 13), (28, 18), (21, 9), (27, 30), (6, 5), (11, 24), (31, 20), (10, 18), (4, 24), (8, 7), (33, 35), (18, 16), (1, 33), (5, 23), (19, 29), (0, 17), (22, 28), (11, 22), (24, 8), (31, 24), (1, 9), (14, 19), (20, 31), (25, 21), (26, 26), (24, 13), (33, 3), (16, 21), (25, 16), (12, 16), (4, 10), (28, 17), (11, 7), (17, 31), (9, 21), (36, 1), (2, 14), (36, 28), (19, 13), (2, 17), (33, 28), (7, 2), (0, 5), (12, 4), (27, 32), (20, 25), (16, 0), (16, 13), (3, 10), (28, 21), (36, 0), (28, 3), (30, 2), (18, 3), (9, 34), (36, 11), (36, 7), (19, 15), (26, 20), (8, 24), (31, 22), (17, 13), (9, 15), (2, 25), (5, 6), (10, 35), (12, 22), (24, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "843008", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (23, 12), (25, 16), (27, 11), (4, 2), (27, 1), (5, 10), (17, 3), (1, 19), (21, 2), (2, 19), (23, 8), (30, 9), (26, 7), (9, 16), (22, 3), (25, 7), (22, 8), (31, 10), (7, 29), (1, 17), (5, 22), (20, 23), (22, 17), (21, 4), (4, 11), (11, 24), (3, 9), (18, 0), (12, 27), (2, 3), (26, 25), (30, 23), (16, 20), (8, 17), (2, 18), (18, 1), (19, 5), (26, 12), (3, 21), (20, 19), (1, 14), (14, 6), (4, 28), (31, 24), (21, 23), (9, 9), (18, 20), (13, 3), (15, 0), (23, 10), (15, 4), (4, 13), (27, 12), (2, 29), (23, 1), (20, 29), (19, 7), (21, 26), (12, 18), (22, 2), (17, 21), (10, 21), (25, 4), (31, 7), (28, 29), (2, 0), (30, 5), (30, 16), (1, 11), (30, 26), (14, 28), (10, 25), (19, 12), (28, 3), (12, 13), (3, 20), (21, 9), (20, 9), (27, 24), (26, 29), (13, 28), (5, 4), (25, 27), (25, 24), (9, 24), (14, 9), (25, 13), (6, 14), (26, 4), (21, 20), (26, 24), (5, 7), (26, 9), (17, 23), (31, 21), (1, 25), (18, 15), (4, 14), (31, 8), (3, 2), (19, 8), (2, 26), (8, 23), (27, 6), (21, 15), (10, 15), (17, 7), (20, 10), (12, 7), (2, 24), (12, 9), (29, 24), (7, 28), (18, 12), (30, 0), (6, 22), (4, 24), (15, 10), (28, 4), (7, 11), (2, 25), (10, 23), (0, 16), (1, 20), (2, 14), (31, 3), (3, 11), (15, 28), (7, 15), (3, 13), (27, 0), (30, 28), (14, 19), (22, 26), (19, 14), (9, 27), (31, 9), (19, 18), (30, 24), (7, 20), (30, 19), (1, 6), (18, 19), (25, 5), (20, 16), (19, 10), (0, 19), (22, 25), (26, 8), (12, 15), (22, 10), (18, 2), (26, 14), (12, 6), (4, 25), (16, 1), (12, 16), (27, 18), (27, 4), (8, 0), (5, 5), (10, 13), (9, 29), (18, 17), (14, 27), (28, 23), (2, 16), (23, 6), (28, 8), (5, 20), (18, 26), (19, 16), (7, 12), (29, 15), (30, 22), (31, 11), (22, 0), (18, 23), (6, 29), (19, 23), (2, 20), (4, 29), (11, 23), (8, 6), (18, 7), (23, 20), (2, 2), (1, 26), (18, 21), (29, 13), (24, 15), (11, 12), (29, 21), (25, 3), (7, 24), (4, 19), (0, 28), (9, 28), (26, 13), (15, 6), (6, 2), (11, 21), (12, 0), (8, 22), (23, 5), (21, 12), (13, 26), (25, 23), (24, 29), (27, 2), (5, 18), (1, 8), (10, 2), (14, 7), (24, 28), (4, 20), (28, 13), (29, 16), (0, 24), (10, 3), (29, 22), (16, 0), (8, 4), (19, 22), (7, 3), (10, 26), (24, 17), (13, 15), (1, 2), (30, 29), (6, 3), (6, 0), (26, 10), (23, 21), (27, 16), (31, 23), (17, 5), (7, 0), (9, 8), (18, 9), (14, 2), (11, 17), (2, 15), (5, 16), (17, 15), (27, 27), (21, 18), (28, 2), (6, 26), (4, 10), (6, 4), (17, 29), (0, 3), (4, 27), (1, 5), (14, 0), (11, 19), (5, 28), (2, 9), (26, 23), (4, 23), (19, 17), (31, 1), (6, 27), (16, 4), (1, 29), (23, 11), (19, 11), (22, 14), (17, 17), (0, 20), (29, 14), (11, 18), (31, 20), (29, 3), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "812904", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 34), (15, 27), (18, 20), (14, 14), (21, 24), (22, 3), (33, 1), (22, 2), (3, 16), (23, 27), (10, 36), (4, 23), (30, 29), (17, 27), (0, 10), (2, 35), (11, 29), (13, 13), (33, 5), (17, 5), (10, 2), (3, 1), (22, 13), (12, 15), (16, 11), (1, 13), (20, 10), (10, 35), (33, 27), (20, 23), (10, 7), (5, 0), (24, 5), (2, 33), (15, 30), (25, 1), (4, 7), (1, 4), (18, 14), (28, 25), (13, 26), (18, 33), (10, 32), (23, 8), (2, 6), (14, 23), (32, 2), (26, 19), (3, 29), (11, 34), (27, 4), (26, 13), (4, 28), (31, 12), (8, 27), (0, 17), (22, 29), (17, 19), (8, 19), (26, 20), (22, 30), (10, 21), (27, 28), (0, 31), (9, 19), (16, 6), (24, 33), (29, 15), (33, 28), (14, 19), (13, 9), (33, 4), (33, 6), (2, 12), (23, 15), (9, 10), (8, 16), (10, 10), (0, 8), (23, 22), (21, 19), (32, 7), (26, 35), (0, 32), (13, 21), (8, 18), (1, 30), (29, 5), (31, 33), (17, 10), (8, 11), (17, 29), (2, 9), (31, 5), (1, 0), (0, 19), (33, 15), (22, 5), (28, 10), (26, 21), (5, 22), (11, 35), (20, 32), (6, 19), (20, 34), (0, 2), (32, 32), (13, 15), (30, 33), (30, 18), (29, 29), (21, 16), (1, 33), (6, 20), (23, 35), (10, 25), (32, 16), (29, 33), (28, 19), (23, 7), (31, 34), (26, 12), (23, 20), (23, 9), (11, 6), (22, 1), (24, 30), (5, 18), (20, 19), (5, 16), (31, 13), (25, 9), (25, 14), (8, 10), (16, 34), (16, 23), (26, 25), (21, 20), (26, 5), (13, 22), (29, 1), (27, 12), (9, 27), (19, 0), (9, 16), (16, 30), (8, 20), (20, 2), (13, 7), (24, 14), (7, 12), (9, 12), (28, 7), (5, 21), (17, 12), (2, 29), (6, 7), (27, 17), (11, 16), (20, 14), (9, 3), (16, 5), (1, 24), (32, 5), (23, 31), (0, 34), (3, 33), (13, 32), (4, 4), (25, 8), (1, 29), (14, 22), (11, 11), (2, 13), (12, 28), (0, 23), (23, 23), (27, 11), (29, 18), (30, 36), (10, 23), (23, 6), (27, 10), (0, 21), (18, 19), (20, 13), (26, 23), (0, 13), (3, 17), (2, 21), (28, 9), (33, 16), (32, 30), (17, 21), (17, 31), (22, 33), (18, 15), (14, 30), (4, 13), (11, 31), (24, 10), (7, 14), (30, 32), (14, 20), (26, 24), (2, 23), (28, 20), (7, 9), (13, 35), (20, 1), (16, 28), (19, 14), (21, 30), (15, 29), (25, 7), (22, 35), (23, 24), (14, 8), (2, 26), (10, 19), (33, 35), (5, 28), (29, 27), (32, 10), (3, 10), (9, 18), (24, 4), (7, 27), (22, 19), (2, 36), (29, 8), (28, 15), (30, 16), (8, 21), (2, 30), (16, 29), (23, 29), (20, 35), (33, 23), (6, 21), (24, 1), (28, 30), (23, 19), (5, 34), (19, 1), (4, 14), (8, 33), (0, 24), (0, 27), (18, 13), (9, 28), (25, 0), (30, 7), (3, 36), (31, 21), (6, 31), (16, 8), (18, 4), (31, 18), (25, 11), (32, 17), (31, 10), (7, 25), (14, 36), (5, 35), (1, 19), (20, 6), (9, 25), (14, 10), (12, 25), (8, 14), (16, 12), (27, 3), (1, 8), (22, 11), (22, 16), (8, 1), (23, 5), (4, 10), (31, 17), (21, 32), (33, 29), (6, 27), (11, 5), (30, 1), (2, 25), (7, 4), (17, 32), (28, 5), (21, 28), (22, 21), (26, 16), (20, 30), (20, 26), (33, 26), (7, 16), (15, 32), (19, 27), (33, 30), (33, 25), (18, 16), (12, 19), (24, 21), (32, 31), (3, 5), (15, 0), (2, 27), (9, 24), (4, 29), (12, 8), (5, 24), (13, 8), (19, 29), (14, 17), (22, 9), (23, 10), (17, 24), (31, 29), (8, 25), (8, 36), (12, 13), (25, 22), (11, 25), (24, 35), (30, 21), (18, 3), (1, 20), (24, 13), (1, 3), (30, 34), (9, 11), (12, 18), (17, 33), (20, 15), (27, 15), (19, 19), (20, 0), (8, 30), (6, 3), (6, 4), (13, 16), (27, 34), (3, 13), (2, 15), (23, 18), (20, 16), (5, 25), (26, 3), (21, 5), (23, 17), (17, 13), (33, 10), (26, 11), (16, 27), (19, 12), (15, 20), (30, 2), (14, 5), (25, 5), (32, 3), (12, 0), (11, 32), (24, 24), (8, 6), (18, 2), (13, 34), (30, 27), (24, 26), (19, 4), (22, 36), (10, 16), (31, 22), (14, 0), (10, 34), (27, 36), (20, 4), (7, 7), (24, 20), (19, 6), (33, 17), (4, 3), (22, 34), (21, 2), (18, 32), (29, 9), (19, 26), (7, 22), (20, 8), (22, 27), (9, 15), (18, 30), (16, 1), (13, 27), (29, 3), (11, 9), (6, 10), (19, 18), (0, 33), (29, 16), (13, 1), (28, 8), (19, 2), (8, 22), (18, 27), (29, 6), (19, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424512", "dataset": "MATH"}
{"messages": [{"content": "In a 31x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 22), (11, 16), (0, 33), (23, 18), (22, 1), (21, 29), (10, 11), (15, 30), (19, 22), (10, 27), (14, 34), (29, 19), (27, 7), (23, 32), (27, 18), (10, 17), (13, 35), (19, 28), (6, 3), (9, 11), (21, 18), (3, 28), (11, 18), (9, 28), (16, 16), (4, 21), (21, 28), (15, 2), (25, 6), (23, 29), (0, 23), (11, 11), (30, 18), (25, 24), (10, 23), (30, 24), (6, 19), (28, 29), (1, 11), (20, 14), (30, 23), (11, 14), (20, 13), (15, 3), (24, 22), (26, 5), (10, 32), (10, 15), (7, 0), (27, 32), (24, 9), (22, 32), (15, 4), (30, 15), (20, 2), (6, 6), (22, 36), (24, 17), (10, 36), (1, 7), (19, 20), (30, 0), (7, 9), (5, 26), (22, 34), (2, 15), (18, 26), (11, 2), (8, 24), (26, 32), (12, 5), (21, 6), (22, 24), (3, 3), (0, 36), (10, 6), (9, 25), (20, 22), (0, 29), (22, 22), (10, 5), (16, 21), (24, 23), (28, 15), (24, 0), (9, 9), (17, 11), (29, 8), (24, 34), (22, 28), (30, 20), (13, 32), (17, 7), (18, 6), (22, 27), (7, 32), (11, 27), (8, 7), (20, 27), (21, 24), (0, 31), (13, 7), (12, 28), (4, 25), (21, 31), (9, 26), (14, 2), (3, 13), (16, 30), (30, 27), (24, 5), (1, 4), (3, 2), (25, 27), (4, 6), (17, 25), (30, 11), (6, 12), (24, 13), (8, 10), (20, 3), (5, 22), (22, 2), (24, 2), (22, 6), (23, 2), (28, 5), (20, 4), (13, 15), (15, 0), (7, 18), (3, 15), (1, 23), (25, 25), (16, 18), (13, 2), (15, 33), (2, 8), (13, 25), (26, 18), (7, 12), (9, 19), (12, 23), (14, 32), (10, 4), (14, 6), (1, 22), (23, 14), (12, 0), (2, 26), (16, 17), (2, 16), (8, 13), (2, 10), (4, 18), (15, 7), (5, 33), (30, 29), (25, 11), (22, 12), (4, 35), (7, 28), (24, 31), (21, 22), (23, 28), (12, 34), (17, 15), (12, 30), (30, 13), (23, 24), (11, 19), (30, 12), (7, 19), (27, 9), (2, 25), (1, 12), (9, 8), (12, 9), (29, 20), (19, 5), (29, 27), (27, 14), (7, 31), (5, 34), (18, 36), (13, 20), (12, 24), (1, 17), (4, 2), (12, 21), (26, 36), (13, 19), (29, 7), (26, 9), (21, 2), (8, 27), (10, 29), (8, 9), (13, 0), (14, 15), (4, 28), (23, 13), (1, 21), (20, 25), (16, 36), (7, 35), (16, 27), (9, 13), (16, 9), (16, 26), (12, 15), (21, 19), (12, 17), (2, 29), (9, 23), (11, 31), (24, 11), (28, 14), (4, 34), (30, 6), (1, 18), (19, 19), (2, 14), (7, 1), (27, 36), (15, 15), (14, 7), (26, 7), (2, 24), (5, 18), (0, 17), (27, 29), (15, 14), (23, 9), (8, 3), (9, 31), (19, 15), (9, 27), (24, 29), (16, 7), (7, 36), (22, 3), (18, 23), (6, 13), (8, 33), (17, 3), (11, 21), (19, 4), (30, 33), (0, 8), (25, 2), (29, 1), (16, 2), (3, 29), (26, 30), (11, 3), (16, 31), (1, 1), (7, 6), (20, 20), (28, 24), (16, 3), (23, 19), (18, 9), (16, 25), (3, 12), (29, 6), (9, 7), (0, 18), (27, 4), (28, 21), (28, 34), (11, 26), (6, 4), (6, 20), (20, 23), (11, 24), (4, 30), (20, 16), (11, 6), (2, 19), (13, 5), (30, 4), (23, 16), (30, 26), (25, 31), (13, 10), (24, 14), (19, 23), (21, 23), (23, 36), (9, 36), (1, 8), (24, 26), (5, 23), (19, 29), (17, 6), (26, 35), (0, 32), (25, 16), (30, 1), (24, 28), (19, 18), (7, 10), (22, 19), (18, 33), (6, 2), (24, 30), (12, 14), (17, 26), (28, 33), (21, 7), (6, 30), (30, 8), (28, 9), (30, 14), (12, 35), (13, 24), (1, 6), (18, 29), (3, 9), (16, 13), (0, 12), (26, 11), (11, 4), (11, 1), (25, 14), (30, 2), (13, 18), (3, 16), (14, 11), (2, 18), (9, 2), (16, 0), (22, 9), (26, 26), (9, 5), (15, 18), (10, 25), (16, 15), (20, 1), (23, 20), (12, 2), (6, 1), (25, 36), (1, 20), (22, 30), (28, 10), (5, 6), (16, 34), (4, 0), (0, 35), (3, 36), (5, 3), (11, 9), (18, 1), (23, 15), (21, 30), (20, 35), (16, 5), (7, 3), (15, 23), (23, 1), (14, 18), (9, 32), (19, 12), (25, 7), (11, 7), (2, 33), (0, 13), (16, 10), (11, 34), (19, 30), (17, 22), (25, 12), (26, 1), (17, 8), (7, 13), (27, 16), (22, 5), (16, 33), (20, 33), (8, 8), (27, 5), (21, 10), (23, 33)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "205200", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (17, 22), (14, 8), (2, 22), (26, 21), (6, 22), (31, 7), (7, 26), (20, 19), (10, 22), (2, 7), (11, 3), (25, 15), (30, 28), (4, 4), (20, 15), (15, 4), (22, 25), (16, 2), (14, 7), (29, 10), (4, 26), (24, 5), (29, 16), (9, 21), (21, 22), (24, 25), (13, 0), (5, 14), (20, 25), (19, 29), (0, 7), (27, 5), (0, 30), (10, 21), (25, 1), (5, 22), (18, 2), (29, 7), (24, 12), (6, 13), (20, 5), (27, 11), (11, 9), (11, 24), (17, 5), (31, 1), (9, 3), (8, 22), (10, 11), (21, 7), (7, 4), (11, 11), (27, 29), (32, 13), (23, 16), (24, 29), (15, 6), (15, 9), (29, 15), (5, 8), (10, 17), (30, 13), (10, 28), (32, 5), (5, 13), (25, 25), (12, 16), (30, 15), (9, 18), (32, 21), (4, 2), (22, 12), (27, 10), (18, 27), (8, 4), (17, 12), (26, 11), (29, 21), (31, 29), (27, 0), (12, 15), (2, 14), (5, 4), (13, 30), (28, 16), (18, 7), (19, 10), (28, 17), (19, 16), (30, 22), (21, 0), (22, 29), (26, 13), (29, 25), (32, 4), (24, 20), (7, 17), (23, 0), (4, 30), (6, 6), (12, 3), (27, 27), (12, 5), (3, 23), (12, 0), (15, 20), (11, 27), (4, 29), (18, 6), (23, 5), (18, 0), (29, 2), (30, 10), (6, 7), (19, 9), (12, 29), (22, 27), (9, 27), (30, 27), (21, 24), (1, 24), (5, 18), (1, 15), (30, 24), (25, 4), (29, 23), (3, 11), (17, 29), (1, 19), (22, 22), (21, 12), (1, 2), (0, 25), (20, 24), (27, 30), (25, 28), (16, 6), (9, 23), (29, 5), (16, 30), (2, 26), (8, 8), (2, 23), (23, 15), (2, 25), (30, 8), (19, 6), (16, 9), (14, 6), (13, 15), (14, 1), (28, 10), (31, 24), (26, 2), (24, 1), (6, 21), (4, 16), (1, 17), (28, 2), (3, 0), (17, 8), (6, 20), (22, 24), (22, 16), (11, 2), (23, 9), (26, 28), (19, 19), (20, 17), (23, 29), (1, 3), (22, 20), (7, 16), (13, 17), (13, 25), (18, 1), (9, 14), (3, 22), (23, 25), (20, 2), (24, 22), (23, 3), (4, 27), (9, 12), (28, 15), (23, 23), (13, 1), (11, 15), (2, 1), (5, 26), (26, 23), (4, 1), (22, 15), (20, 22), (11, 18), (22, 5), (18, 20), (27, 7), (20, 28), (25, 17), (20, 13), (12, 12), (28, 19), (2, 4), (27, 28), (29, 0), (2, 15), (4, 13), (5, 12), (7, 11), (29, 14), (16, 8), (6, 30), (12, 13), (15, 18), (5, 21), (17, 10), (11, 22), (31, 4), (5, 28), (21, 3), (14, 10), (3, 17), (13, 2), (16, 0), (17, 17), (3, 25), (1, 8), (32, 27), (14, 23), (3, 4), (20, 18), (10, 14), (15, 22), (15, 3), (19, 14), (19, 25), (4, 9), (10, 4), (26, 22), (20, 27), (15, 1), (18, 14), (12, 17), (31, 27), (30, 1), (11, 12), (25, 27), (30, 0), (21, 1), (0, 14), (29, 27), (13, 24), (29, 3), (25, 26), (2, 6), (26, 3), (18, 17), (4, 8), (1, 9), (30, 21), (32, 3), (1, 27), (10, 16), (11, 23), (17, 26), (20, 8), (16, 19), (3, 12), (9, 9), (25, 0), (14, 2), (21, 13), (10, 29), (11, 28), (4, 0), (31, 3), (21, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564705", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), 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, 26), (16, 8), (5, 22), (30, 4), (17, 12), (18, 12), (3, 4), (1, 22), (27, 11), (23, 16), (7, 9), (25, 32), (3, 32), (19, 10), (23, 34), (23, 29), (20, 20), (8, 31), (1, 20), (7, 26), (27, 36), (17, 8), (29, 11), (5, 9), (12, 2), (0, 34), (8, 28), (3, 24), (17, 10), (7, 4), (26, 27), (29, 0), (19, 25), (21, 32), (4, 27), (9, 3), (30, 17), (26, 23), (29, 5), (18, 37), (9, 28), (11, 21), (19, 22), (12, 35), (10, 34), (19, 5), (13, 33), (26, 20), (9, 5), (16, 3), (11, 26), (13, 24), (11, 29), (8, 2), (14, 4), (4, 0), (27, 6), (23, 19), (29, 30), (12, 11), (1, 37), (0, 12), (9, 20), (7, 27), (30, 21), (6, 34), (2, 18), (0, 1), (8, 35), (0, 32), (0, 28), (18, 28), (13, 31), (11, 17), (21, 27), (30, 3), (1, 16), (22, 35), (7, 18), (10, 12), (21, 19), (23, 25), (5, 26), (19, 2), (3, 22), (12, 36), (6, 16), (27, 22), (26, 15), (2, 21), (3, 8), (29, 32), (29, 27), (23, 26), (11, 10), (22, 27), (3, 31), (23, 10), (0, 6), (15, 9), (2, 4), (7, 19), (20, 28), (6, 8), (17, 37), (14, 20), (21, 28), (14, 6), (22, 17), (9, 23), (30, 2), (11, 13), (15, 36), (20, 29), (18, 14), (10, 26), (17, 25), (30, 20), (8, 9), (12, 9), (24, 15), (6, 3), (8, 26), (24, 35), (7, 21), (2, 13), (26, 9), (28, 13), (30, 1), (29, 7), (26, 29), (20, 1), (20, 6), (1, 26), (1, 13), (5, 34), (15, 8), (22, 28), (5, 21), (27, 1), (21, 29), (24, 32), (28, 20), (23, 21), (8, 27), (20, 24), (22, 30), (5, 19), (5, 36), (10, 1), (6, 17), (12, 4), (17, 34), (23, 23), (25, 16), (23, 33), (7, 1), (1, 9), (9, 36), (2, 34), (6, 37), (1, 8), (2, 31), (4, 23), (7, 10), (26, 32), (18, 20), (4, 17), (30, 16), (28, 35), (22, 21), (6, 35), (22, 34), (30, 28), (12, 28), (20, 16), (5, 30), (19, 21), (13, 5), (20, 36), (14, 29), (17, 31), (0, 5), (9, 26), (22, 5), (10, 14), (16, 14), (28, 17), (29, 19), (18, 19), (24, 16), (3, 33), (19, 7), (8, 8), (25, 35), (9, 25), (10, 22), (7, 24), (0, 31), (4, 37), (15, 15), (0, 37), (15, 19), (3, 29), (12, 24), (21, 5), (11, 15), (6, 32), (8, 23), (3, 13), (15, 1), (7, 28), (28, 7), (6, 10), (14, 35), (25, 30), (10, 21), (23, 6), (4, 4), (28, 8), (16, 15), (30, 6), (19, 6), (1, 32), (25, 37), (19, 17), (9, 21), (23, 2), (20, 27), (13, 7), (21, 4), (24, 4), (7, 29), (4, 3), (0, 27), (23, 0), (18, 32), (13, 28), (19, 29), (26, 21), (20, 13), (28, 16), (8, 5), (19, 15), (6, 30), (16, 21), (11, 34), (23, 18), (25, 25), (24, 18), (4, 10), (26, 34), (29, 8), (29, 29), (2, 24), (4, 18), (25, 21), (11, 19), (30, 12), (15, 21), (20, 22), (0, 17), (11, 11), (13, 2), (16, 0), (15, 12), (8, 10), (12, 6), (27, 10), (9, 30), (15, 5), (15, 34), (5, 10), (24, 26), (17, 11), (30, 27), (16, 2), (12, 30), (13, 30), (10, 7), (3, 20), (1, 24), (13, 34), (2, 28), (17, 16), (12, 37), (4, 12), (8, 12), (29, 14), (0, 30), (8, 34), (18, 7), (6, 12), (6, 23), (4, 24), (19, 24), (5, 35), (11, 24), (5, 2), (21, 11), (7, 8), (11, 7), (8, 3), (21, 10), (2, 0), (9, 10), (30, 22), (28, 10), (13, 11), (21, 30), (17, 27), (4, 8), (15, 0), (28, 37), (9, 0), (11, 37), (7, 30), (2, 15), (23, 22), (0, 25), (29, 24), (25, 1), (11, 0), (6, 31), (19, 1), (30, 36), (22, 16), (23, 36), (24, 31), (13, 21), (19, 23), (2, 10), (29, 26), (7, 23), (7, 34), (14, 12), (20, 11), (19, 33), (1, 11), (11, 2), (11, 1), (8, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566082", "dataset": "MATH"}
{"messages": [{"content": "In a 32x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 29), 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), (12, 25), (26, 28), (4, 21), (22, 18), (20, 11), (17, 12), (28, 3), (4, 23), (17, 24), (17, 18), (19, 10), (21, 20), (20, 18), (12, 20), (14, 8), (22, 2), (15, 24), (18, 19), (5, 9), (2, 0), (23, 5), (6, 17), (25, 22), (24, 2), (23, 4), (25, 19), (9, 18), (28, 21), (23, 1), (3, 7), (24, 29), (31, 28), (3, 21), (29, 26), (27, 29), (29, 3), (2, 2), (12, 11), (3, 26), (29, 18), (22, 9), (30, 3), (28, 13), (21, 26), (22, 21), (27, 28), (14, 0), (5, 6), (13, 22), (21, 8), (28, 14), (15, 21), (26, 21), (20, 25), (28, 22), (2, 23), (7, 14), (12, 22), (23, 23), (7, 25), (18, 10), (20, 0), (0, 10), (1, 21), (20, 7), (1, 9), (8, 4), (1, 1), (17, 4), (20, 27), (20, 13), (13, 15), (30, 20), (22, 29), (17, 0), (15, 2), (25, 4), (29, 7), (3, 27), (2, 7), (7, 20), (26, 10), (27, 26), (23, 11), (10, 4), (31, 24), (15, 3), (29, 27), (21, 21), (21, 23), (21, 14), (25, 24), (13, 6), (0, 22), (13, 5), (10, 24), (22, 26), (26, 15), (5, 11), (23, 22), (0, 27), (14, 13), (4, 25), (5, 10), (2, 19), (30, 25), (21, 6), (1, 10), (10, 19), (12, 18), (30, 14), (23, 6), (9, 9), (16, 13), (13, 10), (0, 13), (8, 11), (21, 24), (26, 27), (23, 24), (9, 7), (17, 11), (6, 27), (24, 20), (27, 1), (14, 5), (19, 5), (10, 22), (22, 27), (7, 3), (15, 4), (26, 19), (10, 29), (29, 19), (31, 10), (22, 11), (4, 20), (17, 3), (13, 21), (22, 25), (24, 4), (31, 3), (22, 14), (1, 11), (21, 12), (19, 19), (14, 18), (5, 26), (5, 20), (8, 20), (5, 27), (29, 29), (27, 19), (28, 17), (16, 24), (18, 11), (28, 10), (10, 28), (6, 23), (2, 9), (8, 24), (12, 3), (21, 5), (27, 5), (4, 0), (18, 2), (26, 23), (5, 22), (30, 24), (4, 14), (4, 12), (19, 14), (30, 5), (30, 8), (6, 15), (9, 22), (25, 18), (20, 17), (20, 29), (21, 17), (18, 20), (22, 16), (8, 26), (21, 19), (16, 20), (21, 7), (23, 14), (24, 13), (18, 22), (0, 8), (17, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "265068", "dataset": "MATH"}
{"messages": [{"content": "In a 30x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 20), (22, 1), (10, 19), (17, 34), (13, 5), (28, 15), (3, 8), (10, 33), (8, 22), (16, 2), (20, 22), (21, 26), (22, 28), (19, 11), (22, 14), (16, 6), (8, 9), (7, 34), (8, 31), (23, 1), (3, 5), (28, 12), (9, 3), (3, 16), (0, 13), (7, 26), (25, 11), (4, 12), (4, 34), (4, 28), (21, 33), (22, 2), (9, 28), (17, 13), (23, 30), (0, 10), (25, 17), (15, 18), (15, 13), (6, 5), (5, 2), (22, 5), (1, 7), (5, 20), (24, 34), (3, 9), (28, 27), (6, 15), (2, 4), (26, 17), (3, 7), (7, 7), (11, 10), (10, 20), (15, 36), (29, 30), (9, 13), (24, 12), (17, 22), (15, 10), (10, 12), (9, 18), (6, 31), (24, 4), (29, 3), (2, 32), (13, 7), (14, 16), (11, 23), (1, 35), (29, 34), (7, 22), (8, 19), (18, 35), (27, 27), (19, 36), (13, 23), (22, 21), (13, 21), (11, 32), (19, 5), (29, 25), (21, 24), (12, 5), (16, 34), (15, 19), (6, 10), (22, 29), (22, 34), (29, 31), (11, 4), (4, 18), (3, 31), (6, 2), (1, 21), (15, 35), (27, 0), (14, 33), (17, 3), (10, 34), (24, 36), (0, 20), (1, 22), (4, 5), (22, 0), (1, 23), (15, 8), (7, 9), (25, 24), (17, 15), (1, 31), (28, 34), (14, 13), (25, 1), (21, 7), (13, 30), (18, 26), (23, 6), (13, 16), (28, 23), (8, 30), (7, 31), (27, 37), (6, 35), (19, 18), (28, 31), (26, 12), (5, 6), (6, 13), (12, 30), (18, 34), (2, 7), (1, 36), (19, 12), (16, 9), (28, 6), (17, 0), (10, 18), (23, 32), (21, 19), (21, 2), (16, 32), (29, 11), (17, 26), (14, 28), (13, 24), (26, 25), (23, 15), (7, 36), (3, 30), (3, 29), (5, 32), (9, 15), (29, 23), (16, 19), (1, 8), (11, 37), (8, 15), (22, 37), (18, 4), (4, 32), (12, 8), (15, 21), (12, 29), (26, 36), (22, 11), (28, 1), (5, 37), (29, 14), (22, 3), (6, 1), (22, 31), (28, 5), (25, 16), (29, 1), (4, 13), (29, 5), (11, 15), (0, 7), (14, 3), (22, 20), (10, 5), (13, 26), (10, 26), (7, 5), (11, 12), (21, 12), (11, 2), (16, 27), (23, 34), (26, 29), (24, 22), (2, 13), (20, 23), (25, 37), (19, 6), (19, 14), (13, 10), (11, 14), (4, 33), (5, 19), (11, 35), (24, 10), (29, 4), (7, 15), (9, 21), (18, 30), (25, 25), (12, 31), (19, 1), (20, 36), (22, 25), (21, 23), (8, 21), (29, 7), (25, 15), (13, 31), (22, 32), (1, 26), (23, 29), (15, 1), (20, 8), (14, 10), (22, 15), (23, 2), (0, 26), (11, 11), (17, 37), (0, 36), (27, 33), (24, 9), (26, 1), (27, 19), (13, 37), (27, 32), (18, 37), (14, 25), (17, 6), (28, 14), (29, 17), (18, 32), (29, 22), (22, 26), (11, 1), (8, 32), (13, 34), (26, 34), (5, 9), (24, 37), (5, 16), (5, 0), (28, 0), (10, 0), (27, 22), (14, 35), (10, 35), (4, 23), (14, 14), (17, 21), (7, 4), (20, 13), (10, 29), (18, 12), (2, 28), (20, 30), (10, 37), (16, 13), (28, 10), (23, 18), (28, 20), (24, 8), (18, 9), (14, 34), (22, 22), (0, 23), (8, 4), (21, 21), (26, 32), (16, 28), (11, 16), (2, 9), (14, 5), (22, 35), (28, 19), (15, 11), (27, 36), (3, 3), (24, 27), (0, 24), (2, 5), (23, 10), (20, 1), (7, 0), (24, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155232", "dataset": "MATH"}
{"messages": [{"content": "In a 35x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (20, 31), (31, 20), (12, 5), (10, 27), (33, 8), (26, 25), (21, 13), (2, 2), (15, 30), (1, 17), (18, 1), (23, 12), (17, 29), (20, 22), (32, 8), (17, 13), (33, 10), (24, 29), (14, 29), (30, 15), (27, 23), (21, 11), (11, 11), (25, 12), (23, 22), (5, 5), (1, 26), (30, 20), (22, 0), (28, 24), (20, 16), (28, 4), (6, 26), (7, 18), (29, 0), (9, 23), (6, 6), (16, 8), (27, 25), (26, 9), (10, 7), (34, 1), (13, 28), (20, 6), (19, 10), (10, 6), (1, 12), (15, 4), (27, 31), (23, 6), (12, 2), (25, 24), (6, 31), (24, 13), (24, 17), (1, 25), (1, 9), (0, 5), (5, 18), (15, 18), (11, 30), (10, 11), (27, 10), (17, 3), (32, 5), (18, 25), (24, 0), (3, 22), (10, 3), (3, 30), (9, 3), (34, 7), (30, 27), (10, 22), (10, 17), (23, 3), (25, 20), (34, 30), (13, 19), (2, 17), (25, 15), (21, 5), (17, 30), (2, 22), (24, 23), (26, 17), (11, 3), (19, 12), (3, 6), (33, 7), (31, 0), (2, 12), (13, 13), (22, 2), (14, 25), (15, 6), (23, 1), (2, 11), (26, 6), (16, 3), (22, 30), (22, 21), (15, 9), (34, 20), (28, 31), (2, 27), (29, 5), (27, 4), (18, 17), (34, 6), (10, 26), (32, 4), (9, 22), (12, 14), (11, 8), (22, 31), (7, 23), (18, 4), (26, 4), (14, 20), (34, 14), (9, 28), (15, 29), (21, 25), (31, 9), (15, 1), (22, 8), (17, 14), (24, 6), (6, 27), (15, 21), (8, 9), (19, 29), (9, 19), (2, 14), (34, 11), (32, 12), (31, 23), (31, 8), (29, 12), (33, 24), (16, 5), (19, 7), (22, 24), (27, 2), (22, 23), (12, 18), (1, 27), (12, 20), (33, 9), (17, 4), (31, 19), (0, 13), (5, 30), (10, 1), (14, 11), (14, 23), (21, 21), (30, 17), (7, 21), (23, 4), (13, 16), (10, 14), (5, 25), (31, 16), (30, 14), (9, 12), (18, 31), (10, 25), (1, 28), (17, 31), (32, 27), (1, 5), (9, 5), (8, 2), (17, 8), (29, 4), (12, 8), (26, 29), (7, 17), (28, 2), (0, 3), (8, 21), (29, 20), (32, 26), (29, 8), (12, 6), (18, 6), (11, 18), (14, 24), (21, 20), (4, 0), (29, 9), (29, 31), (12, 12), (31, 26), (24, 7), (13, 15), (8, 19), (28, 14), (16, 6), (13, 17), (13, 21), (23, 29), (28, 22), (26, 15), (4, 18), (5, 31), (31, 17), (4, 21), (13, 7), (6, 28), (16, 11), (11, 15), (13, 4), (21, 2), (32, 25), (29, 10), (26, 22), (21, 15), (11, 13), (20, 5), (24, 2), (17, 10), (2, 24), (34, 13), (19, 24), (17, 26), (25, 21), (13, 14), (12, 25), (31, 18), (28, 13), (6, 13), (4, 15), (4, 7), (12, 22), (7, 27), (3, 14), (16, 30), (20, 27), (17, 25), (7, 9), (9, 15), (28, 17), (7, 3), (16, 17), (0, 8), (5, 3), (11, 17), (33, 21), (25, 10), (7, 10), (24, 20), (19, 5), (24, 21), (5, 4), (9, 0), (20, 18), (29, 29), (9, 21), (16, 16), (15, 23), (21, 3), (10, 16), (4, 13), (28, 3), (2, 29), (14, 3), (21, 6), (0, 11), (0, 29), (19, 13), (4, 31), (31, 29), (14, 27), (29, 24), (24, 9), (33, 1), (28, 29), (13, 1), (6, 3), (34, 23), (22, 1), (1, 7), (13, 31), (25, 2), (20, 3), (2, 10), (33, 0), (18, 7), (34, 29), (4, 5), (13, 5), (0, 21), (22, 25), (18, 26), (14, 13), (13, 29), (4, 11), (20, 21), (14, 18), (6, 12), (13, 11), (21, 12), (0, 27), (5, 27), (10, 12), (22, 11), (9, 16), (6, 23), (21, 26), (3, 21), (6, 15), (23, 2), (10, 31), (19, 22), (28, 16), (30, 4), (6, 9), (24, 31), (5, 26), (28, 28), (18, 14), (17, 6), (5, 6), (6, 29), (4, 3), (8, 0), (1, 18), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "964224", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (33, 32), (28, 1), (21, 2), (19, 24), (26, 17), (28, 3), (20, 33), (14, 22), (7, 14), (28, 27), (20, 14), (7, 15), (32, 12), (35, 27), (19, 25), (30, 15), (14, 29), (35, 30), (26, 33), (0, 6), (3, 10), (33, 5), (22, 15), (9, 3), (23, 2), (32, 24), (24, 5), (9, 20), (9, 31), (28, 20), (22, 8), (35, 7), (26, 32), (30, 25), (24, 18), (25, 23), (14, 23), (0, 33), (20, 19), (34, 21), (11, 9), (30, 12), (13, 8), (14, 0), (24, 7), (7, 11), (32, 31), (21, 33), (29, 7), (17, 1), (6, 22), (35, 14), (8, 0), (14, 14), (27, 21), (22, 9), (33, 6), (30, 33), (25, 7), (5, 28), (7, 20), (31, 4), (25, 22), (2, 10), (29, 18), (20, 7), (17, 8), (22, 19), (28, 25), (14, 11), (17, 23), (2, 24), (28, 26), (25, 33), (33, 21), (25, 3), (1, 19), (29, 12), (12, 8), (19, 4), (20, 1), (3, 26), (34, 10), (22, 16), (25, 1), (10, 25), (17, 12), (5, 9), (8, 33), (19, 3), (21, 10), (3, 16), (15, 1), (6, 13), (17, 6), (0, 8), (35, 17), (29, 3), (27, 12), (14, 4), (33, 2), (10, 9), (18, 20), (25, 28), (16, 18), (24, 28), (17, 28), (5, 23), (18, 29), (16, 8), (8, 31), (34, 9), (4, 20), (33, 11), (21, 25), (27, 0), (8, 1), (17, 30), (24, 16), (13, 7), (23, 3), (32, 21), (9, 4), (18, 22), (24, 6), (25, 16), (20, 5), (3, 24), (20, 10), (5, 16), (31, 31), (7, 26), (10, 1), (10, 15), (22, 12), (34, 11), (20, 24), (9, 21), (28, 9), (21, 8), (13, 33), (30, 30), (10, 32), (33, 10), (28, 11), (2, 34), (10, 16), (3, 13), (35, 5), (4, 33), (7, 18), (15, 10), (19, 15), (29, 16), (19, 31), (16, 7), (5, 2), (30, 23), (0, 29), (29, 5), (29, 28), (11, 26), (21, 32), (12, 21), (31, 33), (3, 18), (25, 11), (13, 32), (12, 7), (21, 14), (10, 24), (15, 6), (23, 33), (27, 2), (26, 4), (24, 11), (27, 7), (14, 6), (3, 22), (2, 26), (9, 26), (30, 26), (24, 20), (18, 19), (31, 13), (2, 21), (31, 15), (10, 23), (29, 1), (15, 17), (14, 3), (13, 9), (32, 22), (1, 33), (28, 28), (19, 30), (7, 17), (27, 4), (1, 26), (17, 19), (19, 16), (17, 9), (11, 20), (32, 7), (25, 10), (1, 4), (19, 21), (27, 32), (10, 33), (8, 14), (34, 3), (27, 8), (2, 15), (29, 25), (11, 11), (13, 2), (30, 27), (17, 16), (9, 6), (24, 31), (25, 6), (24, 26), (17, 11), (35, 32), (8, 3), (20, 15), (23, 8), (15, 7), (21, 30), (4, 18), (35, 28), (5, 8), (34, 0), (22, 32), (15, 8), (34, 31), (34, 19), (23, 21), (20, 30), (35, 19), (26, 27), (26, 25), (5, 33), (25, 0), (26, 7), (26, 30), (29, 20), (13, 22), (33, 29), (33, 23), (15, 31), (35, 12), (15, 25), (25, 31), (8, 6), (25, 5), (3, 15), (7, 2), (28, 30), (2, 12), (20, 22), (27, 20), (13, 0), (31, 5), (9, 18), (10, 3), (18, 33), (13, 19), (18, 25), (9, 9), (35, 25), (15, 9), (22, 22), (1, 1), (2, 28), (29, 8), (22, 31), (12, 17), (18, 8), (30, 1), (19, 7), (35, 29), (28, 29), (13, 34), (30, 28), (33, 0), (16, 19), (29, 19), (17, 7), (8, 2), (5, 6), (25, 4), (22, 6), (12, 16), (0, 19), (29, 32), (2, 6), (12, 19), (3, 3), (15, 21), (14, 34), (7, 21), (34, 13), (21, 15), (35, 22), (5, 7), (12, 1), (22, 34), (18, 30), (8, 17), (0, 27), (9, 2), (15, 16), (24, 22), (20, 16), (15, 23), (21, 4), (19, 6), (1, 7), (6, 12), (1, 28), (7, 32), (11, 12), (1, 8), (33, 7), (8, 16), (19, 0), (32, 14), (25, 15), (14, 25), (9, 17), (20, 18), (13, 11), (30, 14), (7, 8), (14, 27), (16, 9), (2, 33), (5, 1), (20, 29), (5, 11), (33, 8), (16, 31), (7, 24), (28, 12), (35, 11), (27, 1), (0, 3), (27, 18), (11, 1), (30, 5), (0, 17), (34, 29), (34, 15), (16, 21), (6, 18), (4, 17), (20, 34), (23, 25), (32, 20), (16, 32), (13, 25), (31, 22), (1, 16), (22, 25), (35, 20), (24, 14), (16, 14), (21, 1), (22, 7), (22, 0), (31, 32), (12, 11), (29, 11), (15, 20), (34, 23), (14, 21), (26, 13), (34, 22), (32, 3), (9, 11), (1, 23), (9, 5), (0, 26), (32, 19), (34, 2), (6, 32), (21, 3), (22, 24), (31, 11), (11, 7), (9, 19), (7, 10), (7, 29), (15, 30), (24, 17), (21, 26), (32, 30), (12, 33), (6, 3), (33, 24), (25, 30), (35, 9), (28, 2), (5, 19), (2, 8), (5, 34), (24, 4), (13, 14), (10, 22), (30, 0), (32, 10), (32, 18), (16, 10), (26, 2), (23, 34), (13, 1), (21, 20), (23, 22), (30, 3), (17, 14), (13, 21), (29, 0), (27, 10), (29, 13), (15, 22), (13, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874944", "dataset": "MATH"}
{"messages": [{"content": "In a 34x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (31, 2), (4, 16), (10, 0), (9, 22), (6, 16), (19, 3), (18, 29), (8, 12), (7, 14), (0, 11), (20, 23), (5, 29), (12, 8), (4, 22), (9, 17), (27, 4), (1, 22), (5, 16), (22, 27), (31, 11), (13, 28), (7, 7), (8, 1), (21, 4), (1, 8), (12, 25), (13, 24), (20, 31), (0, 13), (5, 15), (25, 19), (20, 12), (20, 19), (18, 8), (7, 19), (29, 3), (5, 18), (3, 31), (16, 7), (5, 2), (29, 8), (9, 12), (15, 3), (16, 17), (32, 9), (26, 10), (2, 21), (33, 24), (15, 25), (12, 12), (3, 19), (28, 19), (7, 0), (33, 7), (16, 2), (6, 13), (26, 3), (9, 8), (33, 9), (9, 20), (1, 20), (19, 14), (25, 28), (18, 26), (30, 26), (7, 6), (11, 9), (3, 23), (18, 14), (13, 4), (18, 5), (23, 12), (15, 17), (20, 10), (22, 29), (18, 22), (21, 0), (33, 20), (8, 7), (10, 8), (20, 14), (21, 7), (15, 23), (17, 29), (4, 28), (5, 26), (16, 29), (31, 22), (26, 16), (6, 22), (0, 20), (26, 31), (24, 20), (8, 3), (16, 22), (26, 14), (10, 25), (10, 23), (6, 6), (22, 0), (19, 26), (22, 19), (9, 11), (30, 28), (14, 2), (6, 28), (33, 6), (30, 23), (9, 6), (1, 31), (31, 17), (25, 21), (0, 21), (18, 19), (26, 9), (32, 20), (3, 2), (27, 16), (15, 14), (27, 10), (14, 25), (27, 25), (31, 0), (9, 7), (29, 25), (1, 12), (27, 7), (2, 16), (1, 3), (27, 0), (19, 22), (28, 26), (24, 1), (11, 12), (13, 14), (3, 27), (11, 29), (13, 2), (24, 21), (6, 15), (31, 5), (12, 4), (13, 9), (2, 2), (18, 18), (30, 17), (19, 21), (25, 11), (24, 0), (26, 6), (4, 20), (7, 10), (23, 17), (10, 14), (13, 6), (21, 5), (26, 20), (17, 5), (11, 7), (17, 30), (30, 15), (15, 22), (9, 1), (1, 16), (25, 9), (13, 21), (15, 24), (7, 1), (22, 11), (25, 16), (28, 31), (24, 5), (21, 1), (28, 17), (18, 1), (17, 12), (6, 10), (2, 22), (16, 27), (29, 24), (22, 8), (6, 27), (4, 11), (2, 25), (23, 5), (8, 10), (2, 5), (3, 13), (1, 5), (29, 2), (28, 16), (18, 4), (32, 0), (31, 27), (11, 10), (0, 8), (11, 30), (9, 23), (13, 25), (18, 13), (12, 29), (0, 16), (6, 29), (31, 21), (21, 31), (20, 15), (18, 28), (0, 1), (14, 13), (15, 0), (10, 20), (6, 18), (30, 16), (24, 28), (11, 5), (33, 27), (7, 17), (5, 7), (11, 23), (26, 8), (32, 18), (29, 23), (31, 25), (27, 23), (13, 7), (16, 31), (30, 14), (33, 13), (6, 20), (10, 17), (8, 26), (17, 21), (27, 27), (18, 2), (7, 26), (26, 12), (23, 28), (4, 9), (8, 27), (0, 29), (28, 18), (1, 4), (24, 2), (6, 17), (21, 11), (16, 5), (15, 1), (15, 19), (22, 30), (9, 3), (32, 1), (22, 10), (28, 24), (8, 25), (30, 31), (23, 1), (31, 12), (24, 3), (21, 28), (30, 3), (28, 12), (21, 8), (28, 25), (2, 15), (28, 29), (14, 3), (30, 1), (29, 22), (3, 20), (14, 11), (22, 13), (14, 26), (24, 13), (0, 28), (14, 9), (13, 30), (17, 27), (21, 16), (1, 11), (5, 10), (24, 31), (12, 10), (5, 22), (16, 18), (19, 13), (7, 31), (1, 6), (3, 3), (23, 29), (29, 6), (16, 14), (23, 14), (0, 30), (23, 24), (13, 8), (28, 30), (15, 12), (0, 19), (6, 14), (22, 7), (5, 9), (2, 20), (19, 12), (16, 21), (23, 10), (11, 28), (33, 1), (1, 23), (0, 24), (5, 12), (1, 19), (25, 13), (4, 25), (11, 3), (3, 14), (13, 3), (4, 27), (24, 16), (27, 2), (31, 18), (20, 6), (2, 7), (17, 14), (10, 29), (32, 17), (7, 12), (1, 28), (18, 12), (28, 3), (31, 19), (23, 11), (7, 16), (21, 21), (14, 15), (25, 23), (33, 0), (6, 5), (30, 30), (12, 9), (15, 27), (23, 30), (31, 16), (1, 24), (33, 4), (2, 1), (11, 1), (15, 13), (8, 24), (5, 28), (31, 7), (10, 21), (13, 20), (13, 12), (8, 6), (18, 15), (26, 15), (29, 13), (14, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744480", "dataset": "MATH"}
{"messages": [{"content": "In a 34x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 32), 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), (24, 0), (32, 14), (27, 8), (32, 21), (22, 17), (17, 22), (4, 20), (31, 10), (20, 17), (14, 4), (28, 15), (1, 24), (33, 11), (16, 23), (16, 20), (15, 23), (13, 2), (22, 10), (17, 28), (2, 5), (16, 5), (22, 29), (0, 6), (24, 21), (16, 14), (12, 15), (15, 18), (20, 11), (3, 9), (11, 8), (33, 15), (18, 13), (7, 11), (4, 25), (19, 7), (2, 15), (5, 20), (23, 16), (33, 25), (10, 0), (13, 29), (7, 7), (6, 23), (5, 23), (14, 22), (6, 1), (22, 24), (15, 4), (17, 21), (20, 10), (19, 20), (2, 9), (27, 31), (3, 13), (20, 29), (26, 16), (16, 13), (7, 18), (24, 5), (9, 19), (25, 10), (27, 13), (22, 7), (2, 7), (23, 21), (10, 31), (13, 15), (20, 1), (28, 13), (16, 32), (29, 29), (21, 1), (28, 0), (1, 21), (20, 18), (5, 2), (9, 7), (7, 20), (26, 0), (0, 32), (9, 3), (2, 18), (20, 32), (25, 5), (23, 24), (12, 20), (25, 17), (27, 30), (29, 1), (33, 4), (11, 17), (16, 9), (22, 15), (22, 20), (15, 9), (2, 13), (23, 22), (20, 4), (33, 21), (4, 26), (24, 19), (31, 12), (0, 5), (30, 11), (9, 6), (15, 30), (26, 10), (32, 16), (4, 30), (17, 20), (31, 26), (23, 23), (8, 14), (14, 13), (8, 0), (15, 2), (10, 4), (1, 22), (9, 1), (25, 16), (25, 0), (29, 30), (0, 21), (4, 3), (17, 29), (1, 4), (13, 13), (32, 15), (17, 5), (16, 22), (30, 4), (24, 9), (24, 8), (7, 29), (1, 26), (3, 19), (9, 2), (11, 25), (10, 5), (6, 24), (23, 13), (17, 2), (15, 28), (10, 24), (24, 26), (31, 9), (12, 13), (18, 0), (7, 24), (29, 13), (1, 17), (15, 29), (21, 14), (22, 27), (13, 21), (6, 26), (26, 4), (10, 17), (8, 11), (5, 0), (30, 24), (18, 10), (6, 20), (21, 2), (17, 8), (28, 21), (31, 23), (2, 6), (24, 11), (1, 15), (26, 19), (29, 23), (32, 20), (3, 8), (24, 2), (26, 22), (26, 18), (24, 4), (15, 25), (25, 15), (3, 3), (31, 28), (32, 17), (12, 5), (23, 32), (23, 0), (9, 27), (1, 11), (6, 0), (14, 23), (25, 14), (4, 22), (4, 12), (14, 21), (31, 7), (22, 22), (14, 18), (7, 3), (33, 1), (19, 26), (20, 16), (24, 30), (26, 2), (7, 26), (1, 25), (25, 28), (21, 12), (0, 28), (9, 23), (25, 23), (22, 21), (10, 28), (27, 29), (9, 21), (10, 21), (16, 3), (12, 12), (9, 22), (23, 27), (27, 23), (22, 26), (5, 26), (21, 5), (1, 32), (2, 10), (18, 5), (14, 14), (33, 10), (3, 21), (8, 12), (14, 27), (33, 0), (32, 12), (10, 26), (5, 32), (20, 9), (7, 17), (28, 11), (4, 27), (3, 11), (2, 31), (27, 14), (19, 17), (0, 26), (26, 8), (19, 24), (6, 18), (25, 26), (26, 6), (20, 19), (32, 27), (28, 25), (12, 4), (29, 7), (29, 22), (29, 28), (7, 9), (0, 10), (27, 6), (7, 16), (8, 13), (29, 2), (15, 6), (18, 24), (20, 21), (13, 32), (6, 6), (30, 18), (24, 16), (24, 31), (25, 3), (8, 30), (0, 4), (13, 9), (23, 1), (13, 22), (2, 11), (12, 23), (1, 14), (7, 22), (27, 10), (11, 29), (14, 28), (29, 15), (19, 31), (12, 1), (13, 1), (17, 13), (14, 25), (11, 2), (5, 24), (30, 6), (13, 17), (33, 31), (9, 15), (25, 21), (5, 22), (33, 7), (11, 22), (23, 14), (19, 11), (12, 21), (0, 2), (29, 31), (10, 20), (29, 14), (28, 8), (11, 0), (28, 3), (10, 32), (27, 0), (18, 15), (8, 20), (30, 9), (32, 11), (26, 27), (4, 21), (23, 5), (6, 15), (9, 10), (6, 3), (30, 15), (11, 7), (32, 0), (24, 12), (4, 4), (13, 12), (29, 4), (31, 8), (29, 26), (23, 2), (1, 28), (30, 20), (21, 26), (23, 30), (9, 18), (14, 3), (20, 24), (29, 18), (20, 0), (1, 30), (10, 27), (18, 28), (11, 18), (3, 0), (16, 15), (9, 32), (11, 9), (28, 27), (0, 25), (27, 3), (14, 17), (4, 5), (33, 27), (13, 6), (25, 9), (13, 7), (10, 16), (10, 15), (13, 27), (9, 25), (7, 30), (12, 28), (4, 1), (27, 1), (10, 18), (25, 19), (2, 17), (31, 25), (12, 17), (7, 25), (11, 27), (1, 3), (29, 6), (27, 32), (0, 13), (30, 14), (14, 29), (32, 8), (25, 24), (15, 19), (25, 8), (15, 15), (28, 10), (26, 15), (15, 24), (20, 5), (22, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979200", "dataset": "MATH"}
{"messages": [{"content": "In a 32x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 31), 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), (30, 26), (12, 8), (17, 19), (13, 9), (26, 11), (3, 25), (3, 5), (1, 14), (18, 5), (13, 27), (7, 24), (29, 20), (10, 8), (0, 2), (11, 18), (17, 13), (23, 8), (11, 27), (19, 31), (15, 13), (30, 31), (5, 7), (28, 21), (4, 16), (27, 25), (14, 8), (24, 31), (3, 0), (24, 18), (5, 18), (31, 29), (10, 18), (18, 8), (25, 27), (31, 16), (7, 22), (7, 3), (30, 15), (2, 4), (23, 13), (20, 12), (20, 26), (17, 22), (2, 6), (11, 10), (27, 11), (25, 25), (2, 13), (28, 28), (18, 12), (12, 21), (12, 1), (7, 13), (3, 1), (17, 29), (2, 16), (8, 21), (3, 8), (6, 6), (18, 2), (28, 29), (28, 13), (24, 3), (26, 31), (28, 7), (17, 18), (19, 8), (19, 16), (1, 3), (27, 22), (25, 30), (0, 15), (7, 30), (4, 14), (25, 20), (28, 8), (23, 20), (29, 10), (17, 16), (23, 3), (0, 10), (20, 14), (7, 21), (10, 4), (15, 18), (6, 2), (5, 6), (13, 7), (2, 8), (4, 18), (15, 5), (16, 5), (17, 0), (28, 11), (23, 29), (27, 2), (7, 29), (30, 0), (4, 28), (27, 23), (2, 15), (19, 6), (27, 12), (29, 13), (16, 3), (0, 14), (29, 30), (22, 20), (3, 28), (18, 21), (22, 21), (7, 10), (31, 28), (8, 18), (15, 9), (14, 20), (20, 11), (6, 25), (11, 28), (28, 4), (15, 8), (13, 23), (11, 23), (6, 7), (20, 30), (17, 31), (25, 7), (21, 31), (20, 28), (24, 0), (20, 7), (20, 23), (7, 26), (4, 11), (29, 31), (23, 0), (27, 9), (6, 5), (31, 22), (26, 1), (0, 23), (7, 7), (21, 14), (12, 31), (28, 20), (12, 3), (19, 26), (26, 5), (26, 7), (0, 20), (22, 2), (22, 5), (13, 28), (24, 26), (20, 6), (19, 18), (3, 6), (7, 16), (15, 7), (9, 16), (11, 14), (18, 3), (26, 25), (13, 22), (21, 4), (21, 13), (29, 18), (26, 20), (5, 0), (8, 29), (29, 12), (28, 26), (4, 0), (1, 22), (8, 14), (19, 22), (6, 21), (10, 27), (30, 24), (3, 7), (29, 21), (4, 23), (25, 5), (18, 22), (29, 1), (15, 27), (19, 2), (24, 16), (27, 21), (5, 28), (22, 12), (15, 11), (13, 5), (28, 14), (5, 29), (11, 6), (4, 12), (1, 15), (12, 13), (8, 11), (10, 1), (14, 2), (12, 11), (28, 9), (22, 27), (13, 15), (0, 16), (31, 2), (19, 19), (22, 14), (1, 26), (6, 15), (30, 23), (22, 23), (16, 30), (23, 14), (4, 9), (14, 21), (9, 20), (10, 9), (14, 3), (22, 28), (11, 0), (27, 19), (19, 4), (17, 21), (8, 26), (3, 20), (14, 17), (29, 4), (26, 2), (16, 19), (1, 21), (21, 28), (27, 10), (16, 14), (12, 10), (9, 11), (20, 10), (14, 5), (11, 29), (26, 3), (2, 22), (23, 30), (10, 30), (21, 21), (30, 5), (7, 19), (1, 11), (26, 17), (10, 20), (24, 6), (10, 16), (31, 15), (26, 16), (1, 24), (7, 0), (8, 19), (9, 21), (21, 27), (14, 4), (9, 9), (15, 20), (10, 14), (20, 21), (11, 20), (0, 29), (0, 22), (4, 25), (18, 19), (16, 0), (1, 25), (3, 11), (11, 13), (17, 15), (29, 17), (10, 28), (18, 4), (14, 19), (29, 2), (31, 3), (10, 10), (23, 27), (24, 22), (3, 4), (3, 10), (8, 2), (5, 24), (5, 17), (15, 4), (3, 31), (20, 5), (16, 31), (2, 14), (4, 2), (13, 20), (25, 11), (18, 29), (31, 27), (16, 13), (31, 0), (30, 20), (15, 19), (19, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "758400", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), 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), (22, 28), (32, 7), (29, 2), (33, 25), (2, 33), (33, 21), (31, 17), (11, 24), (16, 33), (29, 25), (18, 0), (24, 12), (2, 1), (8, 28), (24, 20), (36, 16), (35, 8), (23, 25), (21, 33), (10, 18), (12, 12), (36, 1), (23, 28), (0, 1), (31, 12), (17, 11), (3, 18), (10, 30), (25, 5), (32, 17), (1, 27), (7, 4), (19, 26), (22, 7), (29, 13), (16, 4), (22, 15), (11, 13), (23, 31), (34, 2), (21, 1), (31, 32), (8, 33), (25, 31), (22, 22), (12, 3), (13, 22), (14, 32), (4, 3), (11, 18), (0, 8), (31, 0), (16, 7), (35, 31), (7, 5), (25, 3), (26, 12), (14, 22), (11, 11), (35, 17), (14, 28), (4, 28), (10, 7), (35, 2), (0, 26), (17, 2), (28, 27), (35, 28), (7, 17), (13, 20), (20, 3), (6, 2), (21, 20), (6, 33), (35, 21), (1, 18), (27, 19), (6, 30), (30, 10), (16, 1), (14, 4), (18, 2), (21, 31), (27, 8), (7, 30), (3, 27), (33, 12), (21, 27), (4, 21), (33, 8), (35, 19), (6, 5), (2, 4), (12, 22), (6, 25), (27, 7), (5, 20), (14, 7), (2, 10), (13, 11), (23, 22), (29, 17), (12, 27), (11, 29), (7, 1), (10, 12), (23, 19), (6, 28), (11, 27), (15, 28), (28, 32), (32, 3), (5, 3), (24, 7), (22, 23), (24, 30), (0, 25), (23, 33), (26, 16), (2, 17), (18, 19), (31, 27), (30, 5), (6, 27), (19, 22), (6, 23), (11, 20), (19, 23), (27, 30), (25, 2), (26, 24), (21, 13), (31, 9), (25, 23), (2, 23), (6, 1), (26, 4), (19, 28), (24, 10), (2, 3), (21, 16), (35, 27), (18, 27), (26, 28), (0, 12), (31, 10), (8, 16), (27, 2), (24, 9), (9, 12), (1, 19), (9, 8), (33, 6), (27, 6), (36, 24), (18, 28), (29, 31), (34, 20), (3, 13), (29, 26), (5, 8), (26, 18), (31, 16), (18, 10), (28, 16), (36, 11), (6, 29), (16, 10), (26, 9), (9, 28), (34, 30), (1, 16), (12, 16), (15, 33), (2, 11), (22, 13), (11, 23), (3, 15), (19, 1), (31, 8), (18, 31), (0, 27), (18, 22), (14, 18), (19, 20), (31, 18), (4, 14), (36, 3), (24, 13), (22, 12), (17, 33), (36, 19), (9, 14), (17, 0), (2, 20), (20, 19), (32, 16), (22, 9), (26, 32), (23, 5), (33, 1), (28, 28), (11, 10), (22, 26), (15, 13), (34, 31), (16, 11), (16, 13), (2, 27), (8, 8), (27, 27), (13, 31), (0, 11), (14, 33), (27, 25), (34, 25), (15, 23), (23, 12), (6, 3), (4, 10), (14, 31), (13, 17), (14, 3), (28, 4), (15, 1), (30, 1), (30, 24), (35, 26), (28, 9), (20, 15), (10, 20), (9, 32), (13, 15), (25, 32), (33, 2), (10, 1), (27, 20), (2, 12), (22, 1), (2, 8), (35, 22), (28, 19), (29, 14), (21, 15), (28, 12), (14, 9), (25, 14), (29, 30), (23, 7), (3, 30), (22, 6), (1, 17), (1, 23), (19, 2), (12, 5), (11, 31), (9, 7), (26, 0), (9, 10), (20, 32), (25, 21), (5, 11), (30, 21), (16, 24), (14, 5), (23, 32), (8, 23), (6, 20), (6, 4), (17, 13), (9, 4), (29, 32), (34, 5), (16, 18), (8, 12), (12, 24), (25, 28), (24, 6), (26, 26), (1, 9), (11, 26), (26, 14), (3, 4), (15, 3), (11, 28), (36, 10), (24, 25), (9, 21), (24, 21), (33, 32), (28, 33), (11, 12), (28, 22), (16, 22), (0, 17), (4, 12), (16, 12), (24, 3), (32, 26), (5, 27), (26, 2), (12, 21), (3, 23), (10, 21), (28, 3), (5, 14), (6, 11), (32, 24), (13, 26), (31, 14), (14, 6), (20, 28), (23, 20), (7, 12), (27, 33), (25, 1), (19, 33), (15, 17), (23, 4), (8, 25), (2, 30), (5, 5), (4, 19), (10, 22), (29, 12), (0, 19), (12, 2), (23, 6), (30, 31), (12, 0), (23, 26), (19, 19), (22, 3), (5, 24), (18, 11), (30, 11), (2, 13), (13, 27), (26, 22), (23, 2), (10, 5), (21, 0), (35, 9), (27, 12), (19, 15), (35, 32), (4, 13), (18, 30), (10, 15), (6, 31), (13, 18), (17, 27), (26, 33), (21, 25), (4, 30), (20, 25), (26, 6), (2, 22), (35, 11), (23, 13), (1, 33), (34, 1), (23, 10), (5, 12), (24, 31), (24, 16), (0, 14), (24, 26), (6, 17), (8, 1), (3, 25), (0, 23), (21, 32), (2, 31), (15, 29), (19, 9), (34, 8), (8, 6), (19, 16), (30, 7), (4, 23), (30, 23), (5, 4), (11, 4), (0, 29), (3, 22), (9, 1), (20, 24), (31, 5), (20, 14), (31, 15), (13, 13), (28, 29), (24, 4), (15, 9), (12, 18), (22, 31), (31, 33), (34, 18), (13, 32), (36, 18), (5, 26), (17, 18), (3, 32), (5, 15), (29, 6), (33, 28), (1, 14), (16, 21), (9, 25), (16, 32), (22, 32), (17, 5), (17, 22), (6, 19), (15, 0), (4, 0), (15, 30), (3, 2), (33, 33), (31, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "952320", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 10), (8, 11), (28, 26), (31, 7), (21, 20), (21, 28), (7, 19), (11, 2), (22, 24), (0, 14), (19, 25), (8, 5), (31, 14), (15, 2), (25, 31), (10, 25), (13, 10), (30, 32), (24, 8), (0, 2), (8, 18), (31, 12), (23, 32), (30, 27), (26, 0), (24, 7), (21, 23), (8, 19), (4, 10), (13, 25), (12, 25), (17, 21), (26, 7), (28, 1), (19, 26), (3, 25), (11, 10), (16, 11), (31, 23), (4, 15), (25, 10), (18, 5), (29, 15), (1, 4), (13, 2), (12, 20), (17, 23), (5, 28), (31, 32), (32, 28), (31, 3), (6, 15), (7, 6), (6, 9), (15, 30), (15, 4), (19, 11), (19, 8), (7, 25), (15, 26), (25, 33), (4, 31), (30, 5), (11, 3), (11, 13), (8, 4), (11, 30), (8, 14), (10, 4), (1, 20), (19, 19), (33, 9), (25, 19), (27, 7), (20, 25), (18, 7), (27, 15), (17, 7), (7, 5), (30, 29), (26, 16), (31, 19), (27, 11), (11, 29), (25, 8), (26, 23), (7, 29), (9, 33), (1, 29), (16, 4), (17, 8), (25, 6), (12, 3), (6, 6), (14, 12), (1, 28), (28, 17), (11, 31), (21, 0), (18, 30), (17, 27), (9, 4), (19, 4), (33, 22), (21, 29), (1, 25), (29, 32), (16, 29), (7, 12), (33, 8), (28, 11), (20, 4), (29, 5), (8, 10), (0, 18), (28, 4), (2, 31), (21, 33), (31, 15), (2, 13), (17, 9), (4, 4), (23, 20), (19, 13), (33, 7), (26, 15), (9, 20), (22, 5), (0, 25), (33, 5), (24, 12), (27, 20), (13, 14), (4, 9), (12, 8), (32, 25), (13, 20), (1, 21), (5, 3), (30, 2), (26, 14), (7, 27), (9, 18), (19, 21), (18, 3), (6, 10), (9, 23), (30, 21), (7, 18), (29, 14), (14, 9), (16, 14), (15, 13), (11, 9), (22, 31), (27, 24), (13, 11), (33, 11), (27, 32), (6, 4), (26, 33), (32, 13), (25, 9), (13, 30), (21, 26), (21, 15), (27, 0), (18, 23), (6, 11), (21, 22), (14, 2), (32, 24), (5, 14), (26, 1), (25, 0), (13, 18), (13, 16), (30, 25), (1, 3), (13, 22), (30, 11), (16, 15), (25, 28), (7, 32), (2, 29), (32, 31), (9, 31), (28, 7), (12, 19), (1, 8), (11, 11), (32, 23), (17, 31), (15, 17), (9, 16), (5, 9), (22, 1), (11, 16), (14, 21), (2, 21), (12, 22), (7, 31), (21, 13), (23, 7), (1, 15), (3, 19), (20, 27), (9, 2), (4, 2), (19, 18), (3, 2), (15, 27), (32, 29), (0, 19), (3, 1), (24, 29), (25, 30), (26, 30), (4, 7), (11, 32), (0, 22), (30, 18), (23, 4), (1, 0), (29, 3), (6, 23), (27, 1), (24, 4), (15, 19), (22, 10), (10, 21), (5, 0), (19, 20), (27, 30), (9, 14), (28, 30), (3, 27), (25, 32), (33, 3), (16, 30), (13, 17), (15, 8), (23, 25), (23, 23), (23, 0), (15, 21), (6, 12), (12, 4), (6, 31), (14, 25), (30, 6), (15, 15), (13, 12), (1, 5), (23, 9), (15, 1), (33, 25), (10, 14), (7, 9), (4, 27), (14, 13), (26, 6), (17, 6), (31, 8), (30, 23), (3, 11), (27, 4), (3, 15), (18, 17), (19, 30), (1, 18), (27, 22), (2, 1), (24, 10), (7, 20), (1, 12), (19, 9), (25, 24), (3, 32), (31, 1), (0, 16), (2, 22), (13, 27), (3, 3), (31, 4), (4, 28), (22, 7), (7, 22), (24, 19), (26, 27), (27, 9), (3, 26), (26, 31), (31, 25), (10, 15), (7, 23), (9, 11), (3, 20), (31, 26), (16, 26), (32, 14), (32, 27), (28, 16), (10, 3), (23, 1), (8, 31), (20, 24), (16, 1), (23, 16), (10, 28), (4, 8), (28, 29), (5, 8), (5, 16), (27, 16), (23, 33), (13, 19), (28, 31), (4, 22), (25, 12), (19, 10), (2, 27), (28, 9), (16, 18), (32, 5), (21, 8), (20, 20), (24, 31), (20, 31), (3, 14), (30, 20), (16, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845880", "dataset": "MATH"}
{"messages": [{"content": "In a 32x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 33), (9, 15), (3, 20), (15, 1), (10, 14), (10, 20), (18, 19), (8, 35), (27, 16), (27, 27), (31, 17), (25, 14), (10, 17), (20, 12), (8, 0), (28, 1), (26, 34), (12, 25), (7, 22), (14, 29), (22, 6), (1, 3), (29, 8), (16, 12), (1, 6), (2, 15), (12, 31), (19, 5), (16, 16), (5, 14), (5, 29), (30, 1), (10, 25), (5, 31), (31, 25), (6, 35), (6, 20), (28, 4), (30, 31), (6, 22), (22, 22), (12, 7), (14, 9), (4, 20), (5, 2), (17, 30), (6, 9), (29, 24), (23, 17), (25, 7), (12, 21), (8, 7), (3, 22), (21, 28), (9, 28), (14, 26), (3, 34), (15, 34), (25, 0), (3, 16), (9, 10), (5, 34), (20, 19), (14, 17), (4, 10), (18, 13), (4, 25), (17, 0), (4, 0), (3, 12), (21, 20), (7, 24), (1, 0), (18, 25), (0, 31), (21, 30), (15, 5), (7, 11), (14, 5), (10, 34), (16, 21), (6, 1), (19, 13), (3, 26), (28, 25), (21, 26), (31, 19), (16, 24), (4, 8), (27, 1), (14, 27), (30, 27), (10, 12), (3, 32), (13, 33), (30, 16), (17, 17), (7, 15), (8, 29), (19, 17), (10, 5), (16, 10), (21, 34), (8, 18), (21, 1), (15, 22), (2, 34), (27, 30), (19, 26), (28, 10), (1, 18), (1, 28), (0, 12), (21, 24), (29, 11), (22, 9), (5, 28), (31, 23), (25, 35), (20, 21), (13, 13), (3, 24), (30, 30), (9, 19), (20, 7), (15, 10), (11, 16), (4, 12), (26, 7), (16, 7), (17, 26), (29, 23), (3, 11), (8, 19), (3, 2), (16, 6), (4, 7), (30, 32), (19, 28), (12, 28), (23, 8), (14, 16), (27, 31), (25, 9), (22, 27), (11, 12), (15, 21), (22, 4), (4, 19), (18, 8), (5, 9), (8, 25), (15, 14), (29, 7), (29, 2), (24, 35), (23, 13), (14, 35), (13, 22), (26, 17), (26, 5), (21, 18), (8, 31), (1, 31), (20, 30), (31, 30), (9, 25), (27, 5), (28, 17), (11, 26), (16, 22), (25, 25), (9, 2), (8, 26), (4, 4), (15, 31), (12, 14), (7, 1), (18, 18), (9, 9), (5, 0), (12, 19), (2, 18), (10, 33), (0, 6), (11, 7), (13, 3), (29, 1), (14, 8), (9, 35), (6, 19), (22, 5), (14, 19), (8, 2), (29, 20), (3, 23), (1, 20), (9, 12), (4, 5), (7, 26), (1, 30), (22, 20), (18, 16), (0, 27), (13, 35), (31, 7), (27, 17), (8, 10), (7, 28), (6, 13), (3, 33), (2, 31), (30, 29), (26, 20), (26, 22), (0, 26), (3, 21), (0, 13), (16, 5), (1, 15), (18, 21), (5, 8), (16, 18), (25, 1), (0, 30), (14, 3), (25, 4), (1, 4), (4, 1), (8, 28), (19, 2), (25, 31), (16, 3), (2, 26), (2, 32), (6, 5), (5, 20), (13, 27), (7, 2), (18, 35), (6, 10), (20, 26), (18, 17), (2, 8), (17, 9), (11, 29), (3, 0), (0, 32), (29, 4), (9, 1), (0, 10), (4, 16), (17, 27), (19, 6), (5, 30), (5, 25), (6, 18), (9, 31), (5, 5), (10, 0), (7, 6), (4, 21), (13, 28), (7, 34), (12, 24), (9, 17), (3, 13), (28, 26), (12, 32), (21, 25), (13, 19), (10, 19), (27, 23), (23, 24), (30, 8), (16, 26), (12, 9), (18, 15), (17, 16), (8, 17), (0, 4), (0, 15), (6, 2), (11, 6), (6, 14), (22, 30), (15, 15), (11, 33), (24, 13), (30, 17), (28, 21), (5, 7), (14, 25), (25, 12), (16, 30), (0, 28), (1, 23), (15, 19), (21, 6), (6, 17), (6, 23), (13, 30), (7, 13), (17, 31), (6, 6), (10, 26), (20, 35), (22, 18), (24, 9), (29, 19), (31, 18), (13, 18), (13, 7), (17, 18), (27, 32), (8, 14), (23, 4), (24, 11), (9, 3), (0, 17), (28, 12), (20, 24), (23, 21), (26, 19), (18, 1), (5, 33), (9, 11), (8, 20), (13, 1), (7, 27), (15, 17), (22, 13), (13, 32), (28, 30), (10, 7), (30, 12), (29, 29), (7, 30), (11, 0), (2, 17), (16, 29), (20, 27), (0, 20), (25, 2), (12, 4), (19, 25), (7, 14), (25, 5), (5, 27), (7, 4), (28, 27), (16, 17), (14, 32), (16, 9), (9, 27), (12, 16), (0, 21), (27, 11), (19, 15), (13, 16), (7, 16), (1, 1), (12, 10), (15, 16), (26, 1), (21, 21), (12, 18), (26, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "996300", "dataset": "MATH"}
{"messages": [{"content": "In a 31x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (23, 13), (9, 32), (2, 31), (3, 8), (25, 27), (0, 29), (4, 28), (2, 0), (16, 1), (20, 24), (12, 17), (18, 5), (21, 9), (8, 32), (0, 30), (15, 27), (2, 4), (20, 29), (20, 27), (6, 4), (17, 15), (15, 26), (26, 6), (30, 26), (9, 12), (14, 26), (23, 31), (9, 22), (5, 2), (29, 17), (27, 22), (26, 17), (24, 16), (1, 15), (27, 13), (25, 13), (22, 0), (24, 27), (30, 7), (30, 28), (17, 12), (10, 18), (19, 7), (26, 12), (4, 2), (23, 9), (3, 4), (24, 24), (13, 12), (20, 12), (28, 12), (21, 14), (6, 30), (1, 23), (21, 29), (24, 6), (4, 22), (27, 16), (22, 24), (7, 10), (13, 7), (28, 28), (28, 24), (8, 7), (12, 6), (18, 20), (6, 19), (29, 21), (28, 22), (29, 28), (11, 9), (25, 24), (21, 27), (18, 4), (19, 11), (2, 3), (0, 22), (14, 1), (20, 31), (24, 4), (30, 1), (4, 13), (22, 11), (23, 20), (18, 31), (5, 16), (22, 32), (15, 6), (11, 24), (22, 17), (24, 17), (23, 12), (4, 24), (24, 30), (8, 13), (14, 10), (3, 9), (12, 14), (25, 9), (15, 30), (8, 12), (8, 3), (2, 22), (8, 9), (20, 11), (14, 13), (26, 1), (21, 8), (26, 20), (21, 30), (28, 33), (15, 19), (11, 21), (3, 28), (18, 7), (25, 14), (23, 8), (6, 24), (20, 5), (1, 10), (16, 8), (15, 0), (11, 4), (15, 10), (0, 32), (20, 33), (14, 23), (29, 7), (7, 23), (13, 32), (19, 25), (21, 6), (18, 29), (7, 14), (21, 11), (6, 9), (7, 20), (26, 29), (4, 8), (25, 23), (4, 17), (7, 25), (30, 19), (1, 21), (3, 1), (23, 28), (18, 3), (13, 13), (21, 10), (21, 31), (17, 20), (27, 30), (20, 2), (15, 23), (14, 6), (22, 16), (7, 13), (22, 30), (12, 30), (17, 23), (7, 6), (22, 21), (26, 9), (14, 12), (22, 33), (26, 23), (1, 3), (14, 29), (8, 25), (6, 6), (9, 29), (17, 13), (27, 8), (18, 11), (10, 16), (30, 9), (14, 3), (5, 5), (25, 22), (4, 16), (6, 10), (3, 26), (4, 20), (20, 4), (4, 15), (19, 19), (9, 8), (14, 15), (19, 28), (30, 24), (3, 22), (25, 18), (10, 33), (19, 0), (22, 8), (9, 7), (14, 2), (26, 0), (2, 28), (13, 28), (22, 7), (22, 18), (24, 22), (7, 4), (11, 10), (7, 31), (2, 14), (20, 16), (26, 3), (5, 20), (8, 16), (17, 29), (10, 24), (2, 17), (0, 21), (2, 1), (2, 23), (3, 20), (13, 18), (15, 2), (27, 24), (13, 5), (5, 25), (29, 16), (25, 11), (13, 15), (20, 6), (10, 14), (27, 23), (29, 30), (16, 20), (20, 22), (24, 12), (5, 22), (21, 21), (5, 28), (26, 15), (18, 26), (10, 25), (15, 29), (5, 1), (24, 5), (26, 21), (18, 17), (28, 5), (16, 27), (3, 0), (24, 13), (1, 13), (9, 28), (25, 31), (21, 22), (26, 18), (15, 31), (29, 31), (19, 3), (24, 2), (8, 29), (25, 6), (23, 26), (29, 10), (30, 12), (29, 26), (21, 25), (22, 5), (1, 26), (8, 6), (12, 4), (14, 7), (15, 20), (28, 14), (1, 27), (5, 23), (18, 33), (25, 10), (26, 11), (1, 22), (27, 5), (27, 11), (9, 6), (28, 15), (22, 1), (23, 19), (10, 1), (16, 7), (21, 13), (16, 2), (14, 8), (11, 16), (30, 20), (28, 19), (30, 6), (18, 19), (24, 33), (16, 23), (13, 3), (1, 6), (1, 11), (8, 4), (4, 14), (28, 32), (23, 16), (11, 0), (22, 2), (6, 26), (11, 23), (12, 29), (8, 14), (24, 3), (18, 0), (8, 28), (6, 18), (17, 32), (24, 26), (4, 4), (5, 27), (22, 27), (12, 16), (2, 33), (6, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "In a 36x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 32), 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), (29, 15), (12, 19), (3, 22), (17, 0), (4, 1), (0, 29), (8, 9), (8, 14), (33, 21), (10, 18), (13, 6), (26, 32), (11, 31), (26, 6), (13, 28), (30, 27), (12, 32), (0, 10), (30, 22), (0, 8), (14, 8), (12, 8), (0, 20), (7, 32), (18, 14), (33, 28), (16, 18), (25, 5), (23, 12), (8, 12), (32, 6), (22, 20), (1, 31), (27, 0), (8, 8), (33, 32), (26, 25), (31, 5), (34, 15), (27, 12), (26, 12), (14, 7), (30, 3), (12, 26), (16, 15), (29, 23), (18, 24), (15, 6), (20, 11), (1, 27), (30, 18), (32, 9), (3, 27), (35, 6), (25, 8), (25, 6), (34, 29), (23, 8), (23, 1), (14, 23), (21, 22), (16, 31), (8, 15), (8, 29), (23, 7), (15, 12), (34, 21), (3, 25), (14, 31), (27, 4), (10, 28), (7, 19), (11, 5), (9, 7), (1, 6), (5, 9), (19, 22), (34, 24), (35, 29), (18, 10), (17, 23), (11, 25), (28, 3), (21, 4), (28, 18), (5, 12), (2, 4), (16, 17), (22, 32), (16, 4), (18, 4), (24, 7), (0, 25), (34, 23), (15, 23), (11, 11), (17, 3), (19, 32), (2, 18), (6, 9), (10, 20), (18, 3), (24, 18), (14, 14), (15, 28), (16, 12), (8, 21), (5, 26), (0, 19), (22, 25), (17, 26), (22, 8), (29, 13), (16, 16), (30, 25), (3, 9), (22, 27), (2, 31), (24, 23), (30, 9), (34, 17), (13, 19), (6, 24), (25, 12), (16, 23), (8, 13), (21, 31), (19, 7), (33, 19), (9, 9), (0, 18), (7, 8), (26, 10), (10, 0), (21, 28), (3, 8), (24, 24), (29, 28), (15, 7), (12, 3), (27, 28), (15, 8), (2, 20), (18, 9), (15, 14), (8, 18), (18, 2), (6, 28), (0, 28), (32, 18), (23, 9), (12, 7), (17, 22), (28, 11), (24, 20), (32, 30), (24, 15), (13, 0), (15, 9), (29, 20), (3, 2), (21, 1), (1, 7), (35, 27), (9, 11), (18, 28), (1, 9), (29, 8), (14, 28), (15, 0), (11, 27), (17, 32), (9, 27), (3, 16), (32, 13), (23, 30), (18, 18), (6, 19), (15, 21), (33, 12), (30, 23), (9, 13), (17, 12), (6, 23), (21, 16), (27, 20), (25, 3), (16, 11), (5, 16), (0, 24), (35, 9), (21, 10), (3, 14), (9, 28), (16, 6), (10, 12), (14, 9), (4, 6), (4, 11), (22, 4), (2, 16), (32, 1), (18, 12), (22, 22), (26, 29), (31, 2), (33, 24), (35, 8), (0, 27), (2, 19), (30, 14), (0, 7), (31, 10), (8, 27), (27, 25), (33, 8), (5, 32), (13, 1), (21, 26), (2, 23), (34, 22), (9, 21), (29, 27), (14, 17), (5, 24), (27, 24), (16, 29), (11, 9), (15, 20), (16, 10), (6, 15), (33, 11), (20, 19), (4, 15), (14, 21), (7, 13), (20, 0), (35, 20), (31, 7), (24, 21), (2, 17), (35, 1), (17, 28), (10, 30), (24, 3), (9, 0), (4, 9), (21, 19), (24, 22), (21, 17), (18, 29), (27, 17), (22, 10), (6, 10), (6, 21), (31, 9), (16, 25), (27, 15), (29, 26), (11, 23), (19, 6), (9, 1), (10, 22), (16, 20), (0, 30), (21, 3), (14, 18), (28, 6), (9, 24), (11, 17), (5, 2), (4, 32), (31, 8), (35, 10), (14, 24), (22, 23), (34, 9), (6, 29), (8, 30), (5, 11), (11, 30), (1, 11), (34, 26), (12, 10), (9, 10), (25, 0), (11, 8), (14, 15), (29, 32), (23, 5), (2, 29), (1, 16), (5, 31), (1, 8), (24, 30), (7, 5), (19, 18), (6, 18), (10, 4), (32, 26), (22, 6), (10, 6), (23, 29), (0, 31), (6, 6), (17, 8), (12, 31), (25, 28), (13, 24), (3, 0), (4, 20), (15, 24), (25, 18), (0, 14), (13, 10), (31, 18), (16, 1), (12, 28), (4, 5), (9, 8), (11, 15), (19, 30), (16, 24), (2, 15), (10, 26), (2, 0), (8, 16), (33, 15), (13, 17), (29, 19), (0, 11), (19, 13), (2, 30), (23, 6), (32, 14), (12, 20), (3, 7), (33, 31), (23, 23), (8, 10), (9, 2), (11, 26), (1, 30), (28, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "867348", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 22), (18, 30), (1, 3), (16, 18), (8, 0), (22, 15), (18, 18), (17, 24), (25, 13), (3, 5), (19, 15), (19, 13), (14, 17), (24, 5), (7, 22), (33, 8), (6, 7), (22, 26), (13, 12), (22, 24), (4, 15), (25, 9), (15, 15), (15, 24), (20, 10), (23, 30), (2, 21), (20, 25), (29, 1), (4, 2), (5, 2), (28, 20), (12, 4), (5, 8), (28, 14), (19, 3), (6, 4), (10, 18), (9, 1), (36, 16), (12, 14), (16, 28), (30, 19), (20, 18), (19, 6), (27, 18), (25, 3), (29, 18), (9, 15), (17, 13), (19, 11), (25, 2), (14, 16), (25, 18), (6, 0), (16, 22), (26, 28), (8, 5), (25, 12), (33, 20), (33, 9), (32, 21), (7, 26), (8, 4), (24, 4), (19, 12), (7, 21), (3, 20), (17, 20), (30, 23), (34, 1), (15, 19), (19, 21), (16, 12), (20, 12), (33, 22), (14, 25), (32, 12), (31, 27), (11, 23), (11, 1), (28, 1), (21, 8), (18, 3), (21, 26), (7, 16), (6, 28), (1, 1), (36, 22), (33, 4), (11, 28), (32, 20), (18, 4), (28, 7), (22, 7), (2, 0), (27, 14), (18, 10), (17, 23), (22, 17), (30, 14), (32, 14), (25, 29), (13, 2), (14, 4), (35, 10), (25, 25), (13, 5), (8, 25), (8, 29), (35, 6), (22, 3), (22, 27), (11, 14), (13, 0), (20, 27), (29, 8), (26, 27), (6, 27), (1, 19), (5, 5), (12, 9), (14, 30), (5, 19), (18, 9), (8, 27), (30, 13), (16, 19), (33, 24), (6, 20), (12, 30), (22, 29), (0, 14), (27, 7), (15, 28), (23, 14), (20, 1), (3, 13), (21, 27), (32, 30), (23, 25), (6, 17), (3, 25), (9, 9), (1, 30), (6, 25), (18, 24), (24, 25), (21, 15), (19, 20), (12, 13), (14, 6), (2, 2), (19, 9), (0, 10), (14, 2), (19, 8), (1, 9), (31, 30), (27, 8), (17, 29), (7, 10), (17, 12), (13, 15), (10, 1), (10, 19), (15, 22), (24, 11), (3, 27), (10, 27), (12, 16), (36, 28), (27, 0), (0, 27), (6, 30), (5, 6), (11, 11), (11, 21), (30, 18), (23, 6), (23, 15), (15, 3), (24, 18), (25, 8), (30, 16), (1, 16), (7, 23), (15, 14), (8, 26), (16, 7), (1, 5), (7, 14), (26, 25), (2, 28), (28, 11), (7, 29), (32, 16), (19, 27), (13, 28), (25, 23), (36, 21), (16, 23), (29, 27), (36, 29), (12, 8), (13, 30), (20, 5), (18, 23), (31, 22), (23, 10), (19, 29), (2, 13), (12, 12), (7, 17), (36, 23), (19, 10), (28, 13), (33, 27), (23, 16), (19, 14), (36, 27), (16, 24), (13, 22), (35, 9), (27, 22), (29, 11), (13, 19), (24, 9), (8, 30), (7, 15), (17, 27), (9, 22), (19, 16), (1, 2), (20, 28), (21, 29), (29, 26), (36, 6), (30, 3), (28, 17), (6, 5), (22, 4), (2, 11), (29, 7), (29, 17), (19, 1), (5, 14), (2, 22), (7, 0), (19, 26), (25, 6), (11, 3), (5, 3), (26, 8), (18, 17), (17, 11), (2, 23), (27, 10), (14, 27), (19, 30), (12, 25), (21, 7), (36, 25), (14, 9), (1, 12), (32, 27), (19, 4), (33, 16), (28, 6), (2, 4), (21, 6), (36, 0), (0, 9), (16, 27), (33, 26), (12, 23), (29, 13), (12, 28), (36, 5), (34, 10), (10, 28), (13, 16), (21, 24), (29, 6), (19, 17), (5, 20), (29, 25), (28, 0), (26, 21), (17, 19), (0, 20), (7, 9), (4, 16), (31, 16), (30, 9), (36, 19), (19, 5), (3, 19), (20, 17), (33, 19), (25, 20), (12, 17), (28, 28), (17, 0), (23, 21), (16, 1), (8, 10), (25, 30), (9, 17), (29, 22), (8, 28), (27, 23), (5, 17), (34, 16), (28, 4), (10, 23), (13, 8), (8, 12), (18, 25), (34, 6), (8, 2), (1, 17), (3, 26), (30, 2), (25, 16), (10, 29), (7, 13), (33, 0), (23, 20), (9, 29), (8, 22), (36, 13), (2, 6), (3, 7), (1, 23), (17, 25), (17, 3), (24, 28), (28, 24), (23, 22), (22, 6), (27, 6), (27, 20), (11, 26), (17, 17), (32, 4), (19, 7), (16, 16), (34, 13), (21, 30), (14, 24), (0, 17), (21, 25), (17, 6), (36, 26), (30, 11), (25, 5), (3, 4), (0, 15), (24, 21), (9, 18), (31, 8), (36, 18), (3, 24), (0, 21), (15, 29), (5, 9), (16, 26), (12, 1), (5, 0), (13, 23), (29, 5), (30, 12), (35, 23), (12, 18)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604800", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 3), (32, 4), (13, 32), (34, 25), (23, 5), (3, 0), (19, 23), (19, 14), (30, 0), (13, 11), (31, 16), (11, 23), (11, 13), (26, 0), (36, 32), (34, 8), (18, 0), (35, 25), (26, 11), (4, 9), (10, 4), (35, 9), (31, 12), (25, 5), (22, 3), (21, 4), (32, 22), (0, 13), (5, 19), (9, 23), (9, 30), (28, 7), (31, 26), (30, 27), (17, 15), (31, 31), (35, 15), (2, 22), (1, 25), (8, 23), (32, 1), (19, 1), (21, 17), (20, 2), (6, 31), (19, 19), (24, 18), (26, 28), (33, 5), (33, 4), (7, 11), (36, 22), (6, 30), (10, 24), (36, 17), (16, 3), (18, 14), (11, 14), (17, 2), (14, 29), (21, 12), (2, 16), (25, 23), (33, 6), (37, 0), (22, 32), (21, 6), (15, 10), (18, 13), (0, 19), (19, 24), (28, 16), (18, 23), (26, 14), (4, 8), (21, 15), (22, 0), (12, 26), (28, 19), (29, 12), (29, 14), (10, 16), (18, 1), (36, 8), (21, 9), (27, 11), (4, 27), (5, 28), (37, 10), (15, 18), (15, 13), (16, 22), (9, 2), (3, 31), (30, 18), (1, 29), (10, 8), (14, 22), (34, 7), (15, 27), (27, 14), (7, 20), (12, 5), (2, 28), (1, 19), (12, 3), (25, 19), (12, 2), (6, 20), (31, 4), (20, 12), (34, 18), (10, 21), (23, 26), (26, 9), (29, 28), (6, 27), (25, 14), (27, 13), (32, 28), (32, 16), (12, 28), (35, 1), (32, 32), (5, 4), (14, 19), (14, 3), (31, 6), (29, 1), (15, 23), (10, 32), (17, 3), (5, 2), (18, 27), (5, 9), (30, 20), (18, 5), (9, 21), (27, 23), (30, 12), (8, 3), (1, 16), (26, 5), (16, 6), (17, 20), (29, 0), (12, 0), (6, 25), (9, 25), (35, 18), (2, 7), (9, 9), (1, 1), (26, 31), (15, 26), (19, 5), (22, 11), (34, 27), (24, 21), (25, 28), (8, 6), (31, 30), (23, 21), (37, 20), (22, 14), (29, 25), (8, 24), (21, 31), (36, 1), (9, 29), (12, 16), (22, 18), (6, 7), (2, 1), (0, 5), (30, 32), (1, 27), (11, 31), (33, 15), (11, 21), (4, 13), (9, 6), (18, 17), (21, 30), (21, 28), (28, 6), (36, 27), (16, 2), (15, 12), (5, 1), (13, 2), (20, 6), (18, 2), (16, 12), (14, 15), (9, 7), (23, 13), (32, 15), (15, 28), (2, 30), (31, 20), (23, 23), (4, 30), (21, 2), (14, 7), (29, 5), (34, 26), (37, 6), (4, 25), (11, 18), (26, 2), (27, 3), (34, 30), (22, 13), (29, 3), (9, 16), (16, 20), (35, 16), (29, 4), (37, 17), (5, 27), (2, 23), (17, 22), (33, 1), (15, 32), (18, 32), (37, 13), (8, 1), (32, 30), (8, 26), (2, 3), (15, 11), (35, 14), (3, 24), (5, 26), (25, 4), (14, 12), (11, 22), (2, 27), (30, 31), (36, 23), (2, 18), (12, 7), (1, 3), (6, 5), (19, 2), (23, 9), (7, 0), (13, 9), (6, 22), (17, 13), (9, 15), (14, 20), (7, 32), (9, 12), (24, 10), (32, 31), (20, 28), (10, 17), (2, 4), (30, 19), (3, 7), (13, 18), (20, 9), (6, 6), (2, 17), (12, 17), (28, 21), (4, 2), (4, 1), (4, 17), (20, 15), (35, 30), (0, 32), (32, 0), (13, 16), (28, 27), (37, 22), (26, 6), (10, 27), (24, 12), (26, 3), (26, 29), (29, 10), (0, 15), (16, 10), (0, 4), (31, 2), (21, 11), (30, 15), (34, 6), (8, 4), (5, 7), (16, 26), (16, 16), (23, 29), (17, 0), (19, 30), (35, 12), (3, 25), (37, 3), (34, 19), (19, 7), (3, 30), (32, 19), (16, 31), (12, 25), (1, 24), (35, 24), (32, 9), (22, 12), (25, 25), (27, 6), (25, 9), (27, 8), (21, 23), (24, 29), (24, 25), (17, 27), (23, 6), (20, 5), (36, 14), (33, 27), (11, 19), (13, 5), (2, 10), (19, 6), (15, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "620928", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), 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), (21, 15), (10, 29), (15, 5), (16, 17), (27, 29), (30, 29), (2, 5), (1, 26), (34, 15), (32, 25), (22, 18), (4, 24), (35, 24), (14, 20), (2, 23), (18, 18), (17, 2), (21, 23), (25, 29), (11, 25), (28, 11), (12, 22), (38, 21), (37, 23), (37, 0), (38, 8), (24, 24), (27, 7), (20, 0), (27, 6), (32, 9), (5, 15), (32, 20), (17, 4), (5, 7), (37, 31), (35, 29), (16, 3), (0, 15), (25, 17), (6, 17), (30, 30), (0, 22), (20, 20), (37, 18), (11, 16), (31, 27), (25, 19), (10, 14), (4, 13), (33, 4), (12, 29), (8, 12), (1, 3), (5, 8), (9, 15), (18, 27), (19, 11), (19, 9), (4, 7), (10, 26), (18, 19), (30, 12), (7, 24), (38, 26), (38, 0), (21, 28), (24, 27), (13, 2), (5, 11), (37, 22), (7, 11), (35, 10), (9, 13), (25, 0), (5, 4), (11, 7), (26, 16), (18, 0), (2, 27), (12, 0), (19, 13), (9, 26), (6, 30), (16, 24), (14, 0), (18, 11), (21, 18), (36, 12), (30, 27), (36, 21), (20, 12), (20, 1), (19, 31), (26, 31), (21, 29), (31, 7), (15, 22), (0, 19), (26, 12), (33, 13), (32, 0), (33, 8), (35, 14), (7, 21), (6, 16), (7, 6), (2, 10), (1, 4), (2, 25), (6, 31), (11, 20), (25, 30), (36, 5), (23, 3), (10, 7), (25, 1), (6, 27), (35, 4), (18, 24), (29, 1), (7, 19), (1, 24), (13, 27), (33, 31), (7, 8), (13, 4), (10, 6), (28, 4), (23, 0), (20, 21), (27, 10), (25, 5), (19, 18), (29, 8), (9, 0), (17, 20), (24, 2), (0, 29), (24, 26), (37, 13), (20, 22), (6, 12), (0, 7), (10, 12), (29, 7), (26, 26), (10, 4), (10, 8), (9, 23), (14, 27), (28, 15), (5, 9), (16, 4), (14, 7), (18, 1), (35, 7), (7, 3), (34, 6), (2, 13), (33, 12), (6, 6), (34, 0), (25, 11), (1, 13), (24, 13), (6, 10), (9, 3), (29, 31), (12, 21), (12, 19), (22, 23), (11, 27), (37, 3), (3, 22), (22, 17), (18, 15), (10, 9), (28, 18), (30, 9), (36, 15), (2, 8), (25, 3), (20, 8), (8, 8), (5, 27), (8, 10), (8, 13), (6, 8), (30, 25), (27, 22), (13, 3), (33, 3), (3, 3), (29, 27), (24, 4), (12, 2), (24, 21), (10, 10), (23, 27), (21, 5), (25, 27), (29, 17), (12, 15), (31, 13), (37, 6), (21, 30), (35, 22), (10, 18), (38, 20), (14, 26), (38, 14), (1, 31), (13, 29), (9, 25), (27, 1), (3, 27), (35, 26), (15, 26), (34, 7), (21, 12), (1, 21), (27, 27), (0, 9), (21, 9), (8, 20), (27, 14), (2, 16), (15, 8), (5, 6), (11, 19), (33, 14), (10, 2), (36, 25), (7, 28), (23, 5), (18, 20), (6, 24), (8, 3), (34, 11), (22, 0), (23, 31), (32, 8), (30, 4), (3, 28), (22, 20), (2, 24), (11, 31), (14, 5), (19, 20), (21, 21), (33, 25), (37, 8), (32, 14), (23, 18), (9, 4), (31, 11), (7, 16), (25, 14), (13, 6), (23, 16), (32, 3), (31, 16), (27, 19), (33, 23), (26, 17), (17, 14), (32, 5), (20, 6), (18, 31), (37, 28), (10, 1), (37, 25), (12, 24), (27, 24), (19, 6), (11, 14), (2, 2), (29, 11), (22, 7), (16, 14), (20, 31), (31, 29), (24, 28), (33, 27), (16, 5), (25, 6), (8, 16), (38, 5), (15, 29), (11, 21), (3, 5), (22, 22), (34, 16), (17, 17), (36, 29), (4, 10), (7, 17), (20, 18), (31, 8), (22, 31), (32, 6), (7, 22), (32, 1), (25, 20), (26, 14), (35, 2), (6, 5), (36, 20), (22, 10), (31, 9), (15, 21), (3, 11), (33, 20), (8, 29), (25, 12), (0, 27), (32, 28), (3, 16), (7, 14), (26, 29), (34, 22), (14, 21), (24, 18), (5, 13), (9, 10), (20, 4), (19, 28), (15, 6), (35, 3), (28, 26), (8, 22), (21, 16), (35, 5), (4, 8), (24, 14), (35, 18), (4, 22), (2, 19), (8, 25), (12, 1), (28, 22), (38, 3), (10, 27), (4, 11), (7, 5), (23, 28), (35, 20), (16, 23), (1, 25), (25, 21), (36, 6), (21, 3), (19, 1), (30, 26), (21, 14), (31, 15), (10, 24), (28, 23), (13, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688160", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 23), (9, 7), (15, 19), (6, 2), (12, 27), (28, 8), (25, 2), (2, 12), (11, 22), (5, 5), (26, 25), (20, 30), (3, 1), (1, 15), (15, 5), (11, 18), (8, 16), (20, 23), (26, 12), (0, 18), (3, 31), (27, 31), (26, 4), (14, 30), (13, 15), (13, 2), (19, 7), (28, 30), (21, 1), (15, 14), (16, 29), (15, 18), (7, 19), (9, 0), (12, 23), (28, 11), (0, 9), (7, 30), (16, 4), (21, 14), (0, 12), (13, 12), (0, 11), (18, 1), (23, 17), (30, 16), (27, 10), (28, 28), (4, 15), (12, 25), (9, 25), (10, 5), (25, 19), (0, 19), (15, 16), (28, 19), (29, 16), (14, 27), (2, 24), (4, 16), (18, 26), (14, 1), (1, 4), (5, 22), (17, 26), (14, 2), (14, 12), (6, 5), (0, 4), (18, 24), (19, 15), (21, 29), (14, 13), (24, 2), (25, 10), (11, 9), (22, 0), (28, 31), (20, 29), (9, 22), (18, 11), (15, 10), (5, 26), (13, 28), (27, 20), (1, 26), (29, 7), (21, 16), (18, 14), (17, 27), (22, 27), (11, 23), (3, 10), (16, 12), (14, 28), (4, 20), (14, 9), (0, 20), (25, 9), (24, 7), (11, 31), (5, 14), (24, 0), (2, 16), (10, 15), (14, 25), (30, 11), (23, 4), (9, 24), (15, 11), (2, 17), (1, 5), (18, 5), (2, 26), (21, 17), (20, 12), (28, 1), (27, 24), (10, 11), (26, 17), (6, 23), (16, 20), (4, 30), (5, 27), (9, 29), (2, 9), (1, 30), (2, 21), (13, 19), (0, 2), (21, 13), (29, 22), (2, 15), (5, 17), (24, 15), (21, 30), (12, 28), (25, 23), (12, 22), (0, 14), (15, 30), (16, 16), (3, 16), (9, 14), (22, 4), (27, 16), (10, 17), (3, 24), (8, 13), (0, 3), (7, 7), (21, 4), (25, 12), (9, 20), (2, 30), (13, 4), (4, 23), (24, 12), (18, 22), (26, 7), (4, 7), (21, 28), (14, 0), (20, 3), (6, 26), (13, 16), (9, 6), (25, 24), (22, 14), (23, 18), (9, 18), (7, 23), (6, 29), (10, 12), (23, 23), (3, 5), (3, 15), (8, 10), (8, 21), (29, 3), (25, 5), (5, 24), (27, 30), (3, 0), (9, 4), (4, 18), (23, 25), (10, 1), (4, 21), (17, 31), (18, 3), (30, 9), (10, 23), (19, 14), (25, 1), (26, 19), (17, 18), (14, 8), (7, 2), (16, 21), (18, 6), (19, 25), (5, 18), (5, 6), (19, 26), (28, 23), (25, 28), (8, 19), (5, 9), (22, 7), (10, 27), (16, 23), (7, 10), (30, 17), (21, 19), (12, 9), (12, 19), (8, 2), (30, 21), (4, 31), (24, 28), (0, 26), (19, 11), (17, 6), (9, 3), (3, 22), (5, 3), (26, 24), (7, 21), (5, 4), (4, 3), (25, 13), (17, 2), (6, 30), (25, 20), (18, 17), (11, 5), (18, 27), (10, 21), (11, 0), (17, 20), (18, 19), (23, 2), (20, 24), (19, 31), (4, 29), (6, 4), (10, 25), (15, 3), (5, 19), (9, 9), (30, 2), (21, 24), (9, 23), (26, 11), (20, 5), (25, 8), (0, 1), (23, 28), (24, 16), (28, 10), (14, 5), (11, 13), (23, 5), (18, 31), (7, 17), (10, 3), (10, 13), (0, 30), (2, 25), (21, 10), (27, 14), (11, 30), (7, 24), (2, 2)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "793908", "dataset": "MATH"}
{"messages": [{"content": "In a 32x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 29), (28, 31), (19, 25), (4, 33), (29, 19), (3, 13), (27, 9), (29, 6), (24, 15), (3, 18), (18, 27), (23, 21), (24, 5), (27, 17), (22, 25), (2, 22), (5, 2), (30, 11), (18, 19), (23, 17), (18, 9), (11, 32), (8, 7), (3, 19), (2, 13), (31, 4), (24, 20), (7, 10), (25, 23), (0, 13), (23, 8), (13, 23), (7, 33), (28, 7), (12, 11), (14, 1), (26, 31), (21, 23), (14, 22), (18, 30), (29, 5), (20, 23), (23, 12), (8, 3), (30, 6), (17, 24), (20, 8), (14, 24), (7, 6), (23, 16), (9, 3), (20, 13), (4, 2), (4, 31), (1, 14), (10, 29), (3, 27), (17, 8), (16, 3), (13, 0), (25, 29), (0, 14), (10, 20), (29, 20), (1, 25), (28, 24), (8, 16), (19, 4), (7, 0), (1, 5), (10, 7), (3, 17), (12, 13), (23, 3), (12, 33), (9, 12), (3, 20), (25, 12), (25, 7), (6, 30), (7, 27), (7, 4), (9, 13), (6, 12), (16, 0), (11, 3), (29, 17), (11, 21), (17, 9), (6, 17), (20, 18), (20, 5), (8, 14), (19, 12), (21, 19), (10, 13), (20, 9), (29, 13), (28, 17), (22, 27), (15, 33), (12, 22), (13, 10), (30, 33), (16, 31), (7, 9), (18, 1), (0, 33), (26, 33), (10, 31), (9, 27), (14, 2), (27, 7), (23, 4), (29, 23), (17, 26), (27, 24), (15, 22), (13, 7), (12, 3), (24, 28), (0, 23), (17, 31), (18, 12), (29, 9), (13, 24), (12, 8), (20, 14), (14, 7), (25, 5), (27, 10), (11, 18), (26, 28), (11, 13), (22, 16), (7, 1), (6, 33), (19, 1), (20, 12), (15, 18), (27, 27), (13, 19), (20, 16), (6, 0), (26, 0), (31, 19), (3, 3), (15, 0), (14, 30), (20, 27), (5, 29), (0, 17), (21, 32), (19, 20), (27, 33), (22, 33), (30, 10), (6, 18), (18, 18), (19, 32), (17, 23), (26, 18), (10, 17), (31, 1), (15, 17), (27, 29), (6, 25), (8, 0), (23, 23), (10, 2), (0, 21), (30, 28), (24, 31), (9, 11), (15, 16), (9, 17), (6, 7), (6, 14), (1, 21), (29, 7), (29, 21), (15, 12), (20, 28), (30, 32), (25, 22), (0, 32), (28, 0), (22, 30), (18, 13), (17, 28), (7, 16), (7, 26), (26, 25), (18, 16), (6, 32), (27, 13), (15, 11), (8, 19), (10, 14), (17, 17), (26, 6), (9, 0), (17, 14), (29, 32), (23, 24), (31, 23), (3, 5), (23, 10), (25, 15), (29, 30), (21, 25), (9, 4), (14, 0), (16, 26), (10, 10), (30, 16), (30, 12), (28, 16), (31, 7), (3, 29), (3, 22), (8, 29), (26, 10), (13, 11), (23, 2), (18, 15), (13, 27), (1, 28), (30, 14), (28, 1), (4, 24), (11, 8), (2, 7), (24, 30), (11, 16), (5, 8), (23, 18), (7, 30), (26, 11), (13, 31), (30, 1), (25, 24), (30, 4), (30, 13), (29, 18), (15, 31), (30, 8), (27, 20), (19, 8), (8, 21), (9, 19), (22, 32), (4, 27), (17, 32), (27, 15), (13, 4), (21, 5), (26, 12), (14, 23), (28, 22), (0, 4), (1, 6), (9, 23), (7, 28), (14, 5), (30, 24), (14, 6), (19, 9), (0, 26), (20, 19), (27, 1), (8, 5), (14, 4), (22, 17), (15, 1), (22, 31), (28, 8), (22, 24), (21, 7), (5, 32), (5, 11), (4, 26), (20, 4), (31, 27), (16, 25), (27, 4), (30, 27), (12, 19), (0, 1), (22, 20), (16, 14), (24, 13), (11, 1), (4, 17), (11, 12), (7, 11), (12, 28), (20, 21), (17, 13), (21, 16), (30, 22), (11, 25), (3, 30), (8, 31), (5, 12), (22, 11), (5, 15), (10, 28), (17, 11), (28, 33), (23, 33), (29, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277560", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 38), (13, 35), (26, 12), (15, 19), (4, 37), (27, 34), (19, 7), (21, 28), (8, 0), (19, 11), (32, 34), (4, 20), (6, 29), (20, 15), (31, 12), (22, 18), (24, 5), (1, 7), (28, 37), (30, 7), (2, 1), (1, 10), (7, 28), (24, 37), (28, 5), (9, 14), (10, 11), (20, 20), (2, 33), (16, 20), (25, 16), (2, 25), (18, 5), (1, 12), (31, 1), (31, 24), (25, 18), (28, 32), (23, 36), (24, 22), (23, 3), (16, 24), (17, 12), (17, 30), (9, 38), (22, 37), (12, 31), (18, 37), (12, 18), (23, 18), (26, 4), (21, 18), (31, 27), (4, 18), (1, 24), (21, 9), (32, 27), (29, 13), (11, 29), (32, 26), (1, 21), (21, 37), (26, 23), (1, 22), (13, 21), (10, 8), (18, 18), (32, 32), (12, 9), (9, 26), (31, 22), (22, 25), (7, 17), (23, 10), (19, 19), (19, 8), (29, 2), (26, 31), (3, 10), (25, 25), (16, 0), (28, 8), (26, 1), (4, 16), (30, 36), (15, 22), (15, 12), (12, 25), (24, 33), (21, 33), (18, 32), (23, 37), (31, 18), (20, 19), (24, 10), (32, 29), (6, 17), (5, 15), (16, 17), (24, 28), (19, 36), (22, 17), (19, 2), (1, 25), (24, 21), (21, 2), (11, 23), (25, 1), (16, 11), (13, 22), (26, 38), (18, 0), (3, 23), (13, 26), (29, 29), (23, 13), (26, 13), (26, 3), (2, 14), (3, 21), (8, 7), (25, 3), (6, 23), (17, 7), (23, 27), (13, 3), (9, 25), (0, 11), (20, 26), (19, 15), (13, 1), (12, 12), (21, 17), (16, 9), (16, 32), (14, 28), (30, 19), (15, 6), (21, 8), (0, 23), (3, 26), (19, 10), (11, 11), (2, 28), (11, 26), (4, 10), (9, 21), (29, 38), (10, 17), (26, 5), (23, 24), (23, 28), (15, 21), (24, 7), (18, 17), (17, 38), (22, 9), (6, 18), (8, 32), (21, 38), (13, 11), (29, 24), (23, 0), (29, 23), (29, 14), (0, 4), (4, 15), (1, 1), (31, 8), (31, 25), (9, 30), (21, 5), (15, 8), (24, 30), (14, 33), (21, 22), (8, 19), (14, 12), (15, 35), (25, 36), (20, 36), (28, 22), (32, 25), (20, 31), (20, 2), (7, 1), (6, 1), (30, 35), (26, 11), (30, 38), (4, 6), (0, 9), (32, 4), (12, 4), (15, 9), (9, 4), (19, 5), (10, 36), (23, 30), (4, 23), (3, 24), (1, 16), (30, 32), (27, 3), (16, 14), (19, 24), (6, 2), (5, 5), (17, 1), (2, 2), (17, 17), (18, 20), (14, 26), (25, 26), (19, 20), (31, 10), (14, 38), (10, 25), (9, 3), (9, 5), (30, 28), (31, 32), (23, 31), (21, 25), (17, 18), (5, 38), (27, 9), (25, 13), (8, 25), (15, 18), (17, 14), (20, 18), (0, 15), (19, 27), (2, 3), (26, 7), (13, 17), (17, 29), (8, 37), (4, 27), (28, 0), (23, 4), (6, 21), (13, 27), (0, 28), (29, 32), (20, 34), (5, 6), (12, 3), (4, 33), (29, 31), (6, 35), (2, 30), (27, 2), (28, 36), (28, 3), (14, 1), (8, 27), (1, 34), (14, 15), (21, 6), (17, 2), (13, 6), (3, 17), (10, 1), (24, 38), (32, 36), (15, 23), (13, 2), (32, 23), (7, 36), (28, 38), (29, 37), (5, 36), (17, 20), (25, 34), (3, 1), (10, 37), (11, 10), (0, 17), (16, 23), (0, 30), (20, 9), (22, 12), (24, 6), (16, 27), (30, 29), (18, 2), (8, 31), (4, 17), (18, 11), (14, 23), (5, 7), (23, 7), (12, 15), (9, 11), (32, 0), (14, 24), (13, 25), (0, 19), (20, 16), (19, 37), (1, 27), (3, 33), (10, 23), (2, 37), (24, 25), (27, 19), (21, 15), (11, 2), (22, 1), (7, 35), (14, 8), (28, 24), (32, 9), (24, 0), (19, 12), (3, 22), (10, 13), (16, 29), (21, 16), (11, 5), (3, 37), (17, 27), (32, 30), (25, 32), (3, 14), (12, 34), (27, 36), (13, 8), (5, 4), (1, 2), (5, 25), (6, 15), (20, 37), (7, 6), (5, 21), (7, 0), (1, 15), (6, 10), (14, 20), (23, 9), (19, 31), (0, 21), (23, 15), (10, 34), (22, 8), (17, 24), (24, 20), (17, 0), (4, 38), (3, 27), (19, 38), (21, 13), (17, 21), (8, 23), (0, 14), (17, 22), (3, 0), (14, 11), (18, 25), (27, 12), (23, 2), (22, 24), (20, 22), (29, 36), (30, 31), (26, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "911088", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (29, 4), (10, 2), (29, 1), (4, 22), (8, 6), (4, 20), (20, 3), (20, 16), (3, 16), (6, 9), (7, 14), (8, 14), (25, 15), (24, 10), (8, 30), (13, 15), (5, 12), (2, 20), (0, 4), (12, 22), (28, 8), (17, 20), (20, 12), (21, 7), (4, 4), (30, 19), (31, 23), (2, 19), (0, 22), (32, 2), (9, 6), (29, 16), (32, 6), (8, 18), (2, 17), (26, 33), (29, 21), (5, 18), (29, 15), (8, 24), (25, 31), (13, 8), (7, 16), (6, 27), (13, 23), (25, 18), (13, 9), (30, 2), (28, 1), (10, 30), (23, 6), (8, 32), (10, 24), (22, 4), (25, 1), (20, 8), (4, 29), (7, 29), (2, 21), (9, 5), (9, 11), (0, 1), (16, 28), (11, 25), (15, 33), (17, 5), (28, 19), (8, 13), (15, 14), (6, 29), (7, 21), (13, 33), (4, 18), (28, 15), (2, 10), (28, 3), (16, 19), (21, 26), (0, 6), (2, 1), (23, 27), (29, 13), (1, 2), (3, 6), (9, 13), (7, 23), (7, 30), (14, 22), (12, 21), (15, 9), (12, 17), (13, 18), (30, 3), (21, 3), (16, 4), (17, 15), (6, 10), (15, 22), (30, 26), (11, 31), (19, 13), (21, 25), (29, 3), (25, 12), (32, 15), (29, 23), (2, 4), (26, 16), (26, 0), (15, 0), (16, 1), (6, 28), (1, 10), (0, 10), (13, 25), (5, 16), (31, 12), (16, 22), (7, 33), (4, 33), (10, 23), (14, 13), (17, 21), (32, 19), (25, 20), (19, 22), (16, 13), (32, 11), (15, 21), (26, 23), (13, 0), (22, 29), (26, 27), (17, 33), (28, 27), (31, 18), (31, 28), (22, 0), (22, 1), (22, 28), (23, 23), (30, 13), (8, 5), (26, 18), (11, 4), (27, 8), (26, 10), (4, 0), (10, 19), (15, 29), (24, 16), (22, 17), (8, 11), (6, 33), (14, 25), (3, 13), (19, 17), (30, 0), (13, 32), (23, 29), (24, 9), (10, 26), (15, 24), (10, 0), (24, 4), (17, 18), (31, 25), (31, 6), (15, 30), (31, 33), (3, 33), (17, 27), (11, 9), (31, 14), (12, 0), (24, 2), (28, 29), (14, 12), (8, 28), (4, 6), (1, 25), (16, 17), (19, 23), (4, 8), (24, 7), (27, 26), (4, 1), (21, 9), (4, 17), (18, 19), (21, 5), (13, 6), (17, 10), (14, 20), (9, 30), (14, 23), (8, 12), (17, 23), (12, 1), (4, 21), (10, 21), (2, 26), (5, 9), (7, 6), (5, 8), (6, 15), (27, 31), (12, 33), (18, 31), (12, 11), (28, 9), (19, 9), (6, 16), (22, 11), (23, 8), (32, 17), (19, 18), (32, 0), (7, 32), (17, 1), (9, 17), (20, 15), (24, 20), (29, 30), (8, 3), (32, 9), (3, 22), (24, 29), (20, 14), (23, 16), (5, 26), (13, 30), (26, 22), (28, 16), (10, 1), (21, 14), (1, 5), (5, 21), (8, 15), (17, 25), (12, 4), (15, 8), (19, 10), (14, 19), (27, 2), (23, 20), (11, 19), (21, 2), (27, 29), (21, 16), (13, 26), (12, 26), (28, 7), (11, 5), (28, 6), (14, 11), (14, 2), (14, 4), (13, 12), (3, 21), (15, 5), (29, 32), (31, 3), (17, 26), (15, 26), (26, 26), (31, 11), (18, 9), (18, 8), (27, 24), (6, 11), (3, 18), (19, 33), (16, 5), (28, 0), (10, 22), (25, 14), (29, 19), (30, 27), (30, 11), (1, 12), (25, 23), (11, 11), (24, 1), (10, 20), (6, 3), (7, 12), (6, 24), (13, 22), (0, 27), (1, 1), (31, 10), (28, 11), (2, 12), (22, 22), (10, 3), (4, 5), (27, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872760", "dataset": "MATH"}
{"messages": [{"content": "In a 34x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 19), (17, 5), (28, 30), (14, 29), (21, 6), (25, 1), (27, 27), (24, 26), (28, 22), (10, 1), (10, 14), (17, 8), (8, 27), (31, 25), (6, 32), (7, 27), (22, 15), (31, 29), (26, 26), (16, 10), (1, 24), (30, 4), (0, 21), (17, 10), (22, 14), (19, 13), (31, 9), (17, 30), (4, 24), (25, 22), (28, 24), (14, 22), (6, 18), (0, 8), (12, 35), (31, 23), (32, 28), (26, 3), (18, 6), (26, 9), (30, 24), (22, 3), (3, 36), (16, 20), (5, 15), (4, 18), (31, 32), (0, 36), (7, 36), (12, 32), (9, 24), (13, 36), (21, 25), (2, 13), (7, 31), (26, 21), (14, 37), (22, 18), (8, 6), (7, 18), (18, 13), (4, 27), (25, 2), (33, 18), (32, 11), (11, 0), (23, 28), (0, 19), (31, 16), (23, 12), (30, 33), (12, 1), (25, 11), (5, 25), (3, 10), (16, 35), (26, 20), (16, 14), (2, 11), (10, 12), (10, 3), (8, 33), (7, 22), (16, 4), (2, 14), (11, 32), (17, 20), (8, 24), (1, 21), (11, 8), (18, 21), (15, 32), (27, 18), (28, 27), (27, 7), (14, 21), (2, 9), (17, 36), (9, 17), (29, 24), (22, 31), (2, 29), (16, 31), (4, 4), (30, 11), (14, 35), (17, 12), (20, 17), (12, 20), (7, 9), (23, 21), (10, 21), (25, 25), (6, 22), (18, 7), (33, 0), (5, 31), (6, 23), (23, 13), (8, 10), (25, 33), (1, 8), (24, 1), (6, 0), (18, 34), (5, 35), (24, 21), (14, 9), (30, 14), (22, 32), (32, 22), (21, 20), (13, 17), (12, 9), (20, 26), (13, 11), (13, 2), (7, 34), (19, 16), (0, 13), (14, 15), (19, 11), (13, 8), (13, 32), (29, 28), (27, 20), (14, 23), (17, 37), (15, 15), (29, 36), (21, 33), (23, 31), (28, 14), (12, 36), (4, 12), (32, 37), (12, 15), (8, 21), (11, 31), (15, 4), (24, 30), (9, 26), (1, 7), (6, 8), (32, 24), (8, 26), (29, 19), (16, 9), (9, 2), (2, 0), (5, 11), (5, 6), (12, 14), (24, 24), (6, 31), (21, 10), (7, 15), (7, 30), (16, 22), (19, 28), (4, 26), (8, 4), (1, 20), (14, 10), (21, 31), (29, 20), (9, 20), (11, 26), (30, 20), (32, 17), (32, 5), (9, 14), (7, 21), (10, 17), (5, 30), (17, 2), (22, 21), (3, 2), (16, 1), (18, 14), (4, 15), (24, 6), (19, 5), (11, 7), (24, 22), (6, 9), (3, 32), (33, 29), (13, 22), (23, 33), (2, 34), (10, 8), (9, 34), (24, 5), (20, 3), (1, 12), (1, 10), (32, 3), (19, 10), (29, 3), (26, 35), (30, 0), (30, 22), (16, 8), (22, 25), (16, 37), (30, 23), (8, 22), (14, 16), (25, 16), (22, 19), (27, 24), (7, 0), (27, 23), (25, 29), (19, 3), (15, 23), (14, 8), (1, 18), (32, 33), (12, 2), (6, 14), (2, 1), (29, 15), (7, 13), (13, 10), (9, 22), (15, 25), (27, 4), (3, 17), (29, 8), (25, 26), (33, 5), (27, 31), (12, 4), (14, 19), (1, 16), (18, 0), (30, 6), (3, 27), (28, 12), (4, 34), (17, 29), (7, 3), (24, 8), (29, 6), (23, 36), (24, 0), (7, 7), (33, 16), (22, 24), (9, 28), (10, 32), (8, 15), (2, 26), (1, 36), (10, 23), (25, 37), (11, 12), (32, 30), (32, 12), (8, 17), (19, 15), (19, 18), (9, 10), (16, 21), (0, 33), (8, 19), (32, 2), (0, 15), (12, 0), (12, 11), (8, 8), (8, 2), (23, 8), (15, 30), (1, 2), (5, 26), (29, 12), (29, 34), (31, 37), (18, 23), (26, 5), (21, 11), (25, 7), (29, 37), (17, 23), (33, 33), (31, 8), (30, 30), (5, 27), (19, 19), (33, 14), (31, 14), (28, 31), (0, 9), (14, 25), (16, 29), (18, 26), (1, 31), (15, 36), (25, 17), (21, 9), (15, 16), (16, 32), (6, 15), (27, 9), (10, 37), (12, 31), (9, 12), (33, 15), (24, 19), (33, 34), (33, 32), (29, 18), (6, 35), (6, 11), (23, 18), (19, 8), (17, 16), (19, 17), (11, 24), (6, 34), (8, 23), (33, 2), (11, 36), (3, 30), (6, 37), (0, 30), (2, 27), (3, 24), (29, 27), (14, 24), (32, 25), (30, 34), (19, 4), (33, 23), (14, 4), (20, 24), (14, 27), (33, 31), (1, 23), (20, 35), (23, 0), (22, 17), (26, 34), (25, 9), (18, 27), (19, 33), (0, 37), (6, 30), (30, 26), (3, 4), (3, 1), (19, 25), (15, 18), (9, 8), (3, 37), (17, 6), (18, 35), (21, 28), (30, 18), (26, 12), (29, 21), (9, 11), (15, 0), (30, 31), (3, 16), (25, 4), (33, 35), (25, 35), (23, 10), (6, 1), (2, 15), (10, 6), (14, 14), (5, 28), (5, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "553014", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), 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), (23, 3), (26, 15), (9, 14), (15, 23), (11, 28), (34, 14), (19, 20), (30, 26), (21, 27), (29, 32), (8, 30), (7, 29), (32, 20), (8, 9), (12, 7), (5, 10), (22, 12), (25, 4), (0, 33), (32, 11), (27, 29), (14, 15), (16, 30), (30, 12), (8, 17), (10, 3), (13, 3), (20, 29), (11, 32), (29, 22), (31, 23), (6, 13), (19, 15), (14, 16), (14, 0), (22, 17), (1, 9), (26, 5), (30, 33), (15, 11), (17, 20), (7, 16), (25, 33), (12, 13), (22, 34), (16, 20), (16, 14), (24, 31), (10, 12), (2, 2), (10, 37), (26, 11), (27, 4), (23, 0), (4, 37), (19, 9), (4, 33), (25, 12), (16, 37), (17, 11), (4, 16), (8, 6), (6, 17), (5, 5), (32, 7), (23, 16), (33, 18), (28, 28), (32, 1), (8, 12), (28, 33), (19, 10), (33, 32), (14, 37), (33, 33), (12, 17), (11, 5), (12, 6), (16, 7), (11, 25), (30, 23), (10, 22), (29, 10), (14, 2), (27, 9), (34, 23), (11, 36), (8, 24), (25, 0), (4, 26), (34, 32), (9, 12), (25, 28), (25, 14), (27, 8), (21, 13), (21, 2), (11, 27), (22, 10), (10, 30), (14, 8), (16, 18), (22, 23), (16, 26), (8, 22), (14, 7), (34, 26), (26, 34), (19, 8), (10, 8), (32, 23), (24, 9), (30, 28), (21, 35), (3, 1), (34, 15), (11, 22), (31, 33), (11, 7), (32, 16), (28, 3), (24, 18), (26, 35), (13, 37), (30, 34), (21, 16), (25, 21), (21, 6), (14, 33), (3, 7), (28, 10), (32, 27), (24, 17), (14, 23), (18, 32), (6, 32), (26, 23), (17, 22), (19, 31), (29, 6), (30, 11), (21, 4), (16, 36), (30, 36), (24, 36), (4, 13), (32, 36), (20, 18), (4, 24), (19, 24), (18, 34), (28, 30), (25, 35), (24, 35), (31, 29), (11, 11), (19, 33), (11, 16), (10, 26), (20, 13), (15, 9), (12, 10), (3, 11), (29, 24), (7, 28), (0, 16), (31, 0), (13, 1), (6, 5), (15, 35), (28, 7), (26, 18), (32, 14), (4, 25), (34, 27), (6, 3), (34, 29), (15, 14), (29, 30), (27, 7), (9, 5), (12, 21), (27, 12), (28, 4), (22, 7), (22, 19), (17, 13), (25, 2), (16, 9), (34, 12), (17, 27), (5, 28), (24, 14), (5, 30), (8, 35), (19, 12), (23, 26), (16, 1), (9, 15), (13, 16), (23, 14), (6, 21), (8, 23), (27, 31), (22, 11), (14, 11), (16, 31), (16, 15), (3, 8), (11, 24), (25, 10), (17, 12), (23, 12), (1, 36), (5, 20), (23, 7), (11, 13), (27, 16), (23, 23), (13, 2), (22, 20), (34, 36), (19, 11), (3, 27), (3, 5), (18, 15), (30, 25), (24, 33), (9, 23), (14, 10), (23, 24), (17, 3), (18, 29), (20, 22), (18, 35), (7, 17), (28, 34), (0, 36), (11, 2), (19, 34), (12, 35), (26, 1), (4, 12), (20, 28), (30, 19), (17, 9), (12, 27), (15, 29), (6, 22), (5, 37), (24, 19), (21, 28), (21, 18), (21, 8), (25, 3), (2, 7), (22, 36), (23, 30), (32, 17), (16, 17), (2, 11), (17, 18), (1, 7), (22, 28), (24, 27), (12, 2), (7, 5), (1, 21), (10, 4), (28, 15), (1, 22), (2, 20), (11, 6), (13, 5), (23, 29), (19, 29), (20, 17), (9, 29), (21, 12), (8, 18), (23, 10), (16, 28), (8, 34), (3, 10), (23, 36), (19, 22), (13, 17), (28, 12), (25, 25), (7, 26), (29, 31), (28, 20), (0, 9), (6, 37), (3, 20), (13, 19), (22, 32), (5, 14), (13, 26), (24, 15), (30, 17), (16, 27), (34, 22), (14, 29), (28, 18), (27, 23), (30, 32), (28, 27), (29, 7), (5, 6), (13, 20), (34, 2), (17, 34), (4, 10), (29, 28), (9, 31), (34, 25), (33, 12), (1, 8), (25, 19), (28, 19), (33, 6), (26, 21), (30, 31), (22, 21), (18, 3), (15, 19), (4, 11), (8, 21), (15, 12), (13, 33), (8, 4), (9, 37), (21, 24), (27, 28), (24, 4), (6, 0), (7, 9), (1, 33), (14, 22), (24, 16), (12, 32), (5, 31), (3, 6), (17, 10), (10, 16), (0, 32), (4, 36), (17, 14), (14, 31), (4, 17), (33, 31), (19, 7), (11, 23), (0, 26), (33, 3), (4, 0), (25, 9), (18, 9), (24, 20), (20, 35), (11, 4), (30, 30), (21, 11), (26, 10), (6, 23), (15, 22), (19, 21), (29, 34), (18, 0), (15, 33), (25, 15), (34, 16), (0, 6), (12, 22), (23, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "561816", "dataset": "MATH"}
{"messages": [{"content": "In a 37x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 31), (1, 32), (13, 1), (36, 26), (12, 1), (33, 23), (14, 23), (6, 6), (0, 17), (23, 7), (25, 24), (27, 34), (18, 7), (23, 20), (34, 11), (27, 10), (36, 22), (10, 25), (4, 30), (29, 8), (19, 2), (20, 27), (27, 22), (11, 18), (36, 17), (23, 12), (34, 1), (15, 30), (30, 26), (32, 16), (20, 24), (34, 22), (22, 12), (11, 30), (35, 16), (29, 19), (28, 9), (13, 31), (21, 1), (7, 27), (5, 13), (14, 21), (4, 12), (23, 0), (28, 33), (22, 1), (25, 29), (36, 1), (14, 32), (8, 8), (2, 14), (15, 31), (33, 28), (13, 14), (4, 13), (36, 6), (30, 21), (16, 0), (26, 28), (17, 34), (27, 1), (36, 10), (1, 23), (9, 29), (32, 19), (5, 11), (8, 3), (26, 6), (15, 2), (21, 15), (1, 7), (8, 6), (29, 34), (14, 16), (10, 13), (28, 3), (9, 26), (16, 24), (0, 30), (29, 27), (27, 16), (5, 3), (21, 26), (9, 31), (24, 0), (20, 17), (8, 17), (2, 31), (1, 2), (22, 14), (20, 2), (35, 31), (11, 0), (9, 15), (36, 24), (1, 27), (36, 5), (22, 29), (25, 34), (15, 0), (6, 32), (15, 13), (32, 12), (11, 16), (34, 33), (1, 24), (5, 9), (17, 8), (24, 20), (3, 7), (9, 6), (35, 5), (18, 17), (8, 10), (35, 15), (0, 5), (31, 9), (21, 14), (17, 15), (27, 30), (11, 13), (19, 3), (28, 24), (34, 26), (7, 1), (7, 9), (28, 4), (26, 21), (2, 12), (22, 9), (26, 17), (21, 24), (20, 26), (11, 10), (4, 14), (31, 31), (34, 9), (33, 25), (11, 3), (32, 15), (4, 2), (9, 18), (35, 2), (30, 2), (22, 7), (21, 29), (23, 31), (6, 8), (4, 15), (34, 17), (3, 25), (20, 3), (23, 26), (12, 34), (26, 19), (0, 15), (32, 33), (25, 3), (20, 10), (7, 16), (2, 5), (32, 3), (27, 23), (1, 5), (34, 6), (31, 30), (8, 18), (12, 0), (8, 0), (4, 24), (1, 28), (25, 10), (30, 11), (25, 1), (18, 11), (16, 10), (30, 34), (24, 6), (12, 9), (13, 11), (21, 19), (35, 11), (8, 15), (18, 0), (24, 8), (8, 2), (35, 1), (6, 21), (13, 29), (24, 34), (7, 10), (20, 11), (9, 21), (15, 15), (15, 6), (1, 33), (29, 21), (11, 27), (13, 0), (10, 34), (1, 11), (13, 9), (0, 25), (13, 23), (19, 19), (0, 23), (17, 21), (21, 22), (33, 17), (3, 0), (35, 10), (25, 27), (21, 21), (3, 18), (3, 2), (3, 15), (3, 11), (22, 28), (29, 24), (0, 4), (12, 25), (7, 3), (12, 3), (35, 24), (17, 10), (20, 34), (24, 5), (26, 4), (31, 11), (29, 20), (24, 15), (22, 13), (17, 14), (3, 28), (23, 28), (26, 2), (27, 9), (8, 16), (17, 24), (10, 10), (16, 13), (7, 14), (30, 16), (1, 19), (2, 2), (24, 25), (17, 13), (10, 27), (6, 17), (19, 26), (15, 29), (35, 9), (22, 5), (0, 18), (14, 15), (7, 22), (16, 34), (8, 34), (1, 9), (8, 22), (24, 2), (5, 25), (5, 2), (10, 3), (18, 20), (8, 13), (9, 34), (35, 13), (21, 31), (23, 22), (21, 4), (25, 2), (15, 17), (9, 4), (33, 13), (5, 32), (10, 32), (35, 6), (13, 28), (4, 26), (31, 15), (31, 6), (18, 14), (33, 27), (22, 30), (24, 14), (36, 19), (24, 30), (26, 10), (9, 20), (36, 25), (4, 3), (14, 20), (12, 33), (6, 34), (8, 1), (3, 19), (32, 27), (34, 32), (0, 28), (28, 11), (2, 23), (11, 1), (28, 22), (20, 19), (22, 11), (10, 24), (18, 15), (30, 8), (5, 33), (16, 16), (14, 30), (16, 32), (22, 25), (24, 3), (14, 12), (4, 32), (25, 21), (14, 0), (32, 6), (5, 22), (20, 15), (12, 10), (35, 21), (14, 5), (0, 8), (31, 4), (18, 24), (4, 31), (0, 31), (10, 4), (3, 21), (13, 24), (2, 13), (25, 9), (9, 12), (12, 18), (4, 34), (32, 0), (14, 9), (15, 3), (4, 11), (35, 7), (33, 20), (29, 10), (28, 19), (30, 23), (4, 19), (19, 18), (21, 34), (30, 24), (32, 20), (26, 11), (11, 34), (27, 2), (10, 23), (16, 22), (7, 12), (34, 31), (8, 31), (24, 31), (2, 9), (7, 28), (6, 5), (20, 4), (32, 14), (24, 24), (13, 19), (2, 26), (22, 31), (7, 29), (12, 26), (1, 31), (19, 27), (15, 34), (34, 12), (6, 15), (0, 22), (11, 8), (31, 24), (32, 17), (3, 32), (12, 8), (33, 6), (33, 32), (34, 34), (0, 21), (8, 26), (16, 7), (27, 32), (25, 14), (29, 12), (28, 1), (4, 27), (4, 21), (20, 28), (10, 7), (26, 32), (1, 0), (29, 3), (19, 11), (34, 29), (18, 27), (25, 31), (16, 20), (17, 33), (33, 7), (12, 14), (25, 6), (17, 23), (32, 28), (9, 33), (11, 12), (26, 29), (7, 32), (34, 4), (2, 11), (4, 18), (29, 18), (8, 27), (17, 3), (8, 14), (22, 16), (16, 19), (18, 2), (35, 32), (25, 26), (34, 15), (31, 14), (11, 15), (2, 1), (4, 29), (15, 7), (11, 25), (27, 29), (14, 27), (13, 16), (16, 15), (2, 19), (29, 6), (4, 7), (18, 8), (12, 27), (20, 0), (26, 34), (7, 8), (3, 23), (9, 32), (23, 25), (28, 7), (25, 12), (17, 1), (4, 25), (9, 27), (17, 17), (25, 22)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "899712", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), 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), (9, 2), (17, 9), (16, 9), (29, 35), (23, 19), (27, 19), (24, 35), (16, 20), (11, 5), (12, 8), (8, 15), (14, 21), (16, 32), (23, 18), (28, 5), (12, 34), (16, 4), (17, 24), (6, 16), (13, 34), (5, 22), (14, 13), (25, 13), (20, 33), (1, 3), (10, 29), (3, 29), (14, 25), (5, 14), (22, 6), (17, 33), (22, 30), (2, 20), (33, 35), (22, 10), (33, 15), (28, 26), (5, 35), (18, 14), (25, 34), (11, 13), (14, 2), (10, 37), (10, 34), (4, 2), (29, 21), (21, 26), (32, 11), (2, 1), (17, 0), (12, 18), (26, 4), (1, 20), (14, 11), (28, 4), (34, 3), (12, 7), (26, 25), (14, 22), (34, 12), (0, 21), (17, 26), (10, 33), (29, 12), (1, 17), (9, 21), (0, 5), (12, 36), (5, 7), (21, 2), (8, 6), (22, 12), (12, 26), (34, 18), (32, 14), (6, 25), (22, 24), (0, 34), (9, 27), (18, 32), (29, 1), (9, 28), (25, 6), (30, 17), (27, 35), (13, 28), (8, 33), (22, 32), (30, 34), (19, 23), (34, 28), (12, 19), (33, 23), (18, 10), (33, 28), (21, 15), (30, 1), (19, 33), (12, 2), (3, 31), (14, 19), (1, 36), (7, 9), (17, 5), (1, 2), (31, 1), (4, 10), (18, 4), (0, 16), (27, 22), (5, 37), (8, 1), (28, 12), (32, 24), (7, 26), (14, 35), (13, 24), (7, 18), (21, 34), (17, 16), (16, 8), (7, 14), (28, 16), (26, 33), (1, 16), (17, 15), (13, 9), (0, 20), (33, 25), (28, 14), (29, 0), (20, 2), (17, 31), (10, 25), (8, 13), (15, 29), (21, 30), (25, 15), (6, 21), (33, 31), (19, 24), (0, 35), (7, 37), (16, 19), (10, 24), (28, 23), (3, 4), (18, 29), (3, 22), (29, 32), (15, 16), (0, 10), (6, 24), (0, 28), (12, 14), (24, 34), (10, 21), (31, 5), (13, 22), (1, 6), (8, 18), (0, 19), (27, 2), (11, 18), (17, 17), (32, 5), (15, 13), (28, 27), (30, 37), (21, 7), (23, 25), (27, 5), (7, 22), (28, 36), (17, 7), (12, 35), (14, 20), (26, 6), (27, 8), (26, 21), (24, 5), (6, 37), (25, 8), (9, 33), (16, 21), (7, 35), (4, 33), (4, 21), (6, 18), (10, 4), (25, 30), (12, 6), (22, 23), (13, 16), (31, 4), (5, 9), (29, 11), (22, 27), (30, 14), (12, 3), (16, 3), (3, 37), (11, 17), (5, 21), (24, 13), (20, 21), (7, 10), (27, 32), (18, 17), (25, 24), (14, 34), (31, 21), (30, 30), (7, 20), (30, 20), (29, 15), (7, 1), (29, 24), (8, 14), (19, 7), (26, 1), (9, 35), (11, 36), (27, 31), (21, 32), (16, 1), (18, 22), (17, 28), (20, 37), (19, 0), (11, 32), (17, 8), (23, 8), (25, 21), (31, 28), (9, 14), (8, 3), (34, 16), (5, 32), (15, 36), (0, 13), (3, 0), (4, 19), (31, 36), (0, 25), (15, 30), (6, 4), (21, 16), (2, 14), (16, 36), (5, 27), (32, 37), (6, 27), (17, 36), (11, 34), (1, 31), (16, 12), (9, 32), (11, 25), (34, 10), (29, 9), (10, 13), (5, 34), (29, 13), (16, 2), (24, 29), (23, 20), (34, 11), (10, 8), (19, 12), (11, 23), (19, 18), (30, 7), (25, 12), (2, 6), (7, 0), (30, 35), (24, 20), (33, 12), (1, 15), (23, 11), (26, 19), (2, 13), (16, 17), (7, 7), (16, 6), (25, 1), (3, 14), (7, 36), (21, 8), (34, 32), (26, 2), (13, 30), (23, 13), (26, 8), (28, 25), (10, 26), (25, 16), (5, 18), (32, 9), (2, 28), (19, 26), (20, 24), (9, 10), (7, 24), (29, 26), (13, 25), (15, 3), (23, 23), (3, 9), (10, 35), (15, 17), (1, 1), (9, 30), (0, 30), (5, 33), (32, 4), (3, 8), (26, 28), (2, 35), (7, 34), (9, 37), (14, 17), (31, 6), (33, 32), (19, 1), (8, 32), (2, 23), (15, 28), (3, 20), (4, 7), (8, 37), (31, 27), (8, 36), (28, 13), (14, 27), (11, 14), (7, 31), (34, 25), (24, 25), (26, 18), (15, 31), (25, 27), (15, 34), (20, 35), (10, 10), (27, 14), (21, 36), (8, 35), (2, 36), (30, 26), (18, 16), (15, 10), (16, 5), (22, 7), (28, 19), (11, 2), (6, 19), (19, 22), (21, 3), (8, 24), (15, 20), (29, 19), (25, 25), (13, 13), (26, 24), (3, 19), (3, 11), (20, 5), (8, 19), (28, 34), (2, 2), (17, 19), (21, 9), (22, 29), (30, 18), (10, 0), (30, 27), (15, 27), (14, 3), (1, 30), (32, 16), (2, 0), (9, 11), (27, 1), (34, 14), (28, 2), (22, 31), (5, 15), (4, 28), (16, 15), (13, 37), (5, 36), (26, 14), (19, 10), (16, 28), (27, 18), (23, 2), (7, 8), (29, 18), (15, 24), (9, 19), (24, 23), (33, 0), (25, 36), (14, 28), (15, 15), (2, 7), (16, 7), (24, 0), (9, 3), (19, 30), (10, 7), (5, 4), (12, 32), (30, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "645120", "dataset": "MATH"}
{"messages": [{"content": "In a 33x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (11, 8), (30, 5), (15, 8), (32, 10), (5, 29), (16, 15), (24, 4), (26, 30), (30, 16), (5, 30), (24, 24), (23, 14), (9, 0), (12, 2), (20, 11), (26, 25), (17, 28), (20, 33), (9, 33), (9, 30), (19, 15), (7, 26), (29, 29), (13, 22), (5, 11), (32, 4), (4, 27), (17, 10), (31, 32), (15, 25), (19, 6), (19, 23), (32, 22), (25, 22), (11, 18), (17, 12), (1, 28), (11, 5), (22, 18), (15, 11), (28, 31), (28, 18), (21, 12), (32, 20), (13, 0), (17, 2), (13, 24), (21, 28), (22, 23), (20, 21), (28, 27), (29, 12), (27, 5), (7, 3), (20, 22), (26, 24), (4, 4), (16, 10), (25, 21), (4, 8), (9, 4), (9, 26), (18, 33), (1, 4), (16, 8), (23, 7), (12, 26), (12, 22), (27, 28), (21, 0), (17, 1), (24, 9), (15, 12), (17, 29), (10, 7), (11, 10), (32, 9), (20, 23), (5, 21), (23, 4), (15, 14), (30, 18), (29, 9), (17, 21), (6, 7), (26, 6), (28, 12), (30, 17), (30, 33), (21, 19), (22, 4), (8, 27), (18, 0), (13, 25), (12, 0), (17, 3), (20, 30), (12, 29), (28, 19), (30, 9), (13, 3), (15, 9), (11, 26), (25, 3), (25, 28), (32, 2), (6, 29), (16, 33), (19, 26), (23, 22), (17, 11), (5, 1), (18, 5), (16, 6), (1, 7), (3, 27), (28, 0), (1, 2), (20, 3), (3, 18), (22, 31), (3, 23), (26, 26), (5, 14), (22, 20), (24, 3), (32, 14), (27, 15), (21, 17), (4, 15), (14, 18), (4, 19), (15, 16), (19, 29), (30, 0), (7, 21), (28, 20), (25, 12), (24, 26), (17, 22), (21, 23), (15, 15), (11, 17), (26, 22), (29, 20), (30, 10), (10, 13), (21, 24), (0, 4), (15, 6), (13, 18), (27, 6), (28, 14), (25, 2), (20, 27), (20, 0), (30, 27), (22, 21), (30, 3), (12, 3), (23, 19), (18, 18), (32, 1), (28, 6), (25, 13), (0, 17), (14, 22), (4, 11), (3, 30), (23, 3), (9, 10), (13, 17), (22, 16), (23, 20), (11, 1), (0, 6), (28, 23), (21, 31), (19, 11), (3, 21), (16, 22), (0, 33), (13, 1), (0, 22), (20, 31), (28, 15), (15, 23), (6, 26), (21, 3), (32, 8), (21, 27), (9, 14), (10, 29), (25, 10), (0, 7), (14, 21), (30, 14), (24, 21), (29, 7), (26, 2), (1, 32), (9, 28), (20, 13), (30, 7), (6, 17), (19, 4), (15, 4), (27, 27), (5, 6), (31, 17), (4, 2), (8, 23), (17, 5), (8, 30), (22, 3), (28, 2), (9, 18), (28, 4), (27, 24), (12, 7), (20, 2), (3, 0), (25, 16), (20, 18), (18, 25), (2, 31), (7, 17), (5, 33), (4, 5), (13, 2), (32, 12), (3, 22), (17, 17), (21, 29), (21, 13), (10, 25), (25, 7), (17, 30), (18, 14), (22, 12), (22, 30), (22, 22), (24, 27), (22, 26), (23, 2), (12, 23), (27, 1), (15, 24), (11, 31), (10, 16), (4, 6), (17, 14), (5, 16), (19, 1), (23, 31), (17, 8), (2, 2), (9, 15), (8, 13), (25, 27), (8, 8), (17, 26), (2, 6), (12, 27), (30, 1), (20, 1), (5, 4), (1, 30), (8, 32), (14, 24), (8, 20), (15, 22), (7, 11), (13, 29), (6, 19), (22, 10), (17, 4), (9, 6), (1, 20), (4, 24), (7, 25), (10, 21), (32, 23), (9, 22), (25, 8), (30, 26), (28, 3), (29, 23), (7, 23), (27, 3), (5, 10), (10, 24), (10, 8), (11, 20), (6, 23), (4, 32), (11, 22), (29, 14), (0, 29), (11, 21), (18, 28), (16, 21), (25, 15), (19, 20), (6, 31), (14, 16), (22, 28), (31, 10), (17, 20), (27, 23), (2, 28), (22, 9), (20, 28), (16, 24), (31, 29), (12, 15), (18, 1), (20, 24), (32, 3), (14, 27), (8, 4), (7, 20), (16, 1), (8, 6), (8, 31), (10, 10), (27, 22), (21, 32), (31, 9), (30, 28), (23, 29), (4, 10), (13, 5), (13, 6), (18, 4), (3, 24), (4, 23), (27, 18), (2, 29), (24, 10), (29, 11), (23, 16), (13, 10), (3, 4), (9, 13), (32, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3016", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (30, 0), (30, 26), (25, 25), (5, 35), (14, 35), (20, 8), (26, 25), (32, 32), (24, 15), (2, 32), (7, 13), (13, 19), (1, 22), (20, 34), (4, 4), (23, 20), (19, 7), (33, 18), (26, 0), (17, 31), (18, 27), (27, 2), (5, 23), (9, 19), (33, 12), (24, 23), (18, 17), (13, 0), (25, 6), (30, 9), (13, 23), (31, 20), (25, 8), (27, 31), (31, 13), (1, 25), (20, 18), (4, 30), (27, 21), (4, 26), (32, 8), (17, 32), (5, 18), (10, 26), (27, 36), (25, 4), (20, 16), (31, 19), (24, 21), (8, 8), (31, 21), (23, 26), (16, 32), (28, 21), (31, 33), (29, 24), (5, 31), (31, 31), (30, 10), (31, 35), (8, 20), (25, 10), (18, 8), (22, 7), (8, 30), (29, 13), (30, 33), (25, 36), (28, 13), (25, 14), (17, 0), (24, 11), (13, 22), (27, 7), (12, 32), (25, 7), (20, 13), (25, 23), (26, 5), (6, 27), (31, 29), (17, 26), (23, 2), (7, 24), (15, 13), (21, 22), (3, 28), (4, 17), (30, 28), (18, 16), (31, 32), (6, 18), (28, 4), (1, 30), (14, 29), (7, 4), (17, 14), (11, 11), (30, 7), (11, 2), (1, 16), (33, 13), (33, 21), (2, 12), (15, 27), (15, 20), (9, 0), (14, 9), (30, 15), (29, 19), (7, 8), (25, 35), (8, 31), (24, 9), (31, 25), (29, 29), (11, 32), (11, 21), (19, 5), (12, 24), (23, 24), (15, 32), (22, 1), (31, 27), (24, 0), (20, 12), (28, 33), (15, 6), (21, 0), (10, 16), (0, 27), (14, 20), (16, 16), (2, 16), (2, 28), (6, 13), (14, 2), (32, 0), (1, 21), (3, 13), (20, 25), (22, 36), (18, 32), (15, 26), (27, 22), (24, 31), (9, 1), (17, 5), (26, 36), (9, 17), (26, 24), (24, 18), (21, 30), (21, 32), (3, 36), (19, 22), (4, 16), (16, 3), (25, 12), (20, 10), (23, 35), (18, 23), (24, 4), (22, 33), (9, 25), (26, 29), (7, 16), (29, 5), (19, 2), (4, 12), (28, 17), (14, 10), (7, 30), (22, 14), (32, 2), (23, 19), (32, 31), (26, 21), (15, 25), (32, 16), (9, 29), (27, 12), (4, 21), (1, 20), (16, 1), (23, 33), (27, 13), (9, 7), (1, 3), (28, 31), (31, 5), (5, 11), (25, 20), (27, 30), (3, 27), (25, 27), (31, 0), (26, 35), (19, 29), (4, 34), (21, 18), (2, 7), (0, 8), (33, 6), (14, 14), (28, 28), (16, 24), (24, 27), (6, 19), (33, 28), (19, 17), (32, 1), (20, 32), (7, 34), (12, 29), (7, 29), (1, 2), (1, 27), (1, 15), (7, 27), (33, 19), (13, 17), (22, 25), (17, 19), (12, 16), (19, 30), (8, 5), (2, 35), (24, 16), (31, 1), (17, 36), (19, 21), (13, 9), (8, 19), (18, 31), (20, 17), (2, 4), (16, 10), (25, 30), (7, 6), (10, 8), (25, 24), (29, 31), (21, 17), (30, 2), (7, 3), (10, 7), (1, 14), (20, 7), (10, 36), (6, 36), (3, 33), (17, 27), (2, 27), (11, 5), (12, 28), (12, 10), (10, 32), (12, 33), (22, 13), (3, 8), (26, 23), (10, 30), (16, 35), (17, 12), (31, 3), (23, 3), (3, 22), (8, 24), (31, 6), (0, 26), (33, 2), (18, 5), (3, 2), (31, 16), (15, 11), (32, 13), (9, 15), (0, 13), (9, 20), (6, 8), (6, 9), (13, 26), (8, 27), (18, 7), (12, 15), (20, 19), (28, 32), (24, 6), (0, 20), (7, 1), (16, 34), (19, 34), (17, 21), (21, 28), (14, 23), (29, 15), (33, 7), (30, 19), (8, 7), (10, 12), (21, 2), (7, 18), (4, 27), (17, 1), (10, 4), (30, 30), (6, 28), (14, 18), (19, 24), (20, 14), (28, 5), (3, 0), (3, 21), (33, 33), (32, 33), (20, 26), (1, 0), (14, 3), (7, 5), (14, 28), (13, 2), (29, 6), (19, 3), (10, 25), (16, 11), (28, 9), (18, 35), (21, 3), (17, 7), (22, 3), (5, 33), (19, 27), (21, 16), (30, 6), (9, 23), (22, 15), (28, 7), (32, 24), (26, 10), (9, 5), (0, 33), (10, 33), (33, 32), (5, 6), (24, 2), (19, 9), (23, 6), (21, 19), (18, 12), (3, 14), (26, 15), (22, 34), (29, 27), (15, 34), (12, 14), (24, 34), (14, 21), (2, 34), (8, 28), (29, 33), (28, 35), (16, 5), (16, 26), (5, 9), (21, 6), (33, 11), (22, 26), (16, 0), (21, 29), (26, 11), (1, 8), (14, 27), (29, 32), (23, 8), (24, 35), (1, 33), (29, 21), (4, 23), (7, 17), (29, 8), (5, 0), (6, 6), (14, 7), (2, 26), (6, 31), (0, 36), (10, 15), (16, 25), (11, 20), (30, 17), (10, 10), (23, 1), (27, 35), (18, 29), (18, 25), (27, 28), (24, 13), (2, 29), (17, 33), (15, 10), (30, 35), (11, 14), (17, 13), (19, 18), (12, 19), (30, 22), (31, 34), (5, 5), (20, 15), (11, 29), (25, 5), (8, 14), (5, 20), (16, 31), (15, 28), (21, 7), (31, 23), (5, 8), (15, 33), (27, 16), (12, 18), (2, 22), (19, 23), (17, 11), (22, 6), (1, 32), (1, 26), (20, 3), (28, 23), (7, 31), (16, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "632016", "dataset": "MATH"}
{"messages": [{"content": "In a 38x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 34), 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), (28, 30), (17, 18), (28, 0), (31, 32), (1, 22), (37, 3), (23, 5), (8, 19), (14, 18), (17, 12), (33, 15), (16, 13), (20, 30), (25, 16), (9, 15), (21, 8), (20, 18), (23, 13), (9, 4), (2, 29), (26, 2), (14, 22), (9, 20), (11, 14), (8, 11), (26, 4), (8, 31), (21, 2), (4, 23), (6, 18), (6, 12), (31, 26), (18, 11), (29, 21), (15, 31), (29, 31), (13, 17), (28, 24), (7, 9), (12, 34), (37, 19), (22, 32), (26, 15), (28, 22), (24, 32), (8, 4), (14, 4), (24, 12), (16, 14), (0, 6), (6, 29), (33, 34), (3, 21), (0, 20), (17, 28), (8, 9), (18, 24), (25, 17), (34, 16), (27, 13), (20, 12), (15, 9), (2, 11), (37, 16), (22, 9), (29, 25), (32, 18), (21, 34), (22, 12), (17, 9), (36, 19), (25, 2), (8, 23), (13, 6), (22, 21), (26, 9), (1, 0), (0, 32), (12, 24), (4, 10), (6, 30), (21, 28), (32, 16), (1, 12), (36, 5), (35, 26), (2, 31), (12, 8), (0, 4), (23, 6), (4, 32), (15, 26), (8, 25), (27, 2), (21, 19), (12, 0), (6, 20), (35, 12), (0, 18), (36, 32), (9, 32), (1, 20), (1, 2), (35, 3), (11, 24), (36, 29), (34, 19), (30, 27), (21, 14), (0, 10), (31, 20), (19, 13), (2, 5), (33, 24), (29, 0), (10, 0), (20, 1), (27, 19), (8, 6), (35, 2), (8, 10), (2, 18), (4, 0), (1, 21), (21, 29), (13, 30), (18, 18), (30, 0), (25, 32), (23, 33), (14, 23), (10, 31), (30, 26), (20, 24), (30, 32), (31, 14), (23, 0), (33, 5), (31, 34), (33, 12), (14, 32), (23, 17), (4, 11), (13, 32), (14, 26), (34, 2), (37, 10), (33, 26), (9, 28), (30, 31), (35, 31), (13, 23), (11, 19), (29, 12), (24, 19), (22, 26), (26, 29), (11, 18), (21, 4), (13, 19), (36, 0), (27, 5), (32, 19), (27, 28), (32, 4), (28, 16), (6, 33), (18, 25), (17, 24), (24, 16), (30, 13), (31, 1), (17, 26), (28, 33), (26, 23), (6, 4), (30, 21), (32, 23), (6, 3), (28, 18), (11, 0), (31, 3), (31, 11), (30, 17), (4, 9), (30, 33), (33, 33), (30, 4), (6, 22), (29, 8), (31, 23), (33, 23), (18, 16), (27, 4), (10, 19), (22, 0), (19, 16), (5, 27), (3, 3), (23, 9), (10, 26), (18, 23), (10, 29), (25, 26), (30, 1), (20, 6), (15, 21), (2, 23), (11, 27), (33, 20), (4, 28), (10, 4), (16, 2), (14, 0), (22, 19), (26, 21), (20, 5), (20, 13), (13, 20), (32, 32), (21, 10), (21, 21), (6, 17), (14, 21), (17, 20), (18, 21), (7, 26), (37, 23), (25, 7), (15, 23), (14, 31), (31, 16), (12, 1), (16, 3), (15, 13), (16, 5), (6, 27), (3, 26), (14, 7), (11, 4), (11, 8), (16, 21), (13, 21), (37, 29), (33, 1), (37, 20), (37, 9), (14, 16), (13, 16), (2, 8), (19, 15), (32, 29), (28, 2), (10, 25), (3, 13), (9, 26), (17, 1), (0, 27), (33, 7), (33, 11), (7, 8), (37, 26), (31, 29), (11, 34), (6, 21), (29, 26), (11, 3), (13, 2), (13, 8), (16, 4), (31, 13), (21, 7), (1, 13), (8, 32), (9, 9), (14, 9), (23, 23), (29, 2), (15, 14), (27, 11), (25, 1), (18, 14), (16, 0), (0, 7), (1, 4), (5, 24), (16, 6), (18, 29), (30, 16), (19, 5), (1, 7), (19, 22), (21, 30), (11, 6), (26, 1), (24, 8), (16, 34), (15, 12), (3, 24), (12, 9), (11, 28), (8, 27), (34, 15), (6, 23), (7, 20), (20, 32), (2, 7), (15, 24), (19, 33), (0, 19), (29, 20), (6, 6), (3, 0), (24, 18), (15, 7), (21, 31), (21, 33), (35, 1), (29, 16), (16, 11), (8, 0), (11, 12), (7, 19), (14, 34), (19, 2), (28, 32), (5, 6), (29, 6), (35, 28), (4, 27), (27, 29), (4, 22), (2, 34), (10, 33), (32, 33), (31, 7), (23, 16), (37, 0), (16, 12), (20, 29), (13, 25), (19, 28), (23, 1), (10, 16), (35, 22), (5, 14), (30, 30), (33, 28), (27, 17), (34, 32), (26, 28), (27, 30), (9, 5), (12, 30), (21, 26), (10, 2), (12, 27), (12, 4), (25, 8), (24, 17), (34, 20), (35, 11), (33, 9), (19, 6), (18, 33), (23, 29), (35, 7), (20, 15), (10, 7), (5, 34), (14, 29), (19, 21), (7, 12), (5, 3), (30, 9), (14, 13), (26, 19), (10, 30), (35, 0), (17, 23), (25, 25), (29, 13), (26, 32), (25, 13), (28, 10), (12, 14), (33, 2), (23, 14), (11, 32), (6, 16), (18, 22), (3, 25), (30, 3), (33, 8), (11, 11), (20, 17), (19, 19), (10, 28), (34, 34), (10, 14), (17, 22), (36, 34), (29, 32), (3, 5), (28, 20), (13, 1), (25, 19), (16, 10), (1, 27), (18, 15), (35, 14), (13, 10), (28, 13), (12, 25), (10, 23), (27, 27), (4, 34), (1, 34), (22, 10), (7, 17), (5, 29), (34, 12), (25, 21)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "705600", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), 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), (5, 25), (35, 3), (28, 13), (8, 10), (36, 4), (15, 2), (20, 25), (35, 31), (31, 12), (22, 18), (1, 21), (6, 19), (12, 0), (17, 20), (34, 2), (8, 22), (31, 4), (10, 19), (18, 27), (23, 32), (38, 32), (30, 24), (7, 15), (27, 16), (8, 26), (37, 21), (4, 14), (28, 3), (4, 23), (27, 21), (17, 11), (34, 10), (23, 28), (11, 21), (16, 37), (2, 31), (37, 13), (12, 7), (11, 20), (31, 36), (15, 19), (23, 1), (12, 29), (14, 2), (4, 1), (20, 20), (4, 25), (26, 27), (37, 27), (3, 33), (9, 2), (32, 34), (11, 26), (35, 15), (26, 31), (27, 24), (32, 5), (2, 10), (35, 12), (12, 36), (3, 1), (13, 12), (3, 5), (22, 22), (0, 22), (8, 5), (23, 29), (23, 18), (17, 27), (11, 19), (21, 23), (30, 30), (38, 19), (35, 7), (20, 10), (8, 36), (0, 14), (1, 27), (12, 11), (26, 16), (19, 19), (27, 7), (2, 0), (5, 3), (26, 26), (34, 0), (22, 6), (14, 31), (0, 12), (13, 29), (16, 15), (37, 4), (38, 23), (2, 18), (36, 18), (7, 17), (37, 36), (6, 8), (3, 15), (15, 9), (33, 8), (38, 31), (17, 4), (18, 3), (34, 34), (17, 16), (33, 33), (0, 20), (10, 34), (21, 25), (0, 30), (8, 19), (29, 14), (28, 23), (10, 9), (12, 20), (25, 22), (16, 4), (4, 35), (3, 18), (11, 11), (16, 36), (11, 25), (6, 2), (4, 19), (23, 8), (20, 35), (20, 7), (4, 9), (35, 19), (24, 23), (34, 11), (11, 18), (18, 21), (10, 13), (31, 34), (30, 18), (27, 17), (17, 19), (18, 4), (26, 4), (30, 19), (17, 2), (8, 11), (14, 3), (34, 4), (34, 9), (34, 30), (29, 34), (9, 9), (31, 13), (5, 8), (15, 10), (12, 8), (20, 11), (26, 7), (36, 29), (6, 31), (28, 6), (10, 5), (15, 20), (24, 6), (6, 34), (20, 14), (30, 9), (1, 5), (22, 34), (35, 13), (15, 23), (7, 26), (3, 24), (16, 5), (17, 33), (18, 25), (23, 35), (5, 2), (12, 5), (37, 2), (33, 32), (18, 10), (16, 29), (5, 12), (34, 1), (26, 32), (1, 3), (7, 33), (8, 32), (14, 0), (31, 17), (37, 12), (37, 3), (11, 34), (21, 4), (23, 21), (21, 27), (24, 37), (9, 12), (9, 6), (2, 12), (5, 21), (24, 2), (30, 7), (35, 24), (35, 16), (9, 24), (13, 34), (3, 3), (0, 10), (0, 21), (0, 2), (1, 12), (28, 27), (14, 27), (14, 37), (4, 18), (27, 34), (31, 32), (17, 35), (15, 28), (7, 34), (15, 3), (25, 25), (8, 7), (17, 30), (34, 15), (2, 16), (36, 36), (10, 7), (12, 33), (16, 3), (31, 16), (14, 23), (5, 22), (22, 9), (36, 17), (31, 19), (17, 21), (32, 29), (5, 27), (33, 28), (4, 29), (29, 29), (4, 36), (31, 3), (21, 30), (11, 29), (5, 23), (5, 5), (28, 22), (32, 26), (5, 32), (10, 23), (35, 27), (29, 15), (20, 5), (13, 3), (3, 20), (19, 14), (3, 30), (24, 33), (13, 6), (16, 27), (28, 16), (30, 26), (6, 36), (23, 22), (21, 19), (6, 20), (31, 22), (22, 28), (31, 25), (28, 0), (23, 30), (26, 8), (13, 23), (37, 28), (25, 20), (15, 13), (36, 10), (37, 18), (36, 11), (29, 9), (13, 15), (24, 20), (26, 6), (2, 26), (4, 30), (24, 14), (0, 5), (37, 14), (21, 28), (24, 35), (5, 17), (6, 7), (6, 23), (0, 34), (9, 10), (36, 13), (6, 6), (18, 26), (31, 8), (28, 36), (12, 16), (21, 31), (18, 7), (9, 27), (37, 33), (17, 28), (3, 21), (32, 17), (25, 24), (27, 3), (35, 36), (22, 32), (31, 6), (25, 30), (9, 0), (27, 11), (3, 4), (25, 23), (6, 32), (16, 22), (10, 33), (2, 21), (14, 28), (38, 33), (16, 9), (19, 17), (29, 22), (15, 6), (24, 5), (12, 22), (27, 30), (28, 32), (2, 15), (31, 9), (13, 37), (9, 25), (0, 33), (9, 1), (0, 11), (37, 7), (8, 9), (7, 14), (33, 15), (12, 12), (6, 13), (2, 14), (6, 18), (8, 18), (28, 33), (28, 7), (17, 15), (33, 2), (25, 11), (17, 18), (15, 31), (11, 2), (11, 23), (16, 23), (33, 24), (33, 17), (7, 11), (24, 30), (19, 28), (16, 21), (27, 20), (27, 33), (7, 1), (3, 2), (17, 24), (12, 37), (26, 18), (35, 34), (0, 36), (13, 28), (20, 32), (24, 22), (3, 29), (19, 23), (36, 35), (10, 10), (34, 20), (7, 9), (1, 37), (3, 37), (36, 28), (37, 15), (6, 27), (36, 6), (31, 28), (22, 37), (27, 25), (7, 25), (10, 18), (8, 35), (38, 14), (27, 12), (5, 15), (11, 24), (20, 28), (26, 3), (38, 26), (13, 16), (27, 5), (5, 10), (32, 21), (17, 14), (34, 25), (22, 1), (14, 14), (38, 7), (34, 21), (24, 26), (38, 21), (25, 2), (24, 16), (29, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "626688", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), 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), (35, 22), (16, 18), (20, 12), (35, 20), (16, 14), (28, 6), (2, 1), (16, 22), (7, 26), (9, 30), (33, 28), (2, 21), (5, 6), (5, 20), (31, 3), (35, 26), (15, 6), (34, 25), (33, 21), (15, 7), (9, 15), (15, 5), (17, 5), (25, 22), (33, 22), (7, 36), (12, 13), (13, 35), (8, 11), (10, 29), (35, 25), (8, 19), (27, 12), (4, 24), (18, 36), (34, 34), (3, 8), (3, 31), (2, 12), (35, 0), (31, 38), (1, 24), (28, 17), (1, 0), (2, 10), (5, 29), (15, 15), (32, 37), (7, 24), (18, 5), (34, 8), (17, 18), (27, 17), (4, 27), (3, 32), (34, 13), (6, 32), (22, 7), (25, 16), (30, 36), (9, 1), (9, 11), (13, 19), (2, 13), (10, 13), (16, 8), (2, 25), (4, 8), (11, 27), (22, 20), (20, 37), (5, 22), (22, 21), (0, 13), (31, 25), (6, 15), (27, 4), (20, 25), (31, 37), (17, 14), (10, 30), (12, 37), (15, 22), (17, 4), (35, 8), (13, 38), (5, 32), (19, 14), (30, 5), (10, 20), (6, 2), (1, 29), (17, 19), (35, 1), (23, 25), (9, 22), (11, 18), (13, 10), (21, 35), (8, 22), (28, 1), (24, 11), (5, 27), (1, 1), (20, 32), (25, 28), (7, 6), (4, 4), (25, 6), (28, 13), (2, 0), (9, 7), (19, 29), (3, 22), (8, 15), (17, 28), (17, 26), (26, 33), (1, 2), (2, 9), (29, 37), (33, 6), (5, 14), (35, 36), (19, 32), (27, 20), (11, 17), (12, 9), (25, 14), (29, 36), (25, 4), (23, 14), (5, 2), (6, 24), (2, 36), (3, 24), (33, 30), (8, 16), (3, 30), (24, 21), (35, 31), (24, 35), (0, 25), (32, 12), (10, 1), (8, 3), (2, 30), (4, 7), (5, 24), (26, 26), (21, 19), (5, 3), (34, 30), (11, 8), (7, 7), (5, 36), (35, 16), (0, 9), (30, 13), (14, 32), (21, 12), (13, 1), (30, 16), (32, 38), (19, 21), (15, 38), (5, 23), (17, 24), (6, 26), (20, 27), (28, 38), (18, 26), (32, 25), (28, 35), (32, 10), (33, 38), (19, 25), (34, 24), (11, 29), (2, 5), (2, 2), (35, 28), (7, 29), (22, 4), (8, 1), (29, 1), (16, 28), (9, 34), (7, 35), (6, 20), (21, 22), (10, 4), (8, 8), (32, 3), (14, 21), (14, 15), (33, 36), (23, 18), (33, 9), (20, 20), (10, 23), (25, 11), (25, 0), (28, 32), (26, 10), (33, 19), (6, 13), (35, 11), (35, 18), (31, 28), (34, 23), (6, 7), (33, 13), (12, 30), (21, 34), (10, 33), (22, 19), (29, 8), (25, 33), (5, 33), (9, 37), (23, 20), (6, 4), (4, 31), (27, 8), (6, 12), (33, 11), (34, 11), (5, 21), (31, 15), (15, 11), (13, 32), (10, 17), (13, 20), (35, 13), (21, 4), (6, 11), (16, 6), (27, 15), (20, 22), (32, 16), (10, 21), (13, 24), (9, 10), (16, 0), (13, 37), (24, 17), (22, 32), (15, 27), (4, 13), (0, 30), (27, 14), (1, 4), (20, 1), (33, 20), (16, 16), (14, 19), (20, 38), (29, 20), (14, 11), (34, 12), (0, 10), (19, 11), (28, 22), (29, 5), (25, 7), (8, 23), (29, 16), (16, 20), (30, 30), (33, 16), (20, 5), (25, 30), (29, 35), (34, 21), (2, 14), (20, 14), (1, 28), (26, 20), (17, 11), (31, 32), (21, 6), (35, 29), (12, 6), (28, 20), (35, 17), (8, 26), (26, 9), (12, 18), (21, 9), (11, 11), (14, 24), (32, 36), (5, 28), (28, 15), (0, 11), (30, 32), (18, 17), (24, 23), (33, 34), (21, 15), (4, 6), (10, 2), (16, 1), (34, 0), (1, 19), (14, 2), (28, 2), (4, 29), (15, 31), (13, 9), (35, 10), (33, 33), (2, 35), (15, 10), (19, 30), (23, 11), (4, 22), (25, 12), (23, 4), (13, 12), (33, 10), (31, 12), (23, 3), (31, 27), (30, 20), (18, 31), (35, 9), (10, 31), (26, 21), (27, 28), (20, 30), (11, 20), (9, 23), (3, 1), (0, 7), (13, 6), (13, 17), (0, 12), (26, 5), (15, 4), (19, 34), (1, 15), (27, 23), (27, 31), (27, 0), (5, 0), (18, 15), (16, 13), (34, 15), (7, 32), (35, 34), (13, 14), (11, 23), (16, 10), (35, 19), (30, 2), (28, 12), (6, 29), (34, 14), (8, 5), (23, 19), (20, 9), (27, 18), (2, 17), (23, 6), (24, 32), (15, 16), (31, 0), (1, 5), (9, 16), (5, 1), (11, 37), (3, 16), (34, 7), (24, 37), (32, 32), (10, 5), (18, 23), (3, 33), (2, 23), (12, 34), (27, 38), (5, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233280", "dataset": "MATH"}
{"messages": [{"content": "In a 35x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 36), 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), (17, 18), (26, 14), (30, 25), (18, 14), (18, 19), (0, 19), (14, 31), (15, 26), (20, 5), (6, 26), (22, 4), (22, 8), (24, 30), (33, 11), (15, 1), (19, 29), (19, 22), (11, 32), (1, 35), (22, 14), (4, 22), (21, 0), (34, 16), (26, 30), (20, 21), (19, 27), (30, 22), (5, 28), (19, 1), (18, 5), (5, 9), (10, 31), (10, 29), (34, 27), (31, 36), (15, 7), (26, 19), (23, 33), (24, 5), (32, 19), (11, 3), (9, 13), (4, 2), (1, 12), (6, 8), (34, 29), (31, 23), (20, 24), (20, 17), (32, 33), (24, 6), (31, 9), (32, 9), (15, 14), (12, 5), (0, 10), (25, 6), (13, 7), (9, 9), (28, 9), (21, 29), (27, 5), (2, 31), (1, 29), (29, 16), (20, 4), (6, 12), (27, 27), (17, 1), (8, 19), (17, 3), (13, 27), (29, 28), (28, 28), (13, 13), (29, 30), (12, 30), (21, 7), (14, 1), (3, 23), (34, 9), (29, 29), (18, 34), (24, 33), (19, 17), (22, 7), (31, 25), (23, 32), (29, 21), (31, 26), (29, 24), (31, 6), (12, 27), (7, 12), (24, 19), (26, 16), (2, 32), (22, 0), (8, 20), (12, 3), (11, 13), (23, 12), (26, 17), (21, 11), (24, 11), (12, 6), (8, 15), (17, 35), (25, 22), (30, 32), (1, 24), (20, 20), (23, 26), (18, 8), (0, 13), (14, 5), (4, 1), (10, 27), (7, 7), (1, 10), (20, 27), (21, 13), (31, 13), (23, 9), (19, 23), (27, 26), (18, 27), (34, 2), (34, 23), (31, 10), (10, 11), (18, 23), (5, 6), (5, 17), (24, 1), (24, 29), (10, 12), (11, 7), (5, 33), (14, 28), (32, 8), (33, 18), (1, 36), (15, 36), (34, 4), (2, 1), (22, 6), (32, 30), (3, 26), (0, 26), (26, 9), (17, 33), (9, 24), (12, 22), (23, 25), (7, 13), (17, 28), (34, 33), (6, 11), (9, 6), (11, 2), (19, 13), (25, 26), (12, 2), (28, 16), (15, 27), (12, 7), (13, 28), (20, 19), (9, 19), (12, 23), (1, 32), (16, 32), (32, 20), (13, 10), (26, 7), (19, 20), (1, 30), (13, 23), (2, 28), (2, 10), (16, 8), (15, 25), (23, 35), (18, 18), (14, 21), (17, 30), (8, 16), (19, 30), (6, 20), (5, 12), (24, 18), (24, 4), (10, 9), (32, 2), (15, 22), (5, 18), (2, 30), (8, 26), (22, 31), (25, 32), (30, 12), (14, 25), (34, 19), (15, 17), (11, 8), (11, 6), (28, 5), (29, 4), (0, 25), (17, 16), (5, 21), (26, 15), (27, 10), (12, 34), (12, 31), (7, 5), (26, 4), (12, 36), (4, 19), (4, 0), (17, 4), (30, 27), (13, 12), (25, 3), (12, 24), (9, 5), (0, 4), (30, 17), (5, 26), (19, 14), (25, 0), (24, 7), (25, 21), (24, 22), (29, 31), (26, 18), (17, 19), (20, 10), (9, 2), (1, 16), (2, 26), (4, 13), (32, 10), (14, 0), (20, 32), (0, 31), (19, 2), (32, 32), (13, 30), (24, 14), (34, 28), (3, 1), (1, 26), (25, 4), (32, 21), (4, 20), (0, 33), (13, 21), (9, 20), (13, 19), (19, 5), (5, 29), (3, 24), (5, 20), (19, 28), (25, 1), (22, 19), (22, 5), (10, 30), (21, 9), (13, 34), (34, 32), (17, 7), (18, 30), (23, 18), (3, 32), (31, 16), (3, 28), (18, 26), (6, 25), (0, 35), (22, 17), (13, 1), (7, 29), (5, 30), (11, 0), (33, 21), (1, 27), (1, 9), (23, 1), (6, 21), (34, 17), (18, 9), (13, 0), (0, 12), (12, 25), (28, 31), (0, 6), (22, 33), (10, 3), (30, 31), (29, 35), (9, 10), (11, 11), (1, 28), (13, 4), (13, 26), (15, 35), (0, 3), (24, 16), (4, 25), (20, 26), (31, 24), (2, 6), (20, 15), (8, 18), (32, 29), (27, 36), (28, 14), (15, 32), (22, 10), (4, 24), (1, 33), (28, 32), (28, 12), (4, 18), (15, 30), (21, 26), (21, 20), (12, 18), (29, 18), (27, 7), (28, 23), (21, 6), (0, 29), (32, 1), (29, 12), (11, 29), (7, 28), (33, 10), (9, 25), (26, 0), (9, 4), (2, 36), (24, 12), (3, 3), (4, 4), (7, 10), (33, 7), (34, 7), (18, 15), (13, 17), (30, 29), (16, 6), (19, 18), (2, 12), (4, 5), (16, 19), (4, 15), (26, 11), (16, 18), (4, 29), (28, 22), (7, 6), (28, 21), (21, 23), (11, 34), (30, 9), (27, 19), (19, 11), (22, 12), (28, 0), (14, 12), (18, 12), (31, 0), (4, 36), (24, 23), (14, 7), (28, 10), (23, 28), (25, 2), (3, 29), (9, 34), (6, 31), (26, 20), (34, 34), (19, 10), (27, 4), (22, 13), (10, 24), (14, 17), (19, 0), (21, 5), (0, 11), (18, 6), (33, 9), (1, 23), (17, 9), (32, 11), (21, 1), (20, 35), (3, 2), (31, 32), (26, 25), (33, 27), (8, 36), (23, 22), (33, 16), (8, 25), (10, 19), (7, 14), (26, 22), (19, 19), (7, 4), (27, 23), (21, 28), (27, 12), (6, 19), (20, 16), (29, 27), (15, 15), (29, 5), (18, 10), (21, 18), (1, 22), (22, 24), (18, 32), (30, 23), (3, 33), (11, 31), (6, 17), (25, 23), (8, 0), (16, 17), (17, 5), (24, 21), (7, 34), (6, 10), (29, 1), (29, 6), (12, 14), (2, 7), (16, 5), (17, 25), (23, 20), (6, 18), (31, 4), (20, 31), (14, 24), (25, 35), (3, 6), (13, 3), (26, 27), (31, 29), (7, 15), (21, 14), (6, 2), (24, 9), (11, 10), (20, 34), (24, 25), (29, 11), (33, 1), (3, 27), (9, 7), (1, 11), (33, 19), (16, 1), (33, 23), (10, 7), (7, 9), (13, 5), (28, 3), (22, 9), (23, 10), (16, 12), (8, 28), (5, 16), (4, 6), (13, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2508", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 31), (8, 1), (1, 30), (12, 0), (11, 5), (27, 0), (10, 25), (11, 18), (4, 27), (5, 12), (26, 4), (29, 16), (20, 20), (10, 32), (8, 31), (12, 18), (19, 12), (20, 33), (29, 17), (6, 19), (27, 31), (15, 5), (19, 16), (22, 21), (0, 15), (8, 26), (26, 14), (33, 28), (17, 12), (19, 33), (12, 25), (7, 23), (2, 3), (28, 13), (3, 5), (33, 24), (6, 4), (27, 26), (29, 32), (25, 9), (6, 28), (8, 5), (13, 11), (6, 30), (28, 0), (8, 9), (32, 9), (6, 17), (19, 4), (28, 34), (2, 4), (27, 27), (8, 33), (3, 28), (2, 31), (14, 21), (19, 14), (7, 33), (17, 1), (18, 29), (32, 5), (15, 25), (6, 12), (7, 30), (8, 6), (22, 27), (24, 28), (22, 11), (15, 33), (10, 26), (12, 33), (13, 23), (19, 1), (10, 21), (5, 32), (21, 10), (22, 13), (23, 19), (20, 34), (33, 32), (25, 27), (18, 26), (2, 19), (10, 27), (3, 23), (27, 9), (16, 4), (4, 4), (15, 8), (27, 23), (16, 3), (6, 13), (19, 21), (21, 34), (28, 6), (25, 4), (19, 23), (5, 20), (29, 19), (0, 16), (31, 29), (31, 9), (17, 0), (12, 12), (5, 23), (26, 3), (25, 5), (21, 0), (16, 21), (4, 17), (24, 23), (3, 3), (10, 22), (26, 0), (9, 3), (31, 19), (15, 16), (2, 5), (30, 34), (22, 23), (30, 10), (22, 26), (9, 4), (18, 27), (26, 25), (21, 5), (10, 18), (8, 20), (26, 26), (24, 15), (10, 20), (9, 34), (26, 11), (7, 27), (24, 18), (2, 11), (13, 4), (20, 6), (23, 13), (29, 3), (23, 18), (4, 20), (19, 26), (0, 34), (4, 5), (8, 2), (30, 1), (9, 27), (18, 22), (33, 35), (31, 7), (23, 34), (28, 18), (25, 17), (5, 36), (33, 21), (17, 10), (22, 16), (5, 34), (24, 9), (3, 20), (22, 7), (16, 17), (33, 18), (10, 4), (10, 3), (33, 27), (14, 0), (21, 9), (14, 24), (22, 1), (6, 10), (28, 11), (10, 7), (28, 22), (13, 36), (0, 24), (21, 14), (27, 28), (29, 4), (3, 22), (0, 8), (1, 27), (5, 29), (22, 9), (25, 22), (16, 23), (5, 24), (3, 11), (13, 30), (26, 6), (4, 24), (14, 4), (25, 26), (25, 31), (22, 19), (12, 4), (10, 31), (20, 22), (32, 31), (3, 7), (24, 19), (33, 23), (8, 8), (1, 10), (33, 33), (2, 30), (9, 24), (11, 23), (28, 35), (25, 20), (30, 14), (26, 10), (9, 16), (27, 4), (0, 13), (13, 27), (7, 7), (0, 5), (32, 14), (14, 26), (12, 28), (22, 35), (29, 28), (31, 27), (28, 2), (12, 36), (13, 20), (0, 18), (23, 16), (27, 33), (32, 1), (31, 12), (25, 23), (26, 13), (6, 26), (33, 26), (14, 15), (33, 11), (12, 13), (13, 18), (0, 26), (31, 36), (7, 10), (9, 12), (30, 26), (18, 11), (11, 28), (15, 10), (12, 15), (31, 8), (1, 19), (20, 0), (27, 35), (32, 28), (10, 28), (5, 18), (16, 19), (3, 12), (30, 11), (31, 21), (31, 18), (26, 33), (4, 13), (4, 26), (22, 36), (15, 34), (16, 30), (3, 0), (33, 12), (12, 32), (2, 34), (30, 30), (14, 13), (26, 1), (28, 19), (11, 1), (22, 20), (0, 17), (22, 4), (10, 0), (8, 28), (10, 23), (15, 29), (0, 19), (19, 18), (14, 35), (18, 34), (26, 7), (4, 23), (30, 12), (31, 14), (31, 31), (19, 10), (9, 13), (28, 7), (31, 4), (11, 30), (31, 17), (24, 22), (26, 2), (31, 15), (0, 1), (13, 24), (29, 30), (31, 10), (23, 31), (29, 8), (19, 7), (24, 1), (1, 18), (31, 34), (33, 10), (30, 23), (26, 28), (19, 36), (26, 21), (2, 2), (30, 17), (6, 6), (20, 25), (8, 25), (13, 19), (22, 14), (20, 32), (23, 26), (29, 31), (4, 32), (26, 35), (27, 7), (3, 32), (15, 18), (1, 6), (19, 35), (16, 7), (13, 1), (16, 18), (1, 7), (8, 12), (19, 15), (14, 8), (4, 8), (7, 1), (17, 36), (20, 21), (11, 0), (13, 15), (20, 4), (1, 12), (9, 20), (23, 24), (7, 18), (18, 17), (26, 22), (6, 35), (12, 29), (14, 27), (15, 23), (13, 5), (6, 14), (5, 19), (23, 3), (27, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "919940", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), 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), (11, 24), (36, 26), (20, 16), (21, 12), (7, 2), (7, 18), (31, 27), (13, 18), (28, 0), (4, 11), (5, 11), (12, 21), (11, 23), (23, 8), (16, 31), (0, 15), (32, 0), (29, 15), (5, 6), (3, 23), (15, 12), (21, 17), (4, 30), (33, 14), (9, 19), (28, 1), (5, 4), (1, 26), (21, 14), (32, 4), (3, 8), (7, 12), (7, 25), (19, 11), (18, 2), (29, 28), (10, 17), (2, 9), (15, 30), (16, 28), (29, 21), (33, 21), (8, 30), (20, 22), (12, 29), (33, 1), (3, 19), (12, 6), (23, 11), (13, 16), (10, 21), (28, 25), (24, 18), (8, 26), (19, 13), (13, 27), (33, 19), (33, 8), (31, 8), (27, 12), (13, 19), (10, 13), (32, 12), (33, 4), (1, 2), (18, 0), (14, 24), (13, 22), (18, 11), (22, 13), (25, 0), (35, 5), (17, 8), (22, 26), (9, 11), (21, 13), (27, 19), (18, 3), (6, 22), (13, 13), (27, 31), (34, 18), (25, 23), (21, 1), (27, 4), (24, 27), (27, 22), (17, 22), (34, 3), (23, 15), (29, 7), (28, 22), (28, 9), (3, 31), (15, 8), (12, 18), (15, 31), (20, 8), (5, 9), (36, 5), (22, 27), (32, 9), (3, 13), (34, 11), (18, 13), (21, 2), (12, 26), (27, 17), (36, 27), (8, 28), (31, 4), (35, 1), (0, 25), (19, 7), (0, 13), (24, 7), (33, 3), (18, 20), (34, 31), (13, 29), (36, 28), (19, 8), (30, 21), (11, 13), (3, 4), (22, 15), (35, 23), (34, 6), (16, 6), (20, 21), (18, 29), (21, 31), (24, 19), (15, 25), (19, 17), (17, 10), (0, 26), (16, 5), (24, 17), (27, 27), (33, 9), (8, 6), (21, 19), (2, 19), (3, 14), (31, 0), (7, 28), (12, 28), (16, 4), (35, 12), (6, 13), (32, 31), (9, 4), (1, 12), (18, 21), (25, 20), (34, 0), (14, 5), (18, 26), (25, 31), (13, 14), (27, 29), (8, 12), (26, 25), (17, 26), (30, 27), (5, 21), (30, 15), (15, 13), (9, 7), (33, 6), (14, 7), (5, 1), (15, 19), (0, 8), (15, 15), (15, 18), (32, 27), (33, 5), (9, 14), (15, 20), (16, 16), (13, 15), (15, 3), (11, 21), (9, 0), (10, 7), (11, 17), (17, 29), (23, 19), (25, 1), (17, 18), (10, 3), (3, 28), (28, 15), (7, 15), (16, 7), (25, 5), (18, 15), (1, 20), (28, 20), (23, 14), (20, 30), (30, 25), (2, 29), (28, 19), (32, 13), (2, 31), (4, 19), (27, 9), (29, 24), (6, 11), (12, 7), (17, 6), (5, 16), (8, 16), (24, 5), (19, 10), (5, 3), (16, 26), (19, 30), (7, 29), (29, 25), (36, 25), (36, 1), (25, 3), (1, 31), (30, 0), (12, 13), (16, 18), (9, 30), (21, 7), (4, 0), (36, 22), (19, 25), (21, 6), (19, 27), (15, 2), (9, 3), (2, 15), (18, 25), (20, 9), (17, 27), (33, 24), (33, 10), (13, 3), (4, 10), (6, 24), (1, 7), (18, 19), (28, 11), (1, 23), (20, 28), (14, 28), (24, 3), (7, 5), (32, 21), (33, 29), (12, 3), (10, 18), (10, 5), (17, 13), (30, 11), (10, 30), (18, 18), (26, 12), (15, 27), (31, 26), (16, 21), (30, 20), (29, 10), (4, 3), (35, 16), (1, 25), (31, 15), (21, 28), (36, 3), (7, 4), (30, 30), (21, 10), (25, 13), (5, 29), (23, 23), (6, 2), (2, 24), (14, 30), (12, 12), (34, 21), (36, 14), (10, 25), (19, 26), (36, 21), (7, 8), (13, 20), (31, 13), (6, 21), (28, 28), (26, 3), (26, 30), (27, 3), (7, 7), (24, 26), (18, 30), (30, 9), (2, 30), (15, 28), (31, 12), (22, 30), (35, 13), (3, 30), (16, 20), (32, 25), (3, 20), (32, 10), (5, 31), (13, 2), (29, 6), (17, 21), (33, 16), (10, 28), (18, 9), (11, 3), (6, 28), (13, 30), (14, 9), (32, 6), (1, 18), (36, 2), (2, 23), (26, 0), (6, 30), (27, 26), (0, 20), (2, 8), (3, 22), (34, 27), (10, 15), (10, 29), (7, 19), (7, 10), (1, 15), (25, 30), (36, 9), (12, 23), (35, 31), (23, 4), (19, 12), (36, 11), (18, 1), (22, 24), (9, 20), (14, 16), (0, 18), (6, 15), (34, 26), (5, 12), (7, 14), (21, 29), (19, 19), (27, 25), (32, 8), (23, 26), (3, 7), (22, 9), (9, 24), (30, 24), (20, 10), (5, 20), (26, 16), (11, 8), (26, 10), (34, 30), (10, 27), (20, 24), (30, 12), (36, 23), (14, 2), (36, 0), (31, 23), (22, 3), (1, 29), (7, 3), (32, 16), (29, 29), (20, 23), (25, 10), (7, 21), (29, 4), (34, 2), (23, 13), (6, 1), (21, 9), (30, 19)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "381888", "dataset": "MATH"}
{"messages": [{"content": "In a 30x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 22), (3, 18), (27, 10), (28, 15), (26, 15), (7, 17), (28, 22), (20, 34), (3, 8), (19, 10), (27, 23), (11, 21), (13, 20), (6, 18), (27, 9), (26, 9), (27, 15), (1, 13), (18, 12), (27, 13), (4, 24), (5, 11), (10, 16), (28, 6), (3, 9), (5, 9), (18, 8), (21, 22), (10, 22), (13, 13), (11, 18), (10, 30), (22, 18), (19, 7), (26, 7), (7, 13), (25, 6), (28, 14), (20, 22), (26, 3), (17, 13), (23, 0), (19, 12), (0, 3), (17, 0), (16, 26), (27, 20), (27, 17), (11, 8), (19, 21), (3, 0), (3, 20), (4, 26), (25, 11), (23, 14), (10, 24), (16, 0), (2, 16), (11, 24), (25, 5), (10, 3), (1, 5), (1, 21), (24, 5), (28, 20), (20, 19), (5, 1), (14, 4), (6, 25), (22, 29), (2, 2), (21, 13), (23, 20), (24, 33), (11, 17), (17, 32), (5, 13), (17, 14), (14, 26), (4, 25), (1, 29), (8, 21), (5, 30), (9, 11), (0, 34), (0, 24), (10, 32), (3, 28), (13, 0), (4, 31), (10, 7), (8, 14), (23, 27), (24, 34), (19, 34), (19, 16), (29, 17), (11, 10), (21, 7), (13, 6), (19, 24), (5, 0), (14, 2), (14, 21), (5, 23), (19, 19), (11, 27), (20, 3), (13, 5), (22, 31), (23, 1), (24, 16), (20, 14), (24, 21), (1, 26), (15, 32), (12, 21), (11, 30), (25, 23), (19, 25), (14, 28), (16, 9), (1, 25), (2, 29), (21, 14), (12, 14), (17, 18), (29, 13), (25, 13), (15, 9), (7, 7), (22, 20), (11, 28), (5, 34), (2, 30), (14, 5), (16, 13), (15, 10), (15, 33), (6, 28), (25, 30), (21, 1), (22, 4), (29, 32), (16, 24), (22, 3), (1, 10), (28, 24), (15, 22), (17, 26), (4, 5), (22, 19), (7, 32), (4, 14), (26, 29), (13, 29), (3, 13), (13, 21), (23, 2), (5, 21), (17, 5), (22, 5), (26, 22), (18, 18), (1, 30), (1, 33), (13, 8), (8, 29), (0, 27), (24, 22), (20, 29), (28, 23), (17, 11), (13, 11), (12, 20), (1, 12), (13, 34), (4, 1), (29, 23), (2, 9), (22, 27), (26, 27), (21, 33), (2, 31), (17, 33), (4, 11), (19, 15), (10, 12), (15, 30), (3, 25), (0, 8), (11, 26), (20, 7), (28, 9), (14, 17), (21, 4), (15, 34), (22, 17), (10, 5), (29, 9), (3, 33), (18, 29), (4, 4), (10, 20), (9, 29), (5, 6), (7, 2), (3, 2), (13, 12), (28, 31), (15, 15), (2, 27), (9, 5), (5, 19), (12, 5), (1, 32), (9, 31), (10, 10), (3, 4), (18, 22), (26, 28), (26, 12), (15, 2), (0, 30), (7, 33), (9, 18), (23, 31), (9, 25), (20, 23), (8, 32), (2, 4), (7, 18), (26, 14), (17, 8), (20, 20), (4, 23), (20, 21), (6, 34), (29, 6), (0, 17), (24, 24), (22, 13), (12, 13), (14, 19), (9, 9), (21, 2), (14, 1), (16, 28), (10, 31), (29, 29), (0, 10), (29, 14), (16, 34), (11, 22), (18, 5), (16, 30), (11, 34), (29, 4), (0, 19), (28, 13), (6, 0), (22, 11), (11, 1), (9, 0), (27, 8), (24, 19), (22, 9), (25, 15), (15, 1), (27, 12), (29, 30), (6, 14), (17, 17), (24, 32), (0, 22), (7, 19), (17, 10), (29, 10), (19, 4), (6, 1), (7, 22), (13, 25), (24, 13), (0, 18), (19, 11), (5, 16), (26, 21), (29, 27), (1, 9), (5, 22), (16, 11), (7, 8), (14, 20), (24, 25), (11, 25), (7, 11), (14, 25), (25, 17), (13, 9), (2, 20), (24, 27), (5, 7), (1, 0), (21, 8), (1, 18), (8, 8), (5, 12), (13, 26), (25, 31), (20, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "417240", "dataset": "MATH"}
{"messages": [{"content": "In a 34x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 36), 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), (12, 12), (10, 29), (28, 10), (31, 14), (27, 8), (26, 34), (20, 28), (13, 30), (25, 36), (27, 26), (24, 27), (21, 27), (15, 10), (7, 13), (27, 21), (10, 0), (26, 33), (9, 28), (32, 6), (27, 34), (4, 8), (27, 27), (18, 8), (17, 7), (30, 7), (23, 31), (5, 12), (22, 11), (11, 5), (12, 8), (21, 2), (32, 24), (13, 22), (33, 25), (7, 0), (32, 18), (28, 16), (0, 15), (22, 17), (19, 20), (18, 31), (33, 13), (15, 29), (3, 2), (23, 20), (20, 7), (32, 25), (2, 7), (7, 17), (21, 1), (6, 19), (4, 3), (19, 1), (27, 18), (1, 29), (14, 18), (22, 13), (0, 10), (28, 7), (5, 31), (27, 1), (4, 2), (26, 14), (17, 17), (9, 34), (31, 13), (6, 5), (24, 29), (19, 14), (22, 31), (29, 25), (4, 32), (19, 15), (19, 25), (10, 2), (28, 30), (26, 36), (22, 28), (21, 20), (4, 23), (2, 24), (11, 13), (26, 15), (13, 24), (28, 23), (28, 28), (27, 15), (5, 9), (23, 33), (21, 4), (5, 32), (12, 3), (31, 35), (8, 6), (30, 30), (21, 26), (9, 25), (10, 17), (25, 23), (22, 34), (9, 31), (27, 32), (15, 1), (25, 33), (8, 29), (16, 25), (2, 17), (20, 4), (32, 33), (9, 22), (11, 26), (5, 33), (23, 35), (16, 35), (11, 34), (1, 34), (18, 33), (30, 29), (15, 16), (30, 33), (5, 20), (26, 8), (24, 11), (12, 27), (15, 33), (25, 0), (3, 4), (26, 31), (23, 2), (1, 28), (16, 13), (17, 8), (28, 33), (33, 11), (33, 34), (19, 0), (15, 36), (32, 35), (19, 2), (22, 25), (10, 22), (8, 16), (16, 34), (18, 18), (24, 21), (28, 18), (27, 7), (24, 35), (14, 17), (11, 16), (25, 32), (32, 30), (16, 14), (30, 32), (28, 15), (21, 19), (8, 28), (22, 16), (13, 11), (31, 32), (17, 20), (28, 20), (2, 31), (14, 24), (4, 16), (26, 25), (13, 23), (20, 22), (23, 22), (9, 36), (28, 11), (16, 22), (6, 30), (31, 27), (16, 27), (31, 22), (2, 36), (17, 25), (17, 35), (8, 17), (32, 3), (12, 21), (22, 22), (5, 7), (28, 0), (28, 22), (18, 25), (18, 14), (15, 7), (18, 17), (3, 16), (18, 10), (23, 10), (29, 7), (23, 19), (5, 14), (5, 3), (20, 0), (20, 34), (8, 8), (3, 19), (7, 34), (23, 5), (7, 28), (30, 22), (1, 12), (6, 16), (22, 7), (17, 3), (15, 18), (6, 15), (8, 11), (19, 16), (26, 23), (17, 14), (18, 20), (28, 8), (25, 27), (22, 26), (1, 10), (0, 1), (20, 11), (10, 19), (15, 13), (21, 17), (8, 24), (26, 13), (13, 10), (33, 4), (29, 2), (10, 35), (31, 7), (31, 19), (31, 28), (25, 10), (23, 28), (7, 2), (16, 7), (17, 24), (4, 31), (22, 35), (26, 2), (3, 26), (4, 26), (18, 36), (2, 2), (13, 26), (27, 6), (15, 31), (27, 5), (4, 0), (7, 23), (6, 32), (22, 6), (28, 34), (21, 3), (4, 13), (10, 34), (22, 33), (5, 36), (30, 12), (9, 19), (15, 6), (4, 21), (29, 5), (25, 25), (11, 33), (16, 12), (9, 32), (20, 27), (30, 9), (28, 14), (24, 33), (8, 27), (29, 8), (9, 13), (0, 14), (6, 12), (26, 35), (9, 17), (26, 18), (25, 20), (26, 0), (24, 26), (13, 27), (18, 11), (2, 0), (32, 17), (13, 5), (22, 4), (9, 8), (4, 5), (32, 23), (28, 35), (10, 4), (0, 23), (0, 22), (18, 4), (10, 21), (4, 20), (29, 17), (29, 23), (12, 18), (2, 8), (24, 0), (12, 36), (7, 11), (3, 13), (4, 14), (17, 12), (4, 34), (28, 3), (22, 1), (16, 29), (12, 0), (5, 5), (16, 30), (24, 25), (4, 12), (30, 26), (14, 30), (12, 29), (23, 24), (14, 20), (0, 11), (28, 31), (2, 20), (12, 30), (28, 36), (11, 10), (5, 10), (11, 31), (19, 17), (11, 4), (9, 0), (27, 19), (0, 7), (17, 31), (9, 16), (2, 10), (24, 14), (9, 7), (9, 3), (6, 6), (19, 31), (21, 33), (20, 8), (10, 32), (21, 36), (33, 9), (19, 4), (14, 32), (25, 9), (19, 21), (26, 16), (16, 32), (26, 26), (30, 3), (21, 22), (23, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "715368", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), 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), (22, 4), (0, 30), (26, 32), (7, 3), (17, 35), (32, 36), (22, 11), (7, 8), (32, 21), (3, 29), (5, 1), (2, 30), (16, 31), (23, 37), (2, 20), (31, 21), (13, 12), (4, 20), (28, 35), (11, 10), (7, 38), (16, 38), (7, 5), (28, 16), (17, 24), (8, 4), (22, 26), (6, 33), (15, 16), (15, 24), (13, 7), (20, 11), (20, 38), (27, 27), (18, 14), (26, 22), (11, 22), (14, 7), (10, 33), (2, 18), (20, 13), (24, 32), (24, 35), (23, 30), (1, 4), (26, 16), (11, 8), (17, 32), (1, 36), (26, 30), (13, 2), (13, 28), (3, 3), (30, 4), (21, 26), (2, 13), (10, 15), (15, 18), (21, 34), (8, 32), (15, 1), (15, 19), (3, 13), (27, 10), (32, 26), (26, 1), (14, 26), (23, 13), (9, 33), (30, 0), (13, 3), (24, 23), (2, 15), (10, 14), (5, 29), (28, 3), (24, 27), (10, 37), (11, 28), (27, 17), (32, 18), (5, 18), (13, 0), (2, 8), (16, 3), (18, 6), (4, 16), (19, 30), (27, 4), (3, 20), (3, 12), (5, 11), (30, 6), (13, 18), (22, 9), (16, 11), (26, 17), (17, 18), (1, 24), (30, 19), (21, 37), (30, 32), (24, 34), (13, 24), (1, 17), (28, 37), (25, 7), (3, 8), (27, 16), (1, 37), (9, 8), (30, 34), (8, 2), (4, 17), (22, 8), (23, 1), (3, 22), (2, 37), (5, 19), (1, 27), (31, 13), (20, 16), (12, 10), (22, 6), (29, 6), (2, 12), (17, 23), (2, 19), (9, 9), (11, 9), (29, 7), (22, 31), (19, 25), (16, 2), (18, 0), (21, 19), (31, 22), (1, 26), (21, 2), (8, 35), (31, 0), (12, 2), (4, 28), (1, 30), (24, 25), (25, 1), (10, 16), (23, 16), (10, 7), (17, 34), (8, 16), (26, 37), (8, 11), (7, 25), (32, 8), (14, 36), (21, 32), (31, 38), (24, 1), (13, 20), (24, 19), (32, 11), (7, 34), (21, 17), (12, 30), (6, 31), (10, 28), (32, 22), (2, 16), (19, 21), (10, 21), (27, 28), (30, 3), (9, 13), (30, 38), (18, 34), (8, 23), (9, 12), (20, 9), (20, 6), (6, 7), (8, 28), (16, 33), (0, 38), (15, 20), (23, 5), (13, 30), (7, 17), (9, 26), (8, 1), (3, 9), (31, 5), (2, 17), (19, 16), (21, 18), (4, 22), (21, 25), (25, 19), (1, 22), (17, 9), (5, 5), (32, 32), (13, 5), (4, 15), (6, 22), (10, 1), (16, 16), (31, 4), (20, 5), (12, 29), (13, 38), (1, 19), (25, 30), (14, 35), (3, 16), (9, 23), (14, 15), (4, 6), (15, 34), (1, 2), (13, 9), (22, 18), (21, 0), (8, 3), (6, 36), (2, 6), (16, 6), (31, 26), (27, 31), (7, 19), (13, 37), (27, 11), (24, 10), (16, 24), (29, 34), (30, 24), (2, 10), (10, 19), (26, 18), (21, 27), (29, 35), (7, 2), (17, 28), (19, 11), (19, 36), (20, 10), (24, 12), (15, 0), (31, 16), (18, 21), (15, 30), (19, 4), (4, 35), (17, 8), (8, 21), (26, 5), (1, 11), (28, 17), (29, 16), (24, 15), (6, 19), (1, 23), (32, 25), (0, 2), (14, 25), (27, 20), (29, 21), (15, 33), (7, 21), (13, 16), (18, 8), (16, 15), (20, 15), (21, 31), (29, 25), (5, 25), (16, 30), (9, 28), (0, 15), (31, 14), (7, 22), (17, 38), (5, 4), (23, 32), (21, 33), (29, 22), (12, 25), (28, 11), (18, 18), (17, 11), (1, 32), (24, 9), (5, 16), (3, 21), (27, 18), (3, 10), (19, 38), (27, 33), (17, 33), (23, 11), (21, 24), (25, 13), (13, 19), (6, 13), (0, 18), (5, 2), (12, 26), (12, 6), (28, 30), (25, 26), (3, 0), (25, 23), (13, 32), (6, 35), (8, 31), (9, 32), (14, 34), (7, 28), (9, 20), (21, 8), (21, 28), (14, 8), (20, 31), (20, 18), (32, 34), (12, 23), (0, 22), (23, 36), (23, 38), (9, 0), (22, 13), (13, 22), (20, 29), (32, 5), (16, 27), (8, 30), (12, 8), (18, 20), (25, 3), (14, 9), (30, 30), (21, 14), (16, 1), (25, 9), (1, 16), (12, 4), (8, 10), (2, 35), (11, 7), (9, 11), (15, 6), (9, 34), (8, 29), (26, 4), (30, 23), (20, 8), (25, 34), (10, 8), (30, 29), (19, 6), (1, 33), (26, 19), (29, 33), (6, 18), (31, 32), (23, 21), (12, 21), (18, 37), (29, 9), (31, 25), (7, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "440640", "dataset": "MATH"}
{"messages": [{"content": "In a 38x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 28), (35, 1), (23, 14), (23, 9), (30, 13), (14, 4), (0, 21), (35, 18), (19, 2), (36, 31), (5, 27), (8, 16), (32, 9), (32, 10), (33, 11), (27, 24), (2, 20), (18, 11), (8, 30), (26, 21), (34, 32), (3, 3), (22, 11), (20, 32), (17, 17), (9, 18), (19, 26), (31, 2), (3, 30), (23, 11), (34, 27), (26, 18), (31, 26), (32, 23), (4, 24), (8, 22), (9, 27), (11, 33), (12, 15), (19, 10), (20, 30), (30, 24), (35, 25), (19, 25), (0, 16), (9, 29), (1, 14), (21, 8), (9, 16), (2, 31), (23, 10), (19, 29), (0, 29), (10, 33), (31, 23), (16, 12), (6, 7), (6, 33), (0, 24), (12, 28), (5, 21), (21, 1), (36, 2), (17, 20), (15, 8), (21, 6), (2, 30), (37, 17), (27, 3), (24, 3), (32, 25), (0, 1), (20, 4), (0, 28), (17, 1), (10, 17), (35, 2), (37, 15), (14, 3), (26, 28), (22, 32), (25, 1), (10, 21), (14, 0), (14, 31), (29, 14), (14, 27), (18, 28), (7, 4), (26, 32), (25, 16), (1, 24), (31, 8), (31, 20), (0, 6), (36, 7), (12, 18), (34, 28), (14, 19), (23, 31), (25, 17), (20, 3), (12, 6), (30, 9), (7, 31), (6, 24), (0, 7), (28, 24), (10, 23), (15, 12), (14, 17), (37, 23), (18, 29), (9, 12), (32, 0), (16, 15), (5, 19), (35, 8), (17, 28), (11, 8), (14, 23), (6, 18), (37, 10), (15, 2), (7, 32), (36, 21), (24, 10), (15, 1), (15, 3), (24, 25), (34, 8), (25, 11), (14, 21), (21, 0), (27, 17), (5, 15), (37, 18), (28, 22), (27, 6), (32, 5), (33, 6), (16, 3), (10, 12), (22, 28), (25, 31), (17, 13), (4, 12), (6, 16), (9, 8), (35, 13), (23, 25), (6, 8), (18, 2), (14, 12), (13, 14), (32, 16), (17, 25), (28, 20), (17, 8), (15, 23), (28, 11), (0, 11), (26, 30), (7, 18), (3, 4), (19, 22), (23, 5), (34, 17), (7, 7), (4, 21), (7, 12), (27, 28), (18, 1), (29, 24), (16, 33), (31, 1), (20, 12), (18, 8), (10, 3), (35, 6), (23, 20), (11, 30), (14, 25), (1, 25), (23, 27), (10, 25), (12, 11), (6, 31), (16, 18), (4, 29), (31, 11), (26, 16), (35, 9), (22, 4), (11, 1), (22, 15), (18, 18), (7, 20), (22, 12), (30, 2), (11, 29), (12, 33), (24, 0), (29, 18), (1, 10), (26, 0), (33, 1), (25, 8), (2, 7), (12, 30), (20, 18), (37, 32), (8, 9), (32, 15), (31, 18), (20, 29), (16, 8), (9, 6), (11, 11), (33, 30), (21, 24), (31, 33), (23, 2), (36, 0), (24, 1), (13, 29), (24, 14), (6, 9), (13, 20), (8, 28), (21, 23), (13, 23), (31, 9), (23, 22), (9, 20), (22, 10), (15, 9), (8, 25), (14, 5), (32, 27), (8, 29), (1, 21), (31, 27), (3, 25), (12, 1), (6, 19), (25, 0), (30, 6), (23, 21), (5, 2), (7, 17), (24, 23), (10, 30), (4, 14), (20, 20), (30, 10), (25, 19), (13, 7), (27, 13), (29, 5), (6, 15), (8, 26), (33, 28), (16, 13), (19, 17), (28, 30), (4, 1), (17, 10), (34, 19), (0, 30), (27, 22), (35, 30), (10, 4), (0, 12), (9, 26), (10, 26), (2, 33), (15, 0), (19, 28), (8, 27), (0, 33), (25, 20), (16, 0), (28, 19), (20, 6), (8, 31), (33, 31), (33, 0), (12, 21), (14, 24), (29, 0), (12, 29), (23, 17), (9, 33), (28, 9), (25, 10), (30, 4), (6, 13), (14, 26), (36, 14), (11, 32), (30, 33), (0, 5), (24, 30), (22, 0), (32, 14), (5, 25), (8, 33), (37, 30), (28, 16), (27, 33), (0, 27), (4, 30), (19, 33), (29, 30), (35, 20), (4, 19), (16, 24), (4, 31), (0, 18), (15, 30), (4, 8), (3, 10), (11, 4), (13, 25), (24, 6), (1, 16), (15, 14), (32, 18), (0, 8), (19, 27), (24, 9), (17, 27), (29, 3), (25, 15), (12, 8), (15, 28), (2, 13), (26, 8), (36, 32), (31, 19), (2, 19), (22, 3), (37, 3), (6, 2), (33, 2), (36, 10), (37, 12), (34, 13), (20, 26), (22, 22), (12, 12), (18, 9), (33, 29), (37, 8), (33, 4), (32, 29), (35, 11), (28, 18), (10, 22), (7, 15), (9, 9), (32, 12), (2, 0), (23, 23), (10, 24), (29, 17), (10, 27), (25, 30), (3, 32), (22, 19), (32, 30), (6, 26), (7, 11), (15, 20), (10, 1), (21, 5), (36, 17), (13, 2), (5, 18), (30, 3), (2, 10), (13, 21), (29, 2), (18, 4), (6, 25), (1, 4), (13, 13), (2, 3), (35, 28), (27, 27), (2, 24), (26, 2), (0, 25), (15, 18), (9, 32), (0, 3), (5, 28), (17, 2), (32, 19), (29, 33), (31, 28), (21, 14), (22, 5), (14, 8), (19, 16), (16, 6), (13, 31), (13, 24), (24, 33), (32, 6), (15, 26), (8, 10), (33, 10), (19, 6), (15, 25), (24, 15), (0, 19), (25, 5), (23, 13), (26, 15), (26, 31), (32, 11), (22, 8), (29, 1), (6, 3), (29, 32), (35, 21), (7, 3), (17, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "531300", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 21), (11, 0), (8, 24), (38, 33), (11, 15), (36, 17), (30, 12), (34, 29), (10, 23), (8, 9), (7, 33), (16, 20), (33, 15), (9, 20), (2, 1), (18, 11), (4, 15), (28, 9), (6, 24), (6, 25), (21, 20), (28, 23), (30, 32), (1, 27), (31, 11), (4, 5), (24, 6), (23, 34), (14, 19), (15, 17), (10, 22), (17, 0), (29, 11), (12, 10), (33, 8), (30, 20), (15, 13), (25, 14), (31, 28), (27, 22), (15, 20), (30, 5), (33, 29), (36, 25), (2, 14), (12, 29), (16, 7), (0, 34), (3, 22), (22, 2), (21, 21), (38, 28), (23, 25), (31, 33), (28, 10), (9, 13), (17, 11), (22, 19), (22, 23), (3, 25), (35, 24), (34, 18), (2, 18), (38, 27), (19, 27), (19, 33), (17, 27), (25, 4), (9, 25), (15, 23), (0, 31), (36, 2), (33, 6), (31, 5), (25, 33), (15, 9), (4, 3), (15, 1), (2, 11), (38, 14), (6, 5), (29, 0), (27, 20), (10, 30), (18, 3), (37, 11), (4, 0), (6, 14), (26, 30), (34, 3), (8, 13), (16, 5), (4, 26), (32, 30), (12, 3), (29, 16), (7, 6), (36, 0), (33, 17), (4, 1), (1, 20), (5, 5), (19, 22), (37, 30), (38, 15), (0, 12), (20, 9), (0, 27), (7, 25), (7, 27), (27, 17), (7, 16), (20, 6), (24, 4), (20, 16), (19, 29), (23, 12), (31, 8), (3, 19), (34, 13), (4, 6), (0, 20), (21, 26), (29, 28), (17, 14), (23, 31), (7, 1), (27, 33), (21, 18), (12, 26), (12, 5), (14, 10), (23, 15), (31, 7), (21, 27), (32, 3), (31, 4), (1, 17), (30, 3), (30, 15), (36, 10), (0, 26), (29, 26), (26, 23), (14, 34), (36, 15), (34, 11), (20, 34), (23, 9), (36, 3), (9, 15), (13, 5), (18, 33), (8, 0), (26, 22), (30, 8), (23, 28), (5, 28), (12, 15), (0, 10), (3, 23), (17, 7), (21, 22), (32, 33), (30, 13), (18, 10), (13, 3), (34, 6), (7, 12), (12, 23), (30, 11), (0, 29), (13, 1), (34, 0), (21, 19), (14, 11), (19, 21), (10, 6), (37, 29), (38, 0), (24, 20), (26, 11), (32, 34), (25, 6), (12, 27), (31, 17), (36, 33), (32, 29), (27, 19), (17, 15), (15, 21), (14, 9), (10, 25), (7, 5), (19, 0), (8, 19), (17, 23), (25, 11), (8, 27), (16, 30), (14, 12), (33, 21), (6, 9), (26, 17), (9, 28), (24, 24), (30, 23), (1, 29), (23, 32), (29, 27), (38, 1), (20, 2), (30, 19), (21, 9), (32, 1), (6, 17), (25, 8), (24, 10), (19, 24), (23, 21), (24, 27), (35, 1), (26, 32), (9, 3), (16, 8), (35, 10), (10, 12), (30, 10), (17, 18), (20, 23), (7, 10), (35, 9), (33, 13), (19, 34), (1, 23), (5, 4), (24, 31), (17, 26), (15, 25), (34, 1), (18, 2), (26, 6), (13, 30), (20, 3), (23, 11), (27, 32), (23, 33), (30, 30), (23, 29), (25, 13), (8, 10), (19, 7), (37, 0), (20, 21), (9, 23), (3, 30), (2, 29), (18, 30), (29, 1), (30, 21), (18, 17), (31, 25), (7, 34), (13, 19), (6, 11), (25, 32), (24, 33), (37, 10), (1, 4), (5, 29), (6, 23), (38, 30), (23, 8), (5, 1), (33, 10), (29, 9), (26, 2), (15, 6), (18, 24), (12, 8), (37, 27), (11, 13), (7, 3), (4, 11), (11, 6), (19, 31), (3, 21), (11, 33), (10, 24), (29, 13), (19, 6), (31, 34), (21, 16), (5, 27), (11, 20), (28, 12), (16, 12), (2, 13), (33, 28), (30, 9), (33, 4), (19, 16), (34, 20), (22, 1), (7, 14), (21, 28), (2, 19), (35, 0), (37, 5), (34, 9), (18, 8), (9, 16), (18, 18), (13, 2), (36, 14), (27, 5), (3, 8), (15, 16), (33, 3), (16, 13), (14, 0), (2, 34), (1, 9), (35, 31), (36, 1), (28, 13), (7, 20), (6, 15), (35, 29), (29, 33), (19, 25), (37, 4), (19, 13), (2, 27), (32, 16), (32, 24), (10, 1), (0, 28), (4, 4), (18, 31), (31, 22), (1, 32), (26, 26), (15, 15), (38, 12), (28, 3), (15, 27), (18, 16), (38, 3), (27, 11), (2, 4), (2, 5), (5, 21), (6, 4), (20, 26), (15, 14), (13, 14), (33, 24), (6, 29), (27, 9), (24, 0), (34, 12), (9, 10), (6, 28), (36, 16), (16, 24), (19, 26), (0, 18), (32, 0), (35, 20), (18, 22), (6, 33), (16, 32), (18, 12), (20, 20), (24, 29), (38, 16), (5, 14), (36, 26), (7, 19), (27, 7), (15, 31), (28, 34), (4, 25), (30, 0), (6, 32), (9, 9), (17, 30), (10, 14), (18, 25), (22, 17), (33, 5), (35, 34), (1, 19), (9, 0), (31, 26), (6, 8), (14, 18), (9, 7), (14, 5), (33, 9), (29, 21), (27, 28), (8, 25), (29, 2), (20, 13), (14, 24), (17, 29), (16, 1), (20, 33), (11, 34), (4, 27), (14, 28), (38, 23), (34, 8), (20, 31), (18, 15), (16, 23), (17, 9), (11, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132192", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), 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, 0), (20, 29), (3, 35), (29, 31), (26, 19), (12, 32), (17, 2), (6, 3), (12, 33), (11, 4), (30, 33), (31, 23), (30, 5), (9, 5), (32, 34), (29, 13), (26, 8), (31, 25), (5, 22), (30, 7), (5, 7), (0, 25), (15, 36), (16, 28), (22, 18), (8, 7), (13, 32), (12, 4), (5, 21), (29, 34), (8, 33), (11, 1), (35, 4), (18, 9), (9, 28), (9, 33), (1, 24), (22, 0), (30, 24), (12, 11), (23, 9), (28, 12), (31, 34), (14, 0), (9, 6), (15, 24), (20, 15), (25, 32), (8, 26), (17, 22), (21, 29), (8, 2), (30, 0), (16, 7), (9, 35), (26, 17), (32, 33), (0, 24), (5, 5), (22, 29), (3, 22), (24, 21), (0, 10), (18, 5), (32, 14), (14, 1), (30, 22), (34, 23), (8, 24), (27, 26), (7, 0), (29, 19), (16, 5), (11, 3), (0, 34), (26, 10), (25, 31), (33, 8), (13, 30), (19, 31), (9, 0), (12, 16), (32, 12), (14, 28), (20, 31), (24, 10), (25, 9), (17, 34), (7, 19), (3, 23), (18, 22), (6, 4), (13, 34), (32, 28), (21, 12), (2, 5), (34, 8), (5, 27), (26, 21), (3, 5), (16, 27), (30, 6), (32, 23), (23, 8), (15, 29), (28, 5), (5, 3), (8, 4), (35, 25), (26, 0), (19, 5), (35, 33), (15, 4), (3, 1), (7, 25), (1, 26), (22, 11), (29, 4), (14, 30), (8, 30), (21, 10), (23, 26), (33, 26), (23, 27), (35, 12), (24, 13), (12, 5), (15, 26), (9, 25), (16, 1), (6, 15), (2, 33), (2, 25), (29, 33), (35, 3), (28, 17), (8, 27), (7, 16), (29, 20), (28, 24), (25, 3), (14, 29), (28, 18), (5, 9), (30, 10), (2, 3), (30, 4), (6, 33), (25, 34), (23, 19), (21, 6), (20, 2), (3, 14), (22, 20), (9, 12), (21, 28), (2, 16), (35, 18), (2, 15), (11, 34), (2, 1), (24, 33), (1, 22), (18, 35), (10, 24), (9, 26), (17, 10), (32, 30), (26, 32), (14, 32), (5, 32), (24, 4), (4, 6), (8, 1), (24, 5), (31, 3), (8, 11), (24, 17), (29, 5), (34, 4), (35, 1), (12, 12), (23, 3), (27, 1), (31, 26), (18, 29), (19, 26), (20, 17), (27, 2), (0, 5), (24, 2), (6, 11), (11, 25), (25, 16), (15, 22), (30, 29), (32, 36), (23, 24), (10, 10), (2, 0), (25, 4), (16, 31), (8, 10), (11, 9), (15, 3), (22, 25), (10, 12), (25, 0), (8, 19), (13, 15), (4, 28), (19, 16), (3, 3), (35, 23), (12, 15), (30, 17), (1, 3), (18, 13), (31, 18), (12, 9), (0, 14), (33, 31), (16, 25), (23, 22), (25, 26), (9, 20), (24, 16), (34, 10), (4, 1), (12, 29), (33, 9), (8, 35), (0, 7), (18, 12), (11, 11), (0, 16), (35, 7), (23, 30), (34, 11), (20, 6), (20, 12), (31, 10), (13, 33), (1, 33), (11, 18), (23, 21), (19, 22), (22, 9), (9, 23), (21, 19), (1, 34), (28, 9), (25, 35), (14, 35), (13, 28), (12, 26), (18, 33), (35, 31), (28, 30), (1, 6), (2, 19), (9, 22), (13, 8), (24, 14), (12, 6), (6, 28), (5, 17), (14, 10), (25, 6), (12, 35), (6, 25), (23, 11), (7, 4), (26, 24), (32, 31), (22, 7), (2, 20), (6, 36), (34, 0), (19, 7), (30, 31), (33, 14), (26, 29), (4, 35), (17, 16), (26, 16), (0, 27), (29, 15), (2, 18), (14, 31), (11, 30), (15, 20), (25, 33), (3, 36), (4, 0), (19, 14), (31, 29), (11, 20), (31, 8), (1, 4), (10, 25), (2, 21), (31, 6), (17, 14), (10, 20), (12, 30), (31, 13), (10, 14), (16, 21), (17, 31), (21, 3), (25, 13), (31, 11), (35, 29), (2, 11), (21, 18), (27, 24), (3, 30), (34, 25), (19, 21), (34, 34), (17, 15), (22, 8), (7, 34), (21, 1), (7, 32), (10, 2), (5, 31), (34, 20), (9, 36), (19, 20), (18, 1), (14, 26), (26, 31), (26, 5), (21, 33), (10, 17), (29, 28), (29, 12), (3, 21), (29, 1), (27, 21), (35, 15), (33, 17), (3, 15), (9, 34), (1, 23), (30, 12), (7, 27), (13, 29), (26, 26), (0, 13), (18, 17), (9, 17), (3, 19), (21, 15), (10, 36), (18, 14), (16, 22), (32, 18), (13, 18), (20, 33), (2, 31), (22, 23), (32, 0), (33, 27), (17, 21), (23, 33), (5, 19), (19, 19), (5, 23), (9, 15), (22, 6), (21, 4), (27, 23), (10, 26), (6, 27), (18, 16), (14, 20), (17, 9), (11, 36), (16, 11), (6, 10), (23, 34), (27, 9), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464724", "dataset": "MATH"}
{"messages": [{"content": "In a 37x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (10, 33), (13, 34), (26, 17), (15, 28), (12, 23), (4, 18), (11, 12), (4, 7), (5, 4), (34, 5), (14, 12), (25, 7), (5, 24), (13, 24), (26, 27), (16, 5), (20, 2), (15, 22), (32, 20), (31, 14), (10, 13), (30, 9), (33, 15), (33, 17), (18, 24), (7, 16), (8, 32), (32, 32), (9, 24), (27, 15), (2, 18), (15, 32), (31, 25), (0, 33), (19, 2), (24, 2), (28, 15), (1, 9), (11, 31), (6, 8), (33, 34), (7, 24), (15, 19), (14, 19), (5, 34), (31, 23), (31, 35), (10, 26), (23, 24), (28, 29), (23, 29), (12, 17), (34, 21), (17, 35), (29, 11), (27, 8), (1, 5), (14, 13), (25, 23), (1, 30), (30, 13), (2, 33), (30, 18), (9, 34), (11, 28), (27, 17), (9, 9), (26, 12), (21, 13), (5, 10), (12, 35), (15, 15), (3, 4), (22, 14), (32, 19), (2, 6), (26, 31), (34, 30), (8, 27), (16, 27), (32, 6), (21, 26), (19, 1), (22, 33), (14, 1), (24, 4), (21, 28), (20, 5), (11, 24), (12, 8), (20, 22), (17, 25), (24, 6), (25, 30), (16, 11), (2, 22), (25, 32), (12, 27), (18, 11), (6, 29), (31, 19), (4, 26), (15, 33), (24, 33), (6, 35), (0, 35), (0, 22), (25, 9), (35, 13), (36, 19), (29, 8), (29, 10), (32, 25), (1, 35), (25, 16), (18, 28), (11, 3), (15, 12), (2, 13), (1, 10), (25, 11), (22, 10), (24, 22), (6, 28), (10, 11), (31, 0), (26, 3), (21, 12), (19, 5), (19, 26), (2, 5), (30, 30), (23, 23), (33, 3), (15, 7), (9, 6), (33, 4), (26, 9), (28, 24), (19, 21), (4, 1), (10, 27), (35, 20), (25, 27), (33, 30), (4, 10), (27, 5), (2, 25), (1, 16), (32, 21), (14, 11), (19, 14), (2, 19), (13, 30), (5, 35), (22, 15), (27, 3), (23, 15), (21, 3), (12, 20), (9, 26), (9, 25), (28, 21), (30, 20), (15, 0), (35, 34), (8, 15), (7, 7), (13, 23), (13, 0), (3, 22), (5, 31), (15, 24), (8, 29), (23, 18), (28, 0), (35, 18), (8, 23), (10, 8), (17, 26), (16, 4), (24, 21), (7, 15), (34, 14), (10, 6), (14, 32), (25, 28), (0, 18), (2, 4), (36, 28), (18, 6), (1, 22), (5, 29), (29, 25), (11, 14), (0, 1), (26, 11), (18, 33), (22, 31), (2, 7), (24, 26), (18, 26), (30, 17), (32, 33), (2, 28), (27, 35), (28, 12), (7, 18), (20, 29), (36, 31), (28, 5), (24, 9), (30, 32), (34, 23), (4, 8), (20, 12), (17, 9), (15, 9), (32, 9), (36, 2), (22, 18), (35, 33), (1, 18), (29, 12), (31, 21), (31, 18), (10, 7), (23, 14), (3, 29), (15, 16), (2, 27), (22, 8), (30, 11), (26, 25), (33, 21), (19, 30), (32, 5), (19, 11), (7, 28), (5, 16), (29, 23), (6, 6), (6, 0), (10, 9), (18, 32), (9, 22), (4, 0), (28, 6), (6, 11), (21, 4), (32, 10), (35, 2), (20, 23), (18, 2), (15, 10), (22, 35), (12, 14), (18, 17), (26, 26), (10, 3), (35, 19), (33, 16), (3, 26), (8, 34), (5, 1), (36, 10), (10, 22), (36, 22), (36, 11), (21, 0), (25, 22), (10, 1), (35, 25), (23, 8), (2, 35), (27, 23), (13, 6), (32, 16), (16, 14), (12, 10), (24, 0), (6, 4), (0, 17), (5, 11), (35, 30), (3, 2), (27, 20), (35, 31), (4, 33), (11, 29), (6, 24), (3, 21), (5, 19), (3, 8), (5, 5), (29, 17), (19, 27), (1, 27), (19, 34), (5, 18), (35, 16), (17, 14), (0, 11), (7, 5), (11, 5), (29, 3), (18, 18), (21, 16), (29, 1), (14, 4), (32, 14), (26, 6), (19, 22), (34, 10), (27, 19), (16, 8), (15, 11), (24, 13), (6, 26), (21, 34), (14, 6), (1, 12), (1, 4), (17, 15), (10, 5), (26, 10), (12, 26), (22, 6), (12, 12), (34, 27), (3, 15), (28, 19), (18, 16), (26, 21), (30, 0), (8, 31), (28, 30), (29, 6), (4, 27), (3, 18), (13, 12), (4, 34), (22, 7), (33, 8), (36, 20), (10, 16), (22, 0), (7, 6), (7, 26), (28, 23), (1, 2), (31, 6), (33, 35), (25, 18), (9, 0), (9, 16), (12, 2), (24, 1), (23, 21), (32, 2), (19, 8), (25, 0), (9, 21), (25, 8), (36, 29), (16, 20), (30, 21), (8, 11), (6, 23), (3, 14), (15, 3), (24, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "466560", "dataset": "MATH"}
{"messages": [{"content": "In a 36x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (25, 26), (22, 17), (4, 32), (18, 22), (34, 23), (8, 2), (22, 33), (22, 1), (11, 28), (23, 27), (10, 10), (12, 16), (35, 10), (17, 14), (17, 28), (2, 2), (21, 25), (35, 2), (14, 15), (21, 6), (5, 26), (1, 15), (30, 0), (31, 0), (26, 20), (22, 23), (25, 34), (7, 28), (6, 12), (6, 8), (24, 1), (13, 25), (23, 32), (11, 15), (10, 25), (23, 4), (25, 21), (32, 0), (3, 12), (10, 17), (16, 10), (7, 25), (0, 21), (1, 30), (27, 19), (14, 29), (28, 25), (4, 8), (33, 13), (31, 24), (15, 16), (17, 7), (34, 0), (26, 18), (8, 28), (2, 12), (3, 28), (4, 28), (19, 30), (8, 6), (1, 14), (14, 2), (20, 29), (32, 16), (32, 21), (5, 4), (10, 33), (32, 8), (10, 1), (32, 30), (23, 8), (29, 16), (33, 12), (25, 29), (24, 34), (8, 14), (29, 17), (24, 11), (11, 30), (31, 18), (0, 29), (20, 35), (10, 21), (21, 11), (33, 9), (3, 35), (6, 34), (5, 27), (8, 33), (18, 19), (13, 16), (28, 0), (6, 30), (33, 30), (33, 16), (27, 21), (35, 11), (22, 32), (34, 14), (25, 16), (19, 22), (20, 5), (34, 21), (15, 25), (14, 28), (4, 25), (10, 35), (30, 30), (24, 22), (19, 14), (21, 16), (7, 33), (1, 5), (26, 27), (10, 20), (33, 15), (20, 1), (28, 35), (12, 24), (11, 34), (33, 24), (9, 3), (28, 6), (32, 28), (31, 22), (19, 15), (2, 26), (13, 32), (26, 17), (17, 9), (8, 16), (10, 22), (30, 34), (20, 26), (14, 20), (9, 2), (26, 32), (2, 34), (28, 31), (1, 13), (6, 10), (26, 15), (8, 15), (3, 19), (1, 6), (34, 15), (32, 11), (11, 26), (33, 22), (12, 7), (7, 9), (22, 16), (12, 28), (28, 29), (30, 9), (27, 12), (0, 31), (10, 34), (0, 7), (21, 28), (25, 17), (5, 19), (24, 33), (14, 11), (11, 16), (34, 4), (22, 19), (24, 0), (29, 32), (16, 31), (1, 24), (25, 19), (11, 24), (23, 34), (35, 28), (11, 32), (2, 4), (20, 7), (6, 19), (15, 0), (22, 14), (32, 3), (6, 4), (2, 27), (32, 34), (10, 26), (15, 10), (21, 0), (27, 4), (16, 24), (21, 7), (33, 34), (10, 31), (13, 22), (30, 19), (22, 4), (1, 34), (3, 1), (6, 22), (15, 21), (8, 5), (23, 0), (14, 3), (17, 33), (5, 14), (23, 16), (22, 9), (14, 32), (20, 33), (7, 31), (18, 30), (0, 15), (14, 12), (20, 0), (8, 0), (5, 35), (15, 11), (26, 2), (10, 15), (34, 1), (13, 7), (28, 30), (16, 2), (22, 21), (7, 22), (13, 26), (32, 10), (32, 12), (33, 19), (18, 34), (15, 3), (27, 30), (8, 11), (5, 16), (15, 17), (24, 23), (13, 2), (7, 5), (28, 17), (18, 24), (9, 20), (25, 28), (6, 15), (10, 8), (28, 18), (19, 23), (33, 3), (10, 13), (0, 3), (22, 11), (30, 21), (30, 4), (30, 11), (6, 25), (26, 35), (34, 16), (20, 10), (24, 20), (0, 6), (4, 10), (34, 25), (1, 35), (6, 32), (33, 28), (8, 10), (27, 2), (34, 22), (7, 26), (3, 3), (10, 2), (31, 21), (27, 32), (0, 22), (27, 7), (3, 14), (31, 34), (3, 25), (27, 33), (4, 9), (26, 10), (1, 19), (30, 23), (18, 17), (0, 23), (14, 1), (23, 7), (28, 2), (26, 22), (2, 18), (4, 17), (15, 23), (17, 25), (29, 10), (16, 3), (2, 25), (19, 9), (13, 34), (24, 27), (14, 31), (1, 22), (32, 5), (22, 35), (33, 10), (3, 7), (7, 2), (9, 16), (19, 13), (19, 33), (2, 19), (25, 6), (5, 13), (9, 17), (29, 31), (19, 25), (16, 16), (35, 16), (30, 15), (35, 21), (12, 10), (4, 2), (27, 22), (32, 18), (0, 17), (34, 26), (25, 7), (29, 9), (17, 0), (18, 32), (21, 22), (6, 2), (18, 15), (3, 31), (22, 2), (15, 4), (29, 22), (35, 5), (4, 18), (17, 15), (8, 35), (18, 21), (21, 34), (7, 19), (22, 18), (31, 9), (10, 30), (3, 16), (12, 1), (19, 4), (1, 28), (10, 12), (34, 3), (24, 19), (9, 13), (19, 7), (24, 13), (13, 35), (25, 23), (6, 11), (19, 31), (32, 14), (30, 13), (7, 30), (6, 31), (6, 33), (29, 26), (5, 10), (4, 27), (29, 20), (7, 20), (17, 31), (27, 9), (18, 14), (21, 10), (21, 19), (31, 33), (3, 2), (30, 32), (31, 29), (33, 8), (35, 19), (5, 6), (4, 3), (31, 11), (2, 5), (0, 18), (19, 20), (6, 35), (10, 4), (26, 19), (31, 2), (25, 13), (1, 8), (6, 23), (13, 23), (13, 29), (18, 13), (14, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "797280", "dataset": "MATH"}
{"messages": [{"content": "In a 33x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 33), (14, 18), (26, 15), (17, 34), (23, 15), (24, 20), (20, 18), (14, 1), (9, 31), (7, 17), (6, 29), (30, 1), (18, 29), (23, 3), (28, 9), (12, 14), (31, 18), (26, 30), (8, 29), (8, 23), (30, 24), (14, 27), (16, 11), (23, 17), (13, 29), (7, 20), (25, 5), (32, 9), (18, 1), (31, 25), (21, 1), (20, 9), (21, 9), (19, 11), (25, 23), (27, 1), (23, 20), (30, 6), (13, 26), (10, 7), (21, 5), (10, 9), (20, 14), (8, 14), (2, 31), (10, 0), (20, 23), (9, 11), (2, 34), (29, 26), (3, 6), (12, 33), (0, 25), (16, 19), (18, 32), (11, 30), (30, 18), (4, 15), (0, 10), (0, 19), (17, 0), (28, 6), (19, 20), (21, 20), (23, 9), (19, 19), (29, 10), (8, 35), (17, 29), (12, 11), (12, 17), (11, 10), (19, 21), (8, 4), (22, 35), (23, 2), (19, 0), (19, 1), (11, 35), (27, 3), (15, 27), (8, 32), (14, 33), (4, 0), (15, 28), (13, 5), (14, 0), (3, 28), (26, 6), (10, 18), (7, 35), (4, 4), (32, 14), (22, 29), (9, 33), (26, 35), (5, 16), (5, 31), (32, 11), (4, 12), (9, 16), (19, 10), (27, 32), (17, 16), (32, 29), (9, 3), (22, 14), (2, 22), (13, 14), (8, 21), (5, 8), (9, 2), (23, 6), (25, 25), (25, 21), (7, 34), (16, 9), (14, 5), (9, 26), (11, 16), (27, 11), (27, 30), (22, 21), (10, 25), (1, 0), (16, 16), (4, 28), (17, 30), (16, 1), (32, 2), (4, 17), (9, 23), (7, 28), (15, 16), (14, 19), (3, 8), (19, 23), (4, 14), (8, 1), (21, 24), (24, 6), (18, 24), (6, 12), (10, 4), (32, 7), (8, 25), (16, 6), (15, 21), (20, 7), (7, 7), (13, 13), (5, 15), (31, 21), (25, 27), (12, 22), (19, 29), (4, 20), (6, 5), (11, 34), (14, 8), (0, 6), (19, 30), (12, 3), (17, 27), (28, 25), (26, 16), (19, 17), (15, 18), (24, 9), (10, 26), (8, 2), (21, 14), (16, 28), (19, 32), (30, 32), (2, 26), (4, 10), (31, 22), (25, 19), (31, 4), (24, 5), (27, 9), (15, 12), (30, 20), (0, 17), (18, 15), (15, 33), (3, 15), (26, 0), (11, 5), (11, 33), (6, 32), (6, 26), (4, 34), (17, 12), (3, 29), (24, 29), (31, 15), (14, 32), (12, 20), (8, 34), (12, 26), (24, 8), (26, 26), (18, 5), (1, 20), (17, 15), (20, 24), (26, 3), (0, 18), (28, 32), (10, 24), (26, 29), (30, 21), (18, 11), (3, 18), (19, 27), (5, 28), (21, 6), (2, 5), (30, 0), (28, 23), (25, 0), (13, 33), (0, 30), (26, 17), (22, 19), (12, 2), (28, 20), (18, 2), (13, 21), (22, 5), (32, 31), (4, 23), (5, 13), (3, 31), (24, 22), (29, 5), (20, 16), (12, 23), (27, 20), (10, 21), (1, 25), (6, 11), (13, 1), (5, 25), (28, 17), (17, 1), (13, 35), (27, 7), (0, 16), (5, 5), (31, 30), (18, 26), (31, 2), (22, 20), (19, 26), (9, 24), (6, 0), (17, 22), (15, 11), (11, 28), (3, 16), (18, 25), (16, 17), (2, 29), (11, 11), (32, 16), (21, 2), (20, 5), (16, 34), (18, 8), (2, 20), (30, 7), (6, 33), (7, 27), (5, 9), (21, 19), (0, 24), (6, 19), (32, 19), (14, 14), (1, 12), (23, 24), (24, 19), (23, 14), (6, 9), (16, 22), (27, 35), (14, 10), (16, 32), (24, 33), (21, 17), (9, 14), (8, 0), (28, 1), (21, 8), (9, 17), (26, 24), (30, 28), (21, 4), (4, 26), (16, 10), (11, 20), (3, 5), (29, 24), (1, 34), (2, 9), (25, 16), (14, 12), (6, 16), (31, 8), (6, 14), (21, 0), (10, 20), (13, 0), (28, 28), (0, 32), (16, 18), (28, 15), (7, 23), (21, 28), (10, 13), (26, 25), (0, 3), (22, 32), (4, 35), (0, 8), (32, 0), (17, 10), (2, 13), (27, 25), (4, 29), (22, 25), (10, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "749472", "dataset": "MATH"}
{"messages": [{"content": "In a 33x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 28), (26, 23), (22, 27), (26, 22), (10, 14), (17, 27), (6, 5), (30, 27), (30, 31), (13, 37), (21, 8), (29, 31), (23, 31), (18, 30), (17, 13), (30, 37), (16, 2), (12, 22), (1, 17), (6, 32), (0, 7), (9, 20), (10, 22), (6, 4), (13, 27), (27, 7), (21, 29), (30, 33), (6, 22), (22, 9), (19, 22), (10, 33), (21, 34), (28, 9), (4, 13), (2, 16), (31, 0), (16, 15), (25, 31), (19, 4), (27, 27), (6, 12), (23, 30), (21, 12), (26, 37), (6, 25), (22, 4), (32, 28), (18, 11), (31, 30), (11, 19), (20, 5), (5, 20), (6, 14), (26, 12), (6, 3), (11, 9), (11, 38), (7, 29), (17, 5), (31, 32), (0, 17), (4, 12), (3, 7), (8, 38), (6, 16), (11, 0), (22, 3), (15, 27), (0, 22), (3, 32), (32, 29), (17, 37), (9, 1), (15, 31), (4, 7), (22, 23), (15, 25), (32, 33), (10, 0), (21, 17), (29, 11), (32, 7), (5, 38), (6, 33), (5, 34), (30, 22), (11, 22), (25, 37), (6, 18), (5, 11), (6, 7), (25, 14), (30, 19), (32, 20), (5, 19), (21, 24), (8, 36), (14, 2), (1, 2), (14, 18), (27, 30), (16, 17), (11, 34), (3, 15), (30, 24), (21, 37), (19, 14), (23, 33), (17, 20), (12, 10), (7, 0), (16, 26), (25, 32), (26, 31), (3, 38), (30, 29), (10, 20), (0, 6), (22, 20), (5, 4), (24, 12), (21, 21), (2, 31), (30, 23), (24, 26), (20, 35), (2, 38), (22, 18), (4, 35), (24, 25), (23, 37), (15, 1), (31, 12), (24, 13), (0, 30), (7, 23), (21, 5), (0, 5), (7, 26), (17, 24), (12, 9), (25, 35), (2, 33), (26, 17), (26, 4), (1, 14), (32, 17), (30, 36), (22, 15), (29, 3), (29, 34), (30, 9), (12, 21), (14, 5), (29, 33), (14, 24), (14, 4), (23, 20), (24, 7), (7, 14), (7, 11), (29, 15), (26, 0), (26, 13), (22, 24), (5, 36), (19, 12), (0, 4), (32, 1), (23, 10), (13, 12), (18, 14), (0, 29), (27, 28), (6, 2), (7, 25), (19, 29), (4, 17), (24, 4), (22, 6), (11, 32), (3, 0), (12, 23), (0, 27), (13, 19), (23, 15), (31, 17), (19, 36), (12, 5), (26, 26), (12, 33), (25, 11), (5, 6), (14, 14), (28, 25), (14, 10), (19, 23), (11, 29), (8, 28), (29, 0), (22, 21), (11, 1), (29, 18), (20, 25), (15, 14), (17, 7), (2, 23), (18, 27), (22, 31), (9, 21), (4, 24), (7, 19), (1, 30), (28, 18), (23, 16), (6, 24), (18, 9), (3, 25), (9, 13), (4, 2), (29, 17), (10, 29), (18, 7), (23, 8), (17, 6), (7, 31), (14, 12), (30, 4), (20, 0), (18, 28), (27, 38), (10, 26), (14, 20), (4, 25), (18, 10), (10, 8), (24, 28), (12, 3), (24, 16), (20, 22), (15, 24), (6, 31), (32, 2), (8, 7), (11, 14), (16, 0), (31, 13), (15, 8), (9, 17), (4, 18), (21, 14), (28, 27), (31, 6), (15, 33), (15, 6), (23, 12), (26, 11), (24, 11), (28, 23), (19, 20), (8, 23), (8, 33), (12, 8), (8, 5), (16, 35), (27, 16), (6, 37), (32, 23), (0, 19), (15, 32), (24, 14), (12, 35), (31, 34), (16, 14), (20, 4), (9, 37), (10, 23), (28, 21), (25, 34), (26, 29), (29, 20), (20, 16), (22, 13), (11, 28), (4, 21), (10, 5), (32, 36), (20, 17), (15, 29), (28, 31), (21, 35), (25, 1), (19, 32), (1, 4), (16, 36), (8, 6), (7, 7), (6, 10), (20, 31), (10, 28), (31, 5), (3, 19), (16, 32), (32, 15), (10, 32), (30, 26), (6, 9), (3, 26), (31, 35), (2, 11), (18, 12), (26, 21), (32, 37), (9, 36), (9, 9), (15, 2), (20, 9), (17, 12), (29, 16), (32, 0), (17, 30), (19, 38), (24, 20), (13, 36), (30, 28), (10, 2), (20, 7), (24, 31), (12, 0), (9, 33), (14, 3), (0, 23), (9, 3), (27, 10), (18, 4), (13, 3), (16, 16), (3, 37), (23, 13), (13, 20), (10, 27), (3, 20), (6, 11), (11, 3), (28, 16), (30, 14), (32, 14), (8, 27), (17, 35), (23, 5), (20, 24), (14, 26), (20, 28), (15, 9), (13, 17), (9, 34), (17, 34), (1, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "862650", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), 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), (22, 2), (30, 15), (0, 18), (15, 29), (10, 25), (23, 11), (11, 15), (24, 11), (3, 2), (25, 10), (22, 5), (7, 15), (6, 23), (22, 29), (18, 15), (22, 30), (32, 7), (30, 8), (15, 18), (26, 7), (10, 1), (12, 30), (23, 21), (30, 16), (11, 16), (16, 2), (0, 16), (32, 2), (25, 13), (6, 17), (4, 29), (20, 30), (27, 30), (28, 28), (31, 16), (14, 10), (27, 23), (18, 23), (13, 26), (32, 27), (19, 30), (32, 24), (32, 11), (28, 24), (8, 24), (19, 18), (6, 6), (8, 14), (8, 26), (30, 9), (2, 27), (2, 15), (0, 29), (2, 16), (9, 28), (28, 11), (1, 9), (13, 21), (15, 24), (23, 16), (9, 9), (9, 6), (6, 22), (32, 22), (1, 11), (17, 2), (20, 21), (18, 24), (31, 1), (31, 15), (26, 20), (26, 13), (20, 26), (29, 30), (12, 27), (30, 26), (21, 11), (1, 23), (20, 13), (26, 22), (26, 1), (32, 4), (4, 1), (31, 9), (10, 4), (13, 17), (8, 1), (16, 1), (18, 10), (5, 19), (30, 11), (3, 30), (29, 20), (24, 19), (3, 4), (21, 5), (11, 25), (17, 4), (18, 7), (22, 27), (25, 22), (12, 21), (1, 10), (24, 29), (3, 23), (17, 25), (28, 6), (9, 17), (5, 22), (32, 17), (12, 2), (25, 23), (9, 23), (28, 15), (3, 12), (18, 22), (29, 15), (7, 6), (14, 22), (7, 1), (7, 11), (15, 16), (6, 30), (6, 29), (12, 4), (19, 4), (12, 22), (26, 28), (21, 26), (16, 15), (15, 26), (11, 20), (28, 8), (5, 24), (25, 3), (31, 3), (25, 17), (3, 24), (16, 23), (13, 9), (24, 1), (13, 1), (21, 7), (3, 28), (4, 7), (28, 5), (3, 25), (4, 11), (1, 13), (10, 10), (26, 2), (6, 4), (25, 5), (0, 10), (12, 28), (15, 15), (18, 13), (23, 13), (25, 8), (30, 2), (24, 10), (27, 18), (28, 3), (2, 21), (17, 16), (22, 16), (10, 16), (31, 17), (27, 2), (17, 10), (9, 21), (28, 30), (13, 28), (13, 22), (8, 2), (6, 3), (28, 14), (3, 13), (17, 18), (3, 11), (29, 3), (24, 22), (25, 27), (4, 18), (9, 22), (22, 25), (26, 5), (26, 11), (2, 3), (32, 23), (5, 28), (14, 9), (28, 22), (11, 22), (14, 26), (21, 1), (28, 17), (0, 30), (7, 12), (28, 21), (12, 25), (5, 7), (22, 11), (9, 2), (17, 19), (29, 6), (0, 5), (22, 10), (16, 6), (3, 19), (16, 16), (14, 29), (23, 17), (24, 4), (1, 7), (7, 30), (31, 21), (5, 25), (32, 21), (31, 0), (11, 13), (4, 10), (19, 25), (24, 2), (6, 14), (0, 26), (22, 19), (4, 3), (10, 9), (3, 5), (9, 4), (10, 30), (32, 12), (18, 30), (6, 19), (12, 17), (26, 25), (3, 26), (13, 18), (31, 24), (15, 21), (15, 14), (2, 12), (26, 0), (4, 25), (15, 30), (12, 14), (5, 27), (7, 17), (7, 27), (23, 18), (24, 12), (21, 8), (20, 2), (23, 30), (0, 8), (27, 14), (16, 28), (29, 7), (16, 24), (17, 23), (31, 6), (11, 18), (22, 23), (29, 22), (22, 17), (17, 11), (19, 9), (31, 27), (11, 14), (27, 28), (17, 26), (1, 16), (2, 14), (5, 29), (15, 25), (5, 12), (32, 0), (9, 29), (6, 18), (8, 7), (23, 10), (12, 1), (1, 4), (1, 21), (18, 5), (10, 2), (8, 30), (3, 20), (20, 16), (5, 17), (16, 19), (28, 27), (1, 14), (0, 28), (17, 24), (15, 12), (18, 11), (23, 9), (29, 23), (11, 24), (17, 13), (16, 30), (28, 2), (9, 11), (1, 19), (24, 23), (21, 21), (8, 22), (8, 19), (20, 10), (28, 19), (23, 15), (16, 8), (32, 15), (25, 29), (31, 20), (3, 8), (20, 27), (0, 23), (14, 25), (31, 14), (12, 18), (15, 3), (26, 6), (23, 1), (18, 1), (19, 28), (18, 8), (9, 3), (24, 18), (20, 29), (23, 26), (30, 1), (19, 16), (19, 22), (5, 3), (14, 30), (20, 22), (30, 13), (19, 10), (5, 23), (22, 9), (25, 14), (10, 29), (5, 6), (4, 8), (18, 28), (8, 3), (30, 19), (32, 10), (6, 1), (14, 11), (21, 3), (13, 8), (18, 25), (2, 25), (12, 15), (19, 2), (2, 22), (3, 7), (24, 20), (17, 21), (11, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "616320", "dataset": "MATH"}
{"messages": [{"content": "In a 37x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 22), (6, 13), (11, 7), (26, 26), (11, 1), (14, 9), (9, 18), (17, 7), (13, 15), (12, 26), (13, 31), (29, 31), (2, 14), (7, 23), (24, 16), (6, 27), (35, 20), (20, 30), (1, 16), (30, 27), (1, 20), (13, 33), (13, 17), (16, 11), (17, 17), (14, 32), (8, 8), (11, 31), (1, 32), (35, 15), (20, 10), (22, 23), (17, 6), (34, 29), (17, 4), (9, 33), (32, 16), (32, 7), (3, 11), (24, 32), (7, 32), (4, 8), (23, 1), (24, 27), (9, 9), (0, 10), (29, 15), (7, 27), (1, 2), (26, 6), (33, 2), (33, 19), (34, 11), (2, 31), (22, 4), (7, 22), (28, 5), (3, 32), (21, 14), (0, 6), (14, 8), (36, 6), (4, 19), (0, 14), (21, 32), (10, 1), (33, 10), (28, 25), (11, 20), (6, 30), (8, 27), (30, 7), (7, 7), (4, 30), (26, 29), (15, 12), (25, 13), (0, 7), (19, 5), (0, 26), (32, 22), (9, 28), (1, 11), (34, 8), (7, 31), (28, 16), (13, 3), (22, 32), (33, 28), (34, 21), (8, 26), (23, 22), (21, 13), (10, 7), (18, 8), (34, 15), (23, 9), (26, 27), (18, 23), (13, 18), (10, 5), (0, 9), (35, 28), (12, 28), (10, 2), (9, 7), (34, 9), (35, 6), (1, 29), (30, 30), (15, 0), (18, 12), (5, 5), (30, 25), (7, 17), (34, 26), (0, 3), (15, 25), (15, 10), (21, 29), (29, 26), (10, 22), (4, 31), (33, 9), (36, 0), (6, 3), (11, 27), (30, 12), (0, 29), (15, 14), (3, 19), (13, 28), (10, 0), (10, 32), (15, 26), (5, 27), (1, 21), (1, 30), (22, 30), (11, 11), (29, 9), (17, 25), (25, 25), (0, 1), (15, 29), (30, 32), (34, 13), (30, 10), (12, 27), (16, 0), (4, 28), (7, 16), (26, 16), (31, 19), (9, 0), (6, 31), (18, 24), (28, 27), (29, 7), (26, 4), (3, 18), (23, 24), (13, 29), (14, 13), (12, 11), (10, 21), (27, 20), (18, 4), (10, 14), (35, 14), (17, 18), (6, 0), (5, 3), (0, 25), (3, 2), (2, 25), (29, 21), (4, 10), (21, 0), (6, 21), (25, 29), (20, 14), (1, 14), (15, 31), (22, 33), (18, 26), (35, 17), (11, 2), (22, 15), (10, 8), (19, 19), (5, 2), (15, 6), (12, 13), (31, 16), (7, 25), (30, 9), (10, 27), (31, 28), (31, 5), (13, 27), (20, 26), (14, 16), (34, 0), (36, 2), (1, 23), (22, 28), (15, 30), (24, 3), (4, 3), (33, 33), (35, 23), (3, 22), (15, 3), (0, 5), (29, 29), (28, 21), (34, 4), (12, 18), (16, 15), (27, 29), (25, 4), (31, 0), (17, 14), (2, 18), (25, 1), (21, 11), (15, 19), (12, 14), (2, 21), (22, 12), (26, 25), (6, 26), (3, 14), (18, 27), (27, 1), (29, 1), (36, 13), (28, 6), (22, 18), (23, 8), (9, 14), (16, 25), (13, 24), (18, 28), (35, 18), (7, 14), (13, 5), (28, 4), (32, 31), (11, 14), (19, 20), (6, 8), (31, 33), (6, 1), (27, 21), (19, 4), (1, 26), (1, 22), (2, 22), (28, 8), (0, 28), (24, 11), (11, 18), (29, 27), (36, 5), (12, 6), (23, 31), (3, 17), (5, 31), (19, 8), (25, 5), (22, 26), (30, 8), (35, 33), (7, 29), (21, 20), (28, 19), (30, 2), (9, 20), (19, 15), (18, 3), (8, 10), (18, 22), (3, 28), (26, 12), (16, 20), (29, 12), (23, 17), (34, 23), (7, 3), (28, 18), (0, 20), (24, 26), (32, 12), (8, 3), (12, 8), (10, 19), (2, 30), (33, 32), (11, 24), (9, 8), (17, 20), (1, 13), (21, 33), (33, 5), (31, 20), (28, 3), (18, 2), (35, 27), (31, 18), (8, 14), (25, 8), (8, 33), (6, 2), (20, 22), (18, 29), (8, 23), (29, 33), (10, 3), (14, 22), (0, 27), (31, 25), (14, 1), (16, 31), (24, 13), (31, 13), (26, 21), (21, 8), (34, 25), (31, 1), (36, 27), (32, 23), (23, 4), (2, 17), (9, 12), (17, 8), (22, 5), (27, 9), (7, 0), (2, 27), (29, 10), (3, 26), (30, 23), (7, 33), (31, 15), (31, 31), (25, 20), (23, 3), (15, 32), (16, 23), (27, 5), (35, 26), (15, 15), (16, 26), (22, 1), (13, 1), (32, 6), (8, 7), (3, 3), (36, 16), (11, 33), (18, 33), (19, 21), (14, 15), (31, 27), (25, 26), (35, 2), (36, 30), (35, 13), (8, 15), (34, 7), (32, 30), (18, 21), (19, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "601728", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), 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), (24, 25), (29, 25), (19, 19), (11, 9), (18, 24), (6, 8), (33, 12), (8, 14), (21, 27), (21, 15), (6, 5), (33, 13), (32, 29), (16, 14), (3, 24), (2, 22), (9, 1), (33, 28), (14, 5), (17, 26), (32, 12), (16, 9), (28, 10), (27, 3), (15, 16), (28, 9), (1, 12), (27, 2), (23, 4), (25, 18), (8, 23), (12, 5), (14, 0), (3, 23), (19, 17), (14, 14), (16, 23), (0, 12), (31, 25), (33, 18), (14, 18), (21, 19), (13, 21), (16, 18), (23, 19), (30, 18), (17, 23), (1, 3), (17, 19), (7, 6), (28, 29), (13, 29), (23, 6), (18, 22), (8, 29), (33, 7), (4, 31), (23, 21), (21, 11), (29, 24), (19, 11), (3, 31), (28, 28), (35, 24), (26, 3), (8, 5), (21, 13), (8, 7), (15, 25), (19, 16), (13, 8), (16, 16), (3, 20), (23, 25), (30, 7), (27, 19), (22, 7), (7, 20), (8, 26), (15, 19), (22, 1), (24, 30), (14, 13), (22, 23), (13, 4), (6, 3), (14, 26), (5, 16), (28, 7), (26, 29), (35, 10), (7, 3), (10, 10), (30, 23), (27, 16), (17, 16), (3, 11), (9, 17), (9, 20), (26, 16), (11, 15), (4, 29), (3, 10), (12, 8), (27, 7), (0, 21), (21, 7), (26, 11), (17, 20), (18, 5), (8, 16), (15, 0), (15, 13), (5, 8), (26, 2), (12, 18), (14, 2), (21, 28), (18, 23), (23, 15), (21, 16), (15, 20), (22, 9), (34, 16), (23, 17), (2, 23), (0, 9), (6, 18), (21, 25), (0, 17), (20, 21), (4, 2), (7, 15), (12, 26), (33, 24), (2, 2), (11, 22), (5, 24), (20, 20), (20, 17), (10, 21), (5, 13), (2, 15), (10, 8), (21, 10), (27, 0), (5, 21), (34, 0), (31, 22), (9, 26), (19, 31), (5, 4), (19, 14), (17, 21), (8, 10), (33, 29), (19, 21), (16, 25), (34, 18), (21, 2), (31, 24), (29, 5), (21, 5), (34, 8), (30, 8), (32, 8), (29, 6), (8, 12), (15, 11), (35, 14), (7, 9), (15, 2), (5, 29), (12, 0), (25, 30), (18, 7), (33, 21), (27, 23), (8, 21), (17, 28), (33, 9), (0, 22), (31, 4), (27, 27), (10, 22), (33, 17), (10, 4), (19, 28), (11, 2), (2, 10), (28, 16), (17, 13), (14, 31), (28, 27), (16, 24), (31, 3), (32, 13), (25, 22), (12, 15), (9, 13), (31, 13), (35, 18), (32, 5), (18, 12), (23, 14), (22, 26), (7, 22), (20, 11), (4, 9), (19, 6), (16, 8), (23, 7), (5, 9), (4, 4), (7, 27), (9, 30), (32, 19), (8, 15), (9, 9), (22, 31), (25, 12), (25, 23), (19, 25), (13, 27), (12, 4), (2, 27), (0, 30), (35, 2), (12, 22), (24, 24), (8, 6), (8, 18), (16, 27), (29, 29), (7, 14), (0, 26), (14, 23), (29, 19), (22, 4), (11, 20), (7, 21), (17, 0), (7, 11), (7, 25), (29, 7), (20, 8), (34, 26), (11, 3), (23, 18), (12, 28), (25, 28), (15, 3), (26, 15), (30, 6), (10, 11), (25, 15), (31, 27), (30, 13), (31, 10), (13, 6), (28, 1), (25, 6), (16, 15), (23, 5), (3, 27), (18, 3), (9, 22), (9, 3), (24, 16), (31, 6), (25, 4), (6, 10), (26, 14), (34, 2), (16, 26), (24, 0), (22, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83280", "dataset": "MATH"}
{"messages": [{"content": "In a 32x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 25), (3, 20), (24, 23), (10, 32), (24, 26), (0, 8), (30, 8), (27, 18), (29, 13), (14, 6), (12, 24), (28, 26), (18, 1), (0, 4), (18, 2), (8, 3), (11, 12), (13, 17), (24, 10), (6, 24), (2, 4), (18, 14), (21, 9), (14, 18), (15, 11), (11, 19), (22, 26), (7, 13), (18, 0), (1, 17), (10, 2), (12, 17), (31, 0), (12, 1), (0, 15), (30, 5), (25, 21), (2, 24), (18, 29), (28, 32), (9, 11), (18, 7), (25, 32), (4, 2), (19, 24), (25, 5), (16, 22), (19, 1), (14, 26), (27, 24), (28, 30), (19, 11), (6, 8), (16, 12), (9, 1), (4, 14), (21, 31), (21, 11), (27, 29), (25, 1), (18, 32), (11, 18), (23, 22), (4, 11), (28, 8), (17, 21), (12, 19), (6, 29), (5, 27), (22, 30), (25, 30), (14, 29), (19, 14), (3, 10), (10, 14), (2, 25), (31, 10), (3, 28), (5, 20), (4, 28), (1, 31), (30, 22), (18, 5), (14, 9), (20, 3), (31, 21), (20, 21), (18, 26), (8, 9), (20, 31), (14, 10), (14, 17), (1, 23), (2, 2), (29, 15), (10, 4), (8, 27), (5, 25), (20, 32), (21, 32), (7, 20), (17, 27), (22, 13), (23, 25), (9, 23), (4, 7), (10, 26), (11, 10), (7, 24), (4, 20), (10, 29), (2, 11), (5, 26), (1, 21), (2, 18), (6, 19), (21, 26), (5, 4), (21, 2), (23, 1), (16, 14), (10, 10), (13, 25), (9, 29), (28, 12), (14, 14), (16, 15), (22, 28), (12, 2), (10, 3), (22, 25), (1, 2), (24, 6), (5, 5), (27, 19), (8, 0), (21, 6), (25, 7), (20, 25), (11, 0), (24, 14), (16, 26), (7, 7), (7, 32), (13, 19), (14, 4), (14, 16), (31, 11), (6, 5), (9, 14), (15, 14), (20, 30), (0, 9), (16, 3), (24, 3), (3, 11), (10, 30), (24, 7), (0, 5), (2, 20), (7, 16), (19, 26), (21, 22), (5, 30), (25, 15), (11, 32), (8, 24), (3, 25), (4, 17), (2, 31), (19, 9), (8, 13), (26, 26), (25, 14), (31, 27), (4, 24), (19, 12), (7, 25), (0, 25), (7, 8), (22, 5), (17, 8), (21, 28), (26, 10), (5, 1), (4, 5), (12, 5), (20, 1), (9, 2), (12, 27), (26, 13), (22, 7), (18, 31), (6, 22), (29, 18), (7, 26), (11, 21), (25, 20), (26, 1), (31, 15), (8, 20), (23, 32), (6, 17), (30, 23), (15, 16), (1, 10), (21, 30), (15, 20), (22, 22), (19, 8), (7, 14), (20, 17), (13, 9), (14, 2), (11, 30), (24, 22), (13, 31), (26, 23), (28, 19), (18, 27), (4, 8), (13, 29), (19, 28), (0, 32), (27, 17), (12, 8), (3, 1), (11, 8), (22, 24), (14, 27), (27, 6), (31, 3), (26, 15), (14, 20), (12, 28), (17, 20), (6, 0), (19, 13), (29, 32), (20, 7), (19, 2), (21, 16), (8, 22), (16, 17), (22, 19), (23, 27), (8, 25), (27, 2), (4, 23), (22, 21), (20, 4), (31, 9), (0, 21), (15, 32), (1, 9), (27, 20), (28, 4), (7, 29), (15, 29), (27, 31), (30, 6), (7, 12), (15, 5), (24, 8), (28, 29), (8, 15), (30, 27), (1, 13), (8, 7), (30, 29), (17, 2), (29, 24), (26, 31), (27, 8), (21, 29), (11, 11), (12, 6), (21, 13), (15, 15), (13, 7), (19, 3), (3, 21), (13, 1), (4, 9), (15, 6), (15, 0), (4, 12), (16, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86640", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (3, 30), (31, 14), (25, 35), (30, 31), (22, 11), (20, 30), (30, 5), (9, 19), (2, 24), (11, 18), (28, 22), (21, 7), (29, 3), (25, 27), (28, 6), (18, 24), (28, 19), (12, 19), (24, 30), (2, 16), (30, 26), (19, 31), (15, 15), (24, 1), (31, 31), (14, 3), (22, 8), (18, 8), (3, 9), (28, 33), (29, 33), (21, 27), (15, 1), (28, 3), (31, 26), (12, 13), (12, 5), (16, 27), (30, 25), (18, 16), (1, 34), (1, 17), (18, 34), (5, 32), (4, 30), (18, 12), (2, 6), (10, 3), (29, 8), (12, 17), (27, 3), (18, 18), (4, 15), (1, 6), (11, 33), (19, 22), (30, 33), (17, 23), (8, 20), (32, 2), (5, 30), (25, 22), (2, 32), (23, 0), (0, 2), (32, 20), (10, 32), (25, 29), (20, 1), (15, 11), (33, 28), (23, 35), (0, 23), (25, 9), (21, 8), (25, 12), (30, 0), (32, 6), (14, 29), (2, 4), (23, 30), (6, 9), (3, 2), (16, 7), (25, 13), (29, 26), (29, 25), (24, 21), (6, 6), (28, 25), (20, 27), (6, 12), (21, 19), (32, 3), (3, 33), (8, 9), (17, 5), (17, 15), (5, 18), (22, 12), (7, 18), (32, 5), (12, 27), (10, 31), (26, 17), (20, 5), (25, 0), (2, 2), (11, 35), (32, 1), (16, 2), (14, 15), (15, 29), (4, 24), (22, 0), (18, 27), (1, 25), (31, 18), (5, 4), (13, 30), (11, 27), (0, 24), (13, 10), (11, 7), (0, 3), (34, 18), (6, 5), (33, 5), (12, 16), (4, 28), (10, 35), (29, 31), (23, 8), (34, 31), (28, 28), (8, 26), (22, 16), (0, 34), (17, 28), (32, 0), (0, 22), (18, 19), (9, 11), (8, 16), (21, 22), (11, 17), (32, 19), (22, 6), (6, 29), (22, 25), (15, 25), (23, 7), (25, 17), (23, 11), (1, 22), (8, 8), (10, 29), (24, 32), (2, 19), (28, 18), (3, 34), (7, 14), (29, 29), (3, 11), (14, 6), (15, 23), (34, 0), (3, 13), (32, 23), (14, 19), (32, 16), (26, 3), (26, 18), (15, 9), (14, 24), (27, 24), (5, 5), (2, 0), (5, 13), (33, 1), (27, 9), (7, 0), (6, 0), (27, 29), (3, 8), (33, 23), (5, 34), (17, 30), (26, 15), (18, 33), (18, 22), (8, 32), (13, 5), (19, 24), (16, 35), (6, 10), (23, 19), (30, 30), (12, 18), (0, 19), (22, 9), (21, 2), (31, 3), (9, 5), (2, 18), (9, 26), (20, 13), (23, 26), (19, 9), (19, 23), (10, 30), (30, 14), (3, 1), (17, 12), (5, 21), (18, 25), (11, 16), (27, 27), (27, 10), (30, 17), (16, 25), (16, 12), (18, 7), (24, 22), (30, 11), (29, 2), (1, 12), (23, 2), (26, 34), (30, 3), (22, 22), (16, 15), (23, 12), (12, 23), (19, 2), (26, 33), (34, 20), (23, 20), (0, 35), (15, 13), (27, 31), (22, 19), (4, 11), (17, 31), (4, 7), (16, 28), (20, 23), (8, 23), (1, 11), (29, 6), (12, 20), (8, 27), (2, 8), (27, 15), (17, 22), (13, 8), (20, 2), (26, 31), (10, 22), (0, 16), (32, 17), (17, 9), (6, 32), (4, 6), (12, 15), (14, 14), (18, 17), (19, 25), (9, 9), (25, 14), (2, 22), (0, 13), (1, 7), (3, 4), (14, 21), (13, 9), (9, 30), (9, 8), (5, 26), (5, 11), (10, 20), (32, 30), (29, 17), (33, 31), (33, 12), (15, 10), (2, 30), (8, 17), (9, 2), (22, 10), (21, 5), (27, 4), (0, 18), (11, 8), (17, 2), (26, 16), (34, 25), (27, 35), (19, 11), (10, 0), (0, 4), (6, 28), (10, 17), (11, 2), (19, 14), (0, 31), (6, 13), (32, 18), (12, 25), (8, 4), (8, 30), (1, 14), (2, 31), (19, 19), (19, 13), (20, 6), (0, 6), (26, 25), (3, 12), (14, 2), (17, 10), (16, 11), (20, 25), (23, 34), (1, 5), (32, 14), (21, 14), (3, 25), (6, 14), (26, 11), (0, 21), (14, 1), (17, 8), (14, 10), (2, 21), (12, 34), (8, 34), (14, 0), (4, 0), (28, 4), (12, 10), (31, 0), (10, 4), (6, 35), (22, 15), (19, 6), (31, 29), (13, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "271440", "dataset": "MATH"}
{"messages": [{"content": "In a 37x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (30, 0), (20, 4), (26, 3), (33, 16), (35, 7), (22, 10), (23, 2), (25, 8), (5, 16), (2, 25), (29, 16), (12, 22), (3, 27), (7, 21), (1, 29), (26, 17), (7, 27), (26, 8), (5, 10), (2, 26), (20, 19), (34, 24), (31, 30), (12, 8), (30, 14), (29, 30), (27, 5), (16, 3), (24, 3), (31, 1), (29, 22), (21, 3), (19, 27), (16, 22), (17, 6), (20, 27), (36, 2), (13, 23), (10, 13), (13, 22), (27, 8), (6, 0), (20, 20), (8, 20), (9, 25), (14, 1), (16, 6), (7, 23), (4, 7), (23, 1), (2, 31), (31, 29), (14, 13), (28, 4), (3, 15), (24, 24), (12, 20), (7, 2), (27, 1), (1, 2), (5, 5), (21, 26), (24, 29), (5, 28), (10, 23), (34, 31), (0, 23), (18, 14), (18, 0), (9, 28), (2, 14), (31, 12), (30, 1), (24, 30), (14, 19), (16, 2), (18, 15), (27, 22), (26, 28), (26, 2), (17, 25), (25, 10), (9, 19), (33, 23), (19, 0), (5, 24), (25, 18), (10, 14), (18, 16), (6, 20), (10, 11), (14, 6), (35, 11), (10, 17), (11, 30), (28, 27), (4, 6), (27, 21), (12, 23), (9, 6), (1, 1), (9, 4), (7, 15), (2, 30), (22, 22), (2, 1), (11, 16), (21, 23), (21, 5), (6, 29), (0, 1), (22, 8), (32, 3), (17, 30), (0, 12), (0, 4), (12, 18), (21, 20), (13, 25), (35, 9), (23, 29), (36, 1), (11, 12), (28, 7), (28, 14), (35, 19), (20, 15), (30, 28), (9, 31), (34, 32), (19, 7), (9, 17), (23, 10), (26, 29), (28, 29), (4, 27), (34, 15), (7, 13), (16, 15), (35, 21), (3, 22), (28, 5), (32, 21), (19, 4), (29, 6), (23, 9), (31, 15), (20, 0), (33, 14), (31, 6), (11, 21), (20, 8), (5, 31), (4, 23), (29, 0), (22, 31), (22, 27), (33, 27), (32, 0), (30, 7), (8, 11), (27, 20), (4, 21), (0, 30), (17, 7), (30, 19), (10, 0), (23, 24), (20, 6), (15, 24), (4, 16), (26, 6), (24, 21), (34, 2), (4, 9), (6, 8), (36, 27), (31, 20), (10, 21), (4, 28), (4, 13), (25, 2), (1, 24), (11, 9), (34, 7), (22, 11), (34, 29), (31, 5), (32, 1), (25, 20), (17, 3), (27, 4), (16, 31), (25, 6), (25, 17), (25, 25), (27, 25), (12, 16), (4, 18), (20, 32), (18, 17), (18, 1), (32, 24), (26, 30), (11, 23), (21, 30), (9, 16), (13, 11), (10, 4), (32, 11), (10, 5), (35, 12), (19, 1), (9, 2), (25, 29), (20, 9), (15, 22), (15, 6), (22, 1), (33, 6), (13, 10), (11, 22), (24, 15), (32, 16), (28, 3), (24, 23), (29, 14), (22, 32), (19, 5), (2, 28), (19, 10), (30, 16), (3, 4), (0, 13), (32, 15), (3, 24), (14, 32), (1, 31), (34, 4), (9, 12), (11, 5), (5, 26), (24, 19), (34, 10), (5, 29), (15, 26), (20, 11), (10, 29), (24, 28), (1, 9), (11, 31), (1, 8), (30, 17), (12, 14), (6, 23), (17, 29), (25, 1), (3, 19), (9, 9), (1, 28), (17, 31), (13, 7), (16, 19), (34, 0), (32, 13), (21, 14), (6, 4), (17, 11), (29, 18), (28, 31), (4, 20), (17, 19), (24, 10), (6, 9), (26, 10), (12, 27), (14, 11), (16, 24), (30, 29), (9, 24), (16, 23), (20, 28), (26, 16), (31, 18), (8, 13), (14, 31), (27, 11), (5, 13), (29, 32), (18, 24), (24, 25), (32, 26), (15, 4), (8, 8), (6, 19), (28, 15), (36, 20), (27, 2), (14, 12), (33, 3), (35, 5), (2, 19), (18, 21), (23, 16), (35, 30), (18, 31), (34, 12), (27, 3), (23, 13), (17, 21), (13, 18), (27, 29), (23, 15), (34, 5), (1, 16), (26, 18), (18, 13), (35, 4), (22, 26), (5, 3), (16, 28), (17, 2), (32, 29), (30, 5), (15, 27), (21, 1), (2, 10), (21, 8), (22, 16), (10, 15), (19, 29), (4, 30), (12, 26), (25, 24), (20, 29), (27, 13), (6, 17), (5, 19), (15, 17), (7, 17), (31, 19), (13, 2), (8, 9), (11, 26), (9, 11), (11, 17), (16, 10), (19, 18), (9, 13), (17, 17), (5, 15), (25, 13), (6, 12), (21, 22), (22, 17), (16, 12), (28, 9), (32, 4), (26, 19), (30, 4), (2, 18), (0, 22), (28, 19), (34, 16), (8, 23), (14, 2), (29, 7), (27, 12), (13, 24), (35, 26), (3, 23), (0, 31), (17, 9), (30, 20), (13, 30), (1, 7), (35, 32), (30, 2), (22, 20), (6, 6), (34, 23), (18, 26), (12, 31), (31, 0), (27, 19), (23, 21), (12, 7), (4, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688896", "dataset": "MATH"}
{"messages": [{"content": "In a 31x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 3), (3, 17), (9, 13), (11, 12), (12, 12), (15, 22), (3, 16), (15, 17), (30, 33), (13, 0), (1, 10), (1, 21), (13, 7), (23, 17), (11, 15), (24, 10), (20, 24), (3, 29), (27, 22), (21, 4), (1, 20), (21, 0), (1, 13), (27, 7), (25, 33), (26, 1), (24, 24), (20, 7), (5, 34), (10, 1), (7, 0), (15, 29), (7, 11), (22, 13), (24, 25), (21, 30), (8, 0), (28, 17), (7, 26), (24, 26), (2, 20), (30, 13), (7, 17), (17, 19), (10, 19), (0, 9), (18, 19), (16, 24), (3, 34), (6, 12), (14, 16), (10, 34), (30, 23), (16, 28), (22, 12), (22, 33), (24, 13), (1, 4), (19, 22), (5, 23), (30, 4), (13, 24), (27, 12), (0, 19), (2, 29), (19, 29), (18, 10), (28, 28), (14, 33), (4, 10), (11, 3), (24, 15), (2, 15), (9, 25), (17, 20), (27, 9), (25, 1), (28, 9), (24, 29), (7, 20), (7, 32), (30, 24), (25, 35), (10, 30), (21, 35), (23, 34), (20, 23), (3, 21), (4, 28), (19, 21), (11, 17), (1, 33), (19, 17), (26, 6), (10, 24), (21, 3), (10, 4), (23, 30), (0, 16), (24, 0), (16, 13), (27, 15), (11, 14), (14, 19), (3, 30), (20, 13), (8, 8), (22, 0), (13, 17), (25, 4), (0, 14), (9, 24), (12, 21), (9, 0), (12, 15), (18, 20), (12, 35), (11, 29), (2, 35), (14, 29), (23, 28), (10, 22), (1, 27), (6, 27), (4, 23), (16, 20), (26, 17), (14, 3), (21, 9), (3, 9), (28, 1), (11, 5), (0, 26), (26, 5), (8, 32), (9, 4), (8, 20), (2, 21), (16, 29), (0, 32), (14, 10), (13, 26), (23, 10), (15, 33), (8, 3), (30, 26), (14, 31), (18, 28), (8, 33), (10, 23), (18, 15), (25, 0), (19, 31), (1, 32), (16, 3), (12, 2), (13, 27), (5, 11), (15, 2), (11, 9), (23, 15), (0, 23), (28, 6), (26, 22), (4, 35), (7, 29), (4, 3), (1, 2), (24, 19), (2, 14), (9, 1), (23, 14), (12, 4), (4, 33), (30, 1), (21, 29), (29, 5), (12, 23), (5, 15), (27, 10), (28, 34), (1, 22), (12, 1), (16, 27), (13, 34), (10, 35), (12, 26), (0, 24), (22, 9), (2, 26), (25, 9), (24, 34), (20, 26), (20, 33), (21, 5), (0, 12), (17, 7), (29, 23), (25, 29), (13, 4), (2, 22), (26, 20), (29, 1), (23, 3), (16, 32), (19, 14), (9, 31), (26, 24), (21, 1), (10, 32), (8, 16), (18, 14), (12, 13), (28, 35), (20, 17), (29, 22), (23, 20), (22, 6), (15, 19), (17, 12), (0, 6), (4, 31), (5, 1), (12, 16), (21, 13), (14, 25), (26, 35), (11, 10), (15, 6), (14, 22), (25, 27), (28, 11), (8, 19), (5, 32), (3, 22), (16, 34), (6, 29), (30, 20), (24, 8), (10, 18), (12, 20), (9, 23), (25, 19), (25, 23), (18, 16), (22, 14), (12, 30), (3, 14), (6, 6), (19, 5), (8, 26), (16, 16), (19, 20), (19, 26), (17, 35), (7, 25), (3, 28), (11, 1), (2, 4), (16, 31), (15, 34), (4, 4), (6, 15), (3, 26), (8, 4), (3, 23), (17, 6), (6, 9), (5, 14), (20, 34), (14, 7), (25, 20), (18, 5), (13, 18), (30, 27), (1, 18), (16, 2), (29, 13), (12, 10), (30, 19), (17, 23), (15, 3), (17, 32), (29, 28), (22, 25), (12, 3), (23, 29), (16, 18), (12, 19), (2, 34), (30, 32), (21, 17), (28, 21), (8, 28), (17, 5), (0, 10), (0, 28), (8, 17), (12, 0), (22, 11), (6, 14), (10, 21), (28, 26), (11, 18), (29, 6), (28, 23), (10, 28), (30, 2), (27, 24), (18, 30), (9, 2), (9, 33), (1, 31), (23, 24), (21, 19), (25, 25), (29, 30), (1, 15), (22, 5), (27, 2), (13, 16), (5, 0), (8, 11), (7, 16), (12, 5), (5, 3), (21, 27), (5, 26), (25, 30), (15, 15), (5, 31), (0, 20), (8, 12), (7, 35), (5, 19), (15, 27), (23, 1), (1, 19), (5, 21), (10, 31), (23, 9), (16, 21), (5, 18), (25, 6), (1, 7), (4, 20), (18, 8), (17, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "754272", "dataset": "MATH"}
{"messages": [{"content": "In a 37x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 37), 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), (30, 11), (5, 23), (30, 2), (11, 34), (35, 29), (32, 5), (5, 6), (31, 24), (11, 15), (9, 3), (22, 24), (36, 0), (16, 19), (33, 37), (17, 26), (9, 32), (11, 18), (6, 15), (7, 32), (34, 30), (16, 15), (27, 16), (21, 9), (36, 6), (16, 11), (10, 28), (26, 3), (0, 23), (21, 3), (24, 31), (21, 20), (25, 1), (2, 14), (22, 6), (30, 12), (31, 29), (26, 14), (33, 19), (23, 34), (20, 7), (3, 29), (36, 4), (36, 20), (18, 25), (35, 7), (14, 37), (21, 31), (11, 14), (14, 28), (21, 28), (3, 30), (8, 2), (35, 16), (27, 24), (28, 32), (8, 33), (0, 21), (29, 4), (20, 4), (26, 27), (17, 8), (20, 10), (20, 22), (14, 24), (4, 25), (24, 12), (10, 2), (24, 4), (7, 12), (13, 20), (25, 7), (16, 22), (17, 9), (4, 27), (36, 14), (31, 26), (24, 32), (9, 37), (35, 18), (16, 9), (27, 23), (0, 19), (0, 37), (28, 15), (5, 9), (28, 19), (17, 3), (10, 23), (11, 16), (4, 6), (20, 5), (17, 27), (30, 29), (2, 7), (35, 12), (22, 35), (16, 33), (35, 8), (20, 23), (6, 29), (30, 15), (2, 15), (3, 9), (29, 1), (17, 19), (17, 0), (34, 12), (30, 9), (11, 28), (30, 20), (23, 5), (3, 25), (21, 16), (4, 22), (8, 19), (22, 10), (20, 19), (30, 24), (32, 29), (30, 17), (8, 1), (25, 10), (26, 10), (15, 32), (4, 8), (31, 5), (36, 27), (34, 19), (11, 26), (8, 37), (0, 34), (15, 27), (3, 36), (35, 21), (2, 0), (19, 18), (28, 10), (23, 32), (13, 6), (13, 7), (22, 14), (32, 2), (19, 20), (33, 29), (24, 2), (20, 17), (14, 35), (22, 17), (25, 5), (11, 17), (23, 20), (36, 34), (12, 29), (1, 1), (33, 11), (25, 19), (14, 21), (5, 19), (7, 8), (6, 7), (34, 28), (18, 22), (3, 0), (12, 12), (27, 27), (2, 32), (6, 27), (23, 9), (3, 4), (22, 28), (25, 25), (18, 14), (18, 19), (18, 17), (3, 22), (3, 19), (7, 28), (9, 6), (32, 34), (3, 16), (9, 20), (13, 35), (30, 4), (34, 15), (35, 2), (34, 26), (1, 29), (27, 18), (36, 32), (24, 19), (14, 4), (20, 26), (9, 21), (28, 18), (5, 8), (33, 18), (8, 9), (4, 34), (24, 27), (7, 25), (20, 37), (3, 11), (13, 30), (36, 33), (25, 15), (11, 11), (31, 32), (21, 23), (15, 37), (4, 0), (28, 14), (24, 29), (22, 26), (36, 13), (18, 28), (6, 3), (8, 30), (16, 32), (18, 33), (14, 11), (12, 11), (8, 31), (12, 19), (28, 30), (16, 35), (28, 9), (31, 30), (10, 7), (2, 18), (27, 15), (21, 33), (27, 19), (28, 34), (1, 22), (0, 14), (15, 14), (20, 14), (5, 12), (11, 25), (22, 7), (11, 22), (19, 11), (5, 24), (31, 13), (29, 34), (13, 33), (19, 6), (8, 35), (21, 22), (7, 10), (24, 18), (13, 27), (4, 23), (9, 9), (24, 3), (5, 37), (0, 17), (25, 14), (2, 16), (21, 34), (16, 5), (8, 12), (1, 33), (23, 14), (1, 7), (10, 26), (14, 10), (6, 33), (33, 20), (23, 30), (29, 24), (9, 7), (12, 26), (22, 9), (22, 23), (10, 29), (18, 5), (3, 23), (13, 32), (20, 15), (9, 5), (30, 14), (32, 7), (34, 4), (2, 6), (2, 12), (28, 28), (5, 0), (16, 13), (18, 26), (36, 12), (23, 21), (23, 13), (6, 10), (7, 9), (12, 7), (19, 31), (18, 3), (18, 27), (33, 1), (25, 31), (1, 30), (21, 36), (18, 21), (8, 7), (4, 11), (33, 7), (19, 29), (15, 16), (7, 34), (19, 12), (34, 18), (6, 16), (36, 24), (1, 36), (12, 25), (0, 31), (1, 27), (32, 27), (13, 8), (31, 19), (12, 4), (24, 8), (3, 5), (21, 19), (26, 21), (32, 32), (1, 28), (18, 11), (12, 32), (28, 33), (11, 6), (15, 1), (28, 29), (10, 31), (7, 1), (24, 20), (15, 0), (20, 1), (33, 25), (6, 4), (20, 13), (8, 8), (5, 35), (19, 5), (26, 18), (34, 17), (11, 32), (33, 9), (17, 30), (24, 13), (34, 29), (32, 12), (33, 13), (16, 20), (26, 22), (24, 17), (31, 23), (7, 14), (25, 6), (15, 11), (8, 24), (20, 6), (32, 30), (15, 29), (6, 22), (18, 1), (5, 18), (8, 27), (14, 34), (3, 3), (5, 11), (21, 2), (25, 36), (7, 21), (27, 25), (29, 12), (9, 23), (11, 21), (0, 9), (31, 34), (18, 24), (5, 17), (8, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8640", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (7, 9), (8, 34), (27, 13), (7, 1), (2, 4), (24, 11), (11, 32), (15, 30), (24, 19), (26, 0), (4, 16), (29, 23), (14, 11), (15, 28), (14, 20), (8, 9), (29, 14), (32, 19), (28, 16), (15, 31), (25, 26), (25, 32), (16, 17), (29, 3), (31, 15), (24, 14), (8, 22), (12, 1), (22, 18), (23, 31), (13, 24), (2, 15), (21, 19), (18, 28), (15, 25), (10, 7), (32, 8), (18, 16), (28, 11), (17, 5), (11, 34), (1, 6), (20, 37), (4, 24), (16, 33), (34, 4), (21, 17), (18, 33), (1, 8), (22, 31), (31, 14), (14, 37), (2, 17), (5, 13), (4, 21), (30, 20), (20, 34), (23, 5), (11, 8), (2, 34), (30, 34), (2, 19), (2, 35), (4, 14), (10, 6), (25, 30), (7, 0), (4, 0), (29, 5), (9, 2), (34, 16), (31, 7), (5, 27), (8, 26), (26, 30), (25, 2), (9, 32), (28, 2), (29, 4), (32, 22), (34, 32), (18, 29), (29, 17), (1, 22), (22, 28), (31, 20), (16, 28), (26, 12), (24, 21), (30, 19), (14, 5), (11, 24), (27, 22), (27, 17), (29, 16), (27, 9), (9, 14), (18, 22), (22, 37), (28, 14), (18, 11), (32, 12), (14, 26), (15, 27), (31, 17), (1, 1), (15, 26), (21, 2), (23, 30), (19, 15), (1, 36), (20, 23), (30, 33), (21, 26), (19, 18), (8, 28), (14, 23), (27, 36), (13, 2), (7, 2), (7, 30), (12, 14), (30, 7), (11, 12), (10, 21), (19, 2), (33, 7), (13, 18), (31, 3), (26, 18), (30, 9), (34, 30), (27, 37), (2, 10), (20, 6), (32, 37), (25, 7), (13, 29), (27, 33), (4, 17), (32, 18), (15, 3), (15, 6), (24, 13), (5, 29), (23, 22), (29, 31), (33, 0), (11, 31), (2, 18), (18, 26), (17, 15), (15, 33), (31, 5), (9, 1), (12, 7), (19, 0), (33, 35), (22, 23), (9, 22), (20, 16), (19, 12), (10, 4), (21, 31), (25, 4), (32, 35), (10, 22), (25, 24), (10, 10), (8, 5), (2, 0), (6, 27), (20, 15), (31, 0), (14, 31), (2, 29), (20, 5), (6, 23), (33, 24), (15, 34), (3, 37), (4, 20), (6, 26), (25, 36), (11, 22), (24, 2), (25, 17), (5, 1), (11, 2), (18, 19), (22, 12), (16, 15), (27, 32), (15, 5), (18, 34), (23, 23), (0, 23), (3, 29), (4, 3), (25, 5), (9, 6), (4, 28), (1, 13), (21, 10), (4, 30), (22, 9), (18, 36), (20, 13), (10, 37), (27, 26), (26, 15), (28, 35), (32, 14), (29, 22), (30, 22), (4, 35), (21, 27), (5, 9), (24, 20), (27, 20), (23, 27), (26, 14), (17, 10), (10, 28), (26, 8), (3, 23), (19, 16), (21, 24), (30, 17), (29, 10), (23, 1), (12, 26), (25, 21), (17, 12), (33, 22), (9, 26), (21, 1), (17, 36), (5, 30), (3, 7), (34, 35), (11, 13), (23, 36), (32, 9), (15, 20), (28, 20), (12, 15), (23, 19), (13, 28), (27, 8), (9, 30), (9, 29), (2, 27), (25, 6), (17, 17), (24, 1), (4, 2), (11, 10), (19, 30), (9, 28), (1, 30), (24, 23), (28, 8), (30, 35), (24, 36), (34, 24), (4, 5), (11, 26), (5, 24), (4, 15), (0, 3), (24, 12), (6, 8), (28, 26), (32, 28), (3, 30), (14, 32), (6, 28), (21, 35), (7, 10), (5, 5), (17, 1), (13, 11), (15, 14), (33, 20), (33, 27), (7, 20), (15, 24), (26, 36), (26, 4), (16, 21), (21, 6), (32, 7), (1, 4), (33, 12), (23, 32), (14, 10), (4, 27), (0, 12), (23, 25), (19, 3), (1, 26), (5, 11), (12, 22), (16, 7), (34, 2), (23, 17), (18, 21), (21, 37), (19, 14), (26, 24), (20, 2), (14, 16), (25, 27), (13, 27), (26, 5), (10, 32), (27, 25), (22, 25), (17, 3), (26, 6), (0, 18), (28, 29), (33, 28), (34, 11), (14, 28), (15, 13), (9, 0), (27, 19), (2, 12), (24, 31), (8, 13), (6, 33), (8, 0), (12, 33), (26, 31), (18, 15), (12, 29), (34, 10), (7, 25), (19, 22), (0, 33), (13, 31), (29, 1), (15, 19), (33, 37), (19, 29), (9, 31), (0, 34), (32, 20), (11, 19), (32, 30), (23, 10), (3, 2), (24, 3), (20, 14), (32, 10), (17, 16), (23, 0), (8, 11), (0, 30), (1, 0), (25, 8), (27, 0), (15, 2), (6, 4), (11, 14), (16, 23), (21, 25), (23, 29), (32, 32), (24, 16), (20, 29), (33, 34), (11, 4), (5, 4), (14, 21), (6, 17), (8, 24), (11, 23), (8, 17), (17, 9), (1, 12), (5, 16), (32, 0), (24, 5), (10, 17), (17, 18), (14, 13), (21, 14), (24, 29), (23, 6), (31, 27), (11, 9), (34, 31), (17, 13), (3, 26), (11, 36), (10, 16)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "719372", "dataset": "MATH"}
{"messages": [{"content": "In a 34x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 11), (3, 23), (3, 29), (12, 4), (33, 17), (4, 21), (23, 32), (16, 23), (4, 13), (28, 12), (24, 7), (5, 3), (24, 17), (23, 10), (4, 6), (13, 11), (29, 34), (7, 11), (2, 13), (25, 32), (26, 17), (33, 22), (27, 20), (24, 12), (9, 16), (11, 8), (1, 4), (28, 25), (30, 26), (29, 30), (32, 15), (13, 7), (9, 4), (33, 7), (20, 0), (28, 1), (29, 32), (5, 16), (2, 11), (12, 14), (25, 5), (29, 14), (3, 12), (2, 15), (21, 16), (20, 17), (2, 16), (11, 13), (21, 2), (32, 5), (33, 9), (30, 19), (22, 34), (15, 20), (30, 11), (23, 34), (10, 33), (29, 18), (20, 20), (28, 0), (26, 18), (17, 31), (10, 18), (29, 22), (31, 17), (15, 2), (2, 8), (26, 13), (15, 6), (21, 9), (25, 16), (12, 0), (22, 0), (5, 22), (6, 32), (3, 11), (28, 9), (3, 0), (28, 4), (4, 28), (12, 25), (10, 34), (11, 32), (18, 17), (1, 5), (14, 8), (30, 32), (5, 14), (22, 17), (24, 19), (11, 21), (28, 19), (16, 8), (25, 18), (17, 23), (1, 11), (0, 20), (33, 13), (12, 10), (10, 29), (9, 32), (6, 28), (28, 7), (20, 22), (25, 31), (22, 23), (16, 28), (1, 7), (19, 16), (23, 2), (32, 2), (12, 32), (15, 16), (21, 31), (17, 4), (3, 30), (12, 22), (23, 26), (30, 29), (24, 14), (6, 4), (7, 31), (0, 22), (20, 18), (30, 12), (24, 5), (9, 20), (3, 20), (27, 30), (27, 29), (14, 31), (5, 30), (13, 3), (16, 12), (13, 34), (2, 7), (0, 1), (29, 6), (21, 22), (22, 30), (13, 15), (5, 2), (5, 6), (5, 27), (29, 20), (6, 6), (23, 21), (27, 12), (17, 20), (32, 6), (2, 20), (9, 14), (10, 6), (6, 29), (29, 8), (17, 1), (10, 17), (11, 14), (18, 9), (21, 21), (13, 23), (1, 29), (33, 25), (3, 28), (17, 34), (16, 33), (14, 21), (17, 27), (4, 2), (20, 3), (21, 17), (28, 32), (18, 6), (1, 13), (19, 34), (6, 19), (30, 13), (33, 33), (24, 28), (18, 14), (16, 14), (10, 24), (33, 23), (19, 15), (18, 5), (6, 22), (8, 27), (5, 18), (17, 11), (32, 9), (32, 0), (24, 9), (28, 33), (10, 16), (33, 11), (10, 0), (27, 7), (33, 3), (17, 18), (29, 11), (28, 28), (33, 14), (20, 25), (12, 31), (27, 28), (31, 12), (13, 16), (10, 26), (6, 20), (7, 3), (18, 16), (16, 29), (12, 12), (27, 21), (2, 2), (25, 17), (12, 7), (9, 13), (12, 5), (29, 21), (4, 12), (26, 9), (16, 32), (17, 26), (16, 6), (16, 16), (4, 5), (20, 11), (5, 9), (2, 32), (6, 30), (3, 21), (9, 3), (5, 25), (10, 28), (19, 6), (24, 21), (33, 8), (26, 10), (22, 29), (7, 14), (28, 30), (8, 11), (27, 13), (21, 29), (33, 28), (0, 9), (17, 21), (23, 5), (2, 9), (26, 4), (10, 22), (15, 27), (15, 12), (8, 17), (13, 6), (6, 31), (20, 13), (2, 23), (23, 29), (24, 18), (18, 24), (31, 6), (25, 19), (31, 7), (9, 10), (19, 20), (22, 6), (22, 32), (33, 24), (27, 33), (6, 11), (4, 9), (18, 28), (28, 26), (29, 25), (6, 27), (7, 12), (4, 18), (33, 16), (27, 15), (9, 11), (22, 24), (1, 2), (5, 7), (11, 4), (18, 19), (23, 7), (10, 10), (10, 8), (32, 14), (31, 16), (21, 30), (33, 12), (17, 33), (26, 24), (19, 2), (8, 7), (23, 15), (22, 8), (1, 26), (30, 25), (3, 5), (24, 3), (31, 22), (19, 13), (27, 24), (13, 31), (3, 10), (17, 12), (3, 9), (25, 25), (2, 18), (10, 1), (8, 33), (0, 28), (25, 9), (15, 23), (18, 13), (15, 24), (26, 1), (2, 30), (1, 15), (31, 24), (4, 29), (18, 4), (29, 1), (21, 12), (31, 34), (13, 27), (25, 13)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631888", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 6), (11, 3), (15, 19), (8, 15), (2, 20), (25, 13), (29, 14), (14, 23), (17, 15), (33, 24), (16, 10), (28, 8), (12, 20), (30, 0), (0, 8), (30, 28), (4, 28), (8, 4), (20, 15), (27, 3), (11, 10), (36, 27), (22, 29), (1, 2), (14, 25), (34, 21), (6, 30), (25, 28), (36, 14), (25, 25), (16, 0), (18, 16), (33, 11), (32, 22), (21, 12), (18, 0), (33, 13), (19, 19), (3, 12), (8, 9), (9, 5), (22, 22), (0, 9), (3, 21), (15, 25), (9, 7), (34, 3), (4, 22), (34, 27), (20, 7), (17, 6), (20, 3), (23, 1), (10, 23), (14, 30), (18, 22), (23, 0), (21, 0), (19, 28), (33, 30), (13, 2), (17, 20), (25, 21), (5, 18), (2, 17), (19, 11), (6, 17), (2, 18), (26, 21), (16, 17), (30, 17), (11, 23), (31, 10), (34, 5), (24, 10), (24, 12), (4, 3), (19, 4), (16, 28), (22, 25), (5, 13), (23, 4), (33, 5), (19, 9), (30, 3), (17, 11), (36, 18), (23, 24), (22, 19), (36, 2), (33, 21), (20, 12), (3, 23), (8, 21), (22, 4), (1, 15), (26, 3), (36, 10), (14, 27), (13, 26), (31, 7), (21, 4), (2, 4), (18, 20), (18, 12), (6, 12), (4, 18), (8, 2), (16, 7), (25, 0), (18, 29), (9, 27), (27, 29), (4, 12), (22, 17), (21, 26), (31, 0), (34, 28), (3, 20), (25, 3), (27, 26), (18, 3), (7, 13), (18, 11), (7, 6), (30, 13), (15, 24), (18, 30), (9, 17), (13, 30), (35, 3), (5, 20), (29, 5), (9, 21), (10, 12), (23, 5), (11, 1), (18, 5), (20, 2), (32, 29), (4, 11), (20, 8), (2, 27), (32, 26), (25, 1), (35, 15), (35, 10), (25, 15), (4, 23), (1, 5), (12, 30), (10, 22), (10, 13), (26, 8), (29, 4), (29, 7), (32, 25), (29, 17), (13, 22), (26, 19), (0, 30), (12, 23), (4, 9), (23, 22), (11, 0), (6, 10), (9, 2), (15, 27), (0, 19), (13, 24), (1, 25), (12, 27), (21, 2), (8, 11), (3, 26), (19, 20), (6, 4), (16, 6), (27, 6), (17, 17), (35, 28), (20, 26), (35, 5), (35, 21), (32, 0), (8, 6), (23, 3), (7, 0), (29, 16), (15, 11), (27, 11), (12, 10), (19, 23), (34, 30), (25, 19), (1, 7), (31, 23), (24, 0), (24, 8), (20, 11), (11, 18), (32, 18), (14, 29), (36, 26), (30, 8), (33, 0), (27, 9), (7, 15), (32, 15), (4, 19), (16, 25), (7, 3), (31, 5), (27, 27), (25, 4), (12, 7), (26, 2), (7, 17), (24, 14), (13, 16), (35, 7), (27, 20), (24, 25), (28, 19), (14, 13), (2, 29), (29, 30), (16, 9), (33, 17), (17, 2), (15, 14), (16, 29), (30, 18), (30, 26), (15, 13), (0, 28), (35, 16), (8, 0), (10, 7), (25, 5), (35, 4), (5, 3), (30, 21), (5, 30), (4, 10), (2, 1), (9, 24), (25, 27), (29, 2), (4, 15), (4, 2), (31, 25), (3, 18), (8, 8), (13, 17), (24, 6), (24, 24), (13, 18), (13, 10), (12, 18), (0, 21), (27, 5), (25, 29), (25, 12), (15, 3), (28, 0), (31, 1), (11, 11), (9, 25), (26, 4), (14, 6), (8, 22), (10, 2), (26, 10), (18, 24), (23, 20), (27, 19), (6, 7), (13, 15), (14, 18), (26, 23), (0, 20), (30, 7), (5, 25), (1, 14), (16, 23), (17, 23), (36, 28), (24, 9), (23, 21), (25, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "401598", "dataset": "MATH"}
{"messages": [{"content": "In a 34x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 11), (5, 20), (19, 3), (16, 1), (30, 32), (14, 4), (32, 9), (5, 30), (7, 6), (19, 17), (7, 33), (29, 7), (4, 26), (8, 3), (9, 10), (3, 9), (6, 5), (3, 12), (8, 26), (11, 28), (32, 13), (11, 21), (33, 21), (29, 9), (7, 13), (22, 6), (13, 14), (32, 28), (21, 14), (24, 4), (10, 8), (25, 1), (18, 3), (2, 17), (29, 19), (12, 30), (6, 0), (17, 15), (28, 25), (18, 4), (29, 3), (12, 34), (2, 10), (20, 0), (5, 17), (19, 10), (15, 6), (22, 33), (8, 19), (27, 22), (9, 18), (10, 35), (6, 16), (17, 12), (1, 34), (11, 30), (29, 5), (30, 29), (2, 27), (32, 0), (17, 25), (33, 8), (2, 7), (33, 19), (4, 23), (1, 3), (21, 23), (12, 1), (18, 5), (11, 32), (4, 29), (18, 20), (3, 7), (2, 32), (27, 27), (9, 35), (28, 8), (7, 4), (1, 33), (18, 28), (17, 9), (27, 21), (1, 17), (23, 4), (26, 20), (2, 2), (21, 29), (10, 21), (12, 19), (14, 13), (21, 19), (0, 33), (11, 23), (22, 23), (18, 35), (14, 19), (11, 2), (0, 26), (14, 2), (30, 34), (7, 32), (31, 15), (3, 26), (9, 29), (3, 34), (7, 28), (22, 1), (9, 14), (11, 8), (7, 11), (6, 23), (11, 27), (8, 20), (3, 28), (27, 24), (33, 13), (27, 32), (10, 11), (22, 32), (10, 29), (1, 23), (10, 25), (29, 27), (26, 26), (25, 23), (10, 15), (3, 30), (15, 23), (3, 1), (27, 8), (26, 2), (31, 3), (19, 24), (1, 24), (23, 19), (24, 1), (27, 15), (8, 8), (15, 27), (28, 3), (5, 9), (19, 9), (21, 30), (15, 3), (27, 17), (2, 12), (0, 27), (16, 9), (20, 26), (20, 17), (1, 25), (13, 13), (1, 27), (28, 31), (30, 33), (31, 12), (24, 0), (27, 29), (28, 19), (26, 27), (12, 23), (25, 7), (25, 16), (18, 24), (11, 4), (4, 24), (2, 28), (7, 15), (2, 23), (8, 21), (3, 32), (11, 13), (2, 4), (7, 30), (15, 4), (12, 28), (32, 32), (26, 1), (3, 29), (30, 27), (7, 27), (9, 9), (25, 32), (4, 5), (13, 19), (15, 21), (9, 15), (0, 12), (11, 22), (22, 14), (27, 18), (9, 8), (21, 22), (15, 29), (15, 17), (8, 11), (19, 16), (28, 1), (5, 31), (33, 20), (20, 18), (9, 25), (26, 30), (26, 32), (30, 28), (28, 21), (31, 24), (2, 22), (29, 21), (23, 28), (6, 13), (20, 34), (13, 17), (10, 22), (5, 1), (29, 4), (27, 16), (22, 20), (9, 34), (29, 14), (3, 31), (5, 16), (16, 35), (24, 13), (19, 32), (15, 0), (23, 5), (22, 13), (31, 5), (18, 10), (25, 30), (10, 3), (15, 25), (1, 5), (7, 10), (27, 7), (17, 27), (16, 22), (33, 29), (25, 3), (10, 26), (20, 7), (17, 19), (31, 16), (29, 29), (18, 34), (25, 10), (20, 28), (9, 31), (9, 30), (24, 27), (12, 32), (13, 18), (14, 30), (21, 5), (19, 12), (13, 7), (10, 24), (20, 19), (5, 23), (18, 14), (2, 8), (9, 33), (5, 34), (1, 26), (5, 33), (19, 13), (18, 18), (18, 30), (31, 6), (17, 24), (16, 20), (20, 27), (24, 21), (32, 6), (14, 17), (21, 34), (20, 30), (8, 22), (16, 34), (23, 18), (25, 24), (6, 15), (16, 17), (23, 11), (23, 3), (18, 17), (7, 29), (8, 0), (16, 15), (23, 14), (17, 26), (24, 32), (4, 33), (1, 1), (22, 11), (7, 25), (7, 9), (18, 16), (4, 1), (5, 10), (17, 16), (16, 25), (11, 15), (19, 30), (14, 20), (15, 8), (18, 13), (24, 5), (20, 10), (24, 34), (19, 25), (33, 22), (9, 24), (26, 11), (21, 16), (0, 32), (3, 19), (16, 2), (29, 0), (11, 35), (13, 26), (27, 10), (27, 35), (22, 15), (14, 15), (1, 22), (21, 28), (10, 28), (3, 0), (3, 4), (29, 32), (16, 13), (15, 16), (31, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832092", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 25), (20, 27), (10, 25), (9, 29), (22, 30), (20, 15), (24, 13), (32, 11), (13, 23), (28, 31), (5, 25), (1, 18), (7, 19), (21, 22), (0, 2), (6, 7), (16, 33), (5, 31), (3, 25), (23, 2), (2, 37), (20, 28), (4, 21), (13, 17), (6, 27), (15, 29), (19, 33), (31, 7), (33, 23), (5, 19), (1, 19), (17, 18), (18, 26), (30, 24), (21, 14), (26, 8), (23, 36), (9, 26), (8, 2), (26, 16), (2, 7), (27, 35), (7, 36), (23, 35), (34, 15), (18, 7), (0, 28), (15, 3), (2, 18), (2, 0), (8, 14), (27, 15), (3, 21), (24, 5), (1, 20), (26, 9), (25, 35), (32, 6), (15, 1), (17, 12), (11, 4), (2, 26), (20, 32), (34, 3), (29, 26), (15, 33), (11, 18), (4, 24), (21, 27), (32, 22), (22, 33), (14, 21), (4, 35), (8, 1), (14, 32), (16, 18), (28, 34), (10, 30), (17, 25), (14, 23), (7, 13), (8, 20), (4, 10), (30, 29), (33, 31), (21, 0), (18, 8), (22, 3), (11, 24), (1, 32), (32, 5), (5, 5), (33, 25), (16, 28), (27, 20), (32, 15), (17, 2), (20, 10), (4, 25), (16, 1), (15, 4), (9, 20), (31, 26), (0, 27), (13, 21), (21, 18), (30, 14), (13, 14), (9, 35), (21, 29), (16, 14), (1, 27), (13, 0), (21, 36), (4, 6), (16, 25), (29, 28), (3, 28), (28, 26), (3, 30), (33, 15), (10, 11), (32, 18), (32, 34), (29, 2), (33, 17), (32, 29), (1, 2), (23, 16), (16, 16), (15, 20), (7, 34), (30, 16), (18, 0), (31, 36), (32, 20), (34, 9), (9, 5), (2, 19), (24, 19), (14, 30), (9, 27), (14, 4), (34, 18), (9, 24), (10, 18), (24, 30), (29, 35), (21, 8), (28, 22), (32, 2), (19, 0), (22, 37), (18, 6), (25, 22), (4, 17), (24, 26), (13, 28), (3, 17), (20, 21), (21, 21), (28, 15), (26, 0), (8, 7), (9, 36), (27, 0), (17, 4), (10, 1), (29, 13), (12, 7), (30, 3), (19, 2), (31, 3), (13, 6), (4, 31), (13, 7), (1, 33), (11, 17), (15, 15), (13, 3), (13, 30), (4, 15), (12, 34), (13, 35), (23, 26), (17, 9), (23, 24), (29, 37), (26, 11), (6, 0), (3, 15), (33, 9), (1, 28), (0, 9), (27, 4), (18, 11), (19, 20), (14, 28), (1, 36), (11, 35), (34, 28), (22, 10), (16, 23), (10, 14), (30, 12), (17, 20), (13, 19), (30, 0), (5, 9), (24, 0), (33, 8), (34, 36), (19, 24), (30, 7), (14, 25), (32, 1), (20, 9), (15, 2), (0, 35), (33, 32), (6, 2), (25, 28), (5, 11), (30, 30), (5, 3), (7, 26), (10, 9), (8, 9), (34, 1), (5, 32), (24, 8), (32, 21), (24, 16), (22, 6), (5, 30), (8, 11), (30, 36), (30, 23), (9, 22), (22, 25), (26, 3), (15, 8), (18, 16), (21, 6), (27, 24), (2, 2), (7, 7), (30, 22), (17, 24), (7, 5), (20, 35), (33, 21), (26, 17), (9, 28), (14, 24), (13, 25), (21, 19), (1, 0), (4, 8), (25, 6), (31, 15), (26, 28), (29, 27), (11, 16), (20, 3), (2, 33), (19, 5), (27, 21), (12, 32), (15, 5), (3, 12), (30, 11), (8, 31), (18, 12), (8, 12), (10, 33), (25, 1), (16, 2), (3, 33), (21, 26), (8, 21), (23, 21), (2, 9), (6, 20), (20, 6), (11, 10), (22, 4), (19, 4), (4, 19), (20, 19), (22, 12), (19, 16), (0, 23), (30, 2), (28, 32), (32, 19), (15, 7), (5, 4), (32, 14), (2, 24), (12, 37), (14, 2), (18, 17), (31, 32), (13, 9), (33, 20), (12, 24), (12, 15), (10, 17), (6, 32), (34, 11), (23, 11), (4, 23), (16, 26), (12, 14), (32, 3), (28, 17), (27, 26), (28, 4), (7, 22), (12, 12), (11, 2), (21, 24), (18, 22), (1, 10), (13, 15), (8, 26), (10, 20), (3, 7), (9, 13), (5, 34), (23, 34), (2, 25), (27, 7), (19, 3), (15, 18), (32, 16), (30, 25), (34, 20), (12, 11), (24, 18), (10, 37), (27, 12), (7, 21), (11, 14), (5, 37), (22, 16), (27, 18), (31, 28), (2, 10), (27, 16), (30, 5), (27, 13), (9, 34), (28, 29), (5, 14), (31, 9), (10, 27), (6, 6), (6, 18), (0, 4), (15, 27), (28, 20), (19, 11), (14, 33), (30, 37), (24, 37), (16, 6), (26, 20), (34, 24), (22, 24), (0, 21), (10, 5), (34, 5), (17, 7), (1, 25), (30, 21), (18, 28), (21, 4), (23, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "874898", "dataset": "MATH"}
{"messages": [{"content": "In a 35x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 30), 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), (22, 4), (15, 9), (28, 17), (6, 7), (3, 16), (28, 14), (6, 25), (20, 30), (16, 11), (15, 13), (31, 25), (7, 15), (17, 7), (15, 20), (1, 8), (27, 20), (22, 29), (28, 7), (20, 11), (2, 10), (2, 8), (30, 17), (24, 17), (14, 18), (13, 1), (30, 5), (18, 16), (14, 23), (29, 1), (22, 0), (25, 9), (30, 12), (21, 10), (25, 16), (33, 30), (17, 12), (34, 25), (16, 18), (2, 2), (14, 11), (4, 19), (31, 4), (25, 21), (17, 5), (9, 7), (27, 14), (20, 12), (22, 5), (1, 9), (14, 24), (23, 30), (20, 26), (18, 2), (32, 21), (12, 25), (8, 14), (33, 15), (6, 8), (24, 19), (21, 9), (28, 26), (7, 6), (16, 24), (26, 29), (7, 24), (3, 24), (30, 1), (2, 15), (16, 7), (6, 28), (13, 27), (14, 2), (28, 30), (19, 6), (1, 5), (17, 23), (11, 13), (4, 1), (28, 2), (13, 17), (10, 24), (2, 1), (18, 3), (25, 7), (7, 11), (1, 30), (28, 1), (20, 22), (19, 14), (23, 4), (13, 22), (17, 11), (30, 26), (15, 25), (10, 19), (22, 19), (18, 24), (6, 0), (23, 3), (8, 25), (10, 6), (30, 27), (17, 25), (11, 15), (7, 19), (4, 3), (12, 26), (3, 5), (4, 4), (7, 13), (11, 8), (16, 6), (26, 19), (26, 24), (22, 3), (8, 11), (33, 21), (10, 5), (17, 21), (30, 24), (28, 8), (9, 9), (0, 6), (29, 5), (26, 28), (13, 6), (29, 14), (17, 26), (9, 25), (32, 8), (2, 23), (13, 2), (26, 25), (33, 12), (34, 20), (19, 5), (6, 2), (16, 16), (33, 14), (26, 13), (9, 19), (25, 26), (20, 14), (30, 19), (22, 13), (10, 27), (1, 6), (1, 15), (26, 21), (24, 27), (6, 29), (27, 30), (30, 2), (8, 13), (1, 23), (29, 22), (10, 16), (11, 23), (9, 8), (30, 15), (23, 16), (23, 14), (20, 0), (20, 25), (2, 16), (23, 9), (22, 6), (1, 12), (8, 29), (26, 18), (21, 26), (21, 25), (9, 2), (24, 15), (3, 1), (6, 3), (3, 28), (30, 7), (31, 11), (0, 14), (1, 14), (11, 7), (20, 24), (16, 25), (24, 0), (21, 27), (27, 27), (14, 13), (11, 22), (31, 13), (20, 9), (16, 20), (27, 24), (20, 16), (14, 21), (29, 18), (11, 28), (14, 4), (4, 25), (5, 14), (24, 11), (14, 19), (1, 3), (33, 2), (22, 2), (2, 29), (3, 4), (0, 5), (8, 20), (19, 10), (27, 19), (24, 3), (28, 15), (19, 4), (8, 23), (3, 30), (3, 13), (15, 28), (19, 20), (4, 13), (7, 17), (23, 28), (12, 15), (24, 16), (8, 5), (28, 21), (2, 20), (20, 19), (2, 13), (3, 18), (32, 13), (22, 15), (31, 27), (34, 13), (23, 24), (6, 22), (1, 28), (4, 12), (26, 23), (21, 2), (20, 13), (13, 18), (6, 10), (31, 17), (11, 9), (6, 21), (27, 25), (4, 27), (10, 17), (29, 25), (25, 15), (25, 8), (0, 2), (31, 21), (14, 8), (18, 26), (28, 6), (28, 12), (6, 16), (17, 24), (19, 22), (11, 29), (14, 27), (16, 23), (11, 14), (7, 8), (14, 1), (17, 15), (28, 24), (32, 4), (8, 4), (6, 26), (5, 26), (19, 28), (19, 25), (3, 6), (22, 14), (12, 12), (27, 3), (27, 6), (21, 15), (9, 27), (5, 17), (14, 12), (8, 2), (31, 1), (31, 29), (18, 27), (25, 6), (19, 2), (2, 28), (6, 24), (14, 6), (34, 26), (26, 4), (7, 23), (30, 21), (34, 27), (7, 30), (33, 6), (33, 18), (25, 0), (20, 15), (32, 27), (13, 12)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928200", "dataset": "MATH"}
{"messages": [{"content": "In a 36x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (18, 29), (16, 13), (25, 13), (22, 3), (8, 10), (9, 2), (3, 14), (14, 14), (13, 5), (32, 33), (15, 25), (16, 0), (34, 28), (34, 7), (19, 17), (32, 9), (2, 17), (25, 21), (34, 13), (35, 24), (21, 25), (4, 17), (16, 5), (1, 2), (3, 13), (20, 14), (30, 14), (24, 12), (20, 12), (12, 33), (13, 20), (35, 29), (31, 33), (15, 27), (27, 13), (23, 5), (32, 10), (14, 13), (14, 5), (12, 23), (15, 15), (2, 3), (22, 2), (34, 25), (19, 24), (31, 28), (9, 29), (28, 19), (10, 2), (27, 21), (34, 19), (12, 32), (31, 27), (15, 31), (17, 16), (28, 32), (11, 31), (2, 13), (20, 3), (0, 12), (22, 13), (6, 0), (22, 21), (7, 14), (13, 21), (7, 0), (34, 15), (1, 7), (16, 11), (29, 10), (32, 6), (1, 0), (3, 30), (19, 20), (5, 21), (28, 15), (19, 21), (16, 24), (29, 7), (12, 6), (15, 21), (15, 12), (18, 16), (21, 14), (27, 27), (35, 9), (27, 33), (14, 22), (29, 26), (26, 30), (17, 33), (22, 18), (1, 6), (19, 22), (16, 1), (26, 34), (33, 3), (6, 14), (19, 16), (1, 26), (9, 3), (35, 5), (24, 28), (30, 19), (11, 22), (5, 29), (4, 6), (32, 12), (4, 5), (10, 34), (4, 21), (0, 6), (16, 34), (22, 27), (25, 28), (15, 17), (4, 2), (33, 16), (7, 1), (21, 12), (0, 19), (25, 9), (11, 4), (0, 3), (23, 17), (16, 20), (3, 8), (2, 7), (19, 0), (28, 23), (10, 18), (10, 31), (13, 19), (29, 15), (4, 13), (8, 16), (26, 13), (30, 18), (34, 10), (21, 0), (35, 0), (8, 21), (27, 18), (23, 27), (18, 10), (27, 2), (1, 25), (14, 18), (6, 28), (27, 7), (15, 14), (17, 8), (0, 23), (31, 2), (32, 1), (4, 0), (13, 31), (33, 8), (12, 25), (34, 11), (0, 32), (5, 13), (9, 26), (27, 30), (19, 6), (18, 3), (32, 34), (5, 26), (21, 21), (0, 24), (20, 33), (26, 17), (12, 29), (3, 20), (28, 2), (18, 17), (0, 8), (20, 32), (11, 34), (30, 34), (21, 2), (18, 25), (9, 28), (21, 34), (35, 2), (25, 7), (21, 11), (17, 23), (3, 17), (22, 0), (24, 4), (35, 30), (4, 10), (22, 6), (23, 10), (34, 21), (30, 32), (15, 30), (18, 18), (26, 22), (25, 12), (31, 22), (16, 30), (6, 33), (12, 14), (18, 32), (13, 3), (23, 1), (22, 32), (2, 2), (5, 1), (18, 21), (18, 33), (12, 22), (8, 22), (5, 28), (28, 16), (30, 10), (4, 15), (7, 2), (4, 33), (10, 24), (15, 22), (35, 23), (29, 9), (31, 4), (34, 6), (29, 28), (34, 29), (35, 21), (24, 20), (23, 26), (25, 14), (30, 15), (7, 33), (19, 34), (33, 7), (23, 32), (4, 18), (12, 10), (1, 13), (28, 26), (10, 8), (25, 8), (11, 12), (29, 2), (3, 12), (23, 2), (17, 29), (29, 25), (33, 34), (23, 33), (9, 30), (31, 5), (2, 33), (14, 1), (17, 3), (22, 14), (3, 5), (29, 16), (19, 11), (5, 4), (28, 5), (20, 25), (4, 30), (19, 12), (6, 34), (12, 0), (4, 31), (25, 30), (15, 7), (17, 7), (15, 5), (31, 1), (34, 2), (25, 10), (8, 26), (34, 27), (4, 27), (17, 12), (2, 22), (9, 7), (33, 15), (19, 32), (14, 11), (26, 16), (11, 20), (0, 15), (6, 2), (32, 19), (7, 6), (17, 11), (7, 31), (22, 10), (35, 13), (23, 29), (21, 17), (7, 29), (27, 17), (29, 13), (18, 31), (9, 32), (20, 30), (30, 5), (20, 9), (26, 7), (19, 14), (17, 13), (35, 22), (15, 19), (14, 32), (11, 30), (15, 0), (30, 30), (24, 8), (12, 7), (26, 19), (8, 33), (20, 8), (29, 3), (17, 31), (10, 29), (11, 14), (22, 5), (24, 34), (20, 28), (5, 7), (27, 1), (17, 25), (28, 20), (8, 14), (23, 7), (29, 1), (0, 33), (23, 6), (12, 1), (14, 27), (31, 3), (20, 29), (29, 17), (12, 2), (9, 11), (0, 7), (2, 32), (7, 11), (16, 3), (9, 13), (2, 26), (28, 9), (24, 2), (24, 18), (33, 29), (21, 1), (30, 12), (23, 16), (0, 5), (24, 15), (3, 23), (34, 1), (9, 31), (1, 30), (14, 31), (19, 30), (21, 27), (10, 3), (13, 11), (15, 26), (15, 3), (26, 10), (0, 9), (23, 18), (28, 27), (21, 20), (14, 30), (14, 24), (8, 27), (13, 10), (34, 24), (35, 6), (30, 17), (11, 28), (25, 1), (11, 27), (23, 22), (2, 14), (33, 28), (30, 27), (26, 24), (25, 16), (0, 2), (17, 34), (17, 10), (17, 0), (2, 10), (9, 17), (15, 9), (11, 2), (10, 11), (25, 33), (7, 32), (10, 27), (1, 11), (9, 6), (30, 26), (11, 11), (0, 27), (32, 26), (17, 14), (13, 4), (2, 4), (34, 5), (17, 27), (27, 9), (20, 17), (11, 13), (31, 12), (16, 25), (35, 25), (14, 21), (17, 5), (21, 18), (35, 18), (9, 10), (33, 21), (14, 8), (1, 23), (29, 18), (11, 17), (17, 17), (5, 17), (1, 28), (3, 29), (13, 12), (6, 31), (19, 28), (13, 33), (30, 13), (2, 29), (33, 10), (16, 33), (1, 33), (9, 14), (34, 16), (31, 13), (1, 24), (25, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479700", "dataset": "MATH"}
{"messages": [{"content": "In a 33x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 9), (9, 30), (20, 10), (31, 14), (21, 10), (23, 24), (10, 6), (18, 26), (20, 28), (19, 25), (12, 5), (11, 2), (13, 13), (32, 17), (9, 25), (20, 6), (5, 9), (10, 11), (15, 2), (4, 3), (1, 29), (32, 6), (2, 5), (2, 12), (6, 30), (25, 25), (4, 11), (13, 21), (26, 30), (5, 18), (20, 18), (3, 2), (27, 7), (15, 17), (25, 9), (12, 12), (23, 7), (11, 5), (2, 26), (18, 8), (18, 16), (22, 16), (8, 15), (3, 8), (28, 25), (20, 17), (7, 23), (20, 19), (21, 30), (23, 12), (12, 18), (8, 3), (30, 12), (11, 15), (12, 23), (13, 24), (19, 30), (11, 24), (4, 15), (5, 26), (1, 19), (9, 22), (20, 27), (28, 5), (15, 23), (24, 19), (17, 28), (12, 0), (23, 19), (25, 2), (13, 9), (32, 3), (0, 11), (27, 4), (22, 2), (30, 15), (18, 25), (30, 23), (17, 4), (8, 14), (18, 5), (13, 17), (9, 14), (9, 10), (25, 22), (26, 7), (24, 28), (32, 22), (18, 10), (4, 23), (21, 27), (7, 18), (17, 21), (19, 28), (0, 20), (32, 28), (16, 22), (13, 5), (19, 29), (2, 11), (9, 9), (31, 13), (14, 30), (25, 18), (22, 9), (29, 21), (6, 2), (17, 25), (15, 6), (18, 12), (21, 20), (7, 7), (16, 17), (26, 3), (4, 1), (2, 15), (29, 23), (19, 23), (27, 17), (9, 11), (3, 28), (20, 12), (28, 10), (4, 16), (20, 23), (29, 13), (20, 4), (4, 10), (14, 6), (17, 26), (3, 25), (15, 5), (16, 29), (18, 14), (12, 27), (17, 12), (6, 5), (9, 23), (3, 11), (26, 22), (32, 5), (28, 12), (7, 22), (6, 28), (23, 1), (24, 21), (14, 0), (26, 19), (24, 8), (11, 14), (5, 27), (30, 10), (7, 12), (5, 20), (5, 15), (7, 4), (1, 6), (27, 8), (25, 8), (31, 9), (29, 30), (27, 2), (7, 30), (18, 3), (11, 9), (5, 1), (16, 2), (15, 11), (17, 0), (21, 0), (29, 3), (23, 10), (14, 1), (22, 21), (12, 20), (18, 24), (29, 22), (10, 4), (22, 22), (10, 17), (12, 22), (25, 23), (4, 2), (15, 3), (25, 4), (12, 2), (2, 27), (16, 24), (10, 26), (19, 21), (20, 16), (30, 7), (27, 10), (30, 14), (3, 23), (29, 12), (3, 17), (24, 29), (26, 18), (15, 12), (21, 26), (19, 0), (0, 13), (21, 19), (1, 12), (5, 19), (16, 7), (9, 3), (6, 1), (8, 18), (1, 26), (13, 20), (17, 8), (31, 22), (7, 26), (8, 8), (13, 6), (3, 16), (29, 27), (16, 25), (31, 27), (11, 0), (16, 1), (30, 20), (20, 7), (28, 2), (24, 26), (11, 3), (30, 21), (18, 4), (25, 16), (31, 15), (14, 25), (20, 5), (15, 18), (20, 8), (0, 27), (5, 28), (3, 22), (13, 2), (14, 29), (7, 17), (1, 1), (27, 29), (9, 6), (8, 9), (1, 30), (24, 27), (17, 22), (30, 11), (3, 6), (28, 8), (8, 17), (1, 22), (18, 7), (15, 24), (30, 25), (0, 8), (16, 14), (12, 8), (17, 17), (22, 19), (26, 28), (23, 29), (19, 16), (16, 13), (28, 6), (23, 0), (26, 23), (21, 18), (21, 7), (0, 6), (21, 21), (5, 16), (11, 11), (8, 11), (18, 29), (18, 19), (17, 10), (6, 8), (13, 23), (2, 23), (10, 18), (29, 7), (15, 30), (19, 6), (8, 0), (15, 13), (12, 7)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "892100", "dataset": "MATH"}
{"messages": [{"content": "In a 36x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 24), (2, 10), (16, 9), (25, 17), (10, 26), (9, 27), (34, 13), (6, 25), (19, 10), (31, 24), (23, 2), (34, 17), (20, 14), (11, 3), (34, 2), (22, 2), (7, 20), (21, 29), (20, 6), (11, 27), (25, 24), (14, 1), (28, 14), (26, 26), (30, 19), (17, 6), (22, 11), (12, 13), (8, 22), (0, 26), (21, 26), (25, 26), (28, 7), (8, 29), (27, 20), (19, 16), (15, 7), (15, 26), (27, 15), (29, 25), (3, 21), (19, 0), (19, 6), (12, 26), (35, 10), (20, 1), (33, 20), (11, 5), (2, 4), (32, 12), (8, 12), (17, 24), (4, 2), (24, 14), (34, 25), (26, 3), (23, 14), (11, 10), (16, 19), (4, 21), (8, 11), (19, 2), (21, 1), (33, 13), (13, 2), (24, 3), (19, 12), (30, 4), (22, 28), (0, 12), (34, 18), (25, 4), (25, 19), (22, 29), (14, 14), (31, 3), (18, 27), (20, 8), (9, 20), (21, 8), (19, 25), (9, 7), (9, 24), (35, 3), (17, 11), (13, 1), (34, 12), (25, 9), (7, 21), (13, 22), (17, 28), (10, 2), (24, 29), (32, 4), (35, 19), (34, 9), (22, 26), (6, 1), (2, 16), (9, 16), (32, 20), (12, 9), (17, 17), (28, 10), (5, 7), (20, 17), (17, 8), (21, 18), (2, 24), (13, 17), (19, 24), (9, 15), (16, 25), (4, 11), (13, 8), (22, 19), (24, 7), (6, 29), (27, 2), (10, 27), (16, 17), (13, 5), (29, 14), (32, 1), (20, 21), (2, 11), (22, 14), (28, 19), (23, 29), (10, 20), (14, 3), (0, 17), (8, 20), (30, 10), (6, 6), (12, 28), (18, 0), (4, 28), (15, 14), (3, 23), (5, 3), (20, 2), (13, 9), (18, 25), (25, 28), (23, 15), (14, 0), (11, 9), (19, 14), (0, 21), (6, 12), (24, 6), (14, 29), (27, 18), (28, 5), (31, 17), (22, 18), (13, 28), (12, 23), (4, 27), (17, 20), (13, 21), (3, 29), (16, 18), (14, 28), (3, 28), (32, 28), (14, 9), (31, 12), (2, 14), (32, 23), (5, 24), (17, 21), (26, 18), (29, 13), (8, 10), (35, 1), (19, 23), (14, 7), (15, 21), (26, 14), (17, 18), (33, 1), (29, 1), (5, 20), (25, 18), (26, 17), (33, 10), (12, 0), (33, 12), (5, 21), (5, 0), (28, 21), (32, 17), (2, 5), (3, 13), (32, 13), (25, 0), (19, 1), (9, 9), (34, 27), (0, 7), (1, 17), (10, 24), (22, 27), (1, 24), (11, 26), (7, 4), (3, 0), (3, 7), (24, 5), (30, 16), (19, 13), (33, 0), (10, 11), (31, 0), (35, 9), (33, 4), (3, 11), (35, 14), (2, 8), (17, 14), (9, 8), (28, 20), (4, 25), (32, 27), (35, 20), (18, 16), (8, 13), (15, 18), (24, 27), (11, 13), (15, 0), (19, 26), (7, 1), (35, 27), (3, 2), (0, 10), (33, 11), (23, 11), (20, 5), (16, 1), (5, 9), (1, 25), (18, 5), (15, 4), (13, 29), (23, 9), (5, 2), (25, 20), (32, 7), (15, 13), (28, 25), (30, 29), (12, 20), (6, 10), (6, 20), (25, 10), (17, 15), (18, 23), (31, 6), (33, 27), (19, 4), (12, 25), (5, 25), (4, 20), (26, 6), (22, 25), (16, 14), (1, 7), (27, 8), (3, 18), (24, 11), (23, 26), (30, 1), (6, 21), (1, 18), (26, 21), (29, 23), (16, 24), (5, 15), (31, 27), (16, 16), (21, 20), (6, 17), (3, 12), (1, 3), (22, 1), (13, 12), (22, 21), (27, 14), (33, 3), (32, 15), (30, 8), (30, 18), (35, 15), (22, 24), (9, 1), (12, 10), (10, 28), (33, 5), (32, 11), (31, 26), (12, 4), (35, 22), (11, 23), (10, 1), (5, 28), (7, 15), (13, 7), (19, 11), (0, 8), (32, 3), (33, 22), (23, 23), (8, 17), (3, 6), (14, 13), (26, 23), (2, 13), (13, 25), (2, 12), (14, 27), (35, 25), (18, 26), (3, 1), (18, 20), (11, 16), (24, 1), (7, 0), (30, 5), (2, 22), (9, 18), (12, 6)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "462240", "dataset": "MATH"}
{"messages": [{"content": "In a 35x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 17), (7, 7), (6, 4), (19, 11), (6, 25), (33, 10), (31, 24), (30, 26), (6, 10), (32, 5), (0, 9), (18, 14), (29, 31), (10, 7), (23, 22), (19, 33), (2, 25), (33, 17), (24, 9), (29, 14), (1, 31), (16, 30), (28, 13), (5, 31), (11, 11), (14, 29), (18, 34), (12, 34), (12, 28), (26, 0), (16, 4), (18, 15), (33, 21), (34, 11), (11, 12), (31, 17), (11, 23), (9, 4), (30, 0), (27, 25), (16, 6), (34, 13), (7, 2), (29, 32), (24, 33), (17, 13), (18, 24), (9, 31), (15, 13), (20, 26), (13, 8), (20, 11), (23, 23), (6, 20), (10, 23), (12, 17), (18, 8), (33, 23), (25, 15), (29, 11), (25, 33), (1, 32), (23, 10), (29, 20), (1, 8), (32, 22), (22, 25), (24, 10), (26, 7), (2, 7), (14, 0), (20, 0), (8, 25), (28, 14), (25, 4), (34, 1), (11, 10), (8, 34), (16, 28), (33, 1), (22, 34), (21, 20), (21, 11), (12, 3), (25, 34), (13, 26), (26, 12), (15, 1), (12, 9), (10, 0), (24, 5), (4, 29), (22, 23), (14, 19), (32, 19), (21, 27), (11, 29), (16, 2), (3, 23), (27, 10), (19, 18), (3, 4), (34, 25), (9, 2), (28, 8), (19, 34), (13, 6), (4, 34), (3, 14), (29, 7), (22, 13), (20, 4), (19, 13), (30, 8), (34, 3), (0, 15), (34, 9), (16, 32), (20, 16), (6, 17), (17, 7), (23, 20), (24, 13), (15, 34), (14, 13), (11, 17), (24, 18), (5, 30), (11, 8), (31, 28), (24, 24), (8, 20), (14, 9), (3, 17), (2, 1), (13, 12), (1, 5), (7, 3), (15, 18), (6, 13), (13, 3), (2, 27), (34, 19), (0, 5), (21, 15), (26, 8), (14, 21), (23, 13), (12, 15), (29, 18), (10, 14), (13, 30), (33, 13), (28, 31), (17, 6), (5, 12), (2, 10), (12, 31), (20, 32), (4, 1), (25, 21), (32, 34), (22, 14), (7, 24), (30, 7), (13, 32), (6, 30), (22, 30), (30, 2), (17, 31), (29, 1), (19, 12), (27, 23), (5, 14), (1, 4), (29, 27), (4, 33), (5, 34), (6, 11), (32, 30), (31, 14), (17, 8), (21, 28), (10, 34), (18, 25), (24, 6), (4, 2), (5, 22), (21, 2), (33, 31), (8, 29), (9, 30), (14, 16), (18, 18), (31, 8), (1, 26), (11, 27), (1, 2), (19, 29), (31, 22), (9, 8), (8, 26), (32, 26), (14, 25), (11, 9), (18, 17), (32, 24), (28, 30), (9, 12), (4, 20), (9, 9), (8, 32), (1, 34), (27, 26), (10, 24), (34, 23), (8, 6), (13, 24), (25, 9), (14, 30), (32, 16), (17, 2), (0, 33), (7, 10), (20, 23), (24, 12), (28, 12), (23, 16), (27, 33), (12, 19), (7, 29), (10, 11), (13, 28), (26, 17), (10, 17), (24, 15), (6, 31), (30, 25), (6, 21), (17, 24), (23, 6), (2, 19), (32, 29), (1, 28), (1, 18), (25, 26), (2, 16), (31, 1), (26, 18), (29, 4), (29, 0), (5, 13), (0, 31), (28, 0), (18, 29), (5, 24), (11, 3), (11, 21), (12, 32), (30, 1), (32, 3), (31, 19), (27, 17), (14, 28), (21, 34), (12, 0), (17, 34), (25, 27), (29, 2), (13, 13), (25, 17), (32, 2), (27, 8), (31, 2), (4, 15), (0, 12), (11, 24), (17, 0), (19, 7), (17, 4), (19, 6), (4, 7), (28, 34), (3, 21), (21, 6), (26, 19), (29, 16), (0, 14), (15, 14), (4, 12), (3, 2), (32, 20), (15, 31), (30, 13), (15, 22), (16, 27), (5, 3), (30, 28), (1, 16), (23, 9), (20, 20), (5, 11), (15, 4), (27, 3), (11, 6), (23, 26), (11, 26), (15, 24), (0, 4), (19, 24), (23, 7), (25, 28), (25, 8), (0, 17), (8, 18), (2, 31), (31, 6), (11, 1), (6, 9), (24, 27), (21, 31), (7, 27), (25, 30), (33, 29), (18, 2), (17, 29), (1, 9), (16, 1), (8, 31), (7, 15), (27, 24), (9, 0), (34, 16), (4, 22), (15, 29), (28, 6), (19, 25), (20, 8), (3, 33), (23, 29), (18, 1), (4, 6), (13, 10), (3, 10), (15, 30), (23, 33), (6, 5), (11, 20), (12, 14), (32, 13), (9, 24), (13, 34), (34, 31), (7, 6), (15, 5), (12, 11), (13, 5), (2, 8), (18, 28), (7, 22), (12, 33), (34, 26), (21, 8), (9, 18), (29, 13), (11, 22), (8, 3), (24, 11), (3, 19), (0, 20), (30, 6), (33, 4), (26, 29), (5, 27), (22, 10), (7, 18), (22, 9), (25, 31), (32, 1), (24, 3), (14, 1), (11, 31), (17, 11), (33, 22), (31, 4), (18, 32), (23, 2), (34, 10), (24, 4), (30, 3), (22, 28), (33, 16), (7, 14), (26, 27), (28, 16), (12, 25), (25, 5), (2, 3), (28, 28)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80400", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 10), (26, 7), (33, 17), (9, 8), (15, 4), (28, 18), (24, 25), (28, 12), (13, 5), (17, 16), (22, 34), (32, 11), (16, 20), (13, 24), (0, 24), (16, 24), (11, 31), (32, 19), (26, 25), (20, 3), (8, 26), (18, 19), (7, 7), (17, 11), (11, 10), (17, 13), (11, 0), (32, 24), (18, 22), (2, 19), (12, 35), (17, 36), (6, 29), (33, 23), (0, 13), (33, 11), (27, 10), (33, 33), (7, 5), (32, 5), (15, 16), (4, 29), (20, 28), (0, 8), (33, 21), (8, 31), (10, 13), (22, 1), (19, 8), (1, 37), (18, 10), (6, 21), (4, 25), (12, 20), (30, 16), (18, 16), (2, 14), (12, 37), (17, 15), (8, 34), (24, 24), (6, 24), (12, 2), (21, 18), (25, 3), (19, 19), (33, 28), (3, 12), (0, 12), (22, 13), (3, 23), (2, 5), (1, 20), (6, 11), (29, 18), (28, 38), (6, 34), (15, 37), (26, 10), (0, 3), (28, 37), (22, 7), (14, 21), (23, 24), (14, 6), (33, 4), (16, 16), (23, 6), (22, 22), (7, 21), (0, 7), (19, 26), (6, 19), (12, 1), (1, 36), (27, 20), (24, 2), (21, 6), (18, 18), (18, 25), (31, 20), (31, 9), (27, 30), (15, 36), (9, 31), (10, 21), (25, 15), (25, 13), (11, 28), (23, 17), (32, 12), (16, 30), (28, 32), (1, 23), (2, 34), (32, 31), (17, 10), (31, 3), (31, 35), (27, 6), (3, 35), (20, 10), (23, 30), (30, 34), (8, 9), (7, 27), (30, 11), (25, 14), (4, 27), (32, 2), (0, 37), (17, 14), (4, 37), (5, 27), (23, 18), (10, 38), (24, 34), (28, 13), (4, 23), (16, 8), (29, 16), (25, 1), (27, 7), (27, 23), (26, 8), (7, 24), (17, 28), (2, 32), (7, 29), (21, 22), (32, 16), (13, 15), (3, 14), (21, 0), (23, 23), (25, 10), (21, 11), (14, 4), (30, 24), (14, 15), (24, 16), (29, 29), (25, 20), (30, 33), (11, 29), (23, 19), (18, 9), (29, 21), (4, 18), (9, 9), (10, 20), (12, 36), (0, 30), (23, 10), (6, 3), (22, 16), (26, 35), (5, 26), (11, 38), (12, 9), (5, 12), (13, 38), (6, 9), (33, 6), (3, 4), (17, 25), (3, 17), (13, 13), (32, 4), (13, 29), (17, 1), (32, 13), (33, 18), (23, 16), (13, 32), (21, 4), (33, 15), (4, 28), (32, 17), (28, 24), (25, 26), (2, 2), (1, 19), (5, 33), (24, 22), (0, 5), (28, 0), (2, 27), (31, 31), (14, 7), (0, 15), (4, 1), (11, 37), (13, 8), (27, 21), (14, 31), (10, 8), (3, 33), (13, 36), (26, 14), (16, 9), (21, 25), (1, 3), (0, 27), (5, 2), (9, 3), (7, 31), (13, 18), (27, 27), (30, 30), (9, 18), (12, 29), (22, 35), (32, 20), (29, 13), (9, 21), (7, 33), (31, 16), (17, 6), (19, 11), (18, 33), (9, 29), (23, 14), (31, 1), (20, 1), (26, 4), (23, 12), (1, 17), (20, 12), (26, 9), (21, 21), (13, 3), (21, 12), (26, 17), (31, 37), (4, 11), (3, 32), (14, 30), (15, 31), (21, 32), (12, 8), (8, 30), (17, 2), (9, 38), (4, 6), (23, 27), (6, 1), (11, 1), (22, 26), (17, 33), (31, 28), (10, 10), (9, 7), (22, 36), (15, 33), (25, 16), (5, 24), (20, 19), (3, 24), (18, 8), (14, 37), (17, 31), (8, 22), (30, 2), (26, 5), (2, 13), (16, 2), (27, 16), (25, 32), (1, 15), (22, 14), (9, 6), (15, 38), (4, 15), (5, 4), (28, 16), (9, 22), (26, 6), (1, 12), (27, 0), (13, 14), (11, 36), (0, 32), (14, 23), (23, 26), (21, 7), (17, 18), (0, 26), (22, 4), (20, 21), (18, 36), (5, 37), (12, 6), (17, 9), (26, 27), (11, 25), (18, 21), (31, 30), (13, 30), (13, 7), (20, 13), (33, 37), (26, 31), (3, 36), (6, 17), (15, 21), (2, 28), (21, 34), (30, 0), (26, 0), (25, 33), (30, 27), (18, 3), (32, 33), (5, 7), (24, 30), (5, 32), (32, 36), (13, 25), (24, 15), (1, 1), (10, 35), (18, 12), (14, 10), (19, 21), (15, 34), (0, 16), (21, 13), (19, 23), (12, 14), (5, 38), (20, 38), (33, 12), (29, 22), (33, 27), (14, 3), (33, 8), (22, 8), (15, 15), (12, 33), (17, 34), (9, 26), (19, 35), (31, 32), (7, 17), (18, 23), (11, 24), (33, 25), (25, 22), (19, 22), (17, 7), (22, 5), (13, 22), (29, 7), (13, 31), (9, 14), (11, 7), (14, 22), (25, 2), (20, 35), (30, 13), (28, 34), (28, 5), (8, 5), (5, 19), (3, 3), (2, 29), (6, 23), (16, 29), (1, 31), (14, 33), (1, 32), (11, 16), (26, 30), (20, 18), (28, 1), (20, 20), (19, 5), (28, 15), (24, 12), (25, 31), (26, 16), (24, 29), (11, 21), (28, 7), (6, 32), (19, 12), (18, 13), (9, 10), (12, 21), (26, 15), (12, 17), (8, 24), (25, 6), (16, 36), (24, 19), (25, 4), (31, 6), (5, 18), (0, 1), (8, 35), (18, 30), (23, 0), (20, 25)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5760", "dataset": "MATH"}
{"messages": [{"content": "In a 32x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (0, 29), (21, 5), (14, 22), (28, 21), (31, 9), (30, 24), (14, 13), (24, 1), (16, 8), (12, 5), (5, 8), (25, 18), (10, 21), (2, 26), (26, 24), (13, 12), (21, 10), (3, 1), (15, 14), (2, 24), (24, 9), (7, 7), (25, 24), (7, 2), (4, 20), (19, 26), (1, 12), (15, 28), (24, 8), (14, 20), (0, 24), (9, 2), (25, 0), (14, 4), (17, 2), (29, 23), (19, 20), (29, 7), (29, 20), (12, 28), (31, 21), (19, 23), (1, 1), (20, 17), (25, 8), (21, 6), (18, 1), (28, 1), (29, 12), (22, 17), (16, 26), (19, 28), (0, 2), (18, 9), (16, 18), (9, 9), (16, 13), (5, 13), (27, 9), (6, 26), (20, 1), (4, 15), (23, 13), (24, 2), (25, 22), (23, 7), (14, 21), (25, 28), (4, 10), (18, 18), (20, 3), (20, 2), (30, 19), (6, 29), (0, 22), (9, 10), (6, 3), (11, 9), (18, 29), (22, 12), (19, 6), (11, 28), (11, 20), (27, 16), (21, 19), (10, 16), (2, 17), (15, 0), (12, 1), (0, 8), (30, 9), (10, 15), (22, 30), (15, 19), (2, 11), (4, 5), (14, 28), (11, 22), (27, 17), (23, 20), (14, 7), (24, 16), (28, 12), (23, 2), (9, 22), (22, 10), (7, 22), (0, 5), (31, 7), (13, 11), (5, 12), (19, 24), (9, 25), (27, 5), (31, 15), (23, 3), (7, 15), (8, 6), (26, 21), (14, 5), (18, 13), (1, 4), (15, 9), (10, 14), (27, 27), (29, 15), (25, 19), (26, 3), (15, 8), (29, 26), (25, 1), (26, 19), (20, 19), (19, 16), (29, 21), (8, 16), (16, 17), (4, 25), (18, 12), (9, 15), (24, 25), (14, 26), (16, 30), (27, 23), (3, 23), (1, 2), (28, 13), (18, 26), (27, 30), (14, 9), (5, 20), (31, 8), (28, 16), (21, 23), (14, 23), (30, 18), (18, 10), (0, 11), (30, 27), (27, 3), (30, 8), (1, 10), (31, 14), (22, 13), (3, 19), (18, 22), (5, 23), (28, 6), (29, 0), (22, 26), (14, 2), (2, 9), (28, 0), (22, 20), (28, 19), (9, 27), (1, 20), (13, 3), (23, 14), (13, 22), (19, 7), (31, 2), (21, 4), (26, 6), (29, 18), (20, 14), (8, 19), (5, 27), (27, 13), (6, 10), (4, 4), (23, 9), (25, 16), (19, 10), (15, 18), (29, 4), (10, 7), (30, 10), (24, 4), (24, 5), (11, 12), (18, 15), (13, 28), (12, 27), (4, 17), (18, 6), (1, 26), (2, 25), (25, 15), (24, 22), (27, 29), (5, 0), (1, 11), (25, 6), (4, 12), (28, 17), (19, 25), (17, 21), (27, 24), (22, 21), (1, 9), (11, 2), (26, 30), (17, 12), (27, 15), (11, 7), (15, 21), (22, 19), (16, 0), (10, 25), (13, 8), (11, 0), (27, 28), (11, 25), (3, 30), (11, 6), (2, 1), (6, 16), (4, 22), (2, 29), (17, 30), (31, 17), (31, 23), (18, 19), (26, 11), (15, 4), (0, 20), (31, 13), (11, 18), (10, 23), (16, 28), (18, 28), (23, 4), (0, 12), (19, 12), (12, 0), (30, 7), (6, 1), (20, 28), (7, 9), (0, 19), (29, 29), (16, 2), (20, 16), (2, 4), (12, 24), (13, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "818955", "dataset": "MATH"}
{"messages": [{"content": "In a 39x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (34, 8), (5, 3), (13, 16), (9, 12), (25, 7), (28, 35), (22, 28), (37, 0), (17, 19), (10, 35), (29, 5), (3, 18), (29, 17), (23, 35), (31, 9), (11, 34), (8, 4), (3, 29), (25, 12), (23, 1), (13, 6), (4, 29), (8, 19), (12, 18), (19, 15), (18, 35), (28, 30), (0, 18), (1, 10), (37, 5), (11, 9), (30, 6), (32, 13), (37, 36), (10, 3), (9, 3), (11, 4), (24, 28), (34, 37), (21, 30), (7, 0), (38, 12), (6, 22), (28, 21), (8, 29), (32, 0), (14, 5), (28, 18), (25, 31), (0, 16), (33, 26), (15, 7), (31, 33), (23, 28), (27, 1), (18, 22), (18, 30), (6, 29), (21, 23), (22, 15), (30, 18), (38, 33), (0, 35), (30, 28), (35, 14), (11, 29), (18, 7), (19, 28), (16, 1), (34, 11), (1, 17), (10, 33), (32, 9), (31, 32), (0, 9), (24, 9), (27, 36), (1, 11), (24, 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(17, 29), (21, 9), (10, 11), (36, 13), (36, 24), (14, 11), (35, 6), (19, 25), (2, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884736", "dataset": "MATH"}
{"messages": [{"content": "In a 31x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (24, 24), (0, 33), (11, 32), (14, 10), (18, 14), (2, 9), (8, 25), (5, 21), (10, 14), (2, 29), (26, 12), (22, 33), (0, 17), (23, 27), (20, 26), (17, 35), (18, 27), (19, 4), (13, 6), (15, 13), (18, 37), (2, 24), (20, 18), (5, 1), (28, 30), (8, 23), (7, 20), (0, 2), (29, 31), (1, 4), (9, 3), (11, 23), (15, 11), (23, 22), (6, 27), (11, 34), (26, 29), (17, 4), (19, 10), (3, 17), (27, 15), (20, 6), (18, 10), (7, 16), (19, 26), (4, 3), (6, 8), (20, 27), (8, 12), (17, 33), (20, 16), (25, 10), (3, 7), (28, 4), (27, 35), (8, 6), (13, 33), (17, 37), (12, 32), (4, 28), (6, 37), (16, 37), (5, 22), (5, 12), (14, 16), (14, 28), (23, 11), (0, 34), (21, 35), (29, 21), (13, 36), (20, 37), (27, 8), (2, 34), (19, 21), (21, 34), (15, 1), (7, 7), (0, 12), (5, 36), (30, 18), (29, 24), (16, 21), (18, 32), (9, 9), (29, 37), (8, 11), (13, 26), (26, 25), (22, 30), (18, 2), (18, 35), (0, 29), (29, 33), (1, 13), (20, 15), (30, 26), (8, 34), (16, 23), (4, 34), (30, 17), (16, 4), (28, 32), (19, 14), (11, 31), (1, 6), (6, 4), (1, 32), (16, 33), (1, 31), (0, 22), (27, 20), (3, 5), (4, 35), (11, 29), (0, 27), (15, 6), (6, 20), (26, 23), (20, 20), (26, 35), (4, 4), (16, 19), (21, 13), (17, 6), (21, 4), (9, 37), (22, 24), (25, 4), (28, 14), (13, 4), (10, 18), (4, 1), (16, 18), (4, 22), (22, 2), (20, 25), (1, 20), (12, 4), (3, 36), (11, 10), (20, 12), (30, 5), (21, 33), (0, 21), (30, 19), (17, 31), (30, 8), (8, 24), (26, 6), (21, 10), (12, 19), (11, 1), (15, 5), (27, 37), (28, 5), (13, 2), (21, 20), (29, 14), (16, 9), (24, 27), (7, 26), (6, 12), (12, 15), (29, 22), (0, 9), (15, 30), (25, 15), (29, 1), (9, 32), (27, 16), (11, 20), (22, 32), (22, 23), (28, 6), (22, 9), (10, 3), (26, 28), (19, 19), (11, 26), (8, 3), (23, 24), (30, 0), (15, 0), (9, 11), (23, 26), (5, 18), (12, 9), (15, 27), (14, 20), (17, 24), (19, 12), (17, 36), (3, 37), (11, 6), (0, 24), (16, 32), (21, 30), (14, 34), (29, 18), (21, 36), (6, 9), (22, 5), (12, 30), (30, 1), (22, 17), (10, 30), (14, 35), (25, 1), (5, 10), (9, 0), (5, 35), (23, 34), (10, 22), (27, 33), (17, 34), (5, 8), (14, 4), (25, 33), (16, 17), (5, 9), (9, 31), (7, 35), (7, 30), (26, 10), (9, 24), (7, 23), (25, 11), (30, 24), (26, 1), (4, 12), (6, 6), (12, 6), (23, 14), (29, 7), (21, 32), (6, 16), (20, 19), (10, 31), (19, 29), (22, 12), (9, 10), (16, 35), (0, 3), (11, 16), (25, 25), (1, 35), (9, 16), (1, 27), (24, 12), (25, 0), (8, 32), (6, 19), (10, 19), (10, 8), (23, 28), (14, 23), (21, 8), (13, 20), (7, 32), (22, 27), (18, 20), (4, 32), (24, 20), (13, 32), (10, 4), (11, 22), (0, 11), (9, 25), (19, 27), (25, 14), (9, 13), (24, 15), (20, 35), (3, 26), (1, 28), (7, 28), (7, 17), (14, 8), (15, 10), (5, 19), (2, 13), (2, 32), (19, 24), (26, 31), (15, 36), (18, 6), (4, 17), (19, 15), (2, 36), (19, 2), (1, 10), (9, 21), (21, 15), (11, 5), (14, 22), (5, 25), (10, 1), (14, 29), (25, 5), (4, 37), (14, 27), (7, 24), (24, 36), (7, 3), (21, 2), (0, 37), (30, 14), (26, 20), (3, 31), (7, 2), (25, 18), (1, 11), (9, 36), (7, 34), (21, 27), (7, 27), (2, 21), (3, 28), (18, 3), (23, 37), (0, 28), (27, 25), (9, 14), (26, 0), (22, 4), (13, 29), (16, 29), (16, 36), (22, 3), (5, 31), (12, 27), (20, 17), (29, 5), (6, 22), (3, 14), (15, 28), (24, 21), (27, 4), (8, 14), (0, 18), (23, 29), (0, 10), (28, 21), (21, 21), (16, 14), (21, 26), (21, 6), (11, 35), (5, 6), (14, 2), (29, 3), (12, 12), (15, 26), (14, 32), (10, 35), (26, 8), (22, 19), (18, 18), (6, 14), (9, 4), (7, 37), (15, 29), (23, 30), (17, 28), (19, 6), (14, 19), (12, 8), (23, 20), (18, 23), (26, 32), (14, 12), (12, 16), (24, 16), (29, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "872810", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (31, 22), (19, 4), (19, 18), (5, 3), (27, 28), (31, 27), (15, 4), (34, 27), (29, 22), (18, 5), (9, 20), (37, 20), (33, 6), (20, 12), (1, 31), (25, 21), (21, 29), (5, 31), (34, 9), (34, 0), (19, 24), (22, 19), (6, 29), (34, 26), (36, 21), (24, 24), (28, 14), (16, 23), (27, 22), (24, 22), (4, 23), (33, 29), (21, 17), (11, 16), (1, 13), (10, 13), (30, 2), (0, 17), (17, 1), (31, 2), (27, 20), (23, 27), (9, 22), (36, 12), (0, 8), (12, 29), (15, 18), (9, 0), (1, 2), (14, 9), (24, 2), (25, 12), (14, 3), (5, 2), (13, 15), (36, 8), (37, 24), (18, 13), (28, 16), (31, 30), (6, 16), (29, 29), (9, 5), (28, 25), (29, 11), (16, 12), (8, 13), (17, 16), (3, 1), (21, 22), (10, 8), (13, 30), (16, 22), (11, 15), (6, 7), (9, 28), (12, 23), (11, 5), (37, 7), (33, 8), (20, 9), (27, 31), (17, 17), (24, 23), (31, 15), (29, 30), (29, 24), (9, 2), (14, 6), (29, 4), (28, 17), (22, 14), (13, 23), (11, 1), (26, 9), (30, 20), (36, 32), (15, 31), (22, 26), (10, 1), (26, 28), (7, 16), (12, 7), (7, 22), (9, 4), (5, 8), (3, 23), (2, 2), (16, 0), (19, 19), (11, 32), (20, 18), (33, 3), (7, 26), (23, 2), (1, 26), (35, 20), (22, 16), (36, 11), (1, 5), (16, 31), (19, 1), (32, 3), (10, 28), (4, 28), (34, 3), (20, 5), (12, 21), (34, 16), (31, 16), (29, 28), (2, 1), (26, 18), (9, 6), (12, 5), (19, 30), (22, 21), (11, 4), (12, 0), (11, 19), (15, 19), (35, 0), (22, 8), (27, 14), (23, 4), (16, 26), (34, 10), (19, 14), (37, 8), (16, 29), (11, 2), (1, 7), (7, 20), (29, 20), (6, 14), (21, 2), (20, 16), (2, 3), (21, 24), (37, 0), (29, 5), (30, 8), (37, 28), (14, 16), (18, 0), (33, 7), (8, 10), (18, 29), (19, 21), (28, 4), (18, 12), (17, 15), (37, 10), (21, 4), (7, 15), (33, 17), (9, 21), (0, 21), (32, 7), (8, 16), (10, 31), (13, 4), (14, 5), (18, 31), (16, 27), (28, 9), (30, 31), (17, 10), (23, 0), (17, 27), (33, 14), (27, 18), (15, 17), (13, 6), (33, 23), (19, 5), (24, 27), (13, 28), (7, 23), (30, 5), (19, 29), (11, 29), (2, 22), (37, 13), (36, 4), (6, 20), (21, 23), (14, 8), (7, 1), (27, 15), (16, 25), (16, 24), (2, 19), (19, 6), (0, 28), (1, 11), (19, 25), (35, 19), (33, 13), (28, 21), (10, 26), (20, 1), (20, 10), (9, 19), (13, 27), (29, 13), (11, 10), (9, 18), (2, 12), (25, 2), (20, 19), (10, 19), (35, 1), (4, 13), (26, 11), (31, 10), (24, 4), (17, 24), (13, 9), (32, 30), (32, 21), (6, 15), (27, 21), (20, 21), (14, 19), (7, 30), (34, 5), (29, 17), (32, 10), (30, 9), (25, 28), (8, 26), (9, 32), (29, 19), (12, 2), (33, 32), (13, 2), (22, 18), (20, 25), (2, 14), (0, 18), (12, 30), (37, 16), (35, 15), (18, 30), (35, 25), (27, 4), (1, 24), (27, 11), (9, 13), (2, 21), (0, 6), (15, 20), (31, 13), (23, 10), (19, 31), (8, 22), (2, 28), (31, 18), (0, 25), (32, 4), (31, 17), (4, 11), (5, 16), (12, 16), (35, 8), (34, 7), (33, 18), (6, 19), (32, 22), (8, 0), (22, 29), (33, 26), (7, 3), (25, 17), (4, 12), (7, 7), (27, 17), (11, 14), (3, 11), (5, 7), (8, 30), (23, 13), (0, 30), (28, 10), (9, 31), (21, 21), (22, 9), (27, 12), (37, 19), (2, 29), (10, 32), (30, 19), (31, 25), (30, 22), (8, 18), (25, 9), (27, 16), (21, 28), (16, 28), (11, 25), (14, 13), (34, 25), (10, 2), (34, 28), (5, 28), (18, 7), (14, 24), (26, 4), (8, 19), (33, 0), (21, 25), (2, 16), (1, 28), (9, 3), (10, 6), (27, 30), (9, 10), (33, 19), (10, 11), (23, 3), (6, 5), (18, 17), (37, 5), (32, 23), (34, 19), (18, 19), (17, 4), (12, 15), (21, 10), (12, 25), (30, 16), (25, 7), (32, 26), (36, 0), (5, 12), (16, 15), (15, 14), (20, 8), (36, 1), (21, 1), (28, 3), (0, 32), (30, 25), (25, 24), (12, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578340", "dataset": "MATH"}
{"messages": [{"content": "In a 34x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 38), 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), (1, 8), (13, 22), (26, 2), (20, 19), (5, 17), (16, 9), (20, 23), (33, 37), (15, 18), (26, 11), (29, 28), (31, 23), (32, 23), (5, 33), (21, 12), (6, 35), (23, 9), (26, 9), (16, 17), (27, 36), (24, 19), (19, 23), (3, 31), (17, 1), (9, 11), (27, 10), (33, 18), (15, 29), (2, 35), (23, 22), (32, 21), (30, 29), (21, 18), (1, 6), (13, 30), (10, 25), (25, 28), (16, 35), (9, 38), (27, 30), (27, 38), (12, 8), (7, 3), (28, 38), (27, 20), (23, 28), (7, 32), (8, 4), (13, 3), (0, 1), (27, 5), (18, 5), (1, 20), (15, 11), (10, 30), (9, 8), (32, 24), (27, 14), (26, 29), (30, 1), (30, 8), (31, 6), (2, 13), (22, 2), (17, 19), (16, 14), (31, 7), (0, 12), (18, 26), (29, 7), (31, 20), (2, 37), (29, 38), (9, 16), (7, 20), (30, 9), (20, 3), (6, 29), (30, 10), (32, 14), (1, 13), (27, 37), (7, 35), (31, 37), (16, 2), (5, 19), (23, 35), (7, 26), (3, 34), (8, 7), (13, 33), (27, 2), (12, 38), (1, 35), (24, 21), (19, 9), (3, 26), (32, 1), (14, 6), (29, 9), (22, 0), (24, 15), (33, 1), (24, 27), (6, 6), (19, 17), (21, 30), (1, 2), (23, 13), (3, 7), (18, 34), (0, 15), (3, 38), (22, 32), (10, 23), (9, 18), (11, 36), (20, 26), (6, 3), (27, 4), (13, 2), (9, 27), (22, 15), (2, 15), (33, 9), (31, 32), (5, 16), (24, 10), (21, 13), (30, 4), (18, 30), (12, 26), (8, 26), (25, 31), (6, 27), (13, 23), (12, 27), (1, 25), (0, 9), (1, 15), (12, 5), (25, 29), (33, 34), (31, 4), (1, 30), (28, 37), (17, 7), (27, 24), (6, 30), (12, 36), (27, 28), (8, 36), (22, 14), (2, 10), (8, 38), (19, 7), (21, 21), (23, 25), (13, 1), (19, 0), (12, 23), (29, 33), (20, 24), (30, 24), (15, 21), (4, 18), (1, 12), (11, 29), (11, 13), (5, 26), (31, 31), (0, 11), (14, 21), (6, 37), (19, 24), (9, 35), (2, 7), (10, 21), (26, 33), (18, 17), (2, 4), (12, 10), (11, 23), (31, 19), (25, 33), (10, 8), (23, 16), (22, 24), (15, 38), (29, 34), (18, 22), (2, 23), (10, 3), (11, 38), (14, 26), (16, 20), (22, 35), (29, 1), (8, 14), (11, 14), (28, 21), (30, 38), (10, 34), (5, 3), (14, 33), (11, 15), (11, 33), (4, 2), (15, 30), (15, 15), (20, 30), (6, 24), (12, 4), (18, 14), (11, 37), (24, 23), (15, 28), (15, 32), (24, 20), (6, 36), (20, 12), (13, 4), (1, 29), (19, 26), (31, 33), (26, 15), (18, 10), (29, 5), (32, 22), (24, 35), (17, 10), (1, 31), (30, 31), (9, 3), (23, 20), (25, 17), (17, 12), (6, 12), (1, 4), (27, 12), (0, 8), (19, 21), (14, 9), (8, 9), (28, 36), (7, 9), (31, 29), (8, 11), (32, 25), (0, 10), (21, 23), (7, 37), (1, 33), (20, 21), (11, 0), (13, 8), (11, 32), (16, 23), (26, 10), (11, 7), (25, 26), (6, 2), (6, 21), (31, 0), (9, 28), (12, 32), (19, 5), (29, 23), (25, 11), (0, 7), (22, 21), (2, 8), (15, 4), (29, 11), (3, 10), (18, 23), (2, 30), (19, 14), (8, 27), (24, 29), (7, 29), (24, 26), (33, 26), (3, 22), (3, 24), (19, 36), (24, 5), (22, 25), (29, 6), (18, 38), (1, 5), (28, 15), (8, 10), (26, 22), (16, 18), (25, 25), (17, 36), (18, 9), (0, 36), (22, 19), (14, 32), (33, 6), (6, 20), (17, 25), (19, 16), (8, 17), (17, 3), (0, 14), (5, 35), (4, 24), (1, 7), (15, 12), (16, 33), (7, 28), (1, 19), (3, 8), (27, 22), (3, 3), (19, 22), (6, 25), (27, 9), (5, 20), (10, 17), (2, 11), (23, 15), (7, 34), (9, 14), (6, 10), (15, 27), (23, 26), (33, 29), (5, 22), (9, 29), (12, 16), (13, 31), (15, 25), (14, 38), (9, 19), (3, 25), (24, 0), (21, 25), (24, 34), (15, 26), (12, 35), (32, 3), (23, 23), (1, 3), (26, 21), (27, 11), (14, 17), (31, 25), (8, 22), (16, 29), (9, 20), (18, 15), (29, 19), (31, 9), (3, 5), (28, 23), (32, 0), (33, 20), (13, 36), (22, 36), (1, 17), (17, 17), (15, 34), (25, 27), (5, 34), (25, 12), (32, 35), (5, 37), (10, 5), (13, 34), (2, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "302400", "dataset": "MATH"}
{"messages": [{"content": "In a 39x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (6, 29), (7, 14), (33, 2), (36, 24), (32, 7), (28, 23), (34, 3), (25, 9), (20, 30), (17, 21), (34, 22), (24, 6), (11, 3), (20, 4), (15, 8), (27, 1), (34, 26), (3, 21), (12, 31), (26, 22), (2, 15), (19, 9), (2, 5), (19, 3), (32, 15), (21, 25), (6, 22), (31, 19), (2, 31), (25, 26), (22, 14), (22, 21), (25, 13), (26, 18), (6, 21), (16, 0), (35, 23), (4, 10), (12, 2), (21, 26), (10, 31), (11, 7), (21, 29), (26, 3), (16, 3), (17, 17), (3, 23), (0, 30), (13, 27), (36, 16), (22, 5), (34, 0), (1, 12), (24, 29), (5, 12), (16, 13), (29, 7), (5, 4), (33, 5), (8, 12), (37, 24), (38, 20), (17, 19), (1, 29), (23, 13), (26, 7), (8, 16), (28, 6), (8, 3), (20, 17), (8, 15), (13, 22), (27, 28), (9, 24), (38, 18), (34, 19), (19, 16), (8, 1), (9, 30), (14, 12), (34, 23), (5, 30), (13, 24), (27, 0), (34, 29), (30, 5), (30, 15), (15, 6), (28, 13), (12, 30), (33, 4), (16, 17), (30, 7), (13, 10), (14, 9), (2, 6), (15, 31), (36, 21), (4, 12), (12, 7), (31, 10), (38, 23), (27, 6), (32, 13), (37, 4), (37, 2), (27, 21), (26, 19), (33, 14), (24, 28), (34, 4), (37, 1), (21, 21), (22, 23), (27, 8), (15, 5), (28, 5), (4, 24), (22, 4), (10, 30), (11, 2), (0, 19), (8, 18), (15, 26), (31, 1), (22, 9), (6, 3), (16, 5), (31, 12), (17, 26), (37, 11), (12, 22), (5, 19), (7, 25), (28, 18), (19, 8), (15, 9), (2, 13), (36, 20), (12, 15), (0, 29), (21, 19), (20, 1), (2, 10), (11, 1), (26, 26), (23, 10), (26, 14), (6, 30), (6, 19), (12, 23), (13, 0), (34, 30), (0, 20), (25, 31), (25, 10), (36, 7), (18, 18), (8, 27), (23, 12), (13, 9), (29, 23), (27, 10), (21, 8), (2, 9), (20, 19), (27, 31), (0, 14), (11, 14), (18, 13), (35, 14), (30, 0), (29, 21), (23, 23), (0, 28), (28, 22), (4, 22), (17, 0), (36, 14), (36, 29), (23, 8), (16, 9), (35, 21), (30, 21), (29, 29), (2, 12), (29, 16), (24, 7), (21, 20), (24, 15), (20, 16), (4, 20), (32, 25), (12, 20), (23, 26), (28, 10), (27, 4), (38, 29), (34, 9), (1, 13), (0, 27), (22, 10), (18, 30), (12, 6), (17, 5), (37, 3), (19, 21), (21, 28), (1, 17), (7, 4), (32, 2), (16, 14), (35, 8), (1, 21), (3, 28), (1, 8), (19, 20), (19, 5), (31, 25), (14, 2), (25, 1), (13, 23), (38, 13), (38, 26), (3, 29), (19, 25), (0, 12), (3, 16), (15, 29), (20, 28), (32, 24), (10, 27), (9, 4), (29, 5), (24, 5), (26, 12), (3, 4), (13, 3), (6, 16), (18, 9), (23, 25), (23, 31), (15, 15), (20, 0), (17, 7), (25, 8), (23, 7), (21, 1), (24, 30), (7, 0), (31, 20), (12, 13), (12, 28), (20, 29), (19, 23), (33, 22), (25, 15), (11, 0), (7, 27), (31, 21), (19, 15), (38, 9), (36, 23), (9, 5), (22, 6), (26, 1), (14, 28), (5, 7), (13, 14), (7, 6), (23, 28), (15, 27), (32, 28), (30, 17), (1, 5), (1, 1), (19, 7), (29, 4), (33, 19), (22, 27), (9, 13), (30, 19), (19, 4), (34, 6), (4, 5), (27, 26), (36, 1), (38, 11), (28, 16), (29, 19), (19, 26), (30, 30), (14, 14), (9, 22), (23, 1), (33, 0), (30, 9), (5, 16), (3, 26), (34, 11), (20, 25), (10, 17), (26, 23), (9, 12), (35, 4), (4, 17), (38, 1), (13, 11), (8, 8), (34, 5), (37, 22), (12, 10), (26, 9), (4, 4), (20, 24), (22, 13), (9, 15), (6, 25), (22, 20), (8, 11), (36, 26), (6, 8), (23, 9), (7, 13), (24, 3), (16, 16), (18, 3), (10, 0), (8, 29), (26, 20), (33, 17), (29, 17), (12, 11), (38, 14), (4, 16), (32, 14), (10, 20), (11, 20), (0, 18), (13, 29), (12, 29), (7, 11), (9, 2), (12, 5), (19, 6), (17, 24), (37, 6), (8, 22), (18, 4), (18, 28), (17, 20), (22, 2), (34, 21), (9, 16), (31, 31), (12, 1), (33, 25), (1, 14), (35, 10), (14, 8), (11, 27), (18, 24), (12, 24), (17, 30), (9, 10), (26, 10), (14, 10), (12, 12), (36, 11), (33, 11), (2, 19), (7, 10), (27, 30), (26, 8), (31, 17), (20, 27), (10, 3), (20, 3), (25, 5), (14, 27), (22, 12), (8, 0), (8, 19), (1, 16), (8, 7), (3, 14), (22, 22), (3, 24), (37, 13), (6, 20), (27, 17), (27, 22), (30, 12), (21, 18), (8, 2), (18, 16), (22, 0), (30, 8), (9, 31), (29, 1), (25, 29), (14, 30), (0, 10), (29, 20), (22, 25), (5, 10), (14, 23), (21, 10), (14, 17), (30, 29), (27, 5), (29, 14), (17, 4), (27, 15), (31, 28), (18, 10), (1, 28), (25, 27), (36, 25), (19, 11), (35, 1), (7, 1), (4, 30), (22, 28), (36, 0), (25, 21), (7, 19), (23, 17), (36, 17), (37, 10), (19, 2), (3, 25), (35, 30), (22, 29), (5, 3), (2, 18), (15, 3), (7, 16), (2, 29), (7, 24), (22, 7), (26, 28), (3, 31), (29, 27), (19, 18), (17, 23), (28, 17), (33, 31), (12, 3), (10, 23), (2, 23), (24, 21), (27, 9), (36, 15), (19, 0), (34, 25), (36, 22), (26, 30), (13, 16), (14, 1), (24, 12), (11, 15), (16, 8), (36, 3), (35, 18), (17, 15), (25, 6), (26, 24), (20, 6), (15, 23), (37, 31)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944640", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 22), (20, 21), (7, 5), (7, 11), (25, 6), (14, 8), (6, 30), (18, 14), (12, 9), (8, 7), (4, 27), (20, 14), (4, 15), (18, 18), (28, 16), (12, 7), (21, 16), (13, 1), (25, 24), (10, 31), (25, 30), (7, 24), (22, 1), (6, 21), (25, 19), (8, 0), (30, 26), (27, 25), (12, 27), (28, 10), (5, 27), (3, 13), (13, 0), (4, 8), (1, 14), (3, 26), (21, 19), (9, 15), (22, 13), (19, 27), (6, 24), (2, 29), (27, 6), (20, 3), (11, 13), (2, 22), (21, 10), (3, 31), (20, 7), (4, 30), (15, 1), (11, 16), (12, 29), (18, 3), (9, 29), (3, 17), (28, 21), (15, 16), (24, 31), (24, 22), (29, 1), (5, 19), (23, 28), (5, 26), (3, 8), (23, 14), (5, 10), (9, 18), (25, 16), (5, 12), (17, 4), (18, 10), (22, 7), (14, 14), (20, 17), (11, 26), (17, 26), (0, 26), (18, 7), (15, 29), (4, 22), (8, 24), (16, 25), (8, 20), (27, 26), (25, 8), (23, 0), (25, 5), (21, 29), (26, 25), (6, 27), (1, 23), (14, 13), (24, 30), (1, 19), (19, 30), (0, 29), (16, 6), (13, 12), (14, 5), (21, 17), (25, 20), (28, 29), (12, 12), (22, 14), (5, 23), (16, 3), (13, 16), (17, 31), (29, 20), (27, 29), (1, 12), (8, 8), (21, 13), (10, 4), (12, 10), (11, 30), (23, 27), (2, 3), (21, 30), (14, 4), (6, 2), (7, 2), (10, 10), (11, 22), (13, 28), (15, 30), (4, 12), (10, 3), (24, 23), (1, 3), (11, 18), (9, 11), (8, 26), (29, 0), (3, 14), (18, 30), (15, 0), (23, 11), (12, 0), (11, 6), (13, 24), (18, 12), (6, 20), (2, 25), (14, 15), (26, 12), (30, 29), (27, 19), (18, 29), (3, 3), (14, 6), (23, 8), (8, 17), (19, 22), (27, 16), (14, 18), (13, 4), (8, 9), (19, 14), (13, 2), (15, 25), (30, 21), (18, 4), (30, 23), (17, 15), (5, 22), (1, 17), (21, 4), (2, 26), (2, 30), (7, 14), (1, 28), (12, 11), (5, 15), (21, 25), (16, 13), (26, 30), (25, 17), (6, 5), (5, 7), (18, 24), (7, 25), (13, 29), (7, 31), (0, 27), (15, 10), (10, 30), (18, 5), (23, 23), (12, 1), (7, 26), (21, 6), (30, 16), (22, 24), (15, 11), (16, 30), (29, 17), (23, 13), (16, 24), (17, 3), (7, 1), (10, 14), (28, 6), (19, 24), (20, 13), (10, 26), (10, 23), (4, 2), (29, 10), (2, 31), (18, 25), (0, 14), (26, 11), (5, 18), (16, 5), (22, 8), (11, 8), (5, 8), (4, 31), (17, 2), (4, 11), (24, 5), (25, 11), (22, 30), (24, 15), (7, 0), (26, 22), (8, 27), (13, 21), (20, 22), (16, 29), (12, 19), (0, 11), (26, 19), (5, 28), (9, 31), (12, 4), (9, 1), (8, 12), (7, 22), (5, 9), (1, 29), (24, 24), (9, 16), (20, 31), (16, 14), (1, 26), (6, 12), (30, 4), (24, 9), (2, 8), (29, 16), (28, 28), (24, 7), (0, 25), (21, 1), (3, 1), (16, 22), (16, 2), (19, 29), (3, 11), (15, 27), (7, 29), (10, 2), (3, 23), (17, 30), (24, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "864480", "dataset": "MATH"}
{"messages": [{"content": "In a 30x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 32), 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, 12), (21, 15), (0, 5), (28, 22), (25, 23), (13, 15), (5, 22), (19, 7), (29, 1), (26, 21), (22, 12), (14, 32), (21, 11), (27, 30), (21, 1), (26, 23), (24, 17), (8, 29), (1, 6), (13, 13), (12, 32), (24, 9), (15, 0), (19, 3), (5, 0), (25, 14), (26, 22), (7, 9), (2, 1), (26, 19), (20, 17), (27, 18), (16, 27), (8, 31), (10, 22), (12, 26), (11, 24), (5, 6), (6, 26), (29, 12), (29, 22), (16, 6), (17, 24), (14, 22), (28, 1), (12, 12), (22, 3), (29, 16), (7, 27), (23, 8), (27, 8), (4, 9), (23, 30), (27, 14), (18, 17), (9, 1), (17, 31), (17, 23), (17, 30), (5, 29), (22, 15), (10, 1), (24, 21), (10, 20), (26, 12), (25, 16), (20, 32), (12, 28), (15, 9), (22, 29), (21, 10), (4, 12), (11, 13), (22, 6), (9, 13), (28, 25), (12, 25), (10, 19), (23, 29), (28, 10), (11, 31), (20, 7), (0, 6), (16, 14), (29, 0), (7, 19), (0, 8), (3, 5), (4, 25), (14, 24), (8, 0), (18, 5), (8, 11), (28, 8), (19, 9), (27, 10), (9, 26), (0, 14), (5, 3), (13, 30), (11, 7), (19, 19), (10, 14), (22, 14), (4, 28), (17, 21), (27, 6), (18, 9), (24, 20), (16, 18), (6, 9), (14, 20), (27, 13), (12, 21), (16, 22), (25, 32), (10, 28), (26, 6), (6, 25), (1, 3), (5, 32), (23, 20), (26, 16), (7, 5), (7, 17), (11, 1), (27, 15), (29, 24), (19, 14), (16, 29), (2, 24), (24, 26), (4, 20), (21, 8), (14, 2), (0, 2), (22, 10), (14, 8), (3, 21), (13, 12), (24, 12), (13, 6), (29, 2), (12, 16), (14, 4), (14, 19), (2, 3), (15, 12), (27, 19), (4, 14), (20, 0), (3, 31), (12, 11), (13, 25), (25, 20), (6, 0), (9, 22), (21, 12), (8, 21), (13, 4), (7, 8), (6, 27), (2, 29), (11, 19), (9, 6), (18, 2), (20, 26), (16, 30), (22, 21), (8, 24), (23, 2), (0, 13), (1, 10), (22, 13), (14, 5), (19, 32), (19, 0), (3, 22), (2, 6), (0, 28), (25, 25), (7, 24), (28, 3), (3, 28), (28, 13), (6, 18), (10, 11), (2, 27), (9, 15), (23, 28), (20, 16), (29, 10), (7, 18), (11, 11), (18, 6), (20, 31), (26, 31), (11, 3), (10, 13), (16, 0), (24, 11), (23, 11), (10, 12), (20, 6), (26, 17), (4, 23), (8, 4), (26, 8), (22, 8), (4, 27), (12, 22), (15, 7), (8, 10), (12, 5), (22, 2), (27, 32), (21, 25), (20, 22), (18, 26), (11, 30), (24, 2), (4, 5), (25, 6), (2, 30), (10, 10), (25, 21), (5, 4), (1, 12), (6, 6), (27, 5), (22, 17), (24, 25), (0, 7), (17, 7), (5, 28), (7, 4), (25, 9), (3, 1), (18, 24), (9, 18), (23, 27), (15, 3), (20, 27), (21, 17), (12, 10), (28, 12), (22, 24), (18, 28), (26, 25), (27, 3), (13, 22), (2, 7), (8, 26), (4, 11), (15, 15), (8, 28), (13, 7), (28, 14), (19, 16), (27, 31), (6, 32), (22, 30), (29, 11), (13, 27), (15, 32), (10, 18), (15, 28), (16, 20), (11, 27), (1, 30), (5, 13), (0, 27), (14, 17), (8, 25), (10, 8), (5, 14), (3, 23), (16, 21), (4, 15), (23, 14), (13, 26), (19, 13), (13, 5), (22, 18), (26, 11), (8, 16), (18, 31), (16, 26), (11, 9), (6, 5), (7, 12), (0, 12), (21, 9), (25, 8), (1, 32), (9, 27), (17, 16), (24, 15), (13, 21), (6, 4), (10, 23), (15, 1), (8, 20), (28, 4), (28, 24), (13, 2), (19, 20), (21, 7), (0, 18), (10, 16), (8, 12), (27, 7), (28, 31), (28, 26), (25, 29), (12, 0), (16, 1), (1, 24), (5, 31), (29, 27), (24, 27), (25, 1), (22, 16), (16, 13), (16, 8), (16, 5), (6, 22), (21, 26), (21, 28), (23, 17), (21, 4), (29, 6), (26, 14), (14, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "565760", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (32, 9), (35, 28), (0, 20), (27, 35), (7, 5), (28, 2), (21, 0), (11, 3), (7, 11), (24, 30), (5, 13), (5, 8), (16, 28), (8, 28), (13, 7), (9, 11), (34, 35), (2, 33), (8, 35), (2, 23), (20, 22), (10, 11), (25, 23), (27, 34), (22, 28), (10, 21), (26, 16), (36, 33), (36, 16), (36, 18), (19, 2), (14, 26), (9, 16), (3, 24), (26, 33), (23, 33), (25, 36), (1, 17), (26, 23), (21, 23), (9, 32), (25, 14), (10, 4), (23, 28), (21, 10), (27, 37), (21, 30), (10, 38), (12, 3), (35, 17), (37, 17), (6, 38), (16, 38), (31, 28), (31, 35), (35, 16), (11, 18), (4, 33), (25, 1), (35, 8), (36, 24), (12, 36), (4, 20), (9, 10), (13, 34), (22, 24), (5, 31), (33, 9), (13, 26), (37, 14), (12, 29), (20, 6), (23, 30), (14, 23), (0, 16), (17, 7), (22, 38), (37, 21), (0, 31), (9, 4), (20, 30), (21, 27), (34, 14), (25, 2), (15, 20), (7, 17), (36, 12), (28, 27), (3, 16), (28, 7), (27, 7), (18, 11), (26, 10), (5, 5), (18, 24), (9, 18), (3, 10), (8, 8), (10, 1), (3, 7), (23, 31), (3, 1), (3, 25), (11, 8), (9, 20), (13, 0), (1, 16), (32, 21), (36, 14), (19, 17), (24, 22), (24, 35), (34, 11), (20, 20), (36, 29), (34, 15), (14, 11), (4, 2), (35, 26), (6, 18), (8, 18), (1, 0), (30, 24), (28, 35), (0, 10), (17, 1), (1, 3), (35, 23), (33, 5), (2, 18), (18, 17), (16, 35), (13, 8), (4, 13), (10, 29), (7, 1), (16, 9), (5, 37), (36, 32), (24, 1), (34, 24), (3, 8), (9, 31), (36, 36), (35, 19), (27, 26), (2, 26), (15, 14), (9, 28), (14, 14), (1, 14), (2, 15), (34, 17), (21, 38), (25, 20), (11, 9), (5, 30), (31, 14), (30, 4), (22, 37), (17, 32), (19, 20), (12, 32), (15, 21), (36, 13), (25, 10), (7, 32), (12, 20), (10, 24), (22, 29), (20, 10), (12, 17), (9, 26), (4, 27), (30, 0), (8, 5), (5, 32), (28, 16), (36, 7), (30, 21), (6, 22), (22, 4), (1, 29), (21, 29), (33, 7), (37, 16), (9, 9), (9, 17), (15, 32), (20, 37), (15, 1), (34, 30), (19, 12), (33, 19), (0, 12), (12, 11), (23, 34), (6, 32), (31, 27), (9, 5), (16, 17), (8, 2), (19, 1), (30, 31), (17, 10), (33, 33), (5, 1), (15, 19), (12, 9), (27, 21), (34, 10), (3, 26), (35, 32), (18, 25), (18, 2), (29, 36), (22, 6), (7, 14), (10, 12), (34, 27), (18, 21), (33, 29), (37, 32), (5, 24), (6, 17), (23, 36), (22, 20), (31, 16), (9, 12), (10, 7), (15, 27), (16, 23), (13, 38), (20, 32), (7, 3), (17, 31), (18, 26), (30, 26), (18, 20), (28, 26), (37, 2), (32, 33), (13, 10), (25, 28), (1, 7), (24, 24), (0, 33), (15, 17), (18, 19), (5, 17), (26, 14), (5, 34), (8, 13), (19, 4), (20, 9), (36, 38), (2, 2), (34, 37), (1, 18), (10, 19), (11, 15), (14, 28), (29, 10), (16, 36), (32, 34), (8, 38), (37, 13), (34, 20), (9, 22), (22, 22), (18, 12), (3, 15), (0, 13), (29, 8), (35, 37), (37, 12), (21, 4), (6, 29), (23, 21), (19, 38), (7, 9), (23, 11), (11, 29), (17, 37), (19, 15), (27, 11), (8, 23), (8, 21), (7, 33), (6, 9), (22, 21), (2, 13), (13, 21), (36, 37), (36, 6), (24, 20), (3, 0), (37, 22), (32, 25), (16, 2), (20, 36), (7, 18), (29, 15), (31, 9), (35, 35), (35, 13), (21, 31), (19, 13), (9, 15), (17, 30), (32, 12), (25, 22), (33, 10), (10, 20), (10, 25), (24, 27), (36, 21), (6, 23), (19, 32), (19, 8), (18, 30), (4, 30), (12, 18), (9, 27), (31, 34), (9, 14), (14, 12), (19, 28), (22, 10), (13, 29), (24, 13), (30, 17), (33, 6), (16, 21), (35, 33), (35, 7), (5, 3), (33, 13), (36, 15), (35, 24), (19, 33), (27, 8), (11, 21), (10, 15), (19, 35), (6, 20), (4, 35), (34, 25), (22, 25), (23, 24), (5, 29), (13, 14), (16, 25), (33, 32), (24, 5), (13, 1), (7, 35), (17, 9), (9, 35), (33, 24), (30, 9), (12, 14), (0, 36), (4, 9), (28, 19), (25, 6), (4, 6), (21, 17), (23, 38), (30, 22), (30, 11), (25, 19), (18, 5), (34, 13), (4, 10), (17, 38), (12, 35), (16, 19), (2, 12), (29, 21), (17, 14), (35, 14), (16, 22), (14, 22), (20, 24), (29, 12), (36, 35), (16, 37), (19, 36), (11, 26), (31, 32), (1, 5), (36, 25), (1, 31), (23, 12), (28, 36), (32, 29), (14, 10), (5, 23), (23, 19), (5, 26), (15, 0), (7, 8), (8, 7), (37, 0), (11, 34), (24, 21), (20, 25), (30, 35), (26, 24), (22, 31), (29, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23256", "dataset": "MATH"}
{"messages": [{"content": "In a 36x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 14), (28, 7), (14, 16), (3, 23), (16, 4), (28, 29), (3, 6), (31, 10), (23, 15), (22, 12), (1, 4), (20, 20), (9, 21), (14, 17), (9, 9), (4, 13), (26, 19), (17, 17), (2, 29), (33, 19), (22, 23), (27, 25), (21, 7), (22, 11), (14, 25), (31, 2), (10, 6), (31, 29), (25, 17), (30, 23), (4, 3), (2, 21), (19, 24), (13, 11), (32, 30), (16, 2), (6, 31), (12, 8), (9, 0), (17, 4), (10, 19), (34, 29), (17, 10), (28, 30), (14, 21), (31, 21), (13, 21), (35, 18), (10, 26), (9, 22), (29, 7), (8, 29), (2, 22), (5, 26), (20, 24), (23, 2), (15, 0), (17, 25), (6, 16), (29, 28), (12, 30), (6, 28), (24, 28), (26, 3), (4, 6), (23, 17), (28, 19), (24, 10), (0, 2), (35, 25), (21, 29), (28, 21), (7, 26), (18, 4), (34, 15), (12, 22), (14, 1), (27, 11), (0, 5), (30, 12), (5, 7), (1, 6), (4, 17), (21, 17), (33, 2), (27, 26), (11, 30), (29, 30), (14, 29), (30, 30), (16, 9), (32, 21), (31, 9), (12, 17), (17, 13), (9, 1), (23, 6), (18, 5), (31, 19), (33, 3), (26, 27), (26, 4), (35, 10), (18, 17), (24, 16), (23, 19), (28, 3), (21, 4), (12, 16), (20, 18), (24, 8), (33, 20), (1, 21), (21, 30), (7, 4), (31, 27), (8, 5), (24, 24), (13, 2), (3, 14), (16, 17), (6, 22), (30, 18), (15, 27), (16, 30), (5, 15), (14, 14), (22, 27), (2, 10), (19, 14), (5, 17), (23, 5), (26, 22), (3, 15), (3, 18), (29, 14), (24, 27), (9, 12), (15, 4), (15, 25), (24, 12), (12, 11), (11, 15), (13, 10), (25, 5), (34, 13), (27, 2), (25, 27), (16, 5), (32, 6), (27, 27), (34, 2), (9, 23), (0, 19), (3, 24), (19, 6), (34, 1), (35, 19), (14, 30), (32, 2), (10, 30), (7, 2), (33, 30), (34, 28), (32, 14), (5, 18), (28, 25), (20, 2), (12, 29), (7, 3), (4, 10), (19, 22), (11, 24), (0, 29), (35, 5), (22, 6), (0, 9), (21, 5), (19, 2), (17, 27), (20, 8), (21, 19), (21, 13), (26, 1), (19, 4), (5, 1), (19, 13), (0, 14), (21, 9), (18, 3), (29, 6), (6, 19), (10, 24), (20, 15), (3, 3), (12, 13), (21, 23), (32, 27), (3, 5), (17, 7), (27, 20), (17, 31), (4, 21), (27, 22), (24, 4), (10, 31), (34, 7), (6, 30), (10, 11), (18, 23), (32, 25), (19, 20), (15, 31), (11, 23), (8, 23), (23, 27), (26, 6), (27, 18), (5, 14), (3, 12), (35, 23), (27, 29), (32, 22), (14, 10), (13, 20), (21, 8), (34, 11), (8, 13), (26, 8), (24, 13), (20, 31), (32, 11), (17, 12), (27, 28), (11, 22), (26, 14), (27, 12), (30, 14), (33, 1), (30, 17), (22, 3), (23, 0), (17, 30), (25, 28), (5, 31), (4, 19), (32, 10), (13, 29), (7, 7), (28, 9), (35, 24), (31, 22), (8, 27), (22, 15), (20, 7), (30, 27), (17, 28), (3, 13), (13, 16), (15, 15), (13, 22), (24, 20), (28, 13), (14, 4), (27, 4), (12, 19), (32, 0), (3, 11), (25, 9), (14, 28), (0, 8), (2, 0), (27, 31), (22, 16), (19, 21), (16, 21), (2, 26), (0, 25), (23, 4), (14, 13), (25, 4), (15, 10), (11, 17), (23, 3), (10, 29), (16, 29), (13, 27), (0, 21), (3, 21), (16, 31), (31, 8), (22, 0), (12, 25), (2, 7), (8, 21), (16, 3), (12, 1), (14, 24), (16, 18), (15, 18), (28, 23), (1, 0), (22, 13), (3, 31), (1, 23), (15, 2), (34, 9), (21, 20), (13, 31), (16, 27), (8, 24), (3, 4), (25, 21), (18, 11), (23, 30), (21, 14), (8, 26), (8, 22), (18, 25), (24, 7), (21, 3), (13, 0), (25, 2), (17, 20), (32, 26), (29, 22), (20, 9)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "682560", "dataset": "MATH"}
{"messages": [{"content": "In a 30x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 36), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (14, 31), (11, 8), (11, 7), (13, 17), (18, 29), (15, 29), (11, 36), (7, 18), (17, 22), (24, 7), (26, 1), (28, 1), (3, 13), (19, 4), (2, 26), (26, 6), (17, 9), (5, 11), (9, 34), (24, 9), (18, 16), (18, 3), (25, 28), (25, 4), (16, 9), (1, 23), (18, 2), (12, 27), (23, 27), (2, 10), (4, 5), (29, 5), (26, 17), (8, 24), (21, 33), (19, 0), (23, 31), (20, 3), (8, 14), (17, 31), (3, 3), (17, 17), (28, 33), (8, 35), (27, 9), (19, 18), (27, 19), (12, 32), (2, 13), (26, 7), (18, 25), (7, 33), (28, 25), (11, 10), (23, 29), (10, 30), (5, 12), (5, 18), (28, 29), (1, 33), (25, 16), (18, 6), (28, 2), (2, 36), (11, 4), (14, 26), (4, 36), (10, 9), (26, 29), (4, 14), (17, 0), (7, 32), (24, 16), (5, 24), (21, 30), (23, 5), (18, 34), (16, 24), (16, 33), (13, 24), (13, 8), (28, 3), (5, 17), (18, 27), (13, 2), (21, 35), (11, 15), (2, 3), (17, 6), (3, 7), (16, 20), (1, 25), (24, 30), (19, 14), (27, 4), (1, 19), (3, 14), (8, 7), (1, 8), (26, 16), (18, 5), (18, 17), (15, 16), (1, 4), (10, 6), (22, 30), (19, 12), (18, 12), (4, 33), (20, 31), (13, 29), (3, 8), (19, 20), (10, 8), (25, 12), (3, 1), (15, 2), (14, 34), (29, 10), (23, 26), (28, 30), (20, 34), (10, 31), (22, 19), (0, 25), (3, 36), (15, 22), (21, 8), (14, 3), (14, 35), (6, 11), (12, 5), (7, 26), (9, 28), (20, 11), (19, 2), (19, 26), (1, 11), (1, 10), (9, 20), (11, 21), (24, 25), (23, 28), (16, 26), (9, 2), (27, 34), (23, 2), (19, 13), (24, 18), (12, 12), (17, 3), (25, 34), (2, 16), (28, 22), (1, 24), (16, 15), (21, 28), (26, 35), (23, 16), (12, 17), (6, 35), (8, 33), (0, 34), (0, 19), (29, 22), (27, 2), (2, 19), (8, 8), (12, 6), (6, 31), (25, 23), (10, 7), (3, 11), (12, 16), (12, 24), (25, 36), (0, 1), (22, 15), (2, 8), (25, 13), (26, 28), (1, 31), (7, 10), (21, 32), (0, 3), (7, 8), (11, 11), (14, 27), (18, 14), (24, 3), (25, 17), (17, 19), (4, 34), (15, 1), (0, 15), (2, 33), (11, 25), (26, 3), (27, 24), (29, 20), (10, 10), (2, 1), (4, 0), (1, 21), (8, 11), (8, 0), (10, 32), (11, 34), (14, 30), (24, 17), (12, 25), (3, 24), (23, 22), (23, 24), (6, 6), (26, 14), (23, 11), (12, 22), (28, 35), (1, 27), (16, 28), (25, 33), (9, 27), (23, 6), (19, 34), (27, 1), (3, 5), (18, 33), (2, 6), (16, 32), (13, 27), (1, 30), (5, 30), (10, 4), (21, 2), (17, 36), (8, 28), (17, 30), (15, 8), (15, 13), (3, 27), (14, 19), (1, 15), (3, 25), (15, 20), (24, 31), (21, 25), (25, 31), (11, 0), (8, 9), (1, 12), (10, 20), (28, 26), (4, 9), (17, 5), (17, 28), (12, 34), (18, 21), (0, 9), (2, 32), (23, 10), (28, 9), (20, 28), (13, 20), (6, 20), (28, 5), (0, 14), (4, 28), (21, 18), (2, 15), (16, 4), (17, 32), (11, 19), (22, 9), (12, 36), (14, 1), (11, 26), (3, 0), (14, 12), (4, 4), (13, 12), (7, 5), (29, 28), (20, 18), (4, 18), (22, 20), (15, 33), (1, 26), (9, 16), (17, 16), (26, 11), (1, 5), (18, 26), (16, 13), (5, 13), (6, 5), (10, 23), (14, 7), (9, 17), (19, 32), (7, 30), (26, 15), (12, 31), (4, 19), (8, 22), (5, 32), (25, 25), (22, 34), (0, 17), (15, 32), (9, 15), (7, 9), (5, 23), (14, 9), (25, 6), (26, 21), (3, 31), (0, 8), (28, 11), (20, 32), (29, 2), (12, 14), (0, 16), (29, 14), (8, 10), (15, 7), (22, 25), (4, 6), (9, 26), (9, 25), (26, 27), (22, 35), (10, 1), (7, 3)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600336", "dataset": "MATH"}
{"messages": [{"content": "In a 35x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 37), 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), (11, 19), (32, 25), (26, 22), (29, 29), (30, 18), (11, 10), (3, 24), (3, 4), (24, 30), (27, 17), (3, 14), (24, 4), (4, 10), (28, 13), (18, 8), (18, 17), (18, 16), (10, 21), (21, 36), (14, 22), (32, 5), (17, 5), (34, 2), (16, 14), (7, 33), (24, 32), (5, 14), (32, 3), (21, 25), (1, 12), (30, 3), (28, 16), (28, 26), (4, 13), (6, 28), (11, 33), (34, 33), (10, 25), (34, 19), (11, 15), (26, 5), (11, 31), (25, 1), (0, 20), (8, 24), (5, 4), (31, 11), (13, 28), (8, 31), (21, 5), (30, 31), (3, 0), (6, 1), (6, 37), (3, 36), (5, 13), (19, 34), (26, 20), (29, 10), (21, 2), (0, 31), (1, 15), (21, 35), (16, 36), (33, 7), (31, 28), (26, 10), (27, 19), (32, 18), (29, 23), (27, 18), (30, 25), (0, 26), (27, 12), (16, 19), (16, 9), (26, 32), (4, 0), (27, 2), (22, 8), (18, 31), (34, 20), (21, 24), (9, 8), (23, 20), (11, 34), (34, 0), (30, 34), (10, 33), (23, 12), (14, 37), (22, 17), (28, 0), (15, 32), (17, 10), (3, 6), (15, 20), (24, 35), (19, 9), (26, 4), (33, 13), (12, 1), (4, 18), (18, 2), (33, 4), (4, 28), (3, 30), (4, 20), (11, 37), (27, 33), (29, 28), (29, 16), (5, 15), (15, 27), (6, 11), (31, 1), (34, 25), (32, 11), (27, 14), (23, 27), (32, 33), (8, 11), (28, 30), (1, 31), (7, 25), (0, 14), (25, 35), (3, 31), (26, 27), (30, 6), (8, 7), (16, 1), (31, 20), (19, 10), (18, 9), (17, 20), (27, 4), (19, 7), (22, 4), (2, 37), (1, 13), (2, 6), (32, 20), (9, 32), (25, 8), (15, 31), (13, 27), (17, 34), (13, 17), (0, 5), (12, 5), (14, 18), (1, 17), (30, 33), (23, 11), (26, 31), (14, 29), (24, 24), (1, 35), (2, 29), (1, 18), (34, 6), (1, 11), (32, 8), (23, 5), (31, 14), (5, 27), (21, 34), (26, 16), (32, 1), (33, 2), (14, 21), (21, 1), (34, 24), (20, 36), (23, 13), (6, 30), (20, 3), (26, 36), (30, 19), (24, 17), (8, 10), (24, 33), (20, 4), (25, 30), (16, 12), (14, 6), (26, 9), (9, 27), (33, 31), (17, 22), (33, 34), (2, 34), (1, 29), (18, 3), (19, 3), (15, 37), (22, 11), (14, 30), (21, 16), (32, 16), (9, 33), (17, 26), (10, 4), (30, 27), (15, 8), (19, 22), (13, 18), (11, 3), (25, 26), (34, 21), (29, 34), (0, 25), (23, 34), (10, 16), (29, 15), (32, 24), (17, 4), (30, 9), (23, 7), (9, 35), (33, 19), (8, 0), (11, 6), (16, 28), (14, 27), (9, 28), (12, 19), (22, 27), (22, 0), (14, 33), (7, 14), (13, 6), (34, 10), (12, 15), (32, 7), (4, 25), (31, 35), (23, 17), (0, 9), (34, 12), (7, 16), (28, 15), (30, 11), (6, 21), (23, 35), (16, 27), (23, 4), (15, 29), (10, 28), (6, 29), (31, 16), (6, 19), (26, 29), (25, 2), (28, 23), (11, 20), (10, 30), (21, 18), (33, 20), (5, 21), (17, 3), (8, 17), (27, 8), (29, 27), (9, 7), (29, 2), (13, 15), (3, 16), (17, 8), (32, 32), (17, 1), (27, 26), (10, 35), (0, 35), (26, 33), (15, 4), (30, 28), (1, 37), (23, 6), (5, 37), (33, 11), (0, 33), (32, 9), (21, 26), (30, 4), (16, 30), (23, 32), (33, 18), (5, 33), (27, 27), (10, 14), (34, 7), (13, 24), (15, 17), (27, 11), (8, 1), (11, 35), (12, 2), (9, 37), (2, 7), (33, 6), (6, 2), (14, 2), (23, 24), (12, 33), (17, 37), (3, 26), (8, 8), (15, 16), (34, 9), (25, 25), (15, 14), (15, 3), (24, 26), (23, 9), (25, 27), (18, 32), (25, 13), (20, 22), (24, 10), (11, 1), (19, 26), (20, 1), (32, 29), (31, 31), (12, 28), (24, 16), (6, 12), (26, 24), (33, 30), (33, 0), (28, 2), (15, 6), (26, 3), (1, 28), (32, 0), (6, 26), (8, 16), (11, 36), (12, 16), (24, 8), (7, 15), (13, 11), (25, 19), (3, 9), (17, 36), (22, 9), (0, 28), (1, 30), (31, 29), (8, 9), (5, 16), (15, 18), (30, 2), (3, 29), (25, 33), (33, 8), (34, 1), (6, 35), (9, 14), (16, 35), (31, 8), (8, 21), (4, 17), (29, 6), (25, 0), (8, 32), (17, 27), (20, 7), (7, 34), (28, 7), (8, 13), (24, 31), (19, 24), (21, 17), (12, 10), (34, 13), (14, 35), (0, 1), (34, 17), (30, 32), (31, 26), (23, 8), (6, 15), (21, 9), (4, 3), (3, 15), (20, 12), (13, 9), (8, 20), (5, 30), (8, 29), (30, 7), (31, 34), (2, 24), (34, 31), (30, 37), (10, 6), (1, 36), (0, 6), (25, 5), (27, 24), (12, 23), (5, 32), (22, 37), (22, 20), (18, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341568", "dataset": "MATH"}
{"messages": [{"content": "In a 38x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 32), 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), (16, 4), (30, 26), (20, 8), (29, 13), (19, 30), (23, 31), (26, 13), (19, 26), (0, 2), (24, 27), (4, 3), (1, 17), (4, 11), (7, 16), (23, 7), (17, 28), (27, 29), (10, 24), (26, 6), (34, 27), (6, 27), (18, 31), (11, 9), (22, 7), (36, 17), (34, 8), (18, 10), (30, 28), (34, 23), (14, 14), (6, 28), (14, 10), (32, 2), (28, 31), (5, 7), (20, 29), (22, 12), (12, 12), (32, 13), (34, 24), (7, 5), (32, 25), (12, 18), (8, 20), (28, 19), (4, 29), (10, 18), (7, 11), (5, 19), (28, 23), (4, 2), (13, 30), (9, 9), (30, 0), (5, 15), (14, 12), (29, 5), (12, 9), (15, 22), (22, 18), (34, 3), (37, 0), (29, 27), (27, 8), (11, 29), (26, 0), (17, 22), (33, 13), (28, 18), (2, 29), (25, 29), (29, 2), (33, 9), (19, 12), (6, 24), (13, 22), (7, 25), (2, 6), (28, 20), (22, 23), (13, 12), (5, 12), (2, 8), (22, 27), (36, 2), (33, 3), (5, 31), (7, 26), (5, 29), (21, 23), (37, 3), (3, 4), (20, 4), (36, 25), (5, 10), (32, 19), (6, 6), (11, 22), (29, 26), (11, 11), (30, 10), (29, 12), (4, 6), (0, 23), (21, 7), (13, 19), (30, 14), (32, 7), (8, 32), (10, 29), (30, 2), (16, 6), (36, 24), (22, 19), (21, 2), (33, 32), (24, 23), (15, 28), (7, 20), (23, 32), (31, 15), (10, 16), (10, 6), (34, 18), (32, 27), (12, 16), (25, 23), (37, 21), (10, 20), (31, 14), (4, 4), (15, 20), (33, 14), (15, 18), (16, 1), (10, 10), (24, 18), (20, 15), (34, 15), (22, 26), (24, 12), (14, 25), (4, 14), (21, 15), (17, 8), (19, 11), (37, 20), (27, 1), (28, 3), (4, 26), (23, 6), (5, 18), (1, 30), (21, 32), (20, 20), (19, 15), (30, 23), (29, 25), (11, 17), (17, 11), (4, 1), (22, 8), (12, 23), (24, 13), (9, 25), (21, 31), (25, 12), (22, 14), (17, 15), (28, 4), (8, 0), (6, 12), (3, 3), (15, 4), (31, 23), (5, 21), (21, 21), (10, 31), (11, 25), (21, 3), (7, 24), (19, 10), (15, 25), (12, 14), (11, 20), (14, 32), (3, 23), (4, 20), (14, 11), (17, 6), (26, 24), (20, 0), (36, 22), (13, 2), (29, 31), (1, 10), (15, 26), (13, 5), (14, 2), (36, 4), (35, 3), (31, 0), (0, 18), (1, 20), (23, 26), (6, 5), (34, 11), (22, 32), (9, 15), (17, 19), (12, 29), (27, 32), (33, 23), (2, 21), (13, 1), (17, 7), (22, 11), (20, 32), (21, 6), (7, 18), (6, 1), (9, 26), (14, 8), (5, 2), (30, 17), (16, 10), (30, 29), (16, 27), (9, 1), (8, 4), (26, 29), (31, 18), (5, 27), (15, 7), (24, 9), (3, 2), (7, 29), (37, 23), (15, 12), (15, 29), (28, 16), (12, 7), (25, 19), (35, 21), (9, 12), (20, 26), (3, 21), (23, 27), (33, 22), (32, 18), (33, 16), (10, 27), (26, 3), (31, 8), (6, 11), (15, 9), (26, 2), (12, 25), (15, 1), (14, 26), (29, 4), (2, 14), (13, 14), (15, 15), (0, 1), (25, 14), (33, 17), (19, 7), (18, 26), (34, 22), (17, 24), (3, 1), (5, 1), (33, 0), (34, 10), (16, 9), (9, 8), (5, 4), (6, 4), (14, 9), (26, 18), (16, 21), (0, 27), (5, 17), (33, 7), (3, 5), (30, 22), (36, 20), (27, 6), (34, 25), (2, 16), (30, 21), (17, 29), (16, 31), (21, 8), (20, 3), (3, 27), (17, 9), (8, 11), (26, 16), (18, 6), (1, 21), (29, 23), (27, 24), (12, 10), (31, 4), (24, 28), (25, 22), (26, 10), (28, 17), (26, 11), (16, 30), (2, 3), (32, 1), (10, 25), (5, 5), (0, 15), (12, 32), (13, 28), (0, 7), (37, 10), (29, 30), (3, 10), (35, 29), (20, 7), (17, 30), (13, 29), (2, 22), (8, 25), (4, 24), (28, 29), (3, 13), (36, 14), (20, 24), (0, 14), (7, 23), (29, 14), (28, 10), (8, 16), (1, 18), (3, 19), (23, 29), (17, 17), (18, 17), (3, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54720", "dataset": "MATH"}
{"messages": [{"content": "In a 35x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 10), (3, 18), (8, 17), (7, 14), (25, 24), (11, 7), (26, 17), (13, 27), (4, 31), (25, 13), (7, 32), (14, 30), (9, 18), (1, 32), (21, 4), (18, 5), (9, 10), (10, 25), (8, 5), (12, 3), (11, 9), (0, 18), (32, 20), (13, 19), (14, 6), (26, 20), (7, 33), (10, 32), (7, 9), (22, 8), (8, 0), (32, 29), (10, 18), (29, 30), (2, 30), (11, 21), (16, 17), (13, 23), (33, 21), (11, 0), (5, 23), (12, 13), (23, 32), (25, 6), (10, 1), (9, 3), (12, 0), (8, 26), (6, 31), (3, 16), (9, 5), (2, 34), (8, 21), (28, 24), (25, 18), (3, 2), (30, 12), (18, 23), (8, 12), (23, 12), (9, 7), (26, 25), (24, 7), (31, 5), (13, 8), (14, 35), (15, 1), (11, 34), (14, 7), (24, 21), (4, 33), (13, 22), (7, 2), (16, 2), (22, 20), (22, 16), (31, 11), (15, 21), (8, 3), (20, 2), (20, 32), (19, 24), (34, 19), (15, 9), (26, 3), (23, 22), (34, 20), (25, 19), (12, 20), (7, 15), (3, 10), (19, 23), (28, 35), (23, 26), (20, 31), (16, 6), (32, 30), (24, 11), (1, 33), (28, 17), (16, 18), (14, 34), (1, 18), (34, 30), (30, 22), (2, 5), (22, 29), (24, 24), (12, 7), (33, 33), (12, 11), (15, 24), (17, 15), (26, 8), (14, 25), (26, 27), (7, 27), (15, 11), (3, 1), (15, 12), (24, 20), (19, 29), (11, 31), (21, 10), (9, 31), (21, 18), (14, 8), (13, 15), (31, 12), (30, 31), (18, 7), (7, 13), (34, 15), (23, 21), (14, 20), (15, 18), (4, 21), (16, 10), (18, 13), (23, 6), (1, 14), (15, 14), (13, 9), (3, 26), (1, 7), (16, 32), (20, 29), (19, 4), (21, 20), (29, 2), (32, 23), (33, 10), (15, 27), (32, 26), (23, 5), (8, 16), (11, 16), (7, 34), (32, 25), (10, 35), (1, 20), (18, 19), (31, 27), (3, 35), (28, 26), (19, 33), (25, 22), (7, 18), (18, 25), (6, 21), (3, 25), (5, 27), (26, 13), (4, 30), (1, 17), (24, 25), (3, 17), (8, 8), (5, 18), (28, 33), (15, 6), (32, 2), (4, 8), (19, 14), (20, 35), (27, 26), (15, 5), (11, 6), (4, 6), (9, 6), (13, 6), (24, 18), (8, 24), (17, 2), (7, 20), (8, 15), (29, 19), (10, 34), (25, 27), (28, 30), (7, 4), (28, 25), (6, 19), (25, 16), (33, 19), (10, 7), (0, 13), (28, 9), (32, 3), (23, 1), (16, 3), (24, 19), (21, 13), (26, 5), (5, 19), (5, 12), (29, 31), (28, 10), (29, 22), (18, 31), (10, 21), (3, 22), (0, 26), (24, 31), (32, 10), (10, 8), (13, 11), (17, 35), (16, 13), (2, 24), (3, 27), (22, 0), (1, 15), (22, 17), (14, 3), (25, 30), (4, 25), (18, 4), (0, 3), (22, 11), (13, 13), (3, 24), (2, 12), (23, 31), (5, 0), (2, 27), (18, 27), (21, 17), (2, 22), (29, 25), (11, 17), (21, 15), (18, 29), (20, 27), (9, 15), (27, 30), (15, 0), (1, 23), (8, 29), (22, 24), (12, 4), (34, 26), (22, 1), (29, 11), (0, 5), (0, 7), (22, 6), (26, 29), (18, 10), (22, 5), (3, 5), (17, 23), (29, 29), (15, 34), (24, 6), (19, 13), (2, 29), (18, 12), (31, 0), (13, 25), (13, 7), (27, 23), (8, 18), (28, 2), (9, 21), (22, 26), (1, 30), (26, 26), (6, 32), (5, 5), (21, 31), (27, 31), (12, 28), (0, 4), (5, 24), (33, 20), (10, 30), (19, 19), (34, 23), (25, 26), (18, 24), (27, 16), (13, 30), (8, 2), (14, 13), (28, 13), (22, 14), (32, 16), (23, 27), (33, 11), (26, 12), (2, 15), (32, 14), (4, 12), (10, 22), (5, 7), (17, 13), (26, 0), (23, 19), (33, 30), (17, 30), (20, 16), (34, 33), (21, 12), (6, 30), (23, 28), (15, 32), (16, 35), (22, 22), (11, 15), (2, 33), (5, 2), (14, 33), (21, 16), (7, 8), (11, 18), (26, 22), (24, 9), (9, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "232470", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 16), (5, 0), (28, 10), (29, 28), (26, 13), (27, 30), (5, 32), (7, 19), (26, 32), (32, 15), (19, 0), (10, 15), (25, 21), (38, 24), (4, 32), (27, 14), (27, 18), (9, 13), (30, 16), (36, 16), (28, 14), (16, 10), (21, 24), (1, 3), (34, 26), (22, 1), (26, 9), (25, 19), (8, 3), (9, 20), (16, 30), (13, 29), (33, 14), (38, 22), (3, 25), (32, 12), (33, 22), (36, 10), (28, 5), (18, 19), (18, 24), (29, 7), (9, 12), (33, 21), (38, 5), (33, 4), (23, 22), (34, 18), (25, 20), (32, 4), (15, 31), (5, 7), (31, 18), (19, 24), (16, 31), (27, 21), (25, 10), (3, 27), (4, 24), (11, 25), (15, 15), (34, 25), (2, 15), (31, 20), (3, 14), (25, 22), (18, 8), (26, 5), (7, 18), (2, 32), (13, 2), (34, 27), (28, 21), (23, 29), (7, 25), (36, 22), (10, 12), (17, 12), (7, 12), (33, 17), (20, 5), (21, 6), (25, 24), (9, 3), (10, 10), (32, 13), (17, 31), (3, 29), (0, 8), (9, 19), (18, 3), (21, 5), (19, 1), (2, 11), (35, 6), (23, 12), (21, 12), (7, 7), (34, 23), (38, 26), (23, 24), (7, 31), (9, 11), (35, 20), (8, 6), (18, 4), (8, 15), (28, 28), (31, 31), (22, 8), (23, 32), (19, 30), (16, 6), (15, 10), (18, 25), (38, 2), (2, 3), (3, 15), (34, 8), (18, 5), (32, 5), (38, 1), (32, 29), (10, 9), (19, 9), (9, 31), (19, 4), (5, 29), (9, 26), (17, 24), (30, 9), (14, 17), (13, 30), (11, 18), (38, 21), (33, 5), (3, 11), (38, 3), (6, 19), (35, 8), (14, 30), (14, 19), (29, 4), (12, 28), (34, 15), (25, 13), (20, 32), (28, 13), (18, 18), (28, 4), (21, 1), (23, 13), (21, 30), (0, 10), (37, 4), (5, 9), (25, 15), (16, 4), (34, 2), (20, 4), (11, 12), (18, 2), (9, 30), (10, 19), (12, 4), (32, 19), (33, 3), (2, 16), (13, 31), (5, 20), (32, 20), (12, 10), (12, 29), (7, 6), (34, 9), (24, 26), (35, 22), (35, 3), (22, 11), (15, 20), (22, 17), (27, 24), (20, 29), (11, 26), (14, 5), (35, 4), (4, 18), (16, 24), (24, 32), (4, 3), (11, 19), (32, 24), (12, 3), (11, 4), (4, 22), (5, 13), (18, 30), (17, 0), (30, 18), (11, 5), (26, 24), (2, 23), (33, 31), (36, 12), (10, 5), (26, 21), (8, 31), (27, 4), (16, 14), (22, 24), (6, 0), (36, 18), (5, 15), (28, 3), (26, 20), (6, 31), (1, 17), (26, 3), (34, 7), (33, 11), (27, 9), (35, 17), (3, 9), (21, 27), (8, 13), (16, 29), (6, 20), (27, 3), (0, 6), (14, 22), (36, 30), (17, 2), (5, 21), (18, 27), (21, 9), (0, 9), (22, 4), (15, 9), (23, 21), (20, 27), (31, 25), (8, 16), (34, 3), (34, 28), (21, 17), (21, 11), (25, 0), (21, 13), (25, 5), (18, 1), (17, 32), (11, 14), (6, 18), (30, 31), (25, 16), (15, 7), (36, 20), (30, 8), (7, 24), (17, 17), (8, 0), (27, 17), (37, 9), (33, 26), (0, 5), (38, 15), (34, 21), (8, 10), (34, 29), (12, 11), (36, 6), (37, 10), (30, 4), (3, 23), (2, 22), (32, 10), (28, 25), (23, 1), (2, 30), (36, 17), (25, 12), (27, 29), (31, 26), (5, 16), (14, 21), (37, 25), (11, 22), (0, 12), (4, 23), (3, 1), (25, 18), (6, 16), (24, 5), (13, 9), (35, 13), (28, 15), (14, 4), (7, 5), (25, 27), (37, 6), (1, 2), (36, 15), (23, 31), (17, 5), (6, 9), (36, 25), (18, 10), (20, 14), (32, 9), (2, 19), (2, 14), (29, 32), (1, 6), (29, 31), (31, 9), (3, 16), (31, 8), (14, 24), (3, 4), (30, 6), (0, 24), (8, 25), (25, 28), (15, 29), (24, 8), (23, 5), (30, 3), (5, 12), (31, 0), (6, 29), (33, 7), (23, 25), (0, 25), (34, 4), (11, 11), (9, 21), (17, 21), (33, 13), (25, 3), (36, 28), (29, 2), (24, 15), (38, 10), (14, 1), (27, 2), (7, 13), (21, 4), (22, 28), (21, 26), (33, 19), (1, 19), (0, 22), (24, 20), (4, 9), (10, 17), (1, 7), (26, 30), (23, 20), (38, 29), (31, 15), (15, 17), (2, 10), (32, 22), (11, 9), (17, 15), (27, 22), (24, 10), (11, 16), (8, 23), (28, 9), (35, 14), (16, 3), (0, 13), (35, 30), (20, 21), (30, 25), (10, 24), (9, 24), (2, 8), (29, 16), (31, 5), (8, 9), (22, 25), (1, 15), (4, 25), (17, 26), (27, 15), (0, 30), (10, 7), (37, 14), (9, 1), (23, 30), (26, 22), (24, 16), (36, 19), (1, 25), (26, 4), (8, 11), (3, 20), (15, 12), (15, 23), (2, 25), (20, 18), (20, 11), (9, 22), (29, 25), (36, 24), (1, 5), (14, 6), (13, 4), (26, 31), (7, 17), (0, 15), (9, 2), (10, 14), (15, 2), (1, 12), (17, 27), (4, 11), (17, 4), (13, 21), (12, 9), (4, 8), (27, 8), (9, 10), (19, 3), (23, 26), (18, 32), (9, 32), (8, 26), (0, 2), (7, 16), (13, 6), (22, 18), (22, 2), (27, 10), (6, 28), (17, 16), (29, 20), (25, 25), (4, 17), (12, 27), (9, 4), (0, 18), (37, 3), (5, 4), (26, 14), (19, 16), (12, 0), (33, 2), (30, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "516132", "dataset": "MATH"}
{"messages": [{"content": "In a 38x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (5, 28), (17, 18), (5, 12), (37, 26), (34, 3), (29, 14), (27, 0), (15, 15), (29, 15), (11, 24), (33, 18), (20, 26), (14, 11), (23, 15), (18, 26), (33, 12), (16, 4), (29, 6), (9, 13), (26, 21), (30, 3), (20, 29), (37, 28), (3, 6), (32, 21), (25, 8), (14, 21), (28, 23), (20, 14), (37, 19), (12, 19), (23, 20), (33, 10), (28, 18), (15, 18), (28, 29), (2, 13), (33, 23), (5, 13), (21, 19), (2, 12), (23, 5), (32, 30), (26, 18), (35, 28), (30, 17), (30, 6), (27, 11), (15, 3), (33, 4), (15, 30), (20, 19), (10, 26), (15, 23), (3, 19), (12, 31), (6, 1), (10, 8), (33, 17), (12, 9), (12, 8), (21, 1), (0, 10), (3, 28), (30, 29), (2, 4), (29, 3), (17, 17), (0, 17), (11, 26), (20, 4), (3, 11), (7, 1), (8, 6), (0, 7), (32, 1), (16, 18), (7, 15), (37, 0), (27, 6), (35, 11), (23, 12), (7, 29), (24, 21), (5, 6), (11, 4), (9, 3), (22, 14), (23, 25), (20, 31), (33, 7), (24, 7), (22, 10), (25, 10), (17, 23), (22, 18), (34, 31), (31, 17), (27, 1), (20, 13), (36, 6), (0, 12), (16, 20), (29, 10), (20, 11), (19, 18), (35, 8), (25, 25), (17, 28), (11, 12), (25, 12), (21, 0), (8, 25), (22, 23), (21, 17), (31, 12), (10, 25), (5, 22), (7, 24), (7, 27), (18, 5), (17, 4), (13, 9), (27, 25), (25, 26), (6, 16), (0, 27), (12, 10), (16, 13), (36, 31), (32, 18), (0, 16), (28, 22), (6, 30), (4, 15), (37, 22), (26, 11), (23, 4), (28, 12), (22, 12), (12, 25), (27, 13), (13, 8), (34, 28), (23, 18), (3, 2), (18, 8), (4, 30), (30, 11), (15, 27), (5, 7), (1, 23), (0, 24), (34, 26), (15, 4), (30, 30), (7, 0), (37, 27), (27, 16), (13, 22), (26, 22), (20, 9), (1, 18), (8, 14), (31, 7), (6, 19), (13, 13), (6, 8), (16, 12), (28, 30), (18, 18), (20, 17), (17, 20), (24, 1), (5, 1), (32, 23), (14, 18), (9, 5), (37, 13), (22, 28), (15, 22), (34, 17), (2, 16), (13, 5), (30, 15), (29, 5), (5, 16), (30, 27), (31, 2), (4, 5), (25, 13), (2, 1), (19, 12), (20, 3), (31, 24), (32, 27), (23, 26), (19, 9), (1, 11), (18, 17), (16, 29), (6, 28), (21, 26), (0, 5), (16, 25), (18, 25), (17, 29), (26, 5), (17, 31), (1, 6), (34, 18), (18, 1), (13, 27), (3, 9), (19, 25), (23, 31), (18, 7), (23, 24), (20, 2), (22, 15), (24, 30), (18, 3), (23, 14), (11, 0), (4, 2), (31, 1), (4, 4), (16, 26), (10, 12), (10, 0), (18, 29), (15, 8), (33, 3), (37, 18), (2, 29), (30, 22), (21, 25), (33, 30), (32, 3), (21, 12), (12, 21), (23, 8), (24, 10), (1, 3), (13, 23), (17, 7), (4, 19), (19, 8), (2, 3), (27, 31), (26, 16), (2, 15), (16, 2), (10, 22), (26, 27), (22, 16), (36, 4), (36, 14), (24, 18), (16, 14), (21, 4), (30, 24), (21, 29), (29, 13), (24, 25), (13, 3), (5, 5), (27, 4), (35, 24), (15, 14), (31, 29), (20, 18), (18, 30), (35, 29), (30, 28), (10, 16), (32, 8), (2, 27), (15, 7), (36, 1), (10, 18), (9, 27), (2, 20), (35, 2), (12, 15), (37, 17), (4, 26), (35, 5), (6, 12), (35, 30), (31, 28), (35, 26), (13, 30), (13, 20), (32, 28), (21, 24), (34, 25), (9, 10), (8, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "903000", "dataset": "MATH"}
{"messages": [{"content": "In a 32x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (31, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 1), (24, 7), (7, 0), (23, 14), (18, 24), (20, 5), (3, 7), (0, 8), (5, 27), (17, 10), (6, 27), (28, 33), (4, 25), (1, 14), (11, 19), (30, 34), (4, 19), (15, 33), (14, 7), (23, 13), (2, 21), (27, 29), (13, 34), (13, 24), (3, 11), (26, 20), (23, 30), (1, 20), (21, 22), (28, 24), (27, 17), (20, 21), (28, 15), (27, 25), (20, 24), (6, 5), (26, 31), (8, 18), (19, 18), (1, 8), (16, 30), (22, 25), (22, 7), (25, 13), (2, 5), (3, 32), (1, 33), (2, 17), (29, 23), (24, 5), (31, 12), (21, 18), (26, 10), (18, 18), (30, 27), (20, 15), (14, 27), (14, 3), (30, 29), (7, 9), (23, 24), (7, 30), (7, 11), (27, 19), (23, 0), (18, 15), (3, 1), (25, 29), (28, 12), (24, 23), (28, 27), (10, 33), (31, 13), (27, 10), (25, 30), (20, 25), (17, 8), (5, 24), (29, 18), (17, 23), (30, 4), (29, 17), (21, 30), (26, 7), (5, 25), (4, 5), (27, 2), (16, 2), (0, 9), (8, 30), (18, 2), (28, 16), (30, 22), (10, 9), (17, 15), (28, 25), (3, 0), (11, 11), (9, 12), (14, 6), (14, 33), (1, 5), (8, 24), (27, 7), (9, 23), (25, 6), (8, 9), (15, 18), (10, 4), (9, 21), (25, 16), (16, 34), (10, 17), (11, 22), (15, 20), (29, 32), (4, 9), (8, 28), (28, 1), (11, 32), (29, 16), (16, 22), (27, 14), (21, 11), (15, 6), (27, 16), (14, 30), (18, 9), (28, 26), (13, 29), (21, 24), (10, 1), (20, 1), (4, 10), (1, 10), (17, 27), (2, 29), (8, 7), (24, 19), (13, 23), (18, 1), (29, 14), (14, 17), (3, 33), (16, 32), (17, 34), (23, 32), (5, 3), (17, 24), (26, 19), (2, 0), (9, 30), (21, 7), (27, 24), (14, 23), (17, 0), (26, 13), (1, 26), (9, 9), (7, 1), (12, 32), (24, 13), (26, 9), (8, 21), (14, 5), (0, 29), (18, 14), (2, 7), (25, 12), (7, 22), (21, 29), (11, 8), (7, 23), (3, 4), (21, 15), (4, 28), (21, 31), (25, 23), (21, 26), (16, 16), (19, 31), (4, 16), (19, 33), (19, 4), (18, 7), (1, 1), (6, 18), (7, 19), (3, 20), (8, 26), (16, 26), (16, 4), (20, 14), (20, 32), (1, 11), (22, 20), (10, 27), (17, 32), (7, 27), (21, 14), (24, 2), (8, 22), (8, 34), (30, 13), (24, 30), (17, 3), (11, 4), (16, 20), (20, 18), (10, 13), (6, 15), (30, 15), (28, 32), (18, 28), (29, 9), (9, 8), (30, 5), (3, 22), (12, 33), (4, 26), (19, 12), (6, 9), (24, 34), (26, 14), (3, 25), (17, 9), (0, 16), (18, 31), (13, 11), (31, 31), (1, 24), (14, 34), (9, 14), (19, 2), (22, 19), (3, 15), (11, 1), (8, 29), (12, 27), (22, 27), (24, 17), (8, 6), (16, 0), (9, 7), (21, 28), (23, 15), (12, 4), (11, 28), (29, 4), (25, 31), (25, 5), (31, 21), (12, 16), (7, 15), (1, 25), (28, 3), (28, 0), (29, 2), (18, 26), (30, 7), (24, 10), (6, 3), (20, 4), (25, 14), (9, 4), (29, 21), (22, 8), (5, 9), (29, 8), (18, 4), (29, 29), (25, 7), (27, 0), (9, 16), (29, 20), (31, 26), (27, 23), (17, 7), (18, 5), (17, 16), (1, 12), (20, 0), (12, 12), (22, 32), (30, 2), (9, 27), (28, 10), (22, 24), (22, 4), (10, 5), (23, 19), (6, 25), (11, 34), (15, 16), (0, 15), (14, 32), (23, 8), (7, 20), (3, 30), (11, 12), (23, 28), (11, 5), (9, 32), (0, 12), (30, 8), (5, 4), (17, 21), (4, 32), (12, 23), (11, 29), (9, 1), (7, 29), (16, 6), (25, 1), (9, 0), (6, 20), (31, 3), (19, 22), (12, 28), (6, 26), (8, 3), (9, 13), (27, 1), (23, 22), (21, 16), (28, 21), (27, 27)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "877464", "dataset": "MATH"}
{"messages": [{"content": "In a 36x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (12, 32), (3, 18), (8, 37), (13, 14), (0, 14), (25, 35), (8, 34), (28, 17), (32, 4), (20, 3), (21, 30), (31, 29), (7, 27), (17, 31), (33, 34), (24, 8), (31, 3), (15, 6), (26, 5), (15, 16), (29, 7), (13, 12), (13, 33), (15, 3), (9, 35), (15, 7), (15, 25), (26, 18), (35, 23), (24, 1), (13, 9), (9, 30), (4, 22), (17, 10), (21, 27), (13, 6), (15, 13), (3, 20), (26, 17), (26, 23), (17, 25), (29, 30), (7, 8), (31, 33), (27, 7), (13, 23), (17, 35), (11, 31), (21, 31), (4, 10), (20, 22), (8, 8), (29, 19), (20, 10), (11, 8), (25, 26), (1, 26), (11, 22), (27, 38), (22, 3), (21, 2), (33, 36), (21, 22), (25, 30), (31, 34), (7, 34), (1, 37), (2, 27), (29, 28), (2, 26), (11, 14), (6, 29), (31, 14), (29, 15), (13, 20), (31, 11), (35, 29), (21, 1), (1, 25), (27, 15), (23, 17), (26, 30), (16, 25), (13, 29), (8, 4), (24, 29), (34, 20), (31, 7), (11, 29), (27, 0), (5, 13), (15, 32), (14, 13), (35, 10), (19, 19), (17, 30), (19, 4), (5, 21), (26, 10), (2, 12), (17, 24), (18, 7), (1, 5), (0, 15), (19, 37), (20, 17), (29, 16), (8, 0), (18, 19), (21, 34), (7, 3), (27, 8), (24, 32), (4, 17), (23, 37), (25, 5), (17, 0), (6, 24), (12, 4), (10, 19), (26, 4), (5, 24), (13, 25), (18, 3), (26, 13), (5, 16), (12, 29), (32, 8), (4, 3), (35, 37), (15, 35), (19, 8), (17, 28), (30, 25), (3, 33), (0, 18), (8, 29), (9, 11), (13, 2), (8, 5), (35, 6), (9, 16), (0, 11), (2, 23), (7, 32), (35, 26), (3, 15), (17, 29), (30, 1), (31, 20), (14, 36), (24, 34), (12, 16), (2, 35), (22, 2), (17, 19), (5, 6), (4, 6), (2, 9), (6, 30), (6, 28), (8, 21), (1, 30), (5, 12), (13, 17), (22, 31), (14, 31), (24, 20), (34, 30), (3, 11), (23, 14), (18, 38), (23, 33), (13, 32), (33, 23), (15, 20), (17, 9), (35, 8), (20, 26), (10, 11), (23, 12), (9, 28), (18, 31), (2, 3), (35, 25), (25, 6), (20, 15), (32, 33), (34, 18), (21, 11), (6, 25), (6, 10), (8, 25), (32, 34), (30, 4), (20, 16), (4, 0), (34, 14), (34, 26), (7, 28), (20, 11), (34, 34), (0, 2), (10, 38), (6, 38), (16, 4), (15, 37), (24, 27), (34, 5), (4, 2), (21, 19), (1, 19), (17, 4), (34, 22), (34, 13), (9, 27), (0, 29), (29, 2), (33, 20), (13, 3), (25, 33), (22, 0), (8, 27), (2, 36), (29, 29), (0, 26), (16, 11), (0, 13), (30, 31), (30, 5), (27, 14), (26, 11), (6, 1), (27, 36), (3, 12), (33, 35), (31, 6), (28, 30), (27, 28), (4, 9), (1, 17), (11, 9), (30, 2), (23, 0), (8, 28), (32, 32), (34, 23), (11, 20), (33, 37), (17, 5), (2, 22), (32, 18), (27, 5), (17, 3), (3, 13), (6, 6), (35, 15), (7, 26), (7, 14), (20, 28), (6, 11), (3, 27), (2, 34), (5, 7), (3, 32), (20, 9), (9, 5), (25, 31), (27, 13), (7, 24), (10, 24), (14, 12), (13, 38), (1, 38), (14, 15), (19, 0), (11, 4), (25, 7), (4, 7), (9, 3), (17, 13), (24, 11), (3, 30), (28, 13), (23, 23), (15, 38), (15, 18), (13, 4), (9, 13), (27, 6), (19, 33), (34, 24), (25, 23), (35, 13), (4, 15), (20, 14), (16, 36), (21, 7), (26, 3), (29, 3), (20, 23), (12, 2), (17, 36), (16, 12), (30, 8), (22, 23), (23, 30), (7, 30), (8, 26), (29, 24), (19, 5), (0, 23), (12, 23), (19, 30), (20, 1), (33, 12), (17, 27), (25, 38), (21, 10), (5, 17), (14, 6), (12, 24), (0, 21), (6, 26), (16, 32), (30, 27), (14, 23), (29, 13), (11, 21), (7, 21), (25, 21), (9, 36), (2, 0), (11, 1), (13, 7), (9, 7), (6, 3), (7, 15), (3, 19), (9, 14), (24, 24), (19, 25), (26, 2), (14, 11), (34, 0), (6, 12), (18, 15), (25, 11), (15, 19), (6, 13), (9, 21), (10, 6), (28, 33), (2, 7), (7, 6), (10, 18), (4, 30), (10, 4), (21, 28), (12, 12), (8, 6), (15, 9), (27, 29), (35, 3), (32, 14), (32, 20), (3, 21), (16, 28), (27, 10), (34, 37), (32, 25), (5, 32), (25, 10), (23, 7), (14, 3), (19, 23), (15, 27), (25, 27), (19, 3), (31, 38), (5, 10), (25, 15), (9, 6), (23, 3), (28, 36), (6, 34), (31, 26), (11, 13), (10, 17), (24, 35), (30, 26), (1, 4), (14, 19), (1, 23), (8, 3), (30, 28), (13, 34), (8, 10), (31, 22), (16, 29), (4, 37), (2, 17), (1, 27), (16, 3), (24, 33), (3, 9), (0, 1)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "687024", "dataset": "MATH"}
{"messages": [{"content": "In a 38x36 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 35), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (4, 25), (25, 25), (11, 28), (6, 34), (4, 13), (16, 18), (9, 33), (3, 30), (31, 24), (19, 31), (31, 12), (10, 2), (5, 14), (28, 21), (35, 6), (0, 23), (6, 31), (19, 33), (18, 16), (28, 27), (32, 32), (26, 33), (31, 3), (5, 32), (14, 3), (16, 14), (32, 5), (16, 28), (7, 15), (9, 27), (30, 0), (6, 12), (1, 5), (5, 30), (1, 33), (4, 34), (36, 11), (1, 12), (34, 19), (32, 26), (35, 15), (16, 22), (36, 21), (11, 16), (31, 2), (11, 23), (9, 32), (0, 8), (18, 32), (30, 19), (23, 35), (35, 10), (28, 6), (7, 23), (28, 9), (33, 6), (4, 2), (34, 24), (29, 29), (7, 17), (21, 35), (28, 32), (30, 33), (6, 25), (19, 20), (23, 2), (25, 9), (31, 8), (14, 27), (18, 6), (10, 6), (34, 18), (18, 4), (17, 17), (26, 27), (15, 4), (25, 4), (7, 21), (28, 24), (7, 24), (32, 3), (25, 7), (32, 11), (6, 28), (31, 4), (0, 16), (20, 2), (0, 17), (21, 9), (0, 31), (3, 5), (36, 5), (10, 15), (0, 3), (22, 22), (23, 3), (22, 17), (24, 12), (7, 7), (33, 26), (7, 25), (2, 1), (18, 18), (27, 27), (34, 9), (4, 0), (35, 30), (33, 23), (22, 18), (33, 32), (2, 9), (12, 1), (35, 5), (9, 23), (17, 1), (27, 31), (8, 29), (2, 16), (13, 19), (37, 24), (15, 8), (2, 27), (20, 14), (31, 22), (5, 24), (15, 14), (23, 5), (22, 26), (15, 10), (11, 32), (25, 8), (5, 23), (33, 8), (20, 31), (30, 35), (14, 4), (7, 19), (36, 30), (12, 3), (35, 8), (17, 2), (9, 30), (35, 3), (30, 27), (30, 18), (22, 12), (11, 12), (6, 14), (29, 24), (22, 13), (8, 4), (19, 21), (4, 10), (28, 5), (22, 31), (8, 7), (14, 25), (5, 9), (36, 7), (32, 16), (32, 33), (4, 14), (5, 4), (17, 10), (20, 16), (19, 17), (37, 25), (6, 10), (17, 25), (35, 29), (22, 32), (33, 14), (25, 30), (7, 11), (3, 12), (31, 6), (29, 15), (8, 31), (28, 7), (22, 15), (25, 5), (25, 27), (29, 20), (28, 28), (35, 13), (5, 16), (0, 14), (27, 21), (6, 11), (23, 32), (33, 18), (17, 19), (31, 34), (8, 13), (19, 28), (26, 5), (18, 26), (4, 8), (2, 15), (0, 24), (26, 26), (36, 17), (3, 24), (15, 1), (12, 7), (33, 16), (27, 5), (7, 13), (7, 6), (15, 29), (19, 34), (24, 19), (1, 30), (1, 27), (30, 21), (19, 8), (17, 13), (3, 20), (11, 2), (14, 9), (14, 1), (17, 15), (18, 31), (15, 20), (36, 32), (18, 2), (5, 27), (37, 26), (31, 1), (11, 35), (32, 30), (17, 9), (14, 5), (7, 34), (28, 22), (34, 2), (20, 27), (3, 23), (31, 16), (9, 24), (4, 21), (13, 21), (26, 30), (10, 8), (28, 17), (14, 14), (13, 10), (8, 12), (18, 5), (11, 24), (31, 21), (30, 11), (31, 17), (25, 24), (3, 34), (7, 20), (18, 15), (2, 17), (3, 22), (0, 13), (22, 29), (32, 18), (14, 28), (19, 14), (2, 22), (26, 10), (11, 13), (21, 20), (10, 29), (31, 13), (35, 24), (20, 3), (24, 27), (6, 22), (9, 18), (8, 11), (12, 4), (2, 29), (32, 1), (37, 29), (21, 16), (31, 19), (35, 28), (16, 4), (2, 20), (5, 22), (26, 21), (5, 8), (19, 35), (7, 1), (8, 24), (17, 30), (20, 17), (24, 33), (22, 33), (14, 35), (7, 16), (20, 22), (29, 0), (3, 35), (8, 23), (29, 5), (6, 6), (6, 19), (7, 0), (35, 17), (37, 31), (8, 34), (34, 34), (20, 30), (13, 17), (20, 25), (30, 13), (30, 17), (25, 29), (26, 28), (27, 34), (8, 25), (11, 11), (1, 23), (8, 19), (14, 24), (36, 12), (21, 18), (15, 34), (29, 8), (16, 16), (27, 32), (20, 6), (0, 35), (26, 3), (17, 14), (13, 7), (29, 19), (21, 32), (28, 10), (15, 18), (37, 15), (17, 18), (27, 11), (7, 14), (1, 1), (31, 0), (4, 28), (7, 31), (23, 24), (30, 4), (16, 31), (24, 20), (8, 27), (25, 32), (22, 0), (31, 27), (16, 2), (18, 34), (21, 31), (34, 5), (25, 33), (9, 35), (2, 26), (2, 6), (11, 17), (31, 5), (10, 11), (22, 2), (26, 11), (37, 10), (8, 10), (12, 28), (36, 25), (23, 33), (30, 9), (35, 34), (13, 1), (37, 17), (19, 9), (25, 0), (0, 9), (22, 14), (5, 18), (12, 26), (19, 26), (21, 1), (29, 32), (22, 6), (30, 20), (4, 30), (36, 16), (22, 20), (29, 1), (0, 22), (21, 29), (30, 31), (10, 21), (17, 33), (6, 4), (25, 28), (7, 10), (29, 25), (24, 29), (24, 17), (20, 7), (30, 3), (33, 25), (8, 20), (11, 31), (35, 35), (24, 11), (3, 10), (20, 20), (28, 2), (33, 27), (2, 7), (30, 14), (6, 17), (35, 18), (16, 9), (30, 29), (6, 21), (8, 8), (13, 5), (6, 33), (6, 16), (31, 10), (0, 27), (28, 4), (35, 32), (36, 35), (21, 12), (16, 12), (36, 13), (1, 19), (29, 18), (29, 30), (6, 15), (31, 35), (1, 8), (34, 11), (1, 7), (11, 21), (21, 5), (4, 24), (37, 28), (31, 11), (21, 0), (21, 19), (10, 5), (26, 1), (23, 19), (13, 6), (4, 16), (29, 4), (37, 12), (37, 1), (3, 31), (8, 3), (15, 19), (30, 10), (6, 13), (26, 13), (37, 13), (21, 14), (14, 16), (14, 13), (8, 21), (37, 22), (7, 32), (27, 19), (5, 0), (13, 2), (5, 2), (21, 23), (32, 10), (21, 2), (23, 31), (22, 8), (24, 8), (35, 26), (10, 19), (11, 10)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "599676", "dataset": "MATH"}
{"messages": [{"content": "In a 33x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (32, 36), 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, 11), (25, 4), (20, 4), (23, 17), (24, 32), (26, 13), (9, 1), (17, 29), (6, 28), (22, 17), (23, 19), (20, 20), (24, 31), (12, 14), (6, 5), (22, 5), (18, 0), (9, 17), (24, 4), (0, 11), (31, 3), (10, 23), (6, 13), (7, 27), (15, 4), (3, 23), (1, 32), (7, 36), (1, 16), (6, 26), (3, 28), (31, 35), (24, 25), (12, 5), (21, 2), (14, 32), (3, 5), (2, 35), (22, 25), (28, 8), (1, 29), (2, 0), (2, 32), (15, 1), (1, 8), (22, 4), (30, 25), (9, 28), (11, 18), (25, 20), (19, 21), (15, 28), (24, 12), (13, 3), (21, 7), (7, 25), (9, 9), (10, 16), (7, 21), (1, 9), (25, 3), (13, 34), (2, 13), (21, 34), (11, 0), (16, 12), (11, 24), (27, 8), (15, 7), (14, 18), (8, 22), (4, 5), (22, 12), (6, 36), (24, 16), (28, 29), (7, 2), (20, 22), (12, 9), (10, 29), (21, 25), (5, 11), (17, 5), (8, 21), (16, 28), (32, 3), (30, 12), (0, 4), (9, 29), (25, 27), (8, 35), (5, 25), (19, 10), (19, 36), (4, 35), (21, 8), (25, 26), (26, 19), (22, 15), (15, 17), (12, 21), (4, 1), (27, 34), (15, 9), (20, 28), (8, 33), (25, 34), (27, 13), (9, 6), (12, 24), (22, 2), (3, 15), (20, 6), (23, 23), (13, 7), (32, 32), (23, 14), (8, 10), (4, 18), (5, 6), (31, 34), (5, 0), (18, 30), (6, 23), (2, 21), (11, 16), (9, 5), (2, 34), (7, 0), (26, 30), (21, 32), (21, 23), (28, 19), (22, 13), (31, 7), (20, 30), (30, 13), (11, 2), (31, 19), (20, 15), (2, 12), (24, 2), (12, 12), (19, 28), (27, 36), (17, 12), (19, 6), (30, 11), (6, 6), (18, 18), (27, 25), (19, 32), (32, 19), (24, 0), (19, 5), (21, 28), (21, 4), (32, 33), (17, 18), (16, 24), (23, 6), (25, 13), (18, 25), (5, 17), (8, 13), (30, 1), (32, 18), (25, 35), (17, 23), (5, 26), (8, 20), (24, 19), (5, 33), (4, 23), (5, 2), (5, 1), (32, 25), (22, 30), (17, 26), (7, 12), (8, 25), (26, 24), (30, 24), (31, 5), (0, 20), (10, 27), (13, 4), (23, 16), (13, 21), (2, 4), (12, 11), (1, 19), (13, 20), (17, 17), (30, 6), (17, 35), (9, 14), (32, 22), (9, 3), (14, 26), (28, 18), (15, 21), (27, 22), (17, 22), (20, 11), (7, 30), (23, 5), (32, 34), (21, 19), (9, 11), (15, 31), (22, 34), (21, 9), (17, 13), (17, 30), (20, 33), (26, 2), (32, 31), (30, 2), (19, 4), (2, 33), (9, 25), (1, 25), (19, 7), (25, 25), (16, 32), (21, 35), (6, 12), (23, 25), (16, 19), (27, 10), (2, 15), (32, 21), (27, 33), (6, 3), (16, 7), (28, 5), (29, 13), (1, 23), (27, 4), (30, 16), (28, 35), (7, 15), (16, 3), (21, 3), (12, 4), (25, 8), (3, 1), (11, 28), (20, 14), (25, 23), (30, 15), (9, 12), (32, 10), (2, 30), (1, 28), (29, 21), (17, 8), (19, 9), (3, 35), (28, 27), (4, 25), (9, 35), (10, 13), (1, 36), (14, 14), (11, 30), (23, 8), (30, 23), (1, 30), (6, 24), (13, 0), (13, 12), (14, 35), (10, 18), (28, 20), (19, 19), (15, 14), (4, 27), (3, 14), (23, 27), (27, 5), (16, 33), (13, 16), (3, 24), (14, 21), (8, 9), (0, 26), (1, 33), (11, 10), (32, 5), (27, 0), (26, 7), (20, 3), (4, 22), (2, 6), (23, 15), (1, 21), (2, 36), (20, 24), (31, 22), (10, 31), (15, 32), (12, 32), (30, 19), (24, 34), (26, 31), (2, 22), (21, 20), (1, 18), (19, 22), (13, 15), (25, 19), (27, 17), (26, 17), (11, 5), (12, 3), (4, 26), (19, 27), (5, 7), (24, 6), (6, 8), (0, 29), (11, 3), (30, 22), (20, 23), (5, 18), (16, 36), (7, 16), (22, 10), (15, 19), (14, 24), (1, 15), (27, 1), (18, 21), (15, 20), (19, 23), (23, 7), (28, 34), (2, 31), (13, 30), (30, 18), (7, 17), (17, 6), (19, 1), (28, 14), (16, 8), (24, 17), (16, 18), (28, 26), (18, 15), (13, 29), (7, 31), (20, 13), (21, 26), (16, 1), (8, 8), (15, 13), (1, 5), (9, 10), (10, 19), (27, 26), (12, 36), (25, 15), (24, 21), (32, 1), (11, 11), (15, 24), (25, 7), (31, 30), (10, 25), (4, 13), (9, 13), (11, 6), (18, 8), (23, 28), (26, 15), (24, 8), (20, 2), (7, 24), (5, 32), (28, 31), (9, 23), (8, 18), (0, 24), (7, 22), (18, 3), (30, 0), (18, 33), (26, 1), (20, 29), (24, 13), (7, 29), (0, 9), (30, 4), (2, 16), (3, 3), (3, 8), (30, 7), (29, 16), (18, 14), (5, 14), (28, 33), (11, 14), (25, 16), (16, 2), (26, 32), (20, 21), (21, 14), (20, 19), (31, 17), (28, 25), (18, 6), (26, 5), (18, 32), (6, 2), (1, 11), (17, 14), (32, 8), (24, 23), (13, 35), (8, 3), (9, 26), (0, 25), (21, 0), (31, 2), (14, 31), (8, 2), (3, 0), (0, 6), (8, 11), (28, 23), (8, 28), (0, 31), (8, 17), (18, 5), (6, 34), (30, 3), (28, 4), (16, 29), (3, 30), (20, 25), (19, 25), (23, 33), (3, 20), (28, 11), (30, 30), (32, 6), (12, 1), (14, 11)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "984960", "dataset": "MATH"}
{"messages": [{"content": "In a 36x37 grid, how many different paths are there from the bottom left (0, 0) to the top right (35, 36), 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), (25, 4), (34, 5), (17, 32), (9, 5), (8, 16), (27, 20), (28, 30), (30, 24), (23, 19), (0, 3), (26, 29), (35, 3), (28, 33), (4, 13), (21, 2), (18, 4), (23, 4), (33, 28), (32, 29), (22, 1), (33, 20), (17, 18), (8, 23), (10, 22), (3, 5), (34, 6), (0, 28), (33, 27), (32, 1), (2, 0), (18, 28), (27, 34), (9, 31), (13, 23), (19, 18), (12, 2), (23, 15), (30, 9), (13, 7), (8, 18), (14, 21), (8, 29), (32, 4), (27, 10), (11, 26), (2, 20), (30, 33), (31, 3), (28, 7), (26, 36), (15, 27), (10, 23), (14, 4), (13, 4), (26, 28), (9, 14), (8, 2), (23, 21), (13, 8), (33, 17), (23, 14), (29, 6), (21, 5), (12, 25), (1, 30), (1, 27), (14, 1), (20, 22), (31, 35), (14, 16), (2, 4), (16, 7), (1, 20), (30, 6), (4, 27), (6, 30), (11, 22), (22, 13), (15, 29), (3, 0), (11, 16), (2, 23), (28, 3), (28, 13), (28, 21), (23, 3), (18, 8), (19, 24), (22, 29), (35, 16), (20, 14), (16, 5), (5, 16), (7, 23), (1, 6), (29, 2), (8, 33), (7, 16), (20, 17), (14, 33), (29, 0), (29, 30), (2, 30), (33, 0), (12, 28), (23, 1), (4, 29), (21, 11), (29, 21), (19, 28), (3, 14), (22, 16), (7, 9), (21, 1), (16, 34), (26, 33), (35, 8), (33, 7), (33, 21), (31, 34), (11, 17), (12, 23), (4, 7), (12, 10), (10, 36), (24, 15), (23, 6), (5, 31), (15, 4), (9, 34), (31, 7), (17, 1), (15, 10), (4, 15), (30, 26), (2, 18), (6, 7), (24, 21), (10, 24), (8, 36), (6, 22), (18, 35), (30, 30), (33, 5), (10, 6), (31, 23), (8, 8), (29, 18), (22, 19), (8, 9), (12, 21), (19, 16), (1, 0), (35, 32), (25, 9), (27, 13), (34, 0), (26, 7), (31, 8), (9, 32), (28, 28), (8, 0), (1, 10), (25, 7), (16, 33), (21, 32), (34, 8), (15, 32), (25, 23), (33, 35), (15, 24), (10, 15), (20, 4), (0, 4), (22, 7), (21, 18), (12, 31), (9, 7), (21, 9), (23, 20), (14, 24), (22, 26), (27, 35), (20, 34), (17, 33), (24, 5), (6, 13), (30, 32), (10, 16), (32, 36), (23, 7), (27, 25), (22, 8), (7, 28), (20, 21), (0, 29), (25, 19), (5, 0), (1, 18), (21, 36), (16, 12), (3, 4), (2, 12), (32, 9), (26, 4), (1, 36), (13, 5), (27, 1), (17, 10), (24, 28), (28, 35), (35, 33), (19, 7), (11, 4), (8, 19), (20, 26), (9, 25), (13, 16), (26, 32), (23, 17), (8, 21), (14, 18), (31, 19), (28, 20), (22, 35), (10, 5), (31, 31), (14, 31), (5, 14), (6, 33), (9, 28), (11, 18), (14, 25), (32, 35), (12, 0), (16, 19), (32, 21), (28, 0), (32, 7), (17, 3), (18, 31), (32, 6), (24, 25), (19, 20), (10, 0), (5, 1), (20, 36), (8, 30), (24, 8), (4, 26), (13, 15), (6, 25), (25, 11), (29, 25), (2, 27), (18, 10), (33, 30), (12, 7), (14, 9), (5, 9), (0, 6), (0, 18), (3, 7), (10, 32), (26, 22), (3, 17), (30, 5), (10, 13), (9, 21), (12, 12), (25, 13), (20, 30), (24, 0), (27, 33), (4, 28), (7, 31), (15, 18), (8, 13), (18, 36), (12, 17), (22, 24), (15, 23), (12, 30), (30, 13), (6, 5), (25, 33), (20, 25), (9, 26), (26, 20), (29, 36), (27, 36), (17, 24), (15, 16), (2, 21), (33, 1), (3, 21), (13, 32), (23, 30), (10, 31), (22, 10), (28, 14), (25, 0), (2, 7), (1, 16), (24, 7), (17, 19), (27, 3), (33, 10), (17, 21), (15, 21), (35, 22), (1, 19), (18, 21), (20, 29), (10, 28), (0, 5), (21, 14), (1, 2), (6, 34), (30, 11), (34, 33), (0, 14), (28, 8), (11, 25), (31, 11), (25, 29), (34, 15), (18, 19), (22, 22), (5, 17), (28, 4), (29, 1), (18, 26), (5, 4), (12, 3), (13, 36), (29, 9), (8, 15), (6, 3), (25, 28), (27, 23), (1, 31), (12, 9), (35, 6), (33, 33), (7, 33), (21, 3), (17, 0), (18, 13), (3, 27), (4, 30), (2, 32), (6, 15), (27, 24), (0, 34), (29, 26)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590976", "dataset": "MATH"}
{"messages": [{"content": "In a 39x35 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 34), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (28, 31), (24, 18), (9, 2), (0, 18), (24, 31), (19, 31), (24, 32), (7, 16), (38, 7), (32, 26), (22, 26), (14, 24), (34, 4), (17, 3), (14, 7), (12, 22), (13, 26), (38, 16), (35, 6), (1, 22), (5, 7), (10, 33), (38, 15), (25, 32), (8, 18), (20, 18), (14, 10), (18, 3), (19, 2), (19, 12), (25, 22), (19, 3), (8, 9), (18, 33), (6, 4), (2, 33), (14, 34), (2, 22), (21, 7), (29, 4), (25, 2), (22, 1), (24, 15), (6, 29), (20, 32), (11, 32), (14, 11), (4, 27), (4, 25), (10, 2), (5, 14), (36, 28), (13, 30), (0, 23), (25, 24), (18, 6), (2, 11), (19, 10), (22, 10), (29, 12), (35, 1), (17, 15), (25, 11), (19, 1), (13, 1), (2, 8), (17, 19), (13, 10), (38, 30), (5, 28), (33, 23), (31, 17), (28, 24), (37, 0), (15, 23), (13, 31), (10, 24), (23, 33), (33, 0), (28, 26), (34, 26), (3, 31), (19, 19), (9, 3), (15, 6), (34, 22), (22, 5), (16, 1), (33, 32), (28, 0), (25, 34), (13, 28), (28, 21), (17, 10), (12, 5), (9, 6), (36, 25), (6, 23), (22, 22), (23, 3), (7, 20), (2, 27), (15, 24), (26, 32), (6, 16), (36, 22), (20, 31), (19, 7), (9, 10), (24, 10), (0, 16), (0, 9), (8, 32), (15, 0), (26, 21), (23, 6), (6, 19), (20, 6), (7, 5), (1, 27), (23, 5), (17, 11), (20, 30), (35, 28), (8, 10), (5, 9), (33, 16), (17, 31), (7, 6), (15, 10), (11, 18), (14, 20), (5, 15), (6, 30), (26, 19), (36, 0), (19, 11), (28, 30), (36, 23), (35, 30), (5, 3), (10, 20), (34, 18), (6, 13), (20, 1), (28, 3), (6, 10), (18, 27), (19, 29), (16, 30), (4, 32), (1, 4), (16, 17), (11, 14), (11, 17), (9, 5), (13, 5), (28, 11), (13, 22), (22, 28), (37, 3), (32, 16), (24, 5), (14, 32), (36, 7), (37, 32), (35, 13), (2, 4), (12, 9), (5, 21), (5, 19), (21, 9), (32, 8), (37, 17), (11, 34), (34, 8), (17, 28), (18, 24), (33, 30), (21, 23), (13, 29), (2, 21), (17, 0), (6, 18), (15, 1), (19, 14), (22, 29), (5, 2), (4, 33), (27, 15), (4, 11), (27, 19), (5, 30), (36, 6), (17, 1), (2, 30), (11, 31), (12, 11), (11, 26), (34, 23), (35, 18), (32, 1), (5, 11), (33, 10), (8, 19), (4, 21), (29, 7), (18, 1), (20, 8), (4, 5), (22, 31), (3, 15), (15, 2), (21, 34), (15, 18), (5, 4), (14, 25), (11, 10), (20, 19), (7, 4), (4, 6), (24, 25), (31, 33), (14, 26), (30, 4), (20, 11), (29, 21), (30, 29), (4, 8), (32, 3), (31, 3), (12, 17), (36, 27), (6, 2), (16, 7), (29, 34), (9, 21), (32, 29), (0, 6), (11, 11), (22, 9), (36, 10), (2, 31), (29, 29), (5, 6), (32, 31), (37, 6), (1, 23), (32, 27), (24, 23), (8, 23), (31, 20), (6, 7), (33, 2), (30, 26), (18, 8), (31, 14), (37, 30), (13, 6), (20, 0), (2, 10), (27, 13), (18, 4), (12, 21), (36, 19), (21, 11), (19, 22), (22, 4), (30, 20), (32, 33), (9, 16), (15, 21), (6, 24), (35, 20), (1, 24), (29, 27), (14, 18), (9, 30), (1, 20), (15, 19), (1, 26), (3, 27), (27, 7), (1, 18), (26, 15), (36, 33), (16, 14), (0, 27), (32, 9), (28, 33), (21, 31), (16, 10), (3, 9), (6, 3), (28, 13), (38, 9), (5, 33), (22, 8), (13, 33), (21, 24), (14, 0), (24, 4), (1, 12), (7, 29), (19, 0), (31, 5), (4, 31), (25, 19), (19, 25), (21, 27), (8, 7), (7, 15), (10, 16), (33, 26), (32, 15), (24, 2), (8, 0), (24, 19), (37, 28), (36, 34), (38, 6), (22, 14), (25, 1), (34, 9), (22, 2), (10, 29), (3, 1), (16, 34), (20, 25), (23, 0), (1, 10), (23, 15), (18, 23), (37, 11), (20, 12), (0, 34), (33, 25), (1, 15), (18, 28), (36, 20), (23, 28), (31, 4), (20, 29), (2, 18), (37, 1), (17, 2), (31, 32), (22, 34), (19, 21), (37, 22), (4, 19), (28, 27), (23, 32), (17, 25), (24, 26), (12, 32), (3, 2), (31, 25), (3, 30), (16, 19), (27, 34), (14, 14), (37, 33), (9, 31), (6, 27), (21, 17), (7, 19), (12, 34), (23, 12), (17, 26), (37, 13), (9, 32), (28, 7), (29, 11), (32, 6), (27, 10), (17, 24), (25, 14), (13, 13), (23, 16), (38, 23), (26, 1), (23, 18), (28, 5), (35, 23), (18, 32), (32, 13), (7, 27), (17, 6), (13, 8)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176544", "dataset": "MATH"}
{"messages": [{"content": "In a 35x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (34, 33), 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), (5, 23), (22, 11), (26, 6), (13, 9), (15, 31), (31, 15), (4, 16), (4, 8), (15, 27), (30, 14), (0, 21), (12, 8), (4, 31), (4, 24), (24, 23), (1, 28), (26, 30), (5, 6), (0, 2), (24, 25), (4, 27), (14, 27), (10, 10), (27, 10), (15, 22), (13, 7), (6, 33), (18, 4), (27, 7), (8, 17), (10, 1), (20, 31), (6, 24), (31, 20), (31, 16), (33, 21), (9, 20), (21, 13), (5, 32), (2, 14), (5, 25), (1, 19), (9, 5), (22, 14), (20, 15), (22, 8), (16, 30), (2, 22), (25, 20), (13, 24), (22, 0), (19, 17), (16, 31), (1, 12), (22, 30), (32, 25), (11, 9), (23, 24), (28, 2), (7, 14), (18, 26), (28, 22), (19, 28), (13, 14), (0, 22), (19, 10), (3, 11), (25, 33), (20, 13), (34, 0), (22, 28), (9, 32), (9, 4), (33, 12), (17, 30), (25, 1), (1, 23), (17, 32), (7, 16), (19, 7), (20, 30), (26, 23), (29, 1), (13, 33), (3, 21), (11, 7), (0, 8), (21, 15), (6, 23), (21, 28), (13, 31), (11, 25), (3, 28), (1, 11), (18, 9), (23, 13), (21, 27), (19, 8), (18, 32), (4, 30), (29, 30), (18, 23), (23, 6), (34, 22), (26, 27), (33, 19), (27, 16), (34, 8), (34, 2), (18, 0), (2, 13), (23, 1), (14, 33), (5, 11), (10, 7), (33, 33), (9, 23), (32, 33), (34, 23), (9, 1), (25, 29), (10, 33), (32, 30), (34, 5), (34, 25), (27, 5), (9, 15), (10, 14), (26, 24), (17, 6), (13, 23), (6, 17), (19, 5), (2, 6), (28, 8), (24, 18), (31, 9), (29, 6), (21, 1), (29, 17), (23, 8), (16, 20), (3, 12), (1, 17), (2, 30), (14, 4), (18, 21), (2, 28), (13, 4), (28, 1), (6, 14), (5, 28), (28, 18), (34, 29), (28, 29), (8, 23), (4, 32), (15, 18), (16, 8), (17, 23), (6, 1), (20, 26), (21, 10), (4, 14), (24, 4), (16, 18), (22, 15), (16, 16), (8, 7), (18, 11), (12, 10), (9, 29), (14, 24), (5, 8), (22, 16), (26, 11), (26, 25), (29, 25), (15, 8), (18, 30), (29, 19), (20, 21), (15, 15), (32, 26), (14, 21), (8, 15), (4, 25), (0, 32), (2, 24), (4, 0), (30, 5), (13, 20), (12, 16), (24, 31), (2, 27), (28, 20), (15, 13), (10, 24), (1, 25), (12, 30), (2, 5), (29, 24), (4, 7), (4, 23), (5, 10), (7, 32), (24, 26), (31, 17), (13, 22), (3, 29), (22, 33), (14, 13), (16, 6), (16, 14), (12, 25), (14, 25), (7, 4), (33, 3), (2, 8), (26, 28), (9, 21), (10, 19), (13, 8), (24, 28), (20, 8), (12, 5), (18, 33), (14, 17), (20, 32), (17, 18), (20, 19), (30, 28), (6, 32), (10, 15), (32, 13), (14, 9), (12, 33), (5, 31), (12, 31), (23, 32), (7, 2), (26, 18), (14, 1), (0, 25), (29, 32), (7, 30), (21, 33), (24, 17), (14, 15), (9, 6), (8, 10), (14, 8), (12, 17), (20, 28), (33, 31), (13, 29), (12, 20), (34, 9), (18, 16), (11, 11), (25, 17), (34, 10), (13, 3), (33, 20), (1, 27), (22, 18), (30, 31), (31, 22), (32, 20), (21, 5), (32, 16), (23, 28), (17, 22), (20, 18), (12, 22), (16, 25), (9, 11), (19, 2), (28, 6), (21, 17), (29, 14), (6, 31), (5, 20), (15, 0), (16, 3), (6, 27), (10, 25), (2, 2), (4, 26), (6, 28), (0, 9), (30, 11), (19, 29), (6, 7), (2, 23), (11, 27), (29, 31), (25, 22), (30, 16), (27, 15), (23, 18), (17, 16), (1, 22), (5, 9), (0, 1), (2, 26), (9, 17), (24, 27), (30, 30), (21, 12), (19, 15), (28, 26), (21, 30), (29, 13), (18, 7), (33, 18), (22, 2), (16, 21), (17, 25), (10, 18), (14, 12), (5, 12), (21, 4), (8, 11), (0, 23), (2, 12), (14, 19), (16, 24), (8, 30), (11, 29), (33, 26), (19, 0), (23, 15), (17, 5), (3, 16), (26, 15), (29, 21), (22, 19), (11, 26), (34, 30), (23, 20)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841104", "dataset": "MATH"}
{"messages": [{"content": "In a 37x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 30), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (17, 27), (21, 11), (14, 22), (34, 3), (33, 7), (24, 3), (0, 30), (10, 27), (35, 20), (32, 22), (15, 6), (23, 20), (22, 20), (17, 1), (3, 9), (15, 9), (20, 20), (20, 19), (19, 4), (8, 19), (24, 15), (10, 14), (13, 24), (6, 11), (4, 21), (11, 14), (24, 9), (0, 17), (27, 13), (28, 18), (36, 0), (3, 10), (9, 1), (26, 25), (0, 16), (14, 5), (5, 8), (25, 24), (33, 13), (7, 7), (15, 8), (18, 6), (4, 29), (26, 13), (6, 3), (8, 3), (16, 1), (12, 19), (25, 11), (23, 3), (4, 12), (36, 14), (15, 30), (32, 16), (28, 21), (15, 3), (32, 20), (8, 24), (9, 8), (18, 2), (25, 1), (2, 2), (18, 24), (23, 29), (10, 19), (11, 24), (33, 26), (19, 0), (36, 8), (8, 29), (5, 17), (3, 6), (32, 19), (15, 12), (11, 0), (17, 21), (11, 1), (27, 24), (0, 20), (34, 24), (23, 9), (25, 27), (1, 10), (3, 11), (14, 30), (18, 15), (21, 30), (18, 16), (11, 28), (11, 8), (21, 5), (3, 24), (2, 20), (8, 14), (7, 15), (29, 0), (7, 22), (7, 23), (11, 23), (8, 18), (5, 29), (16, 16), (19, 11), (13, 10), (17, 28), (19, 1), (6, 28), (17, 4), (26, 10), (22, 25), (27, 0), (36, 3), (34, 1), (29, 6), (2, 14), (30, 5), (0, 21), (4, 22), (7, 10), (14, 23), (15, 22), (22, 3), (1, 17), (5, 18), (21, 17), (23, 14), (0, 18), (33, 9), (35, 11), (20, 18), (36, 16), (17, 8), (27, 15), (19, 16), (16, 0), (35, 22), (18, 0), (4, 3), (21, 4), (19, 14), (36, 23), (12, 9), (31, 10), (9, 24), (1, 11), (33, 16), (33, 28), (12, 22), (18, 29), (25, 16), (15, 18), (23, 28), (26, 19), (32, 18), (18, 10), (24, 29), (35, 25), (5, 6), (23, 27), (5, 22), (9, 29), (14, 4), (36, 21), (22, 4), (3, 19), (14, 27), (16, 28), (9, 6), (0, 15), (1, 0), (12, 0), (34, 20), (2, 27), (25, 5), (1, 28), (15, 16), (12, 15), (24, 12), (36, 5), (8, 28), (32, 25), (33, 10), (33, 27), (13, 19), (6, 8), (29, 22), (11, 18), (7, 2), (31, 26), (25, 25), (7, 9), (3, 15), (25, 22), (36, 12), (30, 14), (24, 4), (32, 6), (30, 20), (24, 17), (0, 5), (19, 20), (27, 25), (30, 28), (19, 3), (1, 18), (3, 12), (21, 28), (34, 22), (23, 26), (14, 1), (30, 10), (28, 24), (21, 0), (33, 11), (30, 13), (1, 26), (6, 15), (8, 15), (7, 14), (27, 20), (5, 27), (35, 6), (18, 22), (11, 25), (30, 26), (18, 14), (17, 22), (14, 18), (32, 15), (3, 0), (3, 16), (20, 13), (26, 17), (17, 17), (9, 22), (10, 22), (3, 17), (24, 24), (17, 0), (28, 1), (17, 30), (7, 27), (1, 3), (8, 27), (0, 10), (27, 8), (20, 6), (3, 25), (29, 10), (30, 30), (11, 22), (32, 14), (10, 21), (5, 23), (26, 14), (33, 17), (22, 15), (34, 19), (2, 24), (4, 20), (8, 5), (18, 8), (10, 16), (0, 24), (14, 19), (10, 3), (11, 3), (32, 10), (29, 27), (35, 26), (19, 9), (35, 0), (34, 21), (22, 21), (13, 0), (0, 12), (10, 26), (15, 13), (25, 7), (14, 16), (36, 15), (14, 14), (29, 28), (23, 30), (10, 5), (18, 30), (2, 1), (32, 29), (24, 21), (3, 21), (3, 4), (13, 18), (12, 23), (27, 28), (19, 8), (28, 19), (20, 28), (6, 22), (32, 12), (33, 14), (7, 1), (16, 18), (25, 28), (4, 15), (25, 29), (15, 28), (19, 26), (19, 30), (7, 25), (16, 11), (7, 16), (30, 16), (33, 0), (26, 0), (0, 29), (12, 29), (22, 2), (18, 27), (25, 30), (36, 18), (19, 28), (21, 23), (25, 13), (21, 24), (31, 7), (1, 5)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "743550", "dataset": "MATH"}
{"messages": [{"content": "In a 37x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (36, 31), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (21, 27), (30, 16), (27, 5), (29, 0), (28, 22), (18, 20), (21, 31), (24, 18), (25, 2), (1, 3), (13, 15), (28, 3), (23, 28), (4, 30), (2, 26), (30, 4), (8, 29), (24, 16), (2, 28), (32, 19), (20, 31), (20, 23), (13, 17), (27, 30), (16, 12), (1, 29), (36, 5), (28, 15), (19, 26), (29, 22), (33, 16), (20, 14), (31, 24), (3, 6), (0, 27), (6, 29), (10, 6), (17, 25), (32, 17), (30, 29), (15, 11), (26, 25), (17, 13), (36, 18), (27, 1), (20, 15), (10, 28), (24, 5), (13, 18), (23, 8), (30, 10), (22, 7), (22, 1), (2, 27), (30, 8), (26, 1), (23, 11), (14, 28), (9, 17), (26, 26), (24, 27), (20, 8), (27, 22), (21, 30), (18, 7), (23, 5), (14, 31), (30, 6), (12, 5), (31, 18), (30, 12), (9, 29), (10, 19), (2, 10), (32, 14), (27, 12), (36, 1), (5, 5), (17, 16), (14, 26), (17, 12), (14, 27), (18, 31), (19, 30), (32, 18), (26, 19), (0, 4), (28, 5), (14, 11), (36, 0), (13, 26), (19, 5), (34, 2), (18, 13), (6, 28), (20, 20), (4, 7), (19, 4), (10, 22), (35, 15), (17, 15), (16, 0), (15, 3), (32, 21), (36, 22), (8, 8), (3, 12), (15, 31), (28, 31), (9, 18), (0, 7), (20, 7), (18, 0), (23, 12), (22, 23), (14, 1), (12, 15), (31, 8), (23, 1), (29, 28), (35, 3), (3, 0), (25, 8), (9, 16), (7, 3), (18, 9), (21, 5), (19, 20), (26, 28), (11, 31), (5, 30), (22, 21), (6, 4), (5, 26), (8, 15), (24, 21), (15, 2), (8, 26), (33, 1), (24, 24), (12, 22), (27, 4), (19, 3), (24, 14), (9, 5), (7, 28), (9, 0), (23, 14), (3, 27), (14, 24), (14, 2), (15, 28), (15, 25), (28, 6), (28, 21), (15, 7), (36, 11), (2, 14), (26, 29), (18, 1), (8, 2), (34, 12), (19, 13), (10, 16), (7, 0), (4, 25), (32, 12), (32, 30), (18, 26), (12, 7), (14, 20), (20, 28), (16, 7), (31, 5), (12, 6), (29, 3), (19, 23), (24, 28), (34, 8), (10, 13), (16, 29), (25, 10), (1, 17), (23, 6), (31, 1), (20, 25), (5, 13), (28, 1), (35, 12), (0, 10), (11, 29), (24, 30), (0, 14), (0, 11), (15, 19), (2, 22), (7, 25), (36, 30), (35, 4), (26, 0), (12, 13), (18, 27), (4, 2), (5, 12), (36, 17), (19, 25), (24, 1), (35, 30), (16, 26), (5, 28), (9, 27), (12, 16), (6, 3), (18, 5), (3, 22), (19, 7), (5, 16), (15, 21), (17, 29), (8, 1), (4, 10), (5, 17), (2, 16), (4, 20), (8, 9), (33, 24), (13, 2), (13, 0), (31, 27), (11, 30), (36, 28), (27, 10), (35, 2), (7, 23), (19, 16), (25, 15), (13, 25), (22, 30), (18, 14), (26, 18), (5, 14), (34, 28), (22, 12), (31, 22), (0, 13), (1, 13), (1, 27), (25, 19), (28, 7), (7, 29), (9, 8), (36, 23), (31, 6), (5, 0), (11, 20), (34, 11), (5, 10), (36, 25), (9, 24), (22, 10), (9, 25), (29, 29), (30, 0), (27, 2), (35, 22), (23, 23), (22, 16), (30, 3), (27, 7), (20, 24), (27, 6), (36, 16), (3, 31), (16, 3), (4, 3), (27, 23), (2, 13), (21, 25), (28, 16), (1, 16), (19, 27), (29, 25), (12, 2), (10, 18), (20, 30), (0, 26), (23, 27), (26, 9), (25, 28), (4, 16), (33, 29), (8, 20), (30, 17), (13, 22), (17, 21), (28, 9), (23, 4), (12, 11), (25, 25), (2, 23), (29, 7), (6, 26), (35, 11), (11, 2), (31, 30), (17, 10), (31, 21), (7, 11), (34, 4), (14, 23), (15, 0), (16, 14), (17, 6), (10, 21), (2, 15), (12, 8), (29, 9), (7, 21), (24, 9), (35, 29), (35, 13), (33, 18), (33, 2), (21, 9), (23, 13), (29, 31), (29, 21), (25, 5), (6, 8), (33, 30), (1, 10), (15, 14), (25, 29), (15, 27), (30, 18), (32, 2), (18, 18), (4, 27), (16, 22), (32, 29), (15, 17), (1, 26), (16, 23), (35, 10), (0, 6), (28, 28), (14, 30), (8, 4), (21, 6), (15, 1), (20, 2), (13, 9), (26, 2), (13, 6), (4, 28), (9, 12), (25, 4), (26, 7), (17, 31), (20, 21), (1, 12), (13, 20), (19, 17), (5, 4), (30, 13), (23, 24), (20, 16), (8, 18), (7, 5), (29, 8), (20, 29), (18, 17), (30, 1), (0, 21), (28, 10), (16, 25), (5, 11), (2, 29), (21, 16), (14, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631260", "dataset": "MATH"}
{"messages": [{"content": "In a 38x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 38), 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), (22, 23), (11, 19), (18, 26), (36, 2), (6, 30), (28, 38), (25, 13), (15, 14), (33, 5), (5, 9), (34, 6), (21, 38), (13, 24), (22, 26), (27, 33), (14, 9), (13, 6), (20, 27), (19, 36), (30, 14), (37, 3), (37, 8), (25, 32), (31, 32), (0, 31), (7, 26), (5, 27), (20, 15), (13, 29), (16, 31), (0, 26), (33, 38), (23, 20), (16, 6), (21, 5), (1, 37), (25, 17), (2, 15), (20, 25), (36, 36), (25, 18), (1, 4), (12, 16), (6, 0), (33, 28), (28, 16), (17, 16), (31, 26), (23, 3), (33, 29), (9, 6), (25, 27), (23, 17), (29, 28), (3, 10), (9, 16), (30, 1), (14, 32), (32, 0), (4, 31), (27, 27), (5, 8), (23, 8), (13, 21), (20, 9), (36, 9), (17, 23), (2, 19), (8, 32), (13, 9), (19, 18), (3, 30), (36, 8), (27, 22), (6, 25), (2, 0), (35, 27), (35, 22), (3, 11), (35, 1), (31, 31), (2, 20), (23, 24), (28, 13), (5, 33), (19, 21), (8, 19), (27, 21), (4, 29), (16, 14), (21, 31), (31, 36), (32, 16), (12, 0), (21, 29), (32, 34), (23, 1), (14, 19), (15, 5), (33, 26), (30, 4), (10, 6), (30, 33), (9, 3), (33, 13), (33, 35), (33, 20), (24, 11), (10, 20), (32, 2), (26, 35), (29, 12), (12, 27), (6, 21), (26, 25), (28, 28), (14, 23), (12, 7), (33, 8), (34, 38), (19, 23), (0, 4), (4, 30), (36, 30), (12, 29), (16, 36), (28, 23), (28, 17), (10, 24), (15, 6), (6, 28), (19, 3), (1, 6), (2, 13), (23, 12), (9, 1), (9, 17), (18, 19), (21, 8), (28, 24), (16, 21), (13, 16), (37, 20), (15, 16), (20, 26), (30, 35), (19, 22), (13, 1), (21, 4), (13, 28), (34, 23), (23, 37), (28, 2), (24, 6), (13, 7), (6, 26), (34, 35), (2, 37), (19, 38), (0, 37), (12, 8), (0, 25), (21, 21), (23, 11), (7, 13), (20, 12), (29, 3), (31, 5), (11, 13), (25, 30), (16, 32), (12, 5), (29, 18), (14, 25), (36, 17), (26, 2), (33, 31), (14, 27), (0, 28), (21, 12), (18, 4), (25, 7), (10, 38), (12, 22), (24, 35), (18, 24), (8, 27), (17, 34), (23, 26), (1, 20), (28, 11), (28, 31), (11, 16), (30, 5), (14, 21), (20, 19), (22, 4), (18, 17), (22, 9), (1, 33), (4, 17), (24, 33), (20, 36), (1, 26), (5, 38), (26, 19), (15, 27), (13, 34), (24, 20), (13, 32), (15, 28), (17, 8), (22, 0), (31, 6), (17, 11), (15, 3), (10, 29), (12, 20), (24, 14), (31, 28), (13, 18), (1, 28), (21, 23), (21, 10), (28, 20), (33, 14), (28, 18), (17, 24), (13, 12), (30, 25), (2, 16), (0, 22), (24, 9), (21, 25), (29, 11), (33, 27), (10, 35), (11, 20), (0, 24), (13, 0), (29, 37), (13, 31), (6, 17), (11, 21), (7, 6), (3, 3), (10, 0), (37, 13), (7, 38), (0, 9), (7, 14), (28, 9), (35, 0), (19, 2), (10, 17), (13, 27), (11, 23), (37, 7), (34, 5), (0, 12), (21, 37), (14, 10), (12, 10), (16, 2), (20, 10), (13, 22), (10, 25), (1, 36), (26, 13), (18, 27), (23, 14), (18, 32), (20, 7), (3, 25), (26, 37), (26, 5), (0, 17), (15, 29), (3, 15), (34, 32), (1, 9), (7, 16), (8, 4), (15, 35), (11, 18), (27, 35), (35, 32), (7, 4), (23, 6), (34, 9), (8, 17), (3, 35), (10, 30), (12, 28), (31, 22), (28, 35), (1, 0), (23, 38), (3, 22), (11, 34), (36, 0), (12, 33), (0, 14), (29, 36), (5, 14), (11, 11), (9, 13), (33, 32), (31, 20), (37, 33), (7, 8), (36, 26), (25, 24), (13, 23), (1, 31), (0, 7), (22, 5), (13, 35), (15, 26), (20, 38), (31, 30), (33, 21), (29, 10), (29, 31), (32, 7), (14, 38), (12, 23), (31, 38), (5, 25), (14, 30), (30, 3), (22, 22), (14, 17), (18, 11), (25, 31), (35, 12), (6, 20), (26, 36), (10, 4), (2, 25), (4, 34), (31, 21), (15, 38), (22, 19), (26, 14), (7, 23), (4, 1), (32, 31), (29, 29), (19, 27), (2, 9), (35, 16), (12, 13), (30, 36), (10, 23), (4, 37), (36, 20), (30, 16), (24, 36), (16, 35), (20, 11), (35, 30), (23, 25), (22, 6), (6, 3), (19, 4), (28, 34), (37, 34), (29, 38), (3, 38), (3, 27), (30, 19), (17, 26), (28, 6), (17, 25), (32, 18), (36, 21), (8, 7), (32, 17), (15, 8), (17, 9), (8, 26), (11, 10), (4, 27), (32, 37), (9, 38), (32, 6), (24, 19), (37, 25), (22, 16), (16, 33), (23, 15), (22, 35), (20, 4), (32, 19), (11, 0), (28, 0), (8, 18), (11, 4), (22, 30), (20, 31), (24, 38), (11, 9), (11, 29), (8, 31), (25, 21), (1, 38), (6, 27), (25, 33), (12, 14), (32, 5), (3, 12), (3, 14), (32, 8), (17, 17), (16, 16), (18, 16), (29, 9), (27, 13), (31, 16), (11, 7), (7, 17), (6, 16), (4, 3), (32, 20), (20, 35), (0, 11), (2, 32), (27, 31), (9, 4), (22, 28), (18, 34), (7, 25), (34, 15), (18, 33), (19, 13), (2, 24), (10, 22), (28, 1), (16, 17), (19, 6), (6, 9), (13, 3), (32, 38), (35, 33), (23, 19), (20, 18), (18, 36), (23, 2), (29, 14), (3, 1), (37, 27), (26, 15), (15, 12), (15, 22), (19, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55650", "dataset": "MATH"}
{"messages": [{"content": "In a 39x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 30), (5, 16), (16, 17), (26, 26), (6, 11), (12, 8), (25, 12), (38, 12), (28, 1), (35, 8), (11, 2), (36, 0), (27, 3), (0, 21), (33, 14), (0, 1), (12, 14), (37, 13), (10, 6), (13, 6), (37, 0), (25, 2), (0, 22), (10, 25), (11, 6), (36, 19), (38, 27), (1, 5), (22, 22), (21, 22), (4, 0), (5, 7), (25, 30), (37, 3), (30, 9), (12, 27), (18, 13), (21, 24), (4, 10), (14, 2), (33, 4), (7, 9), (21, 27), (19, 26), (15, 15), (26, 0), (0, 11), (13, 20), (17, 23), (30, 33), (18, 2), (13, 10), (18, 6), (31, 18), (25, 0), (27, 14), (29, 21), (7, 2), (34, 1), (5, 3), (34, 9), (23, 25), (11, 32), (7, 26), (7, 3), (34, 25), (22, 6), (22, 2), (36, 7), (27, 5), (4, 2), (22, 25), (27, 26), (13, 32), (11, 21), (19, 28), (7, 29), (11, 1), (20, 29), (32, 13), (4, 20), (15, 4), (28, 8), (30, 8), (31, 24), (20, 10), (19, 29), (21, 12), (28, 19), (22, 29), (34, 5), (33, 33), (19, 20), (2, 17), (35, 26), (25, 29), (24, 6), (28, 30), (13, 33), (5, 31), (10, 26), (0, 12), (35, 19), (32, 11), (20, 3), (34, 0), (6, 5), (30, 17), (15, 3), (38, 11), (19, 18), (7, 10), (6, 29), (17, 10), (30, 2), (15, 9), (4, 1), (11, 0), (35, 1), (17, 31), (26, 12), (13, 7), (17, 21), (31, 4), (12, 26), (1, 14), (14, 3), (35, 13), (30, 19), (31, 14), (21, 33), (12, 16), (6, 17), (10, 9), (23, 29), (10, 12), (3, 15), (27, 31), (7, 1), (17, 26), (2, 11), (15, 6), (23, 1), (10, 27), (35, 7), (8, 4), (16, 16), (38, 1), (26, 23), (33, 2), (17, 2), (9, 3), (20, 22), (10, 16), (29, 1), (15, 22), (24, 24), (32, 32), (35, 30), (4, 30), (20, 27), (30, 3), (9, 4), (11, 18), (34, 13), (35, 3), (38, 31), (21, 4), (14, 9), (35, 27), (1, 16), (5, 2), (18, 14), (2, 26), (23, 31), (33, 20), (9, 18), (8, 23), (20, 1), (9, 8), (8, 10), (12, 28), (16, 4), (5, 14), (25, 10), (14, 14), (27, 1), (30, 14), (31, 33), (34, 18), (29, 11), (31, 0), (23, 15), (20, 32), (21, 32), (27, 27), (2, 19), (4, 11), (25, 19), (38, 29), (10, 3), (8, 25), (23, 8), (3, 19), (20, 8), (38, 15), (16, 3), (5, 12), (21, 15), (22, 14), (12, 21), (24, 9), (21, 31), (9, 12), (38, 17), (33, 15), (12, 4), (25, 11), (4, 6), (32, 9), (4, 8), (27, 8), (0, 16), (28, 16), (12, 23), (23, 23), (36, 17), (1, 11), (35, 0), (33, 24), (10, 15), (18, 33), (33, 11), (6, 20), (3, 9), (21, 2), (15, 16), (4, 7), (35, 2), (3, 29), (2, 30), (36, 24), (20, 21), (9, 5), (26, 4), (16, 1), (2, 0), (15, 30), (29, 15), (26, 16), (22, 4), (6, 21), (4, 28), (36, 29), (28, 25), (34, 10), (12, 10), (34, 8), (11, 11), (1, 20), (13, 23), (26, 27), (6, 0), (14, 17), (18, 7), (6, 14), (23, 4), (13, 26), (25, 17), (14, 4), (22, 15), (19, 25), (34, 12), (28, 9), (36, 3), (17, 27), (34, 21), (26, 18), (20, 7), (0, 5), (25, 31), (6, 7), (11, 16), (19, 3), (28, 23), (28, 3), (21, 20), (5, 26), (5, 33), (33, 13), (25, 33), (37, 5), (34, 30), (6, 22), (38, 24), (5, 19), (38, 14), (6, 12), (27, 15), (5, 6), (29, 10), (34, 22), (17, 18), (24, 7), (29, 31), (32, 15), (3, 1), (32, 19), (21, 10), (33, 3), (36, 12), (22, 27), (1, 9), (37, 9), (14, 25), (18, 0), (8, 3), (38, 6), (33, 10), (17, 33), (13, 2), (12, 24), (12, 12), (6, 25), (1, 8), (38, 28), (6, 19), (37, 25), (12, 22), (21, 26), (11, 5), (18, 25), (22, 33), (30, 21), (24, 25), (32, 17), (1, 30), (37, 22), (8, 2), (7, 5), (7, 27), (17, 28), (5, 28), (22, 11), (9, 30), (12, 25), (15, 14), (18, 9), (22, 28), (23, 9), (14, 28), (28, 6), (34, 7), (14, 24), (3, 25), (30, 13), (15, 27), (4, 13), (15, 25), (6, 16), (4, 18), (1, 25), (28, 32), (1, 21), (8, 17), (31, 20), (37, 6), (32, 5), (24, 16), (16, 32), (22, 32), (21, 17), (30, 6), (5, 5), (26, 5), (12, 15), (12, 18), (16, 25), (26, 31), (31, 28), (19, 4), (35, 28), (30, 31), (3, 28), (36, 10), (28, 21), (1, 4), (8, 24), (23, 27), (38, 7), (19, 21), (16, 14), (14, 26), (2, 24), (27, 23), (24, 26), (20, 15), (36, 27), (6, 18), (1, 15), (30, 18), (19, 12), (17, 12), (29, 9), (14, 13), (16, 18), (33, 27), (3, 33), (23, 20), (12, 29), (19, 24), (31, 25), (30, 15), (31, 10), (35, 31), (16, 26), (20, 16), (37, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "935172", "dataset": "MATH"}
{"messages": [{"content": "In a 30x39 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 38), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 0), (4, 9), (28, 18), (18, 9), (3, 4), (28, 21), (6, 25), (10, 22), (4, 14), (17, 4), (14, 13), (13, 26), (11, 4), (3, 24), (4, 34), (3, 14), (9, 34), (1, 33), (27, 13), (11, 30), (2, 9), (20, 8), (18, 15), (1, 11), (29, 13), (10, 21), (7, 29), (16, 11), (15, 9), (2, 30), (2, 6), (29, 21), (5, 30), (16, 3), (6, 6), (5, 25), (13, 6), (16, 4), (10, 26), (1, 7), (19, 36), (25, 13), (14, 30), (11, 1), (27, 5), (0, 13), (8, 31), (16, 28), (17, 19), (20, 25), (28, 15), (28, 35), (15, 24), (1, 30), (6, 18), (2, 36), (5, 27), (10, 28), (8, 19), (14, 7), (18, 26), (0, 11), (15, 0), (8, 10), (24, 13), (11, 35), (1, 23), (10, 14), (0, 33), (10, 7), (0, 37), (1, 16), (14, 20), (9, 10), (23, 6), (2, 3), (12, 1), (16, 37), (20, 20), (12, 28), (13, 21), (17, 22), (5, 29), (14, 23), (11, 38), (19, 35), (7, 16), (18, 2), (1, 31), (14, 18), (1, 32), (12, 11), (27, 20), (26, 18), (7, 1), (12, 36), (2, 7), (19, 21), (20, 35), (17, 20), (22, 28), (21, 17), (8, 32), (9, 30), (18, 0), (10, 31), (23, 17), (21, 16), (5, 15), (9, 38), (8, 9), (15, 31), (23, 35), (21, 0), (20, 11), (5, 33), (0, 25), (10, 25), (21, 4), (15, 10), (9, 27), (6, 20), (16, 2), (7, 3), (9, 13), (19, 38), (8, 29), (22, 32), (18, 25), (25, 29), (25, 36), (17, 8), (9, 31), (13, 9), (25, 32), (13, 27), (26, 38), (18, 8), (15, 26), (7, 36), (14, 35), (8, 37), (13, 10), (15, 38), (27, 34), (9, 24), (21, 28), (12, 33), (21, 18), (8, 18), (15, 37), (17, 2), (12, 24), (18, 29), (15, 6), (10, 37), (12, 15), (22, 34), (19, 7), (11, 0), (22, 6), (25, 34), (19, 23), (14, 22), (3, 37), (16, 24), (8, 17), (1, 36), (8, 38), (29, 4), (0, 17), (25, 2), (23, 31), (7, 13), (13, 24), (15, 35), (26, 35), (12, 20), (28, 13), (23, 24), (20, 17), (14, 21), (5, 12), (4, 20), (3, 33), (22, 31), (9, 15), (19, 37), (16, 36), (7, 23), (9, 5), (5, 6), (0, 14), (5, 7), (23, 10), (12, 34), (26, 28), (6, 12), (8, 3), (10, 15), (22, 5), (17, 30), (17, 17), (20, 32), (1, 5), (6, 0), (4, 37), (9, 35), (11, 24), (26, 20), (28, 24), (13, 14), (23, 16), (19, 26), (22, 33), (19, 0), (0, 5), (23, 27), (3, 9), (2, 1), (4, 12), (12, 8), (3, 5), (9, 26), (1, 37), (22, 36), (17, 13), (16, 9), (26, 17), (14, 31), (15, 22), (21, 10), (1, 12), (19, 5), (14, 2), (17, 26), (10, 2), (8, 8), (11, 21), (14, 32), (28, 32), (20, 26), (29, 11), (19, 12), (24, 35), (3, 32), (24, 15), (15, 12), (17, 12), (3, 19), (28, 30), (22, 26), (28, 14), (11, 13), (11, 23), (7, 19), (15, 33), (20, 14), (7, 38), (7, 11), (14, 8), (11, 6), (15, 27), (14, 25), (5, 31), (20, 28), (29, 31), (9, 14), (1, 19), (6, 36), (15, 21), (5, 19), (19, 16), (23, 15), (17, 32), (24, 9), (19, 2), (15, 28), (0, 6), (27, 19), (0, 21), (13, 28), (17, 23), (25, 0), (3, 10), (17, 18), (20, 36), (17, 14), (5, 32), (22, 3), (4, 22), (21, 36), (11, 3), (24, 24), (23, 38), (19, 17), (9, 4)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578016", "dataset": "MATH"}
{"messages": [{"content": "In a 31x32 grid, how many different paths are there from the bottom left (0, 0) to the top right (30, 31), 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), (12, 4), (22, 21), (23, 27), (5, 16), (19, 6), (23, 21), (1, 8), (0, 12), (15, 9), (0, 23), (4, 3), (9, 30), (3, 20), (23, 29), (14, 24), (28, 23), (10, 12), (26, 3), (17, 14), (18, 15), (29, 3), (10, 1), (30, 7), (0, 8), (12, 26), (29, 15), (12, 10), (2, 21), (0, 9), (3, 15), (24, 30), (23, 6), (14, 0), (3, 25), (7, 31), (14, 13), (21, 8), (20, 23), (15, 25), (26, 10), (0, 13), (4, 15), (18, 5), (17, 5), (8, 0), (13, 14), (21, 22), (7, 10), (29, 22), (13, 5), (25, 6), (23, 30), (18, 11), (5, 5), (1, 27), (18, 18), (5, 11), (17, 21), (6, 30), (25, 27), (18, 25), (25, 4), (28, 20), (24, 24), (20, 11), (28, 24), (22, 8), (6, 18), (10, 18), (6, 7), (29, 8), (28, 28), (27, 22), (6, 29), (16, 3), (9, 17), (25, 31), (7, 28), (26, 31), (28, 3), (4, 22), (12, 11), (26, 24), (0, 16), (4, 19), (29, 25), (7, 4), (9, 5), (11, 26), (21, 10), (19, 25), (22, 6), (26, 29), (29, 18), (24, 28), (28, 29), (20, 0), (7, 30), (4, 7), (22, 23), (27, 24), (19, 20), (7, 24), (16, 10), (0, 2), (24, 9), (19, 27), (12, 25), (2, 26), (0, 29), (17, 12), (0, 14), (6, 12), (5, 14), (12, 2), (11, 3), (9, 2), (6, 13), (8, 15), (29, 5), (6, 28), (2, 23), (11, 21), (12, 15), (28, 10), (27, 16), (7, 26), (21, 28), (19, 24), (23, 3), (2, 13), (9, 28), (27, 15), (2, 14), (30, 9), (20, 20), (9, 21), (8, 18), (5, 27), (29, 31), (13, 12), (16, 5), (27, 12), (8, 11), (22, 11), (16, 24), (24, 12), (25, 20), (19, 29), (21, 0), (14, 5), (13, 25), (26, 13), (22, 31), (9, 20), (18, 23), (10, 14), (12, 7), (11, 28), (13, 30), (21, 4), (25, 22), (0, 19), (7, 14), (8, 4), (18, 21), (17, 28), (22, 2), (11, 5), (21, 9), (4, 6), (27, 11), (1, 10), (14, 26), (5, 15), (6, 9), (15, 12), (12, 21), (2, 8), (27, 13), (27, 9), (5, 18), (8, 9), (23, 9), (17, 7), (18, 4), (8, 10), (14, 31), (4, 24), (26, 25), (12, 17), (7, 17), (14, 10), (30, 13), (27, 8), (3, 8), (23, 22), (1, 24), (6, 10), (10, 31), (24, 22), (1, 7), (4, 21), (4, 28), (26, 5), (0, 4), (4, 10), (16, 2), (5, 8), (11, 14), (29, 16), (15, 6), (11, 4), (6, 26), (7, 27), (27, 23), (18, 10), (11, 20), (13, 29), (13, 21), (26, 14), (22, 27), (10, 17), (24, 23), (11, 29), (13, 16), (19, 17), (11, 23), (9, 0), (2, 25), (9, 6), (30, 26), (30, 19), (24, 16), (3, 10), (17, 9), (30, 2), (23, 23), (12, 24), (30, 10), (12, 31), (29, 12), (23, 5), (2, 3), (17, 6), (23, 4), (27, 25), (1, 12), (18, 29), (30, 20), (25, 18), (27, 10), (19, 8), (3, 13), (21, 19), (2, 15), (7, 25), (5, 1), (6, 15), (14, 20), (3, 24), (16, 13), (3, 6), (16, 23)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "775656", "dataset": "MATH"}
{"messages": [{"content": "In a 34x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (26, 21), (21, 13), (10, 4), (24, 0), (30, 9), (5, 23), (22, 12), (15, 15), (5, 7), (23, 22), (26, 18), (1, 2), (8, 5), (33, 21), (3, 17), (21, 11), (31, 3), (13, 8), (15, 6), (6, 1), (20, 25), (0, 20), (22, 13), (28, 16), (26, 22), (12, 26), (11, 9), (27, 16), (15, 28), (27, 0), (19, 14), (11, 20), (9, 26), (2, 10), (20, 29), (17, 26), (25, 10), (20, 15), (24, 9), (11, 14), (7, 10), (8, 12), (28, 15), (18, 21), (11, 3), (31, 15), (30, 16), (22, 18), (29, 1), (3, 0), (17, 5), (11, 17), (17, 21), (12, 21), (8, 14), (17, 15), (13, 28), (5, 16), (10, 0), (9, 20), (15, 4), (12, 3), (30, 28), (28, 7), (32, 28), (30, 3), (0, 8), (33, 2), (21, 28), (4, 15), (19, 29), (11, 29), (31, 7), (27, 3), (28, 27), (11, 4), (31, 13), (29, 27), (15, 3), (17, 18), (27, 2), (9, 16), (32, 10), (6, 0), (2, 5), (30, 13), (21, 10), (18, 8), (8, 8), (3, 4), (29, 15), (4, 1), (32, 7), (28, 26), (26, 15), (3, 24), (4, 3), (15, 0), (9, 24), (0, 14), (2, 18), (14, 19), (2, 12), (17, 23), (25, 14), (19, 26), (22, 2), (12, 5), (3, 16), (19, 4), (14, 17), (6, 2), (31, 22), (11, 8), (5, 2), (23, 16), (7, 6), (7, 18), (1, 26), (29, 13), (11, 2), (2, 4), (4, 19), (17, 11), (5, 18), (19, 18), (23, 20), (15, 14), (27, 8), (3, 18), (32, 12), (14, 20), (10, 23), (26, 10), (27, 14), (25, 12), (32, 0), (12, 7), (30, 7), (31, 21), (28, 6), (31, 2), (14, 15), (0, 28), (10, 29), (19, 10), (25, 23), (13, 7), (16, 15), (20, 12), (3, 2), (17, 13), (15, 23), (24, 27), (30, 15), (25, 27), (30, 25), (32, 2), (19, 5), (11, 28), (31, 17), (12, 23), (17, 12), (15, 12), (31, 5), (0, 18), (5, 21), (13, 22), (4, 5), (1, 12), (9, 4), (5, 11), (31, 8), (6, 29), (32, 8), (8, 9), (23, 25), (2, 21), (16, 5), (7, 4), (6, 13), (20, 23), (6, 25), (25, 3), (33, 25), (7, 29), (4, 0), (25, 16), (27, 21), (33, 9), (24, 29), (17, 17), (18, 7), (22, 24), (16, 24), (32, 18), (19, 28), (33, 13), (14, 0), (7, 9), (26, 17), (22, 7), (11, 11), (4, 25), (8, 15), (13, 14), (7, 0), (30, 19), (19, 11), (27, 23), (3, 14), (33, 18), (8, 18), (32, 9), (3, 26), (7, 7), (21, 14), (27, 1), (26, 0), (20, 0), (16, 22), (8, 21), (23, 27), (21, 12), (15, 25), (2, 11), (25, 11), (0, 29), (0, 13), (14, 9), (12, 8), (2, 20), (13, 21), (13, 19), (23, 18), (7, 13), (18, 22), (32, 5), (3, 5), (10, 2), (0, 27), (31, 26), (32, 24), (29, 7), (19, 24), (8, 3), (13, 9), (8, 25), (2, 7), (1, 13), (11, 18), (15, 9), (1, 8), (16, 3), (32, 16), (28, 14), (13, 20), (17, 22), (2, 17), (16, 25), (7, 19), (20, 3), (13, 17), (4, 7), (12, 12), (33, 12), (21, 9), (30, 18), (26, 2), (4, 4), (3, 11), (28, 9), (13, 0), (25, 21), (27, 19), (10, 28), (28, 10), (30, 17), (17, 6), (17, 24), (14, 4), (18, 5), (16, 20), (6, 4), (10, 5), (9, 1), (22, 3), (13, 26), (23, 3), (28, 29), (27, 26), (8, 10), (5, 14), (31, 27), (17, 20), (10, 24), (20, 2), (10, 22), (29, 19), (25, 9), (31, 10), (12, 19), (17, 4), (22, 23), (16, 29), (17, 29), (21, 24), (26, 6), (4, 20), (20, 18), (20, 27), (25, 25), (24, 11), (3, 12), (25, 5), (11, 27), (29, 0), (2, 23), (6, 14), (5, 13), (24, 17), (6, 18), (13, 25), (0, 24), (31, 18), (22, 25), (29, 3), (24, 2), (9, 13), (33, 3), (28, 12), (26, 27), (0, 21), (21, 22), (16, 1), (30, 20), (21, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "768768", "dataset": "MATH"}
{"messages": [{"content": "In a 30x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (29, 33), 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), (15, 11), (2, 17), (17, 11), (21, 9), (4, 32), (12, 22), (14, 14), (27, 10), (21, 8), (23, 13), (21, 33), (3, 0), (18, 30), (6, 5), (10, 15), (15, 6), (15, 21), (7, 5), (25, 23), (28, 16), (25, 10), (15, 12), (23, 30), (14, 15), (4, 26), (21, 6), (2, 31), (20, 20), (6, 19), (21, 1), (13, 31), (9, 9), (27, 23), (8, 3), (9, 23), (16, 5), (13, 33), (10, 9), (0, 33), (13, 28), (8, 2), (3, 10), (21, 10), (10, 32), (8, 10), (4, 10), (19, 10), (11, 17), (2, 21), (6, 12), (1, 14), (9, 33), (11, 21), (21, 5), (10, 18), (12, 33), (0, 16), (6, 22), (15, 30), (12, 2), (26, 16), (13, 9), (4, 19), (10, 24), (11, 13), (27, 18), (28, 29), (10, 26), (29, 20), (23, 6), (20, 12), (24, 30), (24, 7), (6, 10), (12, 24), (29, 17), (9, 7), (25, 16), (24, 16), (0, 22), (28, 33), (20, 8), (22, 4), (1, 25), (1, 11), (7, 24), (20, 13), (0, 28), (27, 28), (9, 10), (24, 4), (5, 12), (26, 10), (24, 0), (14, 27), (18, 10), (2, 32), (2, 6), (15, 20), (8, 30), (1, 15), (24, 10), (7, 10), (14, 13), (1, 23), (4, 6), (23, 28), (19, 12), (1, 29), (17, 27), (3, 5), (12, 16), (9, 5), (16, 25), (16, 27), (4, 24), (10, 12), (4, 22), (2, 23), (11, 24), (13, 25), (24, 20), (5, 21), (23, 21), (20, 16), (8, 5), (18, 15), (6, 27), (25, 19), (6, 26), (19, 27), (15, 28), (21, 27), (23, 19), (9, 26), (19, 6), (16, 16), (11, 1), (25, 0), (5, 17), (12, 3), (4, 3), (0, 17), (23, 32), (27, 27), (11, 31), (19, 16), (8, 7), (27, 13), (3, 26), (18, 0), (8, 15), (16, 12), (26, 33), (2, 19), (9, 17), (13, 1), (8, 19), (20, 33), (22, 16), (2, 3), (16, 32), (9, 20), (12, 14), (18, 14), (6, 14), (5, 33), (21, 28), (24, 29), (25, 14), (28, 9), (28, 20), (19, 3), (3, 6), (16, 21), (1, 32), (14, 11), (26, 6), (18, 32), (16, 30), (10, 22), (21, 21), (15, 26), (22, 8), (24, 6), (14, 28), (15, 18), (22, 26), (13, 32), (12, 27), (18, 1), (12, 23), (15, 33), (24, 11), (2, 13), (21, 14), (5, 4), (22, 12), (28, 27), (29, 25), (5, 5), (20, 30), (26, 22), (21, 23), (17, 16), (13, 11), (9, 30), (9, 8), (28, 28), (4, 13), (2, 28), (11, 18), (9, 32), (15, 14), (8, 26), (28, 26), (12, 15), (16, 29), (24, 1), (25, 11), (1, 13), (19, 8), (4, 12), (23, 12), (23, 27), (10, 29), (11, 33), (2, 8), (29, 11), (7, 31), (14, 3), (28, 4), (11, 7), (19, 29), (29, 5), (19, 21), (18, 18), (12, 10), (8, 31), (12, 30), (6, 11), (4, 20), (29, 10), (7, 26), (21, 22), (0, 4), (10, 20), (22, 22), (26, 25), (15, 32), (5, 29), (5, 26), (27, 14), (28, 12), (16, 9), (5, 25), (1, 26), (8, 28), (26, 3), (25, 18), (0, 21), (9, 16), (10, 10), (13, 5), (28, 8), (26, 21), (11, 12), (18, 28), (17, 14), (21, 3), (26, 7), (8, 29), (21, 29), (14, 12), (3, 16), (3, 21), (5, 7), (5, 15), (11, 23), (10, 16), (20, 26), (13, 4), (10, 7), (25, 9), (12, 17), (19, 24), (4, 7), (16, 7), (24, 33), (5, 11), (29, 19), (20, 6), (16, 26), (3, 25), (4, 28), (28, 30), (5, 3), (3, 27), (8, 16), (26, 28), (20, 28), (20, 24), (25, 17), (6, 15), (7, 20), (17, 17), (12, 20), (3, 22), (27, 7), (13, 24), (24, 9), (29, 0), (19, 4), (15, 27), (0, 31), (24, 32), (2, 5), (17, 15), (7, 0), (10, 5), (19, 11), (20, 22), (9, 1), (2, 15), (3, 31), (8, 23), (29, 18), (16, 19), (18, 19), (22, 7), (29, 1), (8, 8), (18, 33), (12, 21), (22, 30), (9, 28), (28, 31), (17, 28), (11, 4), (8, 4), (29, 13), (21, 4), (27, 6), (28, 24), (16, 20), (21, 16), (11, 14), (20, 21), (19, 17), (3, 23), (19, 9), (17, 1), (17, 29), (29, 12), (23, 11), (24, 18), (28, 5), (10, 8), (24, 31), (13, 22), (23, 3), (26, 32)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604800", "dataset": "MATH"}
{"messages": [{"content": "In a 38x31 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 30), 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), (24, 22), (2, 28), (12, 19), (27, 2), (17, 17), (10, 30), (32, 6), (8, 17), (28, 20), (22, 26), (19, 23), (3, 26), (12, 0), (29, 3), (7, 7), (30, 27), (16, 14), (15, 26), (2, 25), (32, 15), (7, 8), (18, 4), (22, 29), (33, 26), (9, 12), (23, 1), (14, 25), (25, 6), (11, 3), (8, 8), (19, 5), (10, 23), (20, 23), (1, 13), (8, 24), (1, 2), (10, 25), (29, 18), (2, 4), (25, 13), (2, 26), (19, 13), (18, 12), (18, 28), (21, 28), (17, 15), (4, 30), (36, 14), (6, 3), (35, 11), (13, 10), (27, 17), (26, 1), (8, 14), (9, 20), (13, 17), (10, 6), (35, 25), (7, 2), (2, 15), (14, 12), (11, 25), (37, 18), (36, 26), (35, 9), (16, 30), (32, 4), (26, 15), (23, 28), (37, 28), (31, 19), (1, 30), (24, 6), (17, 28), (18, 17), (32, 29), (20, 3), (23, 16), (1, 15), (13, 27), (23, 7), (22, 18), (26, 8), (17, 9), (2, 14), (37, 22), (1, 28), (13, 20), (4, 4), (1, 21), (26, 3), (24, 8), (9, 8), (4, 27), (23, 12), (2, 6), (8, 25), (34, 15), (18, 18), (29, 23), (7, 17), (8, 9), (26, 9), (22, 12), (20, 27), (6, 4), (1, 9), (32, 28), (33, 25), (26, 23), (27, 3), (11, 21), (15, 12), (22, 3), (29, 14), (36, 27), (2, 8), (26, 25), (31, 27), (24, 28), (5, 23), (33, 23), (32, 10), (13, 8), (28, 3), (13, 14), (33, 9), (11, 14), (10, 29), (26, 2), (35, 1), (0, 8), (15, 24), (28, 18), (33, 28), (3, 0), (20, 1), (34, 17), (6, 8), (23, 9), (24, 13), (14, 21), (30, 7), (2, 1), (31, 22), (18, 3), (8, 13), (37, 29), (13, 7), (18, 29), (11, 2), (11, 26), (6, 14), (27, 23), (35, 14), (25, 7), (27, 4), (9, 25), (8, 28), (33, 30), (31, 20), (33, 24), (32, 26), (25, 11), (32, 16), (14, 19), (27, 5), (13, 22), (28, 29), (13, 4), (14, 5), (32, 12), (12, 3), (19, 3), (32, 25), (21, 11), (13, 3), (5, 15), (19, 15), (26, 0), (25, 23), (0, 6), (9, 7), (26, 14), (12, 1), (10, 13), (32, 7), (37, 21), (33, 15), (10, 18), (28, 4), (4, 21), (23, 30), (16, 3), (17, 27), (21, 14), (19, 4), (6, 25), (4, 13), (7, 3), (12, 14), (27, 28), (3, 30), (20, 28), (22, 0), (26, 29), (14, 22), (0, 25), (25, 16), (5, 26), (8, 18), (13, 28), (37, 13), (36, 23), (22, 9), (2, 23), (32, 5), (17, 3), (4, 14), (26, 22), (6, 7), (28, 14), (15, 30), (28, 2), (10, 26), (20, 6), (27, 24), (26, 16), (36, 0), (37, 16), (19, 24), (12, 5), (7, 16), (20, 26), (7, 29), (33, 11), (13, 23), (11, 19), (10, 3), (26, 26), (25, 12), (7, 23), (31, 6), (34, 7), (1, 24), (34, 20), (21, 12), (8, 7), (15, 1), (18, 26), (0, 29), (26, 12), (3, 25), (27, 6), (29, 6), (3, 27), (29, 29), (36, 18), (27, 30), (29, 13), (12, 24), (6, 11), (34, 14), (16, 18), (22, 27), (28, 8), (19, 22), (14, 30), (32, 14), (27, 20), (18, 15), (25, 0), (27, 13), (18, 24), (28, 21), (15, 29), (15, 9), (15, 20), (8, 20), (20, 25), (37, 6), (14, 17), (30, 15), (19, 11), (2, 20), (7, 26), (36, 7), (21, 19), (1, 25), (16, 11), (12, 22), (2, 12), (29, 25), (6, 20), (35, 0), (30, 12), (13, 18), (33, 10), (36, 9), (0, 22), (35, 28), (11, 17), (36, 24), (15, 11), (7, 21), (13, 2), (35, 7), (14, 15), (18, 16), (31, 26), (17, 30), (22, 2), (19, 14), (8, 22), (5, 16), (21, 4), (23, 23), (18, 2), (11, 22), (31, 3), (28, 0), (1, 12), (17, 2), (33, 12), (20, 5), (23, 21), (0, 23), (25, 25), (4, 1), (3, 17), (13, 15), (24, 9), (6, 28), (28, 22), (21, 18), (2, 24), (29, 11), (36, 12), (13, 25), (26, 17), (28, 6), (7, 12), (11, 12), (8, 12), (3, 7), (8, 23), (13, 12), (20, 4), (36, 8), (34, 19), (12, 17), (35, 13), (12, 15), (11, 13), (1, 7), (23, 20), (18, 25), (9, 24), (35, 29)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "752950", "dataset": "MATH"}
{"messages": [{"content": "In a 39x30 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 29), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (22, 26), (6, 14), (36, 15), (35, 0), (26, 8), (14, 26), (28, 18), (12, 4), (35, 23), (15, 24), (20, 16), (33, 11), (22, 24), (20, 19), (28, 8), (23, 29), (25, 14), (9, 7), (5, 12), (2, 15), (37, 1), (15, 3), (12, 3), (13, 14), (29, 24), (6, 18), (31, 9), (17, 18), (34, 1), (11, 21), (27, 11), (14, 23), (34, 0), (35, 2), (11, 27), (29, 8), (10, 10), (18, 7), (7, 1), (27, 5), (23, 19), (29, 17), (37, 8), (27, 16), (5, 26), (22, 28), (5, 4), (38, 28), (35, 26), (30, 22), (7, 25), (20, 3), (28, 0), (29, 21), (22, 8), (0, 12), (23, 27), (16, 9), (35, 13), (23, 10), (11, 22), (8, 8), (21, 18), (2, 6), (30, 1), (1, 2), (24, 27), (24, 24), (31, 25), (38, 20), (31, 8), (17, 25), (19, 26), (28, 24), (22, 13), (22, 23), (28, 5), (16, 2), (37, 16), (10, 3), (10, 11), (3, 1), (24, 7), (13, 28), (10, 7), (29, 25), (28, 25), (20, 18), (30, 28), (9, 28), (12, 5), (35, 10), (2, 23), (6, 12), (19, 23), (22, 14), (22, 2), (1, 11), (0, 11), (0, 8), (4, 22), (22, 5), (28, 10), (38, 0), (10, 12), (0, 13), (2, 16), (8, 20), (37, 15), (17, 4), (24, 5), (8, 22), (4, 6), (2, 12), (35, 7), (0, 10), (18, 20), (1, 0), (34, 25), (15, 26), (31, 23), (4, 16), (4, 28), (1, 24), (36, 3), (12, 8), (36, 6), (10, 9), (6, 20), (23, 21), (16, 3), (32, 25), (5, 0), (24, 19), (7, 28), (8, 9), (27, 14), (29, 2), (15, 6), (9, 10), (8, 23), (29, 19), (2, 20), (13, 6), (6, 9), (8, 12), (22, 19), (34, 12), (25, 9), (17, 0), (20, 25), (20, 14), (4, 5), (35, 19), (23, 23), (34, 16), (30, 18), (30, 12), (8, 19), (14, 12), (26, 18), (0, 5), (32, 13), (32, 26), (27, 7), (2, 11), (11, 14), (15, 16), (4, 27), (27, 28), (13, 13), (30, 11), (20, 17), (28, 7), (24, 25), (25, 8), (13, 5), (16, 26), (36, 18), (3, 14), (14, 3), (30, 0), (30, 6), (21, 13), (15, 27), (21, 23), (19, 5), (5, 21), (26, 12), (3, 24), (34, 26), (26, 19), (8, 10), (35, 6), (22, 25), (9, 5), (23, 28), (17, 27), (21, 2), (7, 21), (15, 12), (25, 25), (35, 21), (7, 5), (32, 24), (3, 28), (38, 24), (20, 4), (1, 18), (16, 14), (31, 20), (19, 6), (5, 8), (24, 4), (17, 10), (6, 17), (12, 16), (34, 14), (22, 21), (3, 11), (17, 15), (25, 22), (36, 14), (30, 24), (1, 4), (30, 23), (22, 20), (35, 15), (25, 5), (35, 16), (30, 29), (13, 26), (11, 7), (12, 24), (7, 2), (25, 29), (13, 18), (21, 19), (1, 6), (23, 8), (37, 25), (9, 19), (1, 15), (4, 12), (1, 20), (22, 16), (8, 14), (20, 12), (18, 27), (32, 3), (2, 5), (11, 25), (12, 12), (16, 6), (9, 18), (37, 19), (14, 6), (17, 28), (10, 25), (19, 21), (19, 4), (26, 28), (34, 28), (12, 28), (36, 17), (13, 7), (1, 14), (38, 15), (19, 25), (22, 9), (33, 19), (24, 12), (22, 0), (3, 5), (11, 15), (27, 13), (9, 21), (20, 24), (16, 11), (3, 26), (29, 5), (17, 23), (3, 6), (15, 1), (31, 4), (34, 9), (25, 15), (34, 10), (35, 8), (4, 7), (25, 12), (18, 13), (33, 2), (10, 17), (12, 26), (31, 17), (0, 14), (30, 9), (10, 29), (19, 0), (5, 2), (7, 18), (20, 27), (32, 15), (27, 21), (25, 18), (19, 22), (19, 3), (17, 3), (28, 9), (14, 17)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "927072", "dataset": "MATH"}
{"messages": [{"content": "In a 34x34 grid, how many different paths are there from the bottom left (0, 0) to the top right (33, 33), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (27, 10), (26, 22), (0, 14), (5, 4), (20, 23), (3, 15), (6, 21), (13, 28), (23, 14), (30, 28), (1, 22), (23, 19), (20, 2), (27, 29), (26, 29), (0, 21), (15, 32), (22, 31), (9, 27), (20, 16), (17, 7), (3, 29), (2, 7), (6, 9), (8, 19), (5, 27), (21, 24), (3, 5), (19, 0), (30, 18), (25, 27), (23, 18), (1, 16), (31, 11), (30, 23), (16, 12), (6, 16), (7, 32), (15, 23), (24, 8), (17, 24), (8, 16), (9, 28), (14, 23), (26, 16), (2, 24), (15, 3), (3, 23), (30, 32), (2, 17), (16, 6), (16, 28), (2, 29), (17, 6), (12, 22), (5, 3), (21, 26), (28, 18), (12, 21), (31, 17), (20, 15), (16, 15), (14, 32), (0, 30), (27, 24), (16, 5), (23, 25), (31, 25), (32, 13), (28, 2), (33, 27), (27, 6), (10, 9), (25, 3), (7, 28), (6, 8), (21, 29), (18, 6), (20, 8), (2, 30), (21, 13), (31, 8), (31, 19), (2, 19), (15, 10), (29, 15), (7, 8), (22, 2), (12, 20), (31, 23), (1, 2), (13, 8), (26, 9), (21, 7), (29, 12), (13, 20), (26, 12), (17, 4), (5, 8), (33, 4), (0, 31), (13, 9), (19, 12), (9, 18), (10, 28), (0, 33), (0, 26), (8, 7), (13, 11), (10, 7), (7, 21), (14, 22), (20, 5), (8, 12), (1, 11), (32, 21), (16, 18), (14, 2), (4, 22), (14, 5), (7, 15), (31, 10), (14, 18), (14, 17), (6, 23), (18, 0), (31, 0), (10, 12), (10, 14), (10, 4), (28, 9), (29, 23), (28, 8), (19, 33), (10, 27), (27, 5), (8, 3), (30, 19), (19, 17), (22, 4), (9, 3), (7, 16), (30, 25), (1, 23), (8, 13), (27, 28), (20, 32), (4, 31), (7, 5), (33, 7), (4, 32), (13, 16), (14, 10), (22, 11), (2, 5), (10, 17), (26, 10), (20, 12), (25, 16), (14, 20), (2, 18), (14, 16), (19, 26), (14, 13), (18, 25), (19, 31), (30, 21), (0, 2), (19, 29), (23, 31), (33, 9), (1, 7), (20, 17), (10, 25), (33, 25), (32, 9), (11, 2), (12, 33), (29, 8), (5, 15), (22, 30), (28, 26), (17, 3), (6, 32), (7, 2), (3, 24), (12, 32), (20, 30), (6, 29), (27, 19), (30, 29), (1, 8), (29, 11), (24, 20), (32, 7), (7, 10), (1, 15), (11, 22), (25, 2), (12, 3), (27, 9), (12, 13), (33, 14), (0, 5), (22, 28), (26, 23), (24, 17), (15, 22), (5, 24), (9, 4), (22, 25), (16, 21), (30, 26), (13, 2), (18, 13), (8, 9), (28, 30), (4, 16), (22, 15), (16, 24), (8, 22), (10, 5), (22, 7), (15, 31), (9, 26), (26, 18), (9, 20), (28, 22), (29, 14), (14, 29), (6, 28), (33, 10), (7, 3), (12, 25), (23, 24), (17, 20), (20, 18), (31, 20), (8, 32), (31, 27), (28, 28), (29, 28), (9, 21), (7, 18), (28, 4), (18, 2), (19, 19), (4, 33), (26, 1), (16, 31), (9, 24), (18, 17), (18, 18), (19, 21), (33, 2), (5, 14), (5, 10), (25, 0), (26, 15), (20, 24), (26, 2), (24, 31), (33, 26), (15, 25), (1, 27), (32, 17), (20, 19), (8, 5), (24, 12), (11, 8), (31, 33), (27, 16), (23, 7), (12, 4), (25, 28), (22, 24), (12, 28), (9, 32), (31, 4), (33, 16), (3, 22), (18, 1), (28, 5), (26, 4), (2, 12), (4, 2), (19, 27), (28, 14), (18, 21), (16, 4), (15, 0), (23, 15), (15, 5), (7, 9), (14, 0), (8, 24), (20, 28), (6, 6), (17, 10), (17, 17), (25, 22), (4, 23), (10, 21), (33, 22), (25, 1), (11, 12), (14, 25), (4, 9), (25, 21), (3, 10), (16, 27), (13, 17), (33, 8), (6, 10), (19, 23), (16, 8), (31, 12), (7, 6), (30, 6), (11, 26), (12, 18), (31, 28), (8, 25), (5, 11), (9, 15), (11, 25), (15, 18), (0, 6), (13, 12), (9, 1), (28, 15)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495000", "dataset": "MATH"}
{"messages": [{"content": "In a 39x33 grid, how many different paths are there from the bottom left (0, 0) to the top right (38, 32), 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), (4, 22), (37, 26), (28, 31), (4, 26), (21, 32), (18, 21), (9, 13), (2, 31), (23, 31), (20, 20), (21, 15), (16, 5), (32, 18), (18, 27), (15, 12), (16, 6), (26, 14), (8, 7), (25, 17), (2, 10), (21, 4), (33, 26), (23, 9), (20, 22), (24, 17), (37, 5), (35, 12), (35, 11), (32, 6), (30, 10), (4, 23), (1, 18), (5, 20), (5, 15), (25, 20), (8, 13), (3, 13), (23, 3), (16, 26), (19, 30), (18, 1), (23, 1), (15, 2), (37, 21), (11, 18), (11, 14), (25, 15), (26, 22), (29, 7), (22, 27), (22, 23), (22, 16), (7, 19), (36, 8), (12, 4), (29, 12), (30, 1), (1, 16), (1, 8), (28, 5), (14, 9), (27, 12), (30, 13), (17, 13), (37, 20), (29, 2), (19, 3), (0, 1), (31, 21), (3, 16), (20, 27), (10, 26), (25, 6), (34, 22), (0, 26), (34, 7), (5, 25), (28, 6), (33, 15), (36, 20), (17, 30), (36, 12), (1, 23), (26, 10), (9, 17), (15, 21), (19, 19), (36, 11), (11, 0), (15, 0), (0, 12), (36, 25), (3, 1), (27, 4), (1, 13), (31, 3), (25, 28), (32, 21), (8, 18), (3, 2), (2, 24), (13, 3), (22, 5), (11, 9), (27, 10), (21, 5), (4, 18), (9, 14), (8, 14), (34, 15), (37, 29), (19, 10), (10, 10), (20, 14), (4, 20), (10, 16), (27, 3), (12, 12), (17, 2), (2, 6), (23, 29), (2, 20), (7, 26), (3, 32), (0, 10), (32, 9), (21, 0), (27, 24), (17, 3), (3, 7), (1, 27), (16, 3), (32, 14), (24, 2), (31, 32), (8, 20), (27, 9), (2, 23), (17, 29), (7, 31), (27, 21), (6, 32), (12, 29), (31, 26), (10, 17), (2, 11), (37, 28), (32, 13), (27, 17), (15, 5), (32, 16), (14, 32), (19, 25), (12, 3), (4, 2), (21, 31), (35, 10), (7, 13), (32, 28), (36, 24), (17, 22), (22, 18), (23, 28), (26, 24), (24, 24), (20, 32), (33, 31), (21, 2), (8, 12), (26, 21), (2, 5), (3, 3), (14, 24), (19, 15), (26, 2), (7, 28), (13, 32), (12, 8), (34, 5), (10, 19), (30, 20), (14, 20), (2, 32), (7, 20), (33, 22), (10, 27), (18, 4), (7, 29), (6, 27), (8, 10), (18, 28), (37, 8), (18, 22), (12, 23), (36, 21), (13, 24), (14, 4), (35, 28), (28, 30), (33, 16), (21, 8), (34, 23), (13, 27), (23, 12), (1, 1), (8, 5), (35, 16), (0, 29), (19, 32), (1, 12), (17, 31), (2, 26), (20, 1), (19, 1), (32, 0), (37, 30), (9, 19), (24, 9), (14, 31), (24, 7), (37, 24), (4, 29), (5, 13), (4, 14), (35, 6), (6, 11), (32, 1), (13, 12), (9, 6), (24, 26), (13, 21), (15, 14), (21, 11), (11, 24), (36, 31), (38, 25), (6, 19), (20, 16), (38, 11), (17, 5), (32, 17), (1, 28), (15, 32), (23, 14), (36, 32), (6, 24), (32, 26), (38, 14), (25, 24), (33, 29), (24, 8), (21, 1), (7, 3), (25, 11), (8, 32), (37, 18), (15, 25), (32, 4), (25, 10), (2, 14), (32, 11), (28, 17), (26, 32), (36, 4), (32, 27), (25, 29), (17, 0), (28, 11), (9, 31), (32, 19), (19, 2), (12, 26), (36, 7), (9, 1), (7, 2), (28, 20), (21, 21), (19, 21), (35, 3), (13, 6), (38, 20), (9, 10), (5, 2), (33, 9), (32, 5), (8, 31), (11, 10), (24, 25), (34, 16), (2, 17), (18, 30), (4, 9), (20, 29), (13, 0), (26, 31), (11, 27), (11, 11), (2, 13), (5, 7), (32, 25), (13, 2), (11, 25), (32, 15), (20, 13), (2, 22), (17, 18), (24, 31), (31, 0), (24, 11), (5, 30), (32, 3), (36, 17), (34, 1), (18, 10), (17, 28), (34, 27), (20, 15), (22, 11), (14, 29), (23, 6), (38, 23), (0, 4), (22, 29), (38, 8), (30, 5), (18, 11), (10, 9), (3, 8), (14, 21), (17, 21), (0, 7), (10, 29), (37, 13), (33, 8), (13, 5), (30, 14), (7, 16), (30, 19), (21, 17), (31, 22), (17, 4), (34, 29), (30, 24), (28, 23), (27, 1), (17, 24), (1, 22), (36, 0), (3, 29), (34, 8), (29, 20), (14, 16), (16, 24), (18, 24), (3, 5), (3, 12), (5, 17), (36, 6), (17, 17), (11, 4), (28, 18), (36, 14), (25, 21), (12, 20), (22, 10), (34, 19), (18, 9), (36, 22), (14, 25), (11, 19), (28, 22), (31, 4), (14, 5), (0, 22), (27, 23), (37, 32), (23, 23), (36, 16), (38, 15), (33, 10), (2, 18), (8, 21), (14, 12), (6, 13), (16, 20), (16, 9), (23, 15), (11, 30), (19, 18), (31, 16), (20, 23), (5, 19), (29, 21), (37, 10), (22, 3), (12, 32), (5, 3), (16, 4), (28, 28), (15, 16), (20, 24), (25, 5), (5, 6), (4, 19), (26, 20), (13, 8), (0, 31), (12, 24), (29, 15), (7, 23), (25, 22), (5, 0)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "631800", "dataset": "MATH"}
{"messages": [{"content": "In a 38x38 grid, how many different paths are there from the bottom left (0, 0) to the top right (37, 37), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (37, 32), (11, 37), (25, 12), (8, 2), (27, 20), (36, 3), (28, 15), (31, 35), (12, 18), (35, 23), (10, 8), (11, 24), (31, 6), (30, 18), (12, 0), (32, 9), (13, 35), (32, 8), (2, 9), (6, 27), (1, 0), (11, 17), (0, 8), (22, 24), (3, 6), (9, 22), (20, 15), (37, 12), (6, 20), (9, 17), (15, 12), (29, 22), (25, 36), (33, 2), (19, 34), (7, 7), (7, 13), (22, 6), (37, 13), (7, 20), (35, 24), (19, 2), (31, 13), (32, 30), (10, 23), (17, 6), (24, 27), (2, 31), (29, 23), (12, 29), (7, 21), (7, 24), (34, 24), (15, 4), (14, 22), (21, 37), (15, 23), (17, 25), (10, 9), (28, 9), (15, 36), (12, 17), (24, 37), (9, 31), (13, 12), (7, 34), (3, 3), (19, 4), (33, 15), (13, 3), (23, 5), (8, 6), (2, 4), (6, 14), (14, 6), (22, 11), (28, 18), (31, 25), (0, 23), (31, 16), (29, 29), (26, 33), (5, 4), (9, 8), (20, 17), (36, 33), (32, 4), (12, 24), (36, 0), (10, 6), (34, 9), (16, 23), (29, 11), (25, 37), (35, 27), (30, 33), (36, 37), (11, 11), (1, 11), (3, 29), (14, 27), (28, 37), (11, 34), (26, 31), (7, 22), (23, 8), (37, 1), (6, 34), (12, 9), (7, 27), (9, 5), (3, 32), (17, 0), (31, 26), (17, 7), (34, 23), (22, 30), (28, 27), (18, 37), (24, 33), (7, 1), (17, 13), (10, 1), (10, 34), (29, 7), (4, 28), (0, 32), (3, 23), (33, 37), (11, 5), (35, 1), (31, 24), (4, 24), (26, 32), (2, 29), (4, 21), (15, 14), (10, 11), (30, 13), (31, 12), (19, 9), (1, 37), (36, 35), (4, 20), (17, 21), (24, 14), (27, 10), (30, 5), (5, 22), (35, 11), (1, 16), (21, 33), (32, 3), (23, 11), (20, 20), (28, 6), (13, 27), (2, 5), (26, 7), (0, 7), (6, 29), (10, 18), (23, 14), (4, 32), (4, 17), (24, 21), (24, 3), (27, 25), (8, 33), (11, 26), (5, 32), (15, 34), (6, 8), (5, 27), (33, 30), (23, 27), (0, 16), (28, 16), (30, 35), (32, 21), (13, 16), (12, 21), (10, 26), (16, 37), (35, 31), (30, 22), (14, 28), (36, 6), (28, 13), (29, 28), (28, 35), (16, 3), (26, 0), (6, 15), (36, 9), (20, 33), (28, 34), (37, 9), (36, 32), (31, 27), (19, 37), (3, 24), (20, 34), (3, 18), (34, 29), (27, 36), (36, 18), (36, 30), (18, 1), (29, 21), (32, 14), (2, 3), (21, 23), (8, 31), (24, 6), (27, 1), (7, 35), (5, 1), (0, 14), (16, 33), (4, 19), (30, 37), (22, 26), (21, 5), (21, 2), (35, 34), (36, 4), (31, 37), (2, 19), (22, 25), (5, 14), (12, 1), (3, 14), (16, 7), (0, 35), (17, 14), (33, 35), (12, 6), (34, 28), (8, 26), (18, 7), (10, 15), (16, 1), (29, 9), (0, 19), (26, 19), (23, 23), (25, 25), (18, 18), (18, 31), (35, 30), (33, 4), (6, 0), (7, 25), (27, 16), (12, 20), (5, 29), (0, 6), (27, 0), (36, 15), (34, 10), (34, 32), (3, 21), (9, 2), (6, 25), (32, 20), (7, 16), (9, 3), (35, 26), (15, 35), (8, 23), (10, 21), (8, 21), (29, 31), (37, 30), (8, 3), (23, 6), (7, 23), (8, 32), (27, 4), (28, 23), (2, 24), (34, 20), (22, 20), (28, 29), (15, 31), (21, 6), (26, 9), (19, 11), (24, 12), (27, 8), (8, 12), (4, 35), (2, 27), (14, 9), (22, 27), (2, 35), (0, 36), (18, 21), (13, 15), (15, 3), (34, 21), (8, 15), (33, 5), (13, 13), (7, 32), (24, 10), (23, 21), (21, 19), (17, 27), (1, 14), (10, 0), (24, 5), (9, 21), (0, 37), (37, 34), (31, 3), (28, 31), (1, 32), (22, 28), (18, 16), (32, 23), (28, 1), (23, 32), (23, 16), (33, 21), (15, 22), (16, 20), (19, 21), (33, 25), (31, 5), (37, 19), (37, 29), (30, 7), (20, 6), (16, 9), (33, 0), (18, 24), (10, 10), (22, 14), (14, 1), (4, 15), (8, 25), (1, 5), (25, 9), (33, 7), (12, 33), (8, 10), (37, 24), (33, 9), (18, 34), (17, 11), (6, 2), (37, 3), (6, 6), (9, 32), (26, 18), (34, 8), (20, 32), (32, 7), (1, 28), (19, 0), (30, 34), (2, 8), (21, 8), (12, 5), (32, 24), (0, 20), (34, 26), (2, 23), (25, 35), (21, 9), (19, 36), (16, 35), (2, 28), (29, 17), (19, 22), (12, 28), (16, 29), (31, 14), (31, 29), (15, 25), (16, 12), (20, 27), (5, 30), (9, 15), (14, 23), (13, 30), (17, 8), (9, 28), (2, 22), (1, 33), (10, 22), (11, 1), (13, 31), (2, 0), (27, 14), (26, 14), (26, 30), (26, 34), (13, 23), (0, 17), (24, 32), (30, 20), (18, 12), (11, 19), (19, 7), (9, 1), (37, 5), (8, 24), (23, 0), (4, 27), (21, 13), (28, 28), (36, 10), (12, 12), (21, 18), (36, 27), (18, 8), (14, 13), (35, 13), (27, 17), (29, 3), (0, 5), (6, 12), (15, 15), (21, 29), (37, 11), (18, 0), (0, 15), (4, 12), (14, 17), (36, 17), (8, 37), (26, 2), (21, 0), (29, 24), (34, 6), (5, 33), (16, 14), (7, 19), (10, 29), (37, 23), (28, 2), (21, 14), (22, 19), (29, 33), (22, 4), (25, 22), (7, 12), (8, 14), (37, 33), (29, 0), (10, 37), (18, 17), (14, 2), (13, 28), (29, 34), (37, 20), (14, 36), (8, 30), (18, 4), (19, 28), (21, 1), (0, 10), (20, 1), (16, 30), (16, 15), (18, 29), (5, 7), (27, 24)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "924480", "dataset": "MATH"}